Aerodynamics and flight dynamics
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Aerodynamics and flight dynamics Document Transcript

  • 1. N A S A T E C H N I C A L - N A S A T T F-542 - ­ T R A N S L A T I O N c?, 1 LOAN COPY: RETURN TO AFWL [WLOL-2) KtRTtANO AFB, N MU(AERODYNAMICS A N D FLIGHT DYNAMICSOF TURBOJET AIRCRAFTTramport Press, Moscozc; 1967N A T I O N A L A E R O N A U T I C S A N D SPACE A D M I N I S T R A T I O N W A S H I N G T O N , D. C. SEPTEMBER 1969
  • 2. TECH LIBRARY KAFB, NM IllllllllslllllllllllllIAERODYNAMICS AND FLIGHT DYNAMICS OF TURBOJET AIRCRAFT By T. I. Ligum Translation of "Aerodinamika i Dinamika Poleta Turboreaktivnykh Samoletov" Transport Press, Moscow, 1967 NATIONAL AERONAUTICS AND SPACE ADMlN ISTRATION For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151- CFSTl price $3.00
  • 3. Table o f ContentsIntroduction . vi Chapter 1 . The P h y s i c a l Basis o f High-speed Aerodynamics . 1 5 1 . V a r i a t i o n s i n t h e Parameters o f A i r w i t h A l t i t u d e . The Standard Atmosphere . 1 52. C o m p r e s s i b i l i t y o f A i r . 5 53. The Propagation o f Small Disturbences i n A i r Sound and Sound Waves . 5 54. The Speed o f Sound as a C r i t e r i o n f o r t h e C o m p r e s s i b i l i t y o f Gases . 7 55. The Mach Number and i t s Value i n F l i g h t Problems . 8 56. F l i g h t Speed. C o r r e c t i o n s t o Instrument Readings N e c e s s i t a t e d . by C o m p r e s s i b i l i t y 9 §7. The Character o f t h e Propagation o f Minor P e r t u r b a t i o n s . i n F l i g h t a t Various A l t i t u d e s 11 58. Trans- o r Supersonic Flow. o f A i r Around Bodies . 14 59. Sonic "boom". 15 510. Features o f t h e Formation o f Compression Shock During Flow Around Various Shapes o f Bodies. 18 911. C r i t i c a l Mach Number. The E f f e c t o f C o m p r e s s i b i l i t y on t h e Motion o f A i r F l y i n g Around a Wing . 20 912. The Dependence o f t h e Speed o f t h e Gas Flow on t h e Shape o f t h e Channel. The Lava1 Nozzle . 22 §13. Laminar and T u r b u l e n t Flow o f A i r . 22 514. Pressure D i s t r i b u t i o n a t Sub- and S u p e r c r i t i c a l Mach Numbers 24Chapter I I . Aerodynamic C h a r a c t e r i s t i c s o f t h e Wing and A i r c r a f t . . The E f f e c t o f A i r C o m p r e s s i b i l i t y 27 5 1 . The Dependence o f t h e C o e f f i c i e n t c on t h e Angle o f A t t a c k . 27 Y 92. The E f f e c t o f t h e Mach Number on t h e Behavior o f t h e Dependence c = f(a) Y . 30 93. The P e r m i s s i b l e C o e f f i c i e n t c p e r and i t s Dependence on t h e Mach Number . Y 31 54. Dependence o f t h e C o e f f i c i e n t c on t h e Mach Number f o r F l i g h t Y a t a Constant Angle o f A t t a c k . 32 55. The A f f e c t o f t h e Mach Number o f t h e C o e f f i c i e n t cx . 33 56. Wing Wave Drag . 36 57. I n t e r f e r e n c e . 38 58. The A i r c r a f t P o l a r . The E f f e c t o f t h e Landing Gear and Wing Mechanization on t h e P o l a r . 59. The A f f e c t o f t h e Mach Number on t h e A i r c r a f t P o l a r .Chapter I l l . Some Features o f Wing C o n s t r u c t i o n . 43 §I. Means o f I n c r e a s i n g t h e C r i t i c a l Mach Number . 43 iii
  • 4. 52. Features o f Flow Around Swept Wings . . 49 53, Wing C o n s t r u c t i o n i n T u r b o j e t Passenger A i r c r a f t . * 53 54. Drag Propagation Between Separate P a r t s o f A i r c r a f t . 59 Chapter I V . C h a r a c t e r i s t i c s o f t h e Power System . . 61 51. T w o - C i r c u i t and Turbofan Engines . . 61 52. Basic C h a r a c t e r i s t i c s o f T u r b o j e t Engines . . 66 53. T h r o t t l e C h a r a c t e r i s t i c s . 67 §4. High-speed C h a r a c t e r i s t i c s . . 69 §5. H i g h - A l t i t u d e C h a r a c t e r i s t i c s . . 71 56. The E f f e c t o f A i r Temperature on T u r b o j e t Engine T h r u s t . . 72 S7. T h r u s t Horsepower . . 73 98. P o s i t i o n i n g t h e Engines on t h e A i r c r a f t . . 74 Chapter V . Takeoff. . 81 51. Taxiing . . 81 92. Stages o f T a k o f f . . 81 53. Forces A c t i n g on t h e A i r c r a f t D u r i n g t h e T a k e o f f Run and Takeoff 84 54. Length o f Takeoff Run. L i f t - o f f Speed. . 87 55. Methods o f Takeoff. . 88 56. F a i l u r e o f Engine During T a k e o f f . . 90 §7. I n f l u e n c e o f Various F a c t o r s on T a k o f f Run Length . . 98 58. Methods o f Improving Takeoff C h a r a c t e r i s t i c s . . 100 Chapter V I . Climbing . . 105 51. Forces A c t i n g on A i r c r a f t . . 105 §2. D e t e r m i n a t i o n o f Yost S u i t a b l e C l i m b i n g Speed . . 107 53. V e l o c i t y Regime o f Climb . . 110 94. Noise Reduction Methods. . 111 S5. Climbing w i t h One Motor Not Operating . . 115 Chapter VI I . H o r i z o n t a l F1 i g h t . . 116 51. Diagram o f Forces A c t i n g on A i r c r a f t . . 116 52. Required T h r u s t f o r H o r i z o n t a l F l i g h t . . 117 53. Two H o r i z o n t a l F l i g h t Regimes . . 120 54. I n f l u e n c e o f E x t e r n a l A i r Temperature on Required T h r u s t . . 121 55. Most Favorable H o r i z o n t a l F1 i g h t Regimes. I n f l u e n c e o f A1 t i tude and Speed . . 123 $6. D e f i n i t i o n o f Required Q u a n t i t y o f Fuel . . 129 57. F1 i g h t a t the " C e i l ings" . 131 58. P e r m i s s i b l e F l y i n g A l t i t u d e s . I n f l u e n c e o f A i r c r a f t Weight . 133 59. Engine F a i l u r e During H o r i z o n t a l F1 i g h t . . 134 510. Minimum P e r m i s s i b l e H o r i z o n t a l F l i g h t Speed. . 136 Chapter VIII. Descent . 138 5 1 . General Statements. Forces A c t i n g on A i r c r a f t During Descent . . 138 52. Most Favorable Descent Regimes . * 139 53. P r o v i s i o n o f Normal C o n d i t i o n s i n Cabin During High A l t i t u d e F l y i n g . . 140
  • 5. 54. Emergency Descent . . 144Chapter I X . T h e Landing . . 150 51. Diagrams of Landing Approach . . 150 52. Flight After Entry into Glide Path. Selection of Gliding Speed . . 151 53. Stages in the Landing . . 154 54. Length of Post-landing Run and Methods of Shortening it . . 158 55. Length of Landing Run As a Function of Various Operational Factors . . 163 56. Specific Features of Landing Runs o n Dry, Ice o r Snow Covered Runways . . 164 57. Landing with Side Wind . 167 58. T h e "Minimum" Weather for Landings and Takeoffs . 168 59. Moving into a Second Circle . 171Chapter X. Cornering . . 173 5 1 . Diagram of Forces Operating During Cornering . . 173 52. Cornering Parameters . . 174Chapter X I . Stability and Controlability of Aircraft . 177 5 1 . General Concepts o n Aircraft Equilibrium . . 177 52. Static and Dynamic Stability . . 178 53. Controllability of an Ai rcraft . . 11 8 54. Centering of the A rcraft and Mean Aerodynamic Chord . 184 55. Aerodynamic Center of Wing and Aircraft. Neutral Center i ng . 185 56. Longitudinal Equil brium . . 188 57. Static Longitudina Overload Stabi 1 i ty . . 190 58. Diagrams o f Moments . . 194 59. Static Longitudinal Velocity Stability . . 195510. Longitudinal Control labi 1 i ty . . 1975 1 1 . Construction of Balancing Curve for Deflection of Elevator . . 199512. Vertical Gusts. Permissible M Number in Cruising F1 ight , . 203513. Permissible Overloads During a Vertical Maneuver . 205514. Behavior of Aircraft a t Large Angles of Attack . . 206515. Automatic Angle of Attack and Overload Device . . 212516. Lateral Stability . . 213517. Transverse Static Stabi 1 i ty . 214518. Directional Static Stabi 1 ity . . 216519. Lateral Dynamic Stabi 1 i ty . . 2i6520. Yaw Damper . . 218521. Transverse Control 1 ab i 1 i ty . . 223522. Directional Controllability. Reverse Reaction for Banking . . 225923. Involuntary Banking (lValezhkal) . 229 V
  • 6. 124. I n f l u e n c e o f C o m p r e s s i b i l i t y o f A i r on C o n t r o l Surface E f f e c t i v e n e s s . . 230 525. Methods o f Decreasing Forces on A i r c r a f t C o n t r o l Levers . . 231 526. Balancing o f t h e A i r c r a f t During T a k e o f f and Landing . 233 Chapter X I I. I n f l u e n c e o f I c i n g on F l y i n g C h a r a c t e r f s t i c s . 236 §l. General Statements . . 236 52. Types and Forms o f I c e Deposi t i o n . In t e n s i t y o f Icing . . 237 S3. I n f l u e n c e o f I c i n g on S t a b i l i t y and C o n t r o l l a b i l i t y o f A i r c r a f t i n P r e - l a n d i n g Guide Regime . . 239 vi
  • 7. I NTRODUCTI ON Jet-powered passenger a i r c r a f t have been adopted and introduced i n t o g e n e r a l use i n c i v i l a v i a t i o n . - / 3* The f i r s t t u r b o j e t passenger a i r c r a f t b u i l t i n t h e S o v i e t Union w a s t h eTu-104, and t h e first f o r e i g n t u r b o j e t s were t h e De Havilland Comet, t h eSud Aviation Caravelle, t h e Boeing-707, t h e Douglas DC-8, t h e Convair 880 ando t h e r s . These a i r c r a f t have been given t h e name f i r s t - g e n e r a t i o n t u r b o j e taircraft. In b u i l d i n g t h e first t u r b o j e t passenger a i r c r a f t , t h e designers attemptedt o achieve long f l i g h t range and t o p e r f e c t t h e high-speed p r o p e r t i e s of t h ea i r c r a f t , thereby compensating f o r t h e heavy f u e l consumption r e q u i r e d by t h ej e t engines. The d e s i r e t o c r e a t e new a i r c r a f t capable o f competing w i t ht h e o l d passenger a i r c r a f t which were equipped with highly economic p i s t o nengines l e d t o a maximum i n c r e a s e i n t h e l i f t i n g c a p a c i t y , and f l i g h t d i s ­t a n c e and speed. The r e a l i z a t i o n of t h e s e q u a l i t i e s became p o s s i b l e onlybecause of t h e appearance of j e t engines. Experience i n using a i r c r a f t has shown t h a t t u r b o j e t passenger a i r c r a f tmay be economic n o t only i n terms of long-range f l i g h t , b u t f o r medium- andeven s h o r t - r a n g e f l i g h t as w e l l . As a r e s u l t , second-generation t u r b o j e tpassenger a i r c r a f t have appeared: i n t h e S o v i e t Union t h e r e a r e t h e Tu-124,t h e Tu-134 and t h e Yak-40, w h i l e abroad t h e r e are- t h e D e Havilland-121"Tridentf1, t h e Bak-1-11, t h e Boeing-727, t h e DC-9and o t h e r s . These air­c r a f t a r e s u b s t a n t i a l l y s m a l l e r i n dimensions and intended f o r u s e on s h o r t -range n e t s . The high power and low u n i t load on t h e wing permit f l i g h t sfrom a i r f i e l d s having r e l a t i v e l y s h o r t take-off and landing runways. Turbojet engines surpass p i s t o n engines i n r e l i a b i l i t y . With t h e i rs h o r t time i n s e r i e s production and u s e , s e r v i c e p e r i o d s o f 2,000 - 3,000hours between maintenance checks have been e s t a b l i s h e d . This i s an importantf a c t i n i n c r e a s i n g t h e economy of using t u r b o j e t a i r c r a f t , because t h e c o s tof t h e s e engines s u b s t a n t i a l l y exceeds t h a t of p i s t o n engines. In t h e FiveYear Plan f o r t h e development of t h e Russian economy from 1966 t o 1970, t h ef u r t h e r development of c i v i l a v i a t i o n is a n t i c i p a t e d and t h e volume o f a i r ­ /4t r a v e l should i n c r e a s e by a f a c t o r o f 1.8. N w passenger a i r c r a f t a r e going ei n t o service i n the a i r l i n e s . Turbojet passenger a i r c r a f t have f l i g h t c h a r a c t e r i s t i c s which d i f f e r fromt h o s e of a i r c r a f t with p i s t o n and turboprop engines i n s e v e r a l r e s p e c t s .These f l i g h t f e a t u r e s r e s u l t from t h e unique high-speed and h i g h - a l t i t u d ec h a r a c t e r i s t i c s of t h e engines, as w e l l as t h e f l i g h t c o n d i t i o n s a t t h e s ehigh speeds and a l t i t u d e s .- ..* Numbers i n t h e margin i n d i c a t e pagination i n t h e f o r e i g n t e x t . vii
  • 8. With t h e appearance o f j e t a v i a t i o n , t h e r e has been a r e s u l t a n t i n c r e a s ei n t h e importance of h i g h - v e l o c i t y aerodynamics, i . e . , t h e motion o f bodiesi n air viewed i n terms of t h e e f f e c t of i t s c o m p r e s s i b i l i t y , i . e . , t h ep r o p e r t i e s t o change d e n s i t y with a change i n p r e s s u r e . . The f i r s t t o i n d i c a t ethe n e c e s s i t y of e s t i m a t i n g t h e e f f e c t of air c o m p r e s s i b i l i t y w a s t h e Russians c i e n t i s t S.A. Chaplygin, i n h i s work "On G a s Flows" published i n 1902. I twas he who developed a method f o r t h e t h e o r e t i c a l s o l u t i o n of problems of t h emotion of gas with allowance made f o r i t s c o m p r e s s i b i l i t y . The S o v i e t s c i e n t i s t s Academicians S.A. Khristianovich, M.V. Keldysh,A.A. Dorodnitsyn, Professors V.S. Pyshnov, F . I . Frankl , I . V . Ostoslavskiy,B.T. Goroshchenko, Ya.M. S e r e b r i y s k i y , A.P. Melnikov and o t h e r s , throught h e i r s t u d i e s i n t h e f i e l d of h i g h - v e l o c i t y aerodynamics , c o n t r i b u t e d muchwhich w a s of g r e a t value i n t h e design of high-speed a i r c r a f t . The S o v i e t turbo j e t passenger a i r c r a f t c r e a t e d by a e r o n a u t i c a l engineersA.N. Tupolev, S.V. I l u s h i n and A.S. Yakovlev, take t h e i r p l a c e s i n t h e rankso f t h e f i r s t - c l a s s aircraft. The s u c c e s s f u l use of new a v i a t i o n technology by*f l i g h t and engineeringpersonnel i s unthinkable without a deep understanding of t h e laws of aero­dynamics . A i r c r a f t aerodynamics, when thought of i n terms of t h e f l i g h t crew, i su s u a l l y c a l l e d p r a c t i c a l aerodynamics. The number of problems involved i naerodynamics i s q u i t e s u b s t a n t i a l . These i n c l u d e s t u d y i n g t h e laws of t h emotion of a i r and t h e i n t e r a c t i o n of a i r flows with bodies moving i n them,t h e i n t e r a c t i o n of shock waves with various p a r t s o f t h e a i r c r a f t , a i r c r a f tf l i g h t dynamics as a f f e c t e d by t h e f o r c e s a p p l i e d t o t h e a i r c r a f t (includingaerodynamic f o r c e s ) , and a i r c r a f t s t a b i l i t y and handiness. I t i s t h e o b j e c t of t h i s book t o examine t h e s e q u e s t i o n s i n terms ofturbo j e t pas s enger a i r c r a f t . viii
  • 9. NASA TT F-542 CHAPTER 1 THE PHYSICAL BASIS OF HIGH-SPEED AERODYNAMICS ABSTRACT. T h i s book p r e s e n t s t h e physical bases of h i g h - s p e e d aerodynamics, and t h e influence of a i r c o m p r e s s i b i l i t y on t h e aerodynamic c h a r a c t e r i s t i c s of w i n g s and a i r c r a f t . Primary a t t e n t i o n is turned t o passenger j e t s . T h e following a r e a s a r e covered: takeoff c h a r a c t e r i s t i c s of j e t s and methods o f Improving them; b e s t c l i m b i n g modes; h o r i z o n t a l f l l g h t ; t h e d e s c e n t ; t h e landing approach; t u r n s and c o r n e r s ; c o n t r o l l a b i l i t y and s t a b i l i t y ; icing and i t s influence on f l y i n g c h a r a c t e r i s t i c s ; and t h e c h a r a c t e r i s t i c s o f modern j e t e n g i nes .5 1 . Variations i n the Parameters of Air w i t h A l t i t u d e . T h e Standard Atmosphere The f l i g h t of a i r c r a f t , l i k e t h a t o f o t h e r f l i g h t v e h i c l e s , i s a f f e c t e dby t h e condition of t h e atmosphere -- t h e s h e l l of a i r surrounding t h e e a r t h . - /5Therefore, i t i s q u i t e v i t a l t o know the processes occurring i n t h e abnos­phere. Only the atmospheres lower boundary, t h e e a r t h s s u r f a c e i t s e l f , i sc l e a r l y d e l i n e a t e d . The upper atmosphere i s more d i f f i c u l t t o e s t a b l i s hbecause t h e d e n s i t y o f air decreases c o n s t a n t l y with a l t i t u d e and even a t ana l t i t u d e o f .lo0 km i t measures approximately one m i l l i o n t h t h a t on t h e e a r t h ss u r f a c e . Normally, t h e upper l i m i t of t h e atmosphere i s considered t h ea l t i t u d e a t which t h e air d e n s i t y approaches t h a t of the gases f i l l i n g i n t e r ­p l a n e t a r y space. Data from d i r e c t and i n d i r e c t observations show t h a t t h e atmosphere hasa layered s t r u c t u r e . In 1951 t h e I n t e r n a t i o n a l Geodesic and Geophysical Unionadopted t h e d i v i s i o n of t h e atmosphere i n t o f i v e b a s i c spheres o r l a y e r s :t h e troposphere, t h e s t r a t o s p h e r e , t h e mesosphere, t h e thermosphere and t h eexosphere. The Troposphere is t h e lcwest l a y e r of t h e atmosphere, which i n t h e middlel a t i t u d e s extends t o an a l t i t u d e o f 10-12 km, i n t h e t r o p i c s -- t o an a l t i t u d eo f 16-18 km, and i n t h e p o l a r regions -- t o an a l t i t u d e o f 8-10 k . This ml a y e r i s o f tremendous p r a c t i c a l i n t e r e s t i n a v i a t i o n , because a l l t h e mostimportant phenomena encountered by t h e p i l o t occur b a s i c a l l y i n t h e tropo­sphere. I t i s h e r e t h a t t h e formation of clouds and f o g s , t h e f a l l o fp r e c i p i t a t i o n , and t h e development of storms occur.
  • 10. The most s i g n i f i c a n t f e a t u r e of t h e troposphere i s t h e decrease i ntemperature with a r i s e i n a l t i t u d e (averaging 6.5" p e r km of a l t i t u d e ) . Thetroposphere i s t h e area of thermal turbulence r e s u l t i n g from t h e unequalh e a t i n g o f l a y e r s o f air a t t h e e a r t h s s u r f a c e and a t v a r i o u s a l t i t u d e s , asw e l l as t h e dynamic turbulence r e s u l t i n g from t h e f r i c t i o n o f t h e air w i t ht h e e a r t h s s u r f a c e and i t s i n t e n s e v e r t i c a l displacement a t t h e boundaries - /5between cold and warm a i r masses of atmospheric f r o n t s . The troposphere ends i n t h e l a y e r of t h e tropopause. The t h i c k n e s s oft h e tropopause f l u c t u a t e s from a f e w hundred meters t o s e v e r a l kilometers.I t i s u s u a l l y a continuous l a y e r which surrounds t h e e a r t h s sphere i t s e l f ,while i t s a l t i t u d e and temperature are f u n c t i o n s of t h e geographic l a t i t u d e ,t h e time o f y e a r and t h e atmospheric processes developing. Over t h e e q u a t o rand i t s neighboring a r e a s , t h e tropopause i s l o c a t e d a t an average a l t i t u d eo f 16-18 km ( I n d i a ) , while i n t h e middle l a t i t u d e s i t i s l o c a t e d a t ana l t i t u d e of 10-12 km, and i n t h e p o l a r regions i t has an a l t i t u d e of 8-10 km,while over t h e p o l e i t may drop t o 5-6 km. J e t a i r c r a f t n o m a l l y f l y c l o s et o t h e l i m i t of t h e tropopause, a c h a r a c t e r i s t i c f e a t u r e of which i s t h ee x i s t e n c e o f c y c l i c bumps beneath t h e tropopause i t s e l f . The s t r a t o s p h e r e i s l o c a t e d above t h e tropopause and extends t o approxi­mately an a l t i t u d e of 35-40 km. Constant temperature with a l t i t u d e isc h a r a c t e r i s t i c of i t s lower l a y e r s . The i n s i g n i f i c a n t content of water vapori n the s t r a t o s p h e r e r e s u l t s i n t h e lack of clouds from which p r e c i p i t a t i o nwould f a l l . According t o d a t a from p i l o t s who have flown a t a l t i t u d e s o f12-16 km, i n t h e lower s t r a t o s p h e r e i t i s most f r e q u e n t l y c l o u d l e s s . The a i ri s s t a b l e and v e r t i c a l motion i s s l i g h t . This a i d s i n smooth f l i g h t . Therei s seldom bumpiness, and only then c l o s e t o t h e tropopause. The mesosphere runs from t h e upper boundary o f t h e s t r a t o s p h e r e t o ana l t i t u d e of 80 km. The thermosphere i s l o c a t e d above t h e mesosphere and extends t o ana l t i t u d e of 800 km. The exosphere i s t h e o u t e r l a y e r of the atmosphere, o r t h e d i s s i p a t i v el a y e r , and i s l o c a t e d above t h e thermosphere. Gases h e r e a r e so r a r e f i e d anda t the high temperatures observed t h e r e have such high v e l o c i t i e s t h a t t h e i rp a r t i c l e s (helium and hydrogen) break away from t h e e a r t h s a t t r a c t i v e f o r c eand move i n t o i n t e r p l a n e t a r y space. Thus we have a b r i e f d e s c r i p t i o n of a s t r u c t u r e of t h e atmosphere. Atmospheric conditions a r e c h a r a c t e r i z e d by t h e various meteorologicalelements -- atmosphere p r e s s u r e , temperature, humidity, cloud cover, p r e c i p i ­t a t i o n , wind, e t c . The atmosphere may be c h a r a c t e r i z e d as a v a r i a b l e medium. As a r e s u l t of unequal h e a t i n g of the a i r masses a t t h e equator and p o l e s ,flows a r e formed which r e s u l t i n t h e passage o f cold a i r toward t h e equator andwarmer air toward t h e p o l e s . The e f f e c t of t h e e a r t h s r o t a t i o n i n t h enorthern hemisphere causes t h e a i r flow t o d e v i a t e t o the r i g h t and move from2
  • 11. t h e south t o t h e southwest, while approaching 30° N i t moves t o t h e west. Therefore, f l i g h t s from west t o e a s t over t h e t e r r i t o r y of t h e USSR a r e - /7 accompanied by t a i l winds, while east-to-west f l i g h t s encounter head winds. The s h i f t from w e s t e r l y winds t o e a s t e r l y occurs a t a l t i t u d e s around 20 km. Whereas p i s t o n a i r c r a f t f l y only i n t h e lower troposphere, j e t a i r c r a f t , i n c o n t r a s t , f l y i n t h e upper and - - t o a c e r t a i n e x t e n t -- i n t h e lower s t r a t o ­ sphere. The f u r t h e r development of high-speed a v i a t i o n w i l l i n t h e n e a r f u t u r e permit us t o f l y a t s u p e r s o n i c speeds corresponding t o Mach = 2.5-3. A t this p o i n t , f l i g h t s w i l l be i n t h e s t r a t o s p h e r e . Before t h e p e r f e c t i o n i n g of j e t a i r c r a f t , i t w a s assumed t h a t a t high a l t i t u d e s t h e f l i g h t s would encounter f a v o r a b l e weather c o n d i t i o n s . However, i t w a s found t h a t a t a l t i t u d e s of 10,000 - 12,000 m cloud cover and bumpiness were sometimes encountered. To t h e s e well-known phenomena, t h e r e were added t h e j e t streams c h a r a c t e r i s t i c of a l t i t u d e s of 9-12 km. The j e t streams are t h e broad expanses o f zones of very s t r o n g winds observed i n t h e upper l a y e r s of t h e troposphere, u s u a l l y a t a l t i t u d e s of 9000 - 12,000 m. Post-war s t u d i e s showed t h a t t h e minimum v e l o c i t y of t h e j e t stream (along i t s a x i s ) e q u a l l e d approximately 100 km/hr, while t h e maximum w a s 750 km/hr (over t h e P a c i f i c Ocean). Over t h e USSR, t h e wind speed i n t h e j e t stream reaches 100 - 200 and sometimes even 350 km/hr, while over t h e North A t l a n t i c and Northern Europe it reaches 300 - 400, 500 over t h e USA, and 650 km/hr over Japan. The j e t stream i s comparable t o a g i g a n t i c h i g h l y o b l a t e channel with a h e i g h t averaging 2-4 km and a width of 500 - 1000 km. These flows run b a s i c a l l y west-east, b u t i n c e r t a i n s e c t i o n s they may vary significantly . F l i g h t speed may be i n c r e a s e d by t h e s e l e c t i v e u s e of j e t stream t a i l winds, while f l i g h t a g a i n s t t h e head wind should be one o r two km above o r below t h e a x i s of t h i s stream. A s a r u l e , t h e j e t streams a r e t o be found i n t h e region where the tropopause i s s i t u a t e d . In studying a i r c r a f t f l i g h t and determining t h e f o r c e s a c t i n g on a i r c r a f t , we may consider t h e a i r as a continuous medium. A t s e a l e v e l , t h e a i r c o n s i s t s of a mixture of n i t r o g e n (78.08% of t h e volume of dry a i r ) , oxygen (20.95%) and i n s i g n i f i c a n t q u a n t i t i e s of o t h e r gases (argon, carbon dioxide, hydrogen, neon, helium, e t c . ) . The a i r a l s o contains water vapors. In t h e troposphere and s t r a t o s p h e r e t h e temperature, p r e s s u r e and d e n s i t y of the a i r vary w i t h i n r a t h e r broad 1 i . m i t s as a f u n c t i o n o f the geo­ g r a p h i c l a t i t u d e of t h e l o c a l e , t h e time of y e a r , t h e time of day and t h e weather. In o r d e r t o achieve a common concept o f t h e c h a r a c t e r i s t i c s of t h e atmosphere (pressure, temperature and d e n s i t y ) , t h e s t a n d a r d atmosphere w a s 3I
  • 12. a r r i v e d a t -- t h e a r b i t r a r y d i s t r i b u t i o n , i n t h e atmosphere, of p r e s s u r e , - /8 d e n s i t y and temperature f o r d r y , clean a i r ( c o n t a i n i n g n e i t h e r moisture n o r d u s t ) of a c o n s t a n t composition a p p l i c a b l e f o r engineering. -- p r i m a r i l y a v i a t i o n -- c a l c u l a t i o n s with r e s p e c t t o t h e i r comparability ( f o r example, i n c a l c u l a t i n g t h e l i f t and drag and f o r graduating v a r i o u s aerial n a v i g a t i o n instruments such as altimeters and o t h e r s ) . I n t h e s t a n d a r d atmosphere, t h e a l t i t u d e i s computed from s e a l e v e l .Normal conditions a t sea l e v e l are: atmospheric p r e s s u r e p = 760 mm Hg, a i r 0 2 4d e n s i t y p = 0.125 k G sec /m , temperature t - 15OC ( o r To = 288OK) and 0 -s p e c i f i c weight of t h e a i r y = 1.225 kG/m 0 3 . Variations i n a i r p r e s s u r e and d e n s i t y with a l t i t u d e , which proceed i naccordance with a s p e c i f i c l a w , are c a l c u l a t e d p e r each a l t i t u d e according t os p e c i a l formulas. The air temperature i n t h e s t a n d a r d atmosphere up t o ana l t i t u d e of 11,000 m drops uniformly by 6.5OC p e r 1000 m. Above 11,000 m ,t h e temperature i s considered c o n s t a n t and equal t o -56.5OC. In f a c t , how­ever, a t t h i s a l t i t u d e it may reach -8OOC. Results of c a l c u l a t i o n s a r egiven i n t h e t a b l e . Below w e p r e s e n t an a b b r e v i a t e d t a b l e of t h e s t a n d a r datmosphere. TABLE 1. STANDARD ATMOSPHERE (SA) -A l t i - f Tempera- Mass lelativ Speed­ Itude , t u r e density lens i t y Ao. 7 of I ,m (tH) > O C a ) - 7 km/hr j kG/m3 m 4 II 1000 21.5 854,6 - 1,3476 1,1374 1,096 1242 0 15 760 : 1O332,3 1,225 0,1250 1,oo 1225 1 000 8,5 674 j 9164,Z. 1.11 0,1134 0,9074 1211 2000 2,o 596 8105,4 1,006 0,1027 0,8215 1197 3000, I -4.5 526 7148,O 0,909 0,0927 0,742 1183 4000 I -1 1 462 6284,2 0,819 0,0636 0,6685 0,754 324.7 1168 5 000 -17.5 405 i 5507,O 0,7362 0,0751 0,6007 0,70 . 320,7 1154 6 000 -24,O 354 i 4809,5 0,659 0,0673 0,5383 0,648 316,6 1139 7000 -30,5 308 4185.3 0,589 0,0601 0,4810 0,599 312,4 ~ 1125 8000 I -37,O 267 3628,4 0,525 0,0536 0,4285 0,553 30S,2 1110 go00 i -43,5 230 3133.1 0,466 0,0476 0,3805 1094 10000 -50,5 188 2694,O 0,412 0,0421 0,337 1078 11000 i -56,5 i 169,6 2306.1 0,363 0,0371 0,297 1063 12000 13000 * 1 -56,5 -56,5 ! 144,6 123.7 1969,5 1682,O 0,310 0,265 0,0317 0,0270 0,253 0,216 1063 1063 14000 ! -56.5 105;6 1436,5 0,226 0,0231 0,185 1063 15000 -56,5 90,l 1226,9 0,193 0,0197 0,155 1063 1 000 6 -56.5 77,l 1047,8 0,165 0,0166 0,135 1063 17 000 -56.5 65,8 894,8 0,141 0,0144 0,115 1063 18 000 -56,5 56,2 764,2 0,120 0,123 OI09S4 1063 19 ooa -56,5 48 ,O 652,7 0,103 0,0105 0,084 106320 000 -56,5 40,9 557,4 0,088 0,009 0,0717 1063Tr. Note: Commas i n d i c a t e decimal p o i n t s .4
  • 13. 5 2. Cmpressibi 1 i t y of A i r Compressibility i s t h e p r o p e r t y of gases (and f l u i d s ) t o change t h e i ri n i t i a l volume (and, consequently, d e n s i t y ) under t h e e f f e c t of p r e s s u r e o r achange i n temperature. I n s o l v i n g t e c h n i c a l problems, c o m p r e s s i b i l i t y i s taken i n t o account i nthose cases when changes i n volume (density) are considerable by comparisont o t h e i n i t i a l volume ( d e n s i t y ) . If t h e volume of water w i t h an i n c r e a s e i n p r e s s u r e of 1 a t . withc o n s t a n t temperature changes an average of only 1/21,000 o f i t s i n i t i a l v a l u e ,i . e . , only 1/210 of a p e r c e n t , a i r , which has a high c o m p r e s s i b i l i t y , r e q u i r e sa change i n p r e s s u r e of only one one hundredth t h a t of atmosphere (0.01 a t . )t o change i t s volume by 1% under normal atmospheric c o n d i t i o n s . Therefore, a l l gases are considerably more compressible than droppingliquid. For example, i f t h e p r e s s u r e i n a given m a s s of gas i n c r e a s e s i nsuch a way t h a t i t s temperature does n o t vary during t h i s change, t h e volumeof t h e gas decreases. When t h e i n i t i a l p r e s s u r e i s doubled, t h e volumedecreases by 50%. .The change i n volume f o r gas i s e q u a l l y high during heating. Differences i n c o m p r e s s i b i l i t y of l i q u i d s and gases a r e explained byt h e i r molecular s t r u c t u r e . In l i q u i d s , t h e i n t e r - m o l e c u l a r d i s t a n c e i s small,i . e . , t h e molecules a r e r a t h e r dense, which determines t h e small c a p a b i l i t yl i q u i d s have of compressing. B comparison with l i q u i d s , gases have an yextremely low d e n s i t y . For example, t h e d e n s i t y of water i s 816 times t h a t ofa i r . The low d e n s i t y of a i r and o t h e r gases i s explained by t h e f a c t t h a t i ngases t h e i n t e r - m o l e c u l a r d i s t a n c e s u b s t a n t i a l l y exceeds t h e dimensions oft h e molecules themselves. Therefore, when t h e r e i s an i n c r e a s e i n t h e pressure,t h e volume of t h e gas decreases due t o t h e decreasing d i s t a n c e betweenmolecules. Thus a r i s e s the e l a s t i c i t y which gas possesses. I n a v i a t i o n problems, t h e need t o account f o r a i r c o m p r e s s i b i l i t y r e s u l t sfrom t h e f a c t t h a t a t high f l i g h t speeds i n a i r , s u b s t a n t i a l d i f f e r e n c e s i np r e s s u r e a r i s e which are t h e cause of s u b s t a n t i a l changes i n i t s d e n s i t y . To e v a l u a t e t h e e f f e c t of c o m p r e s s i b i l i t y , l e t us examine t h e speed ofsound .§ 3. T h e Propagation o f Small Disturbances i n Air. Sound and Sound Waves. The p r o p e r t y of c o m p r e s s i b i l i t y i s i n t i m a t e l y r e l a t e d t o t h e phenomenonof t h e propagation of sound i n gases. The speed of t h e propagation of soundp l a y s a v i t a l r o l e i n high-speed aerodynamics. The e f f e c t of c o m p r e s s i b i l i t yon t h e aerodynamic c h a r a c t e r i s t i c s of a i r c r a f t i s a f u n c t i o n of t h e degreet o which t h e f l i g h t speed of t h e a i r c r a f t approaches t h e speed of sound. Whenair flows a t speeds g r e a t e r t h a n t h e speed o f sound, q u a l i t a t i v e changes occur / 10i n t h e c h a r a c t e r of t h e flow. The s e n s a t i o n which w e p e r c e i v e as sound i s t h e r e s u l t of t h e e f f e c t , on 5
  • 14. our a u d i t o r y apparatus, of t h e o s c i l l a t o r y motion of a i r caused, f o r example,by t h e motion of some body i n it. The displacement of each p a r t i c l e o f a i rduring i t s v i b r a t i o n i s i n s i g n i f i c a n t l y small. The p a r t i c l e s v i b r a t e aroundt h e i r e q u i l i b r i u m c o n f i g u r a t i o n , which corresponds t o t h e i r i n i t i a l s t a t e .However, t h e l a b o r a t o r y p r o c e s s i s propagated a v e r y long d i s t a n c e . The human ear p e r c e i v e s as sound t h o s e d i s t u r b a n c e s which a r e t r a n s m i t t e dwith a frequency from 20 t o 20,000 v i b r a t i o n s p e r second. Those w i t h afrequency of less than 20 p e r second are c a l l e d i n f r a s o u n d , and t h o s e above20,000 p e r second a r e c a l l e d ultrasound. B small d i s t u r b a n c e s w e mean s l i g h t changes i n t h e p r e s s u r e and d e n s i t y yo f t h e medium (gas o r l i q u i d ) . Disturbances being propagated i n t h e medium,such as a i r , a r e c a l l e d waves (due t o t h e s i m i l a r i t y o f t h i s phenomenon t owaves on t h e s u r f a c e of w a t e r ) . The speed of t h e propagation o f t h e d i s t u r b a n c e s i n space ( t h e wavev e l o c i t y ) i s q u i t e s u b s t a n t i a l . The speed of propagation of a sound wave,i . e . , small changes i n d e n s i t y and p r e s s u r e , i s c a l l e d t h e speed o f sound.It i s a f u n c t i o n of t h e medium i n which t h e sound is being propagated andof i t s temperature. I n high-speed aerodynamics, sound i s considered as waves of p e r t u r b a t i o n sc r e a t e d i n t h e a i r by a f l y i n g a i r c r a f t . The speed of sound i n gases i s a function of temperature. The h i g h e r t h egas temperature, t h e l e s s compressed i t i s . Heated gas has a high e l a s t i c i t yand t h e r e f o r e i s more d i f f i c u l t t o compress. Cold a i r i s e a s i l y compressed.For example, a t a gas temperature T = 0 ( o r t = -273OC), t h e speed of soundequals zero because under t h e s e conditions t h e gas p a r t i c l e s a r e immobile ande x e r c i s e only s l i g h t d i s t u r b a n c e s , with t h e r e s u l t t h a t they can c r e a t e nosound . The dependence o f t h e speed o f sound i n a i r on temperature may bedetermined according t o t h e following approximate formula: a = 20 JTm/sec. Within t h e l i m i t s of troposphere, t h e a i r temperature decreases witha l t i t u d e . Consequently, i n t h e troposphere t h e speed o f sound a l s o decreaseswith a l t i t u d e . On t h e e a r t h s s u r f a c e under s t a n d a r d c o n d i t i o n s (p = 760 mmHg, t = 15 s e c ) , a = 340 m/sec. With an i n c r e a s e i n a l t i t u d e f o r every 250 m , ­ /11t h e speed of sound decreases by 1 m/sec. A t a l t i t u d e s above 11,000 m, t h e temperature i s (according t o t h es t a n d a r d atmosphere) considered constant and equal t o -56.5OC. Consequently,the speed of sound a t t h e s e a l t i t u d e s should a l s o be considered constant andequal t o a = 20 4273 - 56.5 = 296 m/sec (Fig. 1 ) .6
  • 15. I § 4. T h e S p e e d of Sound as a C r i t e r i o n f o r the Compress i b i 1 i t y of Gases I n gas dynamics, f o r t h e speed of sound t h e r e is t h e well-known formula: m/sec, AP where A is t h e change i n p r e s s u r e , Ap i s t h e p change i n gas d e n s i t y which it causes. The more compressed t h e gas i s , t h e slower t h e speed of sound, s o t h a t one and t h e same change i n d e n s i t y ec. may b e obtained through a s l i g h t change i n p r e s s u r e . And, i n c o n t r a s t , t h e l e s s t h e com­ p r e s s i b i l i t y of t h e medium and t h e g r e a t e r i t s Figure 1 . The Change i n tt--. Speed of Sound w i t h e l a s t i c i t y , t h e g r e a t e r t h e speed o f sound i n A1 t i t u d e . t h e same medium. In t h i s c a s e , a s l i g h t change i n d e n s i t y may be achieved only through a g r e a t change i n p r e s s u r e . The speed of sound i s taken i n t o c o n s i d e r a t i o n i n any case i n which t h e r e i s an e v a l b a t i o n o f t h e e f f e c t of c o m p r e s s i b i l i t y i n any aerodynamic phenomena, because t h e value of t h e speed of sound c h a r a c t e r i z e s t h e c o m p r e s s i b i l i t y of t h e medium. I f t h e medium is e l a s t i c (compressible), compressions and expansions w i l l vary s u b s t a n t i a l l y from l a y e r t o l a y e r with t h e speed of sound. I f t h e medium is a b s o l u t e l y incompressible, i . e . , f o r any i n c r e a s e i n p r e s s u r e t h e volume o r d e n s i t y remains unchanged, then as can b e seen from t h e formula given above, t h e speed of sound w i l l be q u i t e high. In such a medium, any d i s t u r b a n c e s a r e propa­ gated any d i s t a n c e i n s t a n t a n e o u s l y . A s was shown above, t h e value of t h e speed of sound v a r i e s i n d i f f e r e n t gases and, i n a d d i t i o n , it i s a f u n c t i o n of temperature. With an i n c r e a s e i n a l t i t u d e , temperature and t h e speed of sound decrease. Therefore, t h e e f f e c t of c o m p r e s s i b i l i t y on t h e f l i g h t of a i r c r a f t a t high a l t i t u d e s should appear even g r e a t e r . Let us introduce s e v e r a l values f o r the speed o f sound a t t = 0 ° C : f o r n i t r o g e n i t is 3 3 7 . 3 , f o r hydrogen it i s 1300, and f o r water i t i s 1450 m/sec. For s o l i d b o d i e s , which a r e l e s s compressible than g a s e s , t h e speed of sound i s s t i l l g r e a t e r . Thus, i n wood t h e speed o f sound i s 2800 m/sec, while i n s t e e l i t i s 5000 and i n g l a s s i t i s 5600. A a i r c r a f t i n f l i g h t , r e p e l l i n g a i r on a l l s i d e s , p a r t i a l l y compresses n i t as w e l l . A t low f l i g h t speeds, t h e a i r i n f r o n t of t h e a i r c r a f t succeeds i n being d i s p l a c e d and adapts i t s e l f t o t h e flow around t h e a i r c r a f t so t h a t compression i s i n s i g n i f i c a n t i n t h i s case. A t h i g h e r f l i g h t speeds, however, t h e a i r compression begins t o p l a y a more important r o l e . In t h i s case, t h e r e ­ f o r e , f o r a s c a l e of f l i g h t speed w e must use a c h a r a c t e r i s t i c speed which may / 2 1 s e r v e a s a c r i t e r i o n f o r t h e c o m p r e s s i b i l i t y of t h e medium. Such a speed is t h e speed of sound, inasmuch as i t i s a f u n c t i o n o f t h e temperature and 7
  • 16. p r o p e r t i e s o f t h e gas. § 5. T h e Mach Number and i t s Value i n F l i g h t Problems The r a t i o of t h e f l i g h t ( o r flow) speed t o t h e speed of sound i s c a l l e dt h e Mach number: Let us assume t h a t t h e t r u e f l i g h t speed ( s e e § 6 of t h i s Chapter) o f ana i r c r a f t at an a l t i t u d e o f 10,000 m i s 920 km/hr (255 m/sec). Then t h e Mach 255 -number M = - - 0.85, where a = 300 m/sec. I n o t h e r words, t h e f l i g h t speed 300i s 85% of t h e speed of sound a t t h i s given a l t i t u d e . Thus, i n comparing t h e speed of t h e motion of t h e body i n t h e a i r witht h e speed of sound under t h e same c o n d i t i o n s , w e may determine t h e e f f e c t ofa i r c o m p r e s s i b i l i t y on t h e c h a r a c t e r of t h e flow around t h e body. The Machnumber i s t h e index of t h e air c o m p r e s s i b i l i t y . The g r e a t e r t h e Mach number,t h e g r e a t e r t h e a i r c o m p r e s s i b i l i t y should be during f l i g h t . To monitor t h e Mach number i n f l i g h t , an instrument -- the Mach i n d i c a t o r(Machmeter) -- i s u s u a l l y s e t up on t h e p i l o t s instrument panel. In high-speed f l i g h t , e s p e c i a l l y when maneuvers a r e b e i n g performed which r e s u l t i na l o s s of a l t i t u d e , t h e reading on t h i s instrument must be followed, and t h ep i l o t must not exceed t h e Mach number which t h e i n s t r u c t i o n s permit f o r t h egiven a i r c r a f t . I f f l i g h t speed remains c o n s t a n t as a l t i t u d e i n c r e a s e s , t h eMach number w i l l i n c r e a s e due t o t h e decrease i n t h e speed of sound. F a i l u r e t o monitor t h e Mach number i n j e t a i r c r a f t would r e s u l t i n gravet r o u b l e because knowing t h e i n d i c a t e d speed ( s e e § 6 of t h i s Chapter) and event h e t r u e speed does n o t g i v e t h e p i l o t a f u l l understanding of t h e f l i g h t Machnumber a t any s p e c i f i c a l t i t u d e . For example, i f t h e a i r c r a f t i s f l y i n g a t ani n d i c a t e d speed of 500 km/hr a t an a l t i t u d e of 12,000 m, t h e t r u e speed w i l lbe around 930 km/hr while t h e speed of sound i s 1063 km/hr, s o t h a t undert h e s e given f l i g h t conditions t h e Mach number = 0.875. I f , however, t h ea i r c r a f t i s f l y i n g with an i n d i c a t e d speed of 500 km/hr a t an a l t i t u d e of1000 m, the t r u e speed i s only 525 km/hr, while t h e Mach number = 0.43. I n t u r b o j e t a i r c r a f t , a change i n t h e Mach number may be represented i nt h e following way. A f t e r t a k e o f f and r e t r a c t i o n of t h e landing gear andwing f l a p s , t h e a i r c r a f t p i c k s up speed u n t i l i t achieves an i n d i c a t e d speedof 500 - 600 km/hr and starts climbing. S t a r t i n g a t an a l t i t u d e of around1000 m, t h e Machmeter shows a Mach number of M = 0.5 - 0.55. As t h e a i r c r a f tclimbs, the t r u e speed w i l l i n c r e a s e , t h e speed of sound w i l l decrease, and /13 -t h e Mach number i n c r e a s e . When t h e a i r c r a f t reaches an a l t i t u d e of 8-9 km,t h e Mach number reaches a v a l u e of 0.63 - 0.66 (depending on t h e a c t u a ltemperature a t t h a t a l t i t u d e ) . A t a l t i t u d e s of 10-12 km, during a c c e l e r a t i o nt h e Mach number i n c r e a s e s t o 0.80 - 0.85. A t high a l t i t u d e s t h e Mach number8
  • 17. w i l l b e g r e a t e r when t h e same t r u e speeds are maintained. Turbojet a i r c r a f t ,l i k e many o t h e r high-speed a i r c r a f t , have a l i m i t t o t h e i r Mach number becauseof conditions o f s t a b i l i t y and handiness (more w i l l b e s a i d concerning t h es e l e c t i o n of t h e Mach number i n Chapters 7 and 11). Therefore ( e s p e c i a l l y a thigh a l t i t u d e s ) , i t i s i n s u f f i c i e n t t o monitor f l i g h t simply with r e s p e c t t ospeed; t h e Mach i n d i c a t o r m u s t a l s o be observed.5 6 . F1 i g h t Speed. Corrections t o Instrument Readings Necessitated by Compressibility Aircraft speed i n d i c a t o r s measure d i r e c t l y n o t only t h e speeds, b u t t h e 2v e l o c i t y head q = pV /2. The a c t u a l f l i g h t speed i s n o t t h e same a s t h i sspeed, which i s i n d i c a t e d by t h e instrument, because t h e a i r - p r e s s u r e s e n s o ri n d i c a t e s the e f f e c t of p e r t u r b a t i o n s c r e a t e d by t h e aircraft and t h e a i rcompressibility. In a d d i t i o n , t h e v a l u e of the a c t u a l f l i g h t speed dependson i n s t r u m e n t a l c o r r e c t i o n s . Therefore, t o e l i m i n a t e t h e above-mentioned e r r o r s i n t h e instrumentr e a d i n g s , t h e following c o r r e c t i o n s a r e introduced: aerodynamic, whichaccounts f o r t h e d i f f e r e n c e i n the l o c a l p r e s s u r e s ( a t t h e p o i n t where t h ea i r - p r e s s u r e s e n s o r i s located) from p r e s s u r e s i n t h e undisturbed i n c i d e n tflow, c o r r e c t i o n s f o r c o m p r e s s i b i l i t y , and instrument c o r r e c t i o n s * . The speed which would be shown on an i d e a l ( i . e . , e r r o r - f r e e ) speedi n d i c a t o r i s c a l l e d t h e i n d i c a t e d speed V The speed which i s read from t h e iinstrument (read from t h e wide n e e d l e ) , does not as a r u l e equal t h e i n d i c a t e dspeed. Therefore, a s p e c i a l name has been c r e a t e d f o r i t -- instrument speedinst The t r u e a i r speed i s t h e speed of t h e a i r c r a f t s motion r e l a t i v e t o t h ea i r (and i s read from t h e t h i n arrow on t h e i n s t r u m e n t ) . The KUS11200 combined speed i n d i c a t o r , which j e t a i r c r a f t f l y i n g a tMach speeds up t o 0 . 9 a r e equipped w i t h , shows t h e instrument speed and t h et r u e a i r speed. During l o w - a l t i t u d e f l i g h t (where t h e a i r d e n s i t y i s c l o s et o t h a t of t h e e a r t h s s u r f a c e , equal t o 0.125 kG - sec2/m4), t h e instrumentand t r u e a i r speeds agree and both arrows on t h e instrument move t o g e t h e r ,being superimposed. With an i n c r e a s e i n a l t i t u d e , t h e t r u e a i r speeds u r p a s s e s the instrument speed and t h e arrows diverge, forming a "fork." /14Knowing t h e true a i r speed and wind speed, i t i s p o s s i b l e t o determine t h eground speed, i . e . , t h e speed of t h e a i r c r a f t s displacement r e l a t i v e t o t h ee a r t h . In f l y i n g and aerodynamic computations, both t h e i n d i c a t e d andinstrument speeds are used. And what i s t h e d i f f e r e n c e between them? Toswitch from instrument speed t o i n d i c a t e d speed, we must introduce an aero­dynamic c o r r e c t i o n and a c o r r e c t i o n f o r a i r c o m p r e s s i b i l i t y : * M.G.Kotik, e t a l . , F l i g h t T e s t i n g o f A i r c r a f t , Mashinostroyeniye, 1965 (Available i n N S t r a n s l a t i o n ) . AA 9
  • 18. ins t = vi + 6Va + 6Vcomp = vi + 6Va, gwhere Vi = i n d i c a t e d speed, 6V = aerodynamic c o r r e c t i o n , a = correction f o r compressibility, and "comp Vi = i n d i c a t e d ground speed. g For high-speed a i r c r a f t , an e s s e n t i a l c o r r e c t i o n i s t h e c o r r e c t i o n f o ra i r c o m p r e s s i b i l i t y , whose value may range from 10 t o 100 lan/hr. The e f f e c tof a i r c o m p r e s s i b i l i t y i n c r e a s e s the speed i n d i c a t o r reading, s o t h a t 6Vcompi s always negative (Fig. 2 ) . 400 600 800 l0 o0 1200 1.~70 Vi , km/hr & i Figure 2. Nomogram f o r Determining t h e Correction f o r Air Compressibility The aerodynamic c o r r e c t i o n may reach values from 5 t o 25 km/hr and may b e - /15e i t h e r p o s i t i v e o r negative. Whereas t h e c o r r e c t i o n f o r c o m p r e s s i b i l i t y i si d e n t i c a l f o r a l l a i r c r a f t , the aerodynamic c o r r e c t i o n i s b a s i c a l l y a f u n c t i o nof t h e type of a i r c r a f t o r , more s p e c i f i c a l l y , t h e p o s i t i o n and f e a t u r e s of10
  • 19. P t h e engine. Therefore, each a i r c r a f t h a s i t s own graph o f aerodynamic corrections. The i n d i c a t e d speed w i t h t h e c o r r e c t i o n f o r c o m p r e s s i b i l i t y i s c a l l e d t h e i n d i c a t e d ground speed: V. = Vi + 6 V A t sea l e v e l , i r r e s p e c t i v e o f a i r 1 comp * g temperature, vi = vi. According t o t h e nomogram i n Figure 3 , w e may f i n d t h e . E f l i g h t Mach number b e i n g given t h e v a l u e of Vi , and t h e n determine t h e t r u e g f l i g h t speed: V = aM. For example, we m u s t determine t h e true speed and t f l i g h t Mach number f o r t h e a i r c r a f t i f a t an a l t i t u d e o f 10,000 m y Vinst ­ - = 500 km/hr. = -10 km/hr, we f i n d : Taking t h e aerodynamic c o r r e c t i o n 6 V a Vi = 490 km/hr. For t h i s speed, according t o t h e nomogram (Figure 2 ) , w e g o b t a i n GVcomp = -23 km/hr. Then l e t us determine t h e i n d i c a t e d speed Vi = ins t - 10 - 2 3 = 500 -33 = 467 km/hr. The t r u e f l i g h t speed may b e found from t h e following e x p r e s s i o n : V. - 467 V = - - -= 810 km/hr, 1 0.58 t & where f o r H = 10,000 m, A = 0.337, a d = 0.58 ( s e e t h e t a b l e f o r t h e T / 16 - s t a n d a r d atmosphere). Or, f o r speed V = 490 km/hr, according t o t h e nomo­ i g gram (Fig,. 3 ) , w e o b t a i n a Mach number of 0.75. Knowing t h e speed of sound a t H = 10,000 m and t h e f l i g h t Mach number, i t is easy to. determine t h e t r u e speed: Vt = a = 300 M - 0.75 - 3.6 = 810 km/hr. The accepted v a l u e 6Va = -10 km/hr i s c h a r a c t e r i s t i c of modern high- speed a i r c r a f t w i t h i n t h e range o f t h e i r i n d i c a t e d speeds o f 220 - 600 km/hr. Later we w i l l determine t h e c.orrection f o r a i r c o m p r e s s i b i l i t y i n each c o n c r e t e case according t o t h e nomogram i n Figure 2 , while we w i l l assume t h a t t h e aerodynamic c o r r e c t i o n i s 6 V = -10 km/hr. a 5 7. T h e Character o f t h e Propagation o f Minor P e r t u r b a t i o n s i n F l i g h t a t Various A1 ti t u d e s I n an example of a i r c r a f t f l i g h t , l e t us examine t h e manner i n which s l i g h t f l u c t u a t i o n s i n d e n s i t y and p r e s s u r e , i . e . , minor p e r t u r b a t i o n s , w i l l b e propagated i n t h e a i r flow. The a i r c r a f t , being t h e s o u r c e of t h e per­ t u r b a t i o n s , has an e f f e c t on t h e a i r p a r t i c l e s l o c a t e d i n f r o n t of i t and p e r t u r b a t i o n s a r e s e n t forward from one p a r t i c l e t o t h e n e x t a t t h e speed of sound. L e t us f i r s t t a k e an a i r c r a f t f l y i n g a t below t h e speed o f sound (Fig. 4a). 11
  • 20. P Figure 3. Nomogram f o r Determining t h e Mach Number -- -/ I I .-- _ . Figure 4. Propagation C h a r a c t e r i s t i c s f o r Sound Waves12
  • 21. When t h e a i r c r a f t passes through p o i n t A t h e p e r t u r b a t i o n s c r e a t e d by ita t t h a t given moment, propagating along a sphere a t t h e speed of sound, overt a k e the aircraft. A f t e r a s h o r t t i m e , t h e Mach wave reaches p o i n t B y whileduring t h i s t i m e t h e a i r c r a f t has succeeded only i n progressing t o p o i n t C;t h u s , i t s f l i g h t speed is below t h e speed o f sound. Passing through p o i n t D,it again c r e a t e s p e r t u r b a t i o n s which w i l l be propagated with t h e speed ofsound and i n a s h o r t while reach p o i n t E . The a i r c r a f t , however, during t h i stime w i l l n o t have reached p o i n t E b u t w i l l be located between p o i n t s C andE. Thus, t h e a i r c r a f t remains c o n s t a n t l y w i t h i n t h e s p h e r e c r e a t e d by i t ssound wave. I f , however, t h e a i r c r a f t f l i e s a t t h e speed of sound (Fig. 4b) ,then p o i n t B i s reached simultaneously by both t h e a i r c r a f t and t h e soundwaves, i . e . , t h e p e r t u r b a t i o n s c r e a t e d by it a t p o i n t s A, C and D. Thus, i n f r o n t of t h e a i r c r a f t t h e r e a r e always Mach waves which,becoming superimposed upon each o t h e r , f o n a dense s e c t i o n o f a i r c a l l e d t h ecompression shock o r shock wave. If t h e a i r c r a f t f l i e s above t h e speed o f sound, it moves ahead of t h es p h e r i c a l waves i t has c r e a t e d (Fig. 4c). The a i r c r a f t w i l l reach p o i n t Ca t t h e moment when t h e p e r t u r b a t i o n i t c r e a t e d a t p o i n t A has reached onlyp o i n t B y while t h e p e r t u r b a t i o n c r e a t e d a t p o i n t D has reached p o i n t E . Thus,behind an a i r c r a f t f l y i n g a t s u p e r s o n i c speed a Mach cone i s formed whichc o n s i s t s of an i n f i n i t e number of Mach waves propagated along t h e sphere a tt h e speed of sound. However, t h e air mass w i t h i n t h e Mach cone i s d i s p l a c e d ­ / 17r e l a t i v e t o t h e e a r t h a t t h e a i r c r a f t s speed. The g r e a t e r t h e a i r c r a f t sspeed, t h e s h a r p e r t h e angle a t t h e t i p of the Mach cone. This angle i sdetermined according t o t h e formula (Fig. 4c): 1 sin 4 = - MIf t h e Mach number i s 1, then $ = go", while t h e f u l l angle is 180" (normalshock); f o r M = 2 , s i n 9 = 0 . 5 and t h e angle $ = 30" ( f u l l angle 6 0 ° ) . Compression shocks a r e both normal and oblique. A normal compressionshock i s one whose s u r f a c e i s p e r p e n d i c u l a r t o the d i r e c t i o n o f t h e i n c i d e n tflow, i . e . , which forms an angle B = 90" w i t h i t (Fig. Sa). Oblique shocksa r e those whose s u r f a c e forms an a c u t e angle of f3 < 90" w i t h t h e d i r e c t i o nof t h e i n c i d e n t flow (Fig. 5b). The g r e a t e s t speed l o s s e s and i n c r e a s e s i n p r e s s u r e a r e observed whent h e flow passes through a normal compression shock. The braking of t h e flowon t h i s shock i s s o s u b s t a n t i a l t h a t behind the shock the flow v e l o c i t y must /8 1be below t h e speed of sound (by a s much as i t was above t h e speed of soundi n f r o n t of t h e shock). I n an oblique shock t h e l o s s e s are l e s s than with a normal shock,s p e c i f i c a l l y , p r o p o r t i o n a t e l y l i t t l e t h e more t h e shock w a s i n c l i n e d i n t h ed i r e c t i o n o f t h e flow, i . e . , t h e l e s s t h e angle B . The i n t e n s i t y of anoblique shock i s a l s o s u b s t a n t i a l l y l e s s than a normal shock. If t h e angle B 13
  • 22. i s c l o s e t o 9Qo, then behind t h e oblique shock t h e speed of t h e flow i ssubsonic, while somewhat g r e a t e r than t h a t which would be obtained i f t h eshock were normal. Streams p a s s i n g through an oblique shock change t h e d i r e c t i o n o f t h e i r motion, d e v i a t i n g . from t h e i r i n i t i a l d i r e c t i o n . During flow around a wing o r f u s e l a g e with a speed exceeding t h e speed o f sound, an oblique shock developes i n f r o n t of t h e wing o r f u s e l a g e . oblique compress i g n A i r c r a f t intended f o r t r a n s - and super­ s o n i c speeds must have i aerodynamic shapes which perturbation f do n o t g e n e r a t e normal y- boundary compression shocks. The forward edge of t h e wing on s u p e r s o n i c a i r c r a f tFigure 5. Formation of Normal ( a ) and O b l i q u e must b e k n i f e - l i k e , and( b ) Compress i on Shocks. t h e wing i t s e l f must be quite thin.5 8. Trans- o r Supersonic Flow o f Air Around Bodies In t h e case of low-velocity flow around b o d i e s , t h e flow is deformed a ta s u b s t a n t i a l d i s t a n c e from t h e body and a i r p a r t i c l e s , i n breaking away, flow - /19smoothly around i t (Fig. 6a) . When t h i s o c c u r s , t h e p r e s s u r e c l o s e t o t h e body v a r i e s i n s i g n i f i c a n t l y , which permits us t o consider a i r d e n s i t y as constant. As a MC 1 r e s u l t of t h e d i f f e r e n c e i n p r e s s u r e s under and over t h e wing, l e f t i s c r e a t e d . I n t h e case of s o n i c o r s u p e r s o n i c flow I Mach around a body, l o c a l a i r p r e s s u r e and d e n s i t y v a r i a t i o n s a r i s e which, propagating a t t h e speed of sound, form a s o n i c o r s u p e r s o n i c shock wave i n f r o n t of t h e body. This occurs because t h e speed of t h e a i r p a r t i c l e s c l o s e t o t h e body suddenly v a r i e s i n both amount and d i r e c t i o n . When t h i s occurs, t h e flow i n a s e n s e "encounters" anFigure 6 . Subsonic ( a ) and o b s t a c l e which, depending on t h e s i t u a t i o n ,Supersonic ( b ) Flow Around may be t h e body i t s e l f o r an " a i r cushion" i na Wing P r o f i l e . f r o n t of i t and form a compression shock14
  • 23. (shock wave). A t t h i s compression shock t h e r e i s an uneven change i n t h eb a s i c parameters c h a r a c t e r i z i n g t h e conditions of t h e a i r , i . e . , speed V,p r e s s u r e p , d e n s i t y p and temperature T. Shock waves may b e formed e i t h e ri n f r o n t of t h e p r o f i l e o r c l o s e t o i t s t r a i l i n g p o r t i o n . P r e c i s e c a l c u l a ­t i o n s and measurements have shown t h a t t h e thickness of t h e shock waves - o rcompression shocks i s n e g l i g i b l y small and has an o r d e r of length o f t h e freepath of the molecules, i . e . , 10-4 - 10-5 mm (0.0001 - 0.00001 mm).§ 9. Sonic Ibooml Supersonic f l i g h t i s accompanied by t h e c h a r a c t e r i s t i c s o n i c %boom. This phenomenon i s t h e r e s u l t of t h e formation o f a system of compressionshocks and expansion waves i n f r o n t of t h e nose o f a f u s e l a g e , t h e cabin, o rwhere t h e wing and t a i l assembly j o i n t h e f u s e l a g e . * The most powerful shockwaves a r e formed by t h e a i r c r a f t s nose and wing, which during f l i g h t are t h ef i r s t t o encounter t h e a i r p a r t i c l e s , and t h e t a i l assembly. These shockwaves are l a b e l e d bow and t a i l shock waves , r e s p e c t i v e l y (Fig. 7a). I n t e r imediate shock waves e i t h e r c a t c h up with t h e bow shock and merge with i t o r /20 f a l l behind and merge w i t h t h e t a i l shock. Behind t h e bow shock, t h e a i r p r e s s u r e i n c r e a s e s unevenly, becoming g r e a t ­e r than atmospheric p r e s s u r e , and then decreases smoothly and becomes even l e s sthan atmospheric, a f t e r which i t again i n c r e a s e s unevenly u n t i l i t i sp r a c t i c a l l y atmospheric again a t t h e t a i l wave. The sudden p r e s s u r e drop i s t r a n s m i t t e d t o t h e a i r around i t i n ad i r e c t i o n perpendicular t o t h e wave s u r f a c e . Persons on t h e ground f e e l t h i sdrop as a s t r o n g Ifboom." Sometimes a second Yboom" i s heard -- t h i s i s ther e s u l t of t h e s u c c e s s i v e e f f e c t s o f b o t h t h e bow and t a i l shock waves. Figure 7. A i r Pressure Changes during a "boom" i n t h e Vertical Plane b e l o w t h e A i r c r a f t ( a ) , and t h e I n t e r c e p t i o n of t h e Conic Shock Wave w i t h t h e E a r t h s Surface ( b ) . . .* A. D. Mironov, Supersonic "Floc" i n Aircraft. Voyenizdat, 1964. 15
  • 24. Repeated observations have e s t a b l i s h e d t h a t t h e two s u c c e s s i v e s o n i cbooms are d i s t i n c t l y heard only when t h e r e i s more than 1/8th o f a secondbetween them. The longer t h e a i r c r a f t , t h e longer t h e time i n t e r v a l between t h eoccurrence of t h e bow wave and t h e t a i l wave. Therefore, two "booms" ared i s t i n c t l y heard i n t h e c a s e o f an a i r c r a f t with a long f u s e l a g e . And, i nc o n t r a s t , an only vaguely s e p a r a t e d "boom" i n d i c a t e s t h a t t h e a i r c r a f t hassmall dimensions o r i s f l y i n g a t a r e l a t i v e l y low a l t i t u d e . If t h e a i r c r a f t f l i e s a t a constant s u p e r s o n i c speed, t h e " b 0 0 m " i sheard simultaneously a t d i f f e r e n t p o i n t s on t h e e a r t h s s u r f a c e . If t h e s ep o i n t s were t o be j o i n e d by a l i n e , we would o b t a i n a hyperbola forming asa r e s u l t of t h e i n t e r c e p t i o n of t h e conic shock wave with t h e p l a n e o f t h ee a r t h s s u r f a c e (Fig. 7 b ) . One hyperbola corresponds t o t h e bow wave, andt h e o t h e r -- t o t h e t a i l wave. The l i n e s of simultaneous a u d i b i l i t y of t h e"boom" a r e d i s p l a c e d along t h e e a r t h s s u r f a c e , following behind t h e a i r ­c r a f t and forming unusual t r a i l s . A t t h e same time, d i r e c t l y below t h e a i r ­craft. t h e r e i s a s u b s t a n t i a l l y louder Itboom," which a t t e n u a t e s as a f u n c t i o n ­ /21of d i s t a n c e and under c e r t a i n circumstances it i s completely i n a u d i b l e . Theground observer who h e a r s t h e tboom" from an a i r c r a f t f l y i n g , l e t us s a y , a tan a l t i t u d e of 15 km with a speed twice t h a t o f sound w i l l not observe t h ea i r c r a f t above him; a t an a l t i t u d e of 15 km, i t takes sound approximately50 s e c t o reach t h e ground a t an average speed o f 320 m/sec, while duringt h i s time t h e aircraft w i l l have covered approximately 30 km. To g e t an i d e a of t h e e f f e c t of a p r e s s u r e d r o on b u i l d i n g s t r u c t u r e s ,l e t us p o i n t out t h a t t h e overpressure A = 10 kG/m3 c r e a t e s a s h o r t - l i f t pload o f 20 kG on a door with an area of 2 m 2 , f o r example. A f i g h t e r with af u s e l a g e length of 15 m a t Mach 1 . 5 and H = 6000 m c r e a t e s A = 11 kG/m2. p Aheavy, delta-winged s u p e r s o n i c a i r c r a f t weighing 70 t o n s w i l l , f l y i n g a t ana l t i t u d e of 20 km and a t Mach 2 c r e a t e A = 5 kG/m2, and a t low a l t i t u d e s p(5-8 km) a drop may reach 12-18 kG/m2. I t i s a known f a c t t h a t i n t h e i rdesign, b u i l d i n g s are planned f o r t h e s o - c a l l e d wind load, which correspondst o t h e f o r c e of t h e p r e s s u r e o f a i r moving a t a speed of 40 m/sec, i . e . ,g r e a t e r than 140 km/hr. This type wind w i l l c r e a t e an overpressure o f 100 kgon 1 m2 of wall s u r f a c e . The p r e s s u r e i n t h e "boomT a t p e r m i s s i b l e f l i g h ta l t i t u d e s i s 1/5th o r 1 / 6 t h t h a t of t h e design allowance f o r wind load. The c h a r a c t e r i s t i c s of t h e e f f e c t of p r e s s u r e drops i n shock waves during"booms" are given i n Table 2. For example, on a w a l l with an a r e a o f 1 2 m2during an overpressure o f 50-150 kG/m2, t h e r e i s a s h o r t - l i v e d load o f 600­1800 kG. Under t h e e f f e c t of such a load, wooden s t r u c t u r e s may c o l l a p s e .Therefore, a i r c r a f t are forbidden t o a c c e l e r a t e t o s u p e r s o n i c v e l o c i t i e s below9-10 km o v e r populated areas. In t h e opinion of f o r e i g n s p e c i a l i s t s , a s o n i c"boom" with an i n t e n s i t y of 5 kG/m2 i s t h e most which can b e t o l e r a t e dharmlessly . Therefore, f u t u r e s u p e r s o n i c j e t a i r c r a f t with heavy f l i g h tweights (140 - 170 tons) w i l l have t o f l y a t a l t i t u d e s of 18-24 km i n o r d e rt o minimize t h e e f f e c t of p r e s s u r e drops. In t h i s case, they w i l l have t oclimb t o a l t i t u d e s of 9-10 km a t subsonic l i g h t regimes (Mach number = 0.9 - ­ / 220.92), while beyond t h a t at up t o scheduled f l i g h t a l t i t u d e a t Mach M = 1.0 ­16
  • 25. 1.2, and only at t h i s a l t i t u d e w i l l they be a b l e t o a c c e l e r a t e t o supersonicc r u i s i n g speed. TABLE 2P res su re Drop, kG/m2 Relative Loudness and Resultant Destruction 0.5 - 1.5 Distant b l a s t 1.5 - 5 Close b l a s t o r thunder 5 - 15 Very c l o s e , loud t h u n d e r (window g l a s s r a t t l e s and s h a t t e r s ) 15 - 50 Large window panes s h a t t e r 50 - 150 L i g h t structures collapse The sound of t h e s o n i c boom i s a f u n c t i o n o f t h e f l i g h t a l t i t u d e , Machnumber, a i r c r a f t s angle of a t t a c k , f l i g h t t r a j e c t o r y , atmospheric p r e s s u r ea t sea l e v e l and a t t h e f l i g h t a l t i t u d e , and wind d i r e c t i o n with r e s p e c t t oa l t i t u d e . For example, t h e ttboomt from an a i r c r a f t f l y i n g a t an a l t i t u d e of15 km and a t Mach 2 (V = 2120 km/hr) i s heard t o a d i s t a n c e of 40 k from t h e ma i r c r a f t s p a t h , while a t an a l t i t u d e of 11 km i t i s heard only t o a d i s t a n c eof 33 km. During f l i g h t a t an a l t i t u d e of 1.5 km a t Mach 1.25, t h e "boom"i s heard only w i t h i n a b e l t 8 km wide. A t a i l wind may d i s p l a c e t h e shock wave, r e s u l t i n g i n d i s p l a c e o f t h ea u d i b i l i t y zone. The climbing and descent speeds and t h e angle of i n c l i n a t i o n0 o f t h e t r a j e c t o r y have s i g n i f i c a n t effects on t h e s i z e of t h e a u d i b i l i t yzone and t h e loudness of t h e "boom." F o r example, i n gaining a l t i t u d e a t anangle of 0 = 15 a t H = 5 km, t h e tboomt i s heard on t h e ground a t M > 1 . 2 .In descending from an a l t i t u d e o f 10-11 km a t an angle 0 = - l o " , t h e "boom"reaches t h e .ground only a t M = 1.03. In conclusion, l e t us dwell on t h e e f f e c t of t h e shock wave c r e a t e d bya s u p e r s o n i c a i r c r a f t on a passenger a i r c r a f t i n f l i g h t . A s has already beens a i d , t h e p r e s s u r e drop during a compression shock i s 5-18 kG/m2. If f o r t h emean value we s e l e c t 10 kG/mZ, i t amounts t o l e s s than 0.1% of t h e a i rp r e s s u r e a t ground l e v e l (p = 10,332 kG/m2 = 1 a t . ) . The v e l o c i t y head f o ra j e t passenger a i r c r a f t f l y i n g st a speed o f 850 km/hr and a t an a l t i t u d eof 10 km i s approximately 1200kG/m2, i . e . , more than 100 times t h e p r e s s u r edrop i n t h e "boom." Consequently, such a drop has e s s e n t i a l l y no e f f e c t onan a i r c r a f t i n f l i g h t . However, t h e r e may be a c e r t a i n e f f e c t on t h e a i r ­c r a f t s behavior as c r e a t e d by t h e accompanying j e t from t h e a i r c r a f t f l y i n gby; t h i s e f f e c t i s comparable t o t h a t of a s l i g h t g u s t ( a s i n g l e g u s t o f"bumpy a i r " ) , d i r e c t e d along t h e propagating l i n e of t h e shock wave. As ar e s u l t , t h e a i r c r a f t w i l l experience s l i g h t bumpiness. 17
  • 26. § 10. Features of t h e Formation of Compression Shock during F l m Around Various Shapes o f Bodies Let us now look a t t h e f e a t u r e s of t h e formation of compression shocksf i r s t with t h e example of flow around t h e a i r i n l e t o f a j e t engine durings u p e r s o n i c f l i g h t , and t h e n l e t us consider flow around t h e p r o f i l e . The e x i s t e n c e of a normal shock at t h e i n t a k e t o t h e d i f f u s e r leads t os u b s t a n t i a l l o s s e s of t o t a l p r e s s u r e ( k i n e t i c energy) o f t h e air e n t e r i n gt h e compressor and t h e combustion chamber. During d e c e l e r a t i o n i n t h e d i f f u s e r , t h e s u p e r s o n i c flow i s transformedas i t passes through t h e normal compression shock. When t h i s occurs, onep a r t of t h e k i n e t i c energy of t h e a i r is used f o r i t s compression, while t h e - /23o t h e r i s transformed i n t o h e a t ( l o s t energy). However, during f l i g h t oft h e Mach number M < 1 . 5 , l o s s e s a t t h e shock a r e small. A s a r u l e , t h e r e f o r e ,f o r such f l i g h t speeds i n t a k e devices a r e used on subsonic a i r c r a f t . A t f l i g h t g r e a t e r t h a n 1 . 5 Mach, however, l o s s e s a t t h e normal shockbecome g r e a t e r . To e l i m i n a t e t h i s , t h e process o f a i r d e c e l e r a t i o n i n t h ei n t a k e device i s achieved through t h e c r e a t i o n of systems o f o b l i q u e shockswhich terminate i n a weak normal shock. Because o v e r a l l energy l o s s e s i na system of o b l i q u e shocks are l e s s than i n one normal shock, t h e p r e s s u r e a tt h e end of t h e d e c e l e r a t i o n w i l l r e t a i n a high v a l u e . Thus, t h e normal shockis divided i n t o a s e r i e s o f oblique shocks. S t r u c t u r a l l y , t h i s i s achievedthrough s e t t i n g up i n the d i f f u s e r a s p e c i a l s p i k e i n t h e shape of s e v e r a lcones whose t i p s a r e d i r e c t e d according t o f l i g h t (Fig. 8 a ) . When f l i g h t speed i s decreased, t h e angles o f i n c l i n a t i o n of t h e obliqueshocks i n c r e a s e ( t h e angle B tends toward 9 0 ; see Figure 5 ) . A s speed i si n c r e a s e d , t h e r e v e r s e occurs, and t h e s e angles decrease. This h i n d e r s t h eoperation of t h e i n p u t device inasmuch as t h e f r o n t f o r a l l t h e shocks w i l ln o t pass through t h e i n p u t edge of t h e cone (Fig. 8b). Therefore, sometimest h e s p i k e i s a d j u s t a b l e , s o t h a t i n t h e event of changes i n speed, i t sp o s i t i o n can b e v a r i e d a x i a l l y , thereby h e l p i n g t h e shock t o pass through t h eleading edge of the a i r i n t a k e a t a l l f l i g h t speeds. O t h e wing p r o f i l e , t h e formation of compression shocks OCCUTS even ns u b s t a n t i a l l y below t h e speed of sound. As soon as t h e flow speed o f t h econvergent stream exceeds t h e speed of sound somewhere on t h e p r o f i l e , Machwaves appear which, i n accumulating, form a shock. I t must be noted t h a tt h i s shock wave i s formed first on t h e upper p r o f i l e s u r f a c e c l o s e t o somep o i n t corresponding t o t h e maximum of t h e l o c a l speed and t h e minimump r e s s u r e on t h e p r o f i l e . As soon as t h e speed of t h e flow s u r p a s s e s t h e speed ­ /24of sound, a shock wave forms on t h e lower p r o f i l e s u r f a c e as w e l l (Fig. 9 ) . 1. A t p o i n t C t h e p o i n t of l e a s t p r e s s u r e on t h e p r o f i l e , t h e speed o ft h e motion of t h e a i r has a t t a i n e d t h e l o c a l speed of sound (Fig. 9 a ) . TheMach waves move from t h e source of t h e p e r t u r b a t i o n toward p o i n t C and,running i n t o each o t h e r , form a weak normal compression shock.18
  • 27. F i g u r e 8. Formation of Compression Shocks a t t h e Intake t o t h e Diffuser of a Turbojet E n g i n e a t Supersonic F l i g h t Speeds: a - l i n e drawing o f i n p u t device w i t h cone: O A , BA -- oblique compression shocks, AK -- normal compression shock; b - operational c o n f i g u r a t i o n of supersonic d i f f u s e r d u r i n g f l i g h t speed below i t s design speed. Figure 9. The Formation of Compression Shocks a t Various Streamline Flows. 2. As t h e speed of sound i n c r e a s e s somewhat ( a t V2 > Vl), t h e speedof t h e flow around t h e p r o f i l e i n c r e a s e s (Fig. 9b). Behind p o i n t C y t h espeed of t h e flow becomes g r e a t e r than t h e speed of sound. A s e c t i o nappears where t h e flow moves a t s u p e r s o n i c v e l o c i t y , r e s u l t i n g i n t h eformation of an oblique shock. 19
  • 28. 3. A t a speed o f V3 (V3 < a ) , regions o f s o n i c and s u p e r s o n i c flow a l s oform on t h e bottom of t h e p r o f i l e , r e s u l t i n g i n t h e formation o f compressionshocks (Fig. 9 c ) . 4. A t a speed o f V4 c l o s e t o t h e speed of sound, t h e compression shocksare d i s p l a c e d toward t h e t r a i l i n g edge, thereby i n c r e a s i n g t h e s e c t i o n o f t h ep r o f i l e which encounters s u p e r s o n i c flow p a s t i t (Fig. 9d). 5. When v e l o c i t y V5 becomes somewhat g r e a t e r t h a n t h e speed o f sound, abow wave forms i n f r o n t of t h e p r o f i l e and a t a i l wave forms behind i t (Fig.9e). During flow around a b l u n t e d body, t h e compression shock forms a t a ­ / 25s l i g h t d i s t a n c e from i t s forward s e c t i o n and assumes a c u r v i l i n e a r form(Fig. l o a ) . A t i t s forward edge, t h e shock i s normal -- h e r e i t i s perpen­d i c u l a r t o t h e i n c i d e n t flow. Depending on t h e d i s t a n c e from t h e body, t h eangles of i n c l i n a t i o n o f t h e shock decrease. During s u p e r s o n i c flow arounda knife-edged body such as a wedge with a l a r g e open angle (Fig. l o b ) , t h eshock i s formed a l s o a t a s l i g h t d i s t a n c e from t h e bow p o i n t and a l s o has ac u r v i l i n e a r form. If t h e open angle o f t h e wedge i s small enough, t h ecompression shock " s e a t s i t s e l f " on t h e s h a r p edges (Fig. 1Oc). Figure 10. T h e Formation of Compression Shocks a t I d e n t i c a l Flow V e l o c i t i e s : a - i n f r o n t of a b l u n t e d body, b and c - i n f r o n t of knife-edged bodies.§ 1 1 . C r i t i c a l Mach Number. The E f f e c t of Compressibility on t h e Motion o f Air F l y i n g Around a Wing The c o m p r e s s i b i l i t y of t h e a i r begins t o m a n i f e s t i t s e l f g r a d u a l l y asspeed i s increased. Up t o a Mach number o f 0.4, t h e e f f e c t of c o m p r e s s i b i l i t yon t h e aerodynamic c h a r a c t e r i s t i c s of t h e wing i s only s l i g h t and may i npractPce b e ignored. With a f u r t h e r i n c r e a s e i n speed, t h i s e f f e c t becomesmore and more n o t i c e a b l e and can no longer b e ignored. S t a r t i n g a t f l i g h tspeeds of 600 - 700 km/hr and above, drag i n c r e a s e s s h a r p l y because o fc o m p r e s s i b i l i t y . This occurs due t o t h e f a c t t h a t l o c a l speeds of t h e motionof t h e a i r o v e r t h e wing and a t p o i n t s where t h e wing a t t a c h e s t o t h e f u s e l a g es u b s t a n t i a l l y surpass t h e f l i g h t speed. In flowing around t h e convex s u r f a c eof the wing, f o r example, t h e air streams are compressed and t h e i r20
  • 29. c r o s s - s e c t i o n decreases. However, because t h e span across t h e stream m u s tremain c o n s t a n t , t h e speed i n i t i s increased. A t any s u f f i c i e n t l y high f l i g h tspeed, t h e l o c a l air speed a t any p o i n t on t h e wing o r o t h e r p o i n t on t h es t r u c t u r e comes t o equal t h e l o c a l speed of sound (Fig. 11). Lava1 nozzle / Profile local=a Figure 1 1 . T h e Formation o f t h e Local Speed of Sound i n Flow around a P r o f i l e . The f l i g h t speed a t which t h e l o c a l speed of sound w i l l appear anywhereon t h e wing i s c a l l e d t h e c r i t i c a l f l i g h t speed Vcr, while i t s correspondingMach number i s c a l l e d t h e c r i t i c a l Mach number Mcr. Higher values f o r t h e ­ / 26l o c a l speeds a r e observed on t h e upper a i r f o i l p r o f i l e . A s t h e speed of t h ei n c i d e n t flow o r t h e f l i g h t speed i n c r e a s e s , t h e l o c a l speed reaches the speedof sound f a s t e s t a t t h i s p o i n t . Let us examine t h e a i r stream surrounding t h e p r o f i l e (Fig. 11). Letus s e l e c t two c h a r a c t e r i s t i c c r o s s - s e c t i o n s of t h i s stream: t h e l a r g e one Iand t h e small one 11. The l o c a l a i r speeds i n s e c t i o n I1 w i l l be g r e a t e r thant h e l o c a l speeds i n s e c t i o n I as a r e s u l t of d i f f e r e n c e s between t h e areas oft h e s e s e c t i o n s . If we i n c r e a s e t h e speed of t h e i n c i d e n t unperturbed flow,t h e l o c a l speeds i n c r e a s e i n both s e c t i o n s , b u t i n s e c t i o n I1 it i s g r e a t e rthan i n s e c t i o n I . This is explained by t h e f a c t t h a t as a r e s u l t of t h ei n c r e a s e i n speed t h e r e i s a drop i n d e n s i t y which i s more i n t e n s e t h e f a s t e rthe speed of t h e stream. To r e t a i n t h e s t e a d i n e s s of t h e mass flow weightr a t e o f a i r along the stream, t h e speed i n s e c t i o n I1 must i n c r e a s e addition­a l l y i n o r d e r t o compensate f o r t h e g r e a t d e n s i t y drop i n t h i s s e c t i o n . A tt h e t h r e s h o l d , t h e l o c a l speed of t h e flow of a i r i n s e c t i o n I1 may come t oequal t h e l o c a l speed of sound. From t h i s i t follows t h a t during f l i g h t with speed Vcr, t h e l o c a l speedo f sound i s achieved a t t h e narrowest p o i n t o f t h e stream. I t has beene s t a b l i s h e d t h e o r e t i c a l l y t h a t a t t h i s i n s t a n t t h e c r i t i c a l p r e s s u r e dropforms between s e c t i o n I and I1 which i s equal t o pII : pI = 0.528. I t i s w e l l known t h a t i f t h e speed of sound i s achieved a t t h e narrowestp a r t of t h e stream, t h e speed i n c r e a s e s and becomes s u p e r s o n i c i f t h e streamcontinues broadening. Therefore, a f u l l y s u p e r s o n i c zone o f flow i s formeddown w i t h p o r t i o n of t h e p r o f i l e s u r f a c e during f l i g h t with M > Mcr. 21
  • 30. The g r e a t e r t h e f l i g h t speed, t h e g r e a t e r t h e zone of s u p e r s o n i c speed w i l lbe. However, f a r behind t h e p r o f i l e t h e speed must b e t h e same a s t h e f l i g h tspeed. Therefore, a t some poHnt on t h e p r o f i l e t h e r e must develop d e c e l e r a t i o nof t h e a i r from s u p e r s o n i c t o subsonic speed. Such d e c e l e r a t i o n , asexperience has shown, occurs only with t h e formation of a compression shock.§ 12. T h e Dependence o f t h e S p e e d o f t h e Gas Flow on t h e Shape o f t h e ­ / 27 Channel. T h e Laval Nozzle A means f o r o b t a i n i n g s u p e r s o n i c speeds i n t h e motion o f t h e gas w a s .developed by t h e engineer Laval (Switzerland) during h i s work i n t h e 1880son improving a steam t u r b i n e he had invented. Laval o b t a i n e d a s u p e r s o n i cflow of vapor as i t flowed from a s p e c i a l n o z z l e . This nozzle, subsequently c a l l e d t h e Laval Nozzle (Fig. l l ) , i s a t u b ewhich i s f i r s t compressed and then expanded. The narrowest s e c t i o n of t h etube i s c a l l e d t h e c r i t i c a l s e c t i o n . If a vapor o r gas i s run through sucha nozzle a t a s l i g h t p r e s s u r e drop i n which t h e speed o f t h e flow i n t h ec r i t i c a l s e c t i o n becomes subsonic, i n t h e expanded p o r t i o n o f t h e n o z z l e t h espeed w i l l drop; i n t h i s c a s e t h e Laval Nozzle o p e r a t e s as a t y p i c a l Venturitube. However, i f t h e d i f f e r e n c e i n p r e s s u r e s a t t h e i n p u t t o t h e n o z z l e anda t i t s o u t p u t a r e s u f f i c i e n t l y g r e a t , i n t h e c r i t i c a l s e c t i o n t h e speed oft h e flow becomes equal t o t h e l o c a l speed of sound. In t h i s c a s e , beyond t h ec r i t i c a l s e c t i o n , i . e . , i n t h e broadened p o r t i o n of t h e n o z z l e , t h e speed o ft h e flow does n o t decrease b u t , on t h e c o n t r a r y , i n c r e a s e s . Thus, it wasobserved t h a t i n sub- and s u p e r s o n i c flows, t h e dependence of t h e speed oft h e flow of gases on t h e shape of t h e channel i s d i r e c t l y o p p o s i t e . Subsonic flow accelerates i n t h e compression channel and d e c e l e r a t e s i nt h e expansion p o r t i o n . In c o n t r a s t , however, s u p e r s o n i c flow l o s e s i t sspeed i n t h e compression s e c t i o n , while i t i n c r e a s e s i t i n t h e expansionsection Therefore, i n Figure 1 we s e e t h e appearance o f s u p e r s o n i c speed a f t e r 1t h e stream has passed through t h e narrow s e c t i o n ( p o i n t K ) . However, s u p e r s o n i c speed does n o t i n c r e a s e along t h e e n t i r e length o ft h e nozzle; a t some p o i n t i t must d e c e l e s a t e t o subsonic speed. And h e r e i nl i e s t h e cause f o r t h e formation of t h e compression shock.§ 13. Laminar and Turbulent Flow o f Air Under t h e e f f e c t of i n t e r n a l f r i c t i o n due t o t h e v i s c o s i t y of a i r andt h e roughness of t h e s u r f a c e of t h e body around which t h e flow moves, t h espeed of air a t t h i s s u r f a c e becomes equal t o zero. Depending on t h e d i s t a n c efrom t h e s u r f a c e , t h e speed o f t h e flow i n c r e a s e s and reaches t h e speed off r e e flow. The l a y e r of a i r i n which t h e r e i s a change i n speed from zerot o the speed of f r e e flow i s c a l l e d t h e boundary l a y e r . I t i s w e l l known t h a t t h e flow of a i r i n t h e boundary l a y e r may belaminar ( s t r a t i f i e d ) when t h e gas flows without being mixed i n t h e neighboring22
  • 31. l a y e r s and t u r b u l e n t when t h e r e i s random mixing of gas p a r t i c l e s throughoutt h e volume o f t h e flow. The boundary l a y e r a l s o e n t a i l s phenomena such as - /28b u r b l i n g (flow s e p a r a t i o n ) , t h e formation of s u r f a c e f r i c t i o n drag, aero­dynamic h e a t i n g , e t c . The i n t e r a c t i o n of t h e boundary l a y e r and t h e compression shocks r e s u l t si n t h e following. If t h e flow i n t h e boundary l a y e r i s laminar (Fig. 1 2 ) , an oblique compression shock developes d i r e c t l y on t h e a i r f o i l p r o f i l e . Behind t h e shock t h e r e i s s e p a r a t i o n and turbulence of t h e boundary l a y e r ; i n t h e t u r b u l e n t region a normal shock developes. I n g e n e r a l , t h e o b l i q u e and normal shocks are combined. When t h e r e is an oblique shock, t h e i n t e n s i t y of t h e normal shock w i l l be s u b s t a n t i a l l y l e s s because t h e flow approaches i t , having already a t t e n u a t e d i t s speed somewhat i n t h e oblique shock, with t h e r e s u l t t h a t t h e drag d e c r e a s e s , Therefore, 1,aminarized a i r f o i l s , i . e . , a i r f o i l s with very smooth s u r f a c e s , a r eFigure 12. Compression s u i t a b l e i n t h a t they o f f e r t h e l e a s t s u r f a c eShocks on the Profi le: 1 - f r i c t i o n drag and wave drag a t s u p e r c r i t i c a lSupersoni c Zones ; 2 - Com- f l i g h t Mach numbers.pression Shocks; 3 - S u b -son i c Zones. A f t e r t h e normal compression shock t h e r e begins t h e s o - c a l l e d wave flow s e p a r a t i o n ,which i s accompa.nied by a decrease i n t h e l o c a l a i r speed. This i n t u r nr e s u l t s i n a s h a r p drop i n t h e a i r f o i l l i f t . During t u r b u l e n t flow around an a i r f o i l t h e r e i s no oblique shock andonly one normal shock. The appearance of l o c a l shocks on t h e a i r f o i li n s t i t u t e s t h e s o - c a l l e d shock s t a l l . P a r t of t h e k i n e t i c energy i n t h e shocki s transformed i n t o h e a t which i s then i r r e v e r s i b l y propagated. A t high f l i g h t speeds, t h e c h a r a c t e r i s t i c s of t h e compression shock a r ea f u n c t i o n of t h e n a t u r e of t h e boundary l a y e r . Experience has shown t h a tflow i n a boundary l a y e r i s u s u a l l y laminar over a c e r t a i n p o r t i o n and thenswitches t o t u r b u l e n t . The p o s i t i o n of t h e t r a n s f e r p o i n t s o f laminar boundary flow t o turbu­l e n t depend on t h e shape of t h e p r o f i l e , j.ts t h i c k n e s s , roughness, e t c . Thes u r f a c e of a body i n laminar flow experiences l e s s f r i c t i o n and less aero­dynamic h e a t i n g a t high speeds than does one i n a t u r b u l e n t l a y e r . The s t a t e of t h e boundary l a y e r i s r e f l e c t e d n o t only i n t h e wing drag,b u t i n i t s l i f t i n g c a p a c i t y as w e l l . I n t h e boundary l a y e r a flow s e p a r a t i o narises which determines t h e c r i t i c a l angle of a t t a c k and i t s correspondingmaximum l i f t ratio. 23
  • 32. § 14. Pressure Distri-bution a t Sub- and S u p e r c r i t i c a l Mach Numbers /29 P r e s s u r e d i s t r i b u t i o n along a wing p r o f i l e under flow conditions i s showni n Figure 13. The arrows r e p r e s e n t t h e values o f t h e d i f f e r e n c e s between t h e l o c a l and atmospheric p r e s s u r e s at each p a i n t on t h e p r o f i l e . b ) y c The p o s i t i v e overpressure (atmospheric p r e s s u r e l e s s -1 I- than l o c a l ) i s i n d i c a t e d by arrows p o i n t i n g toward t h e contour, whereas n e g a t i v e p r e s s u r e o r r a r e f a c t i o n (atmos­ p h e r i c p r e s s u r e g r e a t e r than l o c a l ) is shown by arrows p o i n t ­ t i O P ed away from t h e contour.Figure 13. Diagram of t h e Pressure To determine and computeD i s t r i b u t i o n s along the A i r f o i 1 Pro- t h e f o r c e of t h e evacuation onf i l e : a - v e c t o r a l ; b - expressed by those points of the p r o f i l e a tt h e pressure c o e f f i c i e n t ( 1 - upper which p r e s s u r e measurementsw i n g s u r f a c e , 2 - lower s u r f a c e ) . were taken, t h e p r o f i l e chord f o r a l i n e p a r a l l e l t o the chordi s p r o j e c t e d , then t h e measured v a l u e s f o r t h e p r e s s u r e a r e p l o t t e d a t as e l e c t e d s c a l e from p o i n t s s p e c i f i e d along t h e p e r p e n d i c u l a r t o t h e chord:p o s i t i v e overpressure i s u s u a l l y p l o t t e d below and evacuation i s p l o t t e d above.The p o i n t s thus obtained then merge i n a smooth curve. In diagrams used i n aerodynamics, normally t h e p r e s s u r e c o e f f i c i e n t s(Fig. 13b), which r e p r e s e n t t h e r a t i o of t h e o v e r p r e s s u r e a t any given p o i n ton t h e p r o f i l e t o t h e v e l o c i t y head o f t h e t u r b u l e n t flow are p l o t t e d a tp o i n t s on t h e p r o f i l e r a t h e r than t h e o v e r p r e s s u r e , as f o l l o w s : Pover - P l o c a l - P a t . p=-­ 9 v2where pl0 - i s t h e a b s o l u t e p r e s s u r e a t a given p o i n t ; cal Pat. - i s t h e s t a t i c p r e s s u r e i n t h e unperturbed flow, i . e . , t h e atmospheric p r e s s u r e a t f l i g h t a l t i t u d e s ; 9 - i s t h e v e l o c i t y head i n t h e unperturbed flow, determined by t h e f l i g h t speed and a l t i t u d e . From t h e above it follows t h a t t h e p r e s s u r e c o e f f i c i e n t characterizes /30 -t h e degree of d i f f e r e n t i a t i o n ( i n u n i t s of t h e v e l o c i t y head) o f t h e l o c a lp r e s s u r e a t any p o i n t on t h e upper and lower p r o f i l e s u r f a c e s from t h e s t a t i cp r e s s u r e i n t h e unperturbed flow. The c o e f f i c i e n t w i l l be negative i f t h el o c a l p r e s s u r e on t h e g r o f i l e i s below atmospheric p r e s s u r e . Consequently,a n e g a t i v e v a l u e f o r p corresponds t o t h e presence on t h e p r o f i l e of r a r e ­f a c t i o n , where a p o s i t i v e value i n d i c a t e s an i n c r e a s e d p r e s s u r e .24
  • 33. ..- . , , . .. . . .. . . . . . -. . . ~ ~I ~~ ~ A t small Mach numbers, t h e diagram f o r t h e p r e s s u r e d i s t r i b u t i o n f o r each angle of a t t a c k has i t s own constant form because t h e a i r c o m p r e s s i b i l i t y has no e f f e c t on t h e n a t u r e of the d i s t r i b u t i o n o f t h e p r e s s u r e c o e f f i c i e n t s on t h e upper and lower s u r f a c e s . A t high Mach numbers (0.6 and g r e a t e r ) , t h e r e i s an i n c r e a s e i n t h e r a r e f a c t i o n i n which g r e a t e r r a r e f a c t i o n arises t o a g r e a t e r degree. This i n c r e a s e i n t h e r a r e f a c t i o n i s explained by t h e e f f e c t of c o m p r e s s i b i l i t y -- d e n s i t y decreases as speed i n c r e a s e s . Consequently , t o maintain t h e constancy of t h e speed flow r a t e around t h e p r o f i l e , it must i n c r e a s e f u r t h e r , which i n t u r n causes a f u r t h e r i n c r e a s e i n t h e r a r e f a c t i o n . A t p o r t i o n s of t h e p r o f i l e where t h e flow around it has i t s g r e a t e s t speed, i . e . , where r a r e f a c t i o n i s g r e a t e s t , t h e a f f e c t o f c o m p r e s s i b i l i t y w i l l a l s o be greater. To f u r t h e r i n c r e a s e t h e speed o f t h e i n c i d e n t flow (above Mcr), the rare­ f a c t i o n on t h e leading edge of t h e a i r f o i l p r o f i l e decreases while i t i n c r e a s e s s h a r p l y a t t h e t r a i l i n g edge, s o t h a t h e r e t h e flow becomes s u p e r s o n i c and there is additional rarefaction. The r e s u l t a n t zone of s u p e r s o n i c speed culminates i n a compression shock behind which t h e l o c a l speeds become subsonic. Such a c h a r a c t e r i s t i c i n t h e change o f t h e l o c a l speeds f o r flow around an a i r f o i l p r o f i l e q u a l i t a t i v e l y changes t h e s i t u a t i o n with r e s p e c t t o p r e s s u r e r a r e f a c t i o n along t h e p r o f i l e as compared t o s u b c r i t i c a l flow. From Figure 14 it i s c l e a r t h a t a t t h a t p o i n t on the p r o f i l e where t h e compression shock formed t h e r e A d d i t i o n a l rare f ac t i on i s a sharp and i r r e g u l a r p r e s s u r e i n c r e a s e ( i . e . , de­ c r e a s e of r a r e f a c t i o n ) . A t Mach numbers g r e a t e r than c r i t i c a l , the increase i n p r e s s u r e i n t h e leading p o r t i o n of t h e p r o f i l e and an i n c r e a s e i n r a r e f a c t i o n i n t h e trai l i n g p o r t i o n leads t o a s u b s t a n t i a l i n c r e a s e i n t h e drag co­ e f f i c i e n t . Shocks a r e normally manifested on t h e upper t h e n lower s u r f a c e i n modern pro- f i l e s a t p o s i t i v e angles of Figure 14. Pressure D i s t r i b u t i o n Along attack. t h e P r o f i l e f o r Mach Numbers Below (broken l i n e ) and Above ( s o l i d l i n e ) Let us look a t t h e p i c t u r e t h e C r i t i c a l Mach Number M c r . of p r e s s u r e d i s t r i b u t i o n along t h e chord of a symmetrical p r o f i l e a t a given angle of a t t a c k f o r various Mach numbers (Fig. 1 5 ) . I f a t small Mach numbers t h e values of t h e p r e s s u r e c o e f f i c i e n t p a r e small, then with an i n c r e a s e i n t h e speed of t h e i n c i d e n t flow t h e r a r e f a c t i o n on t h e upper p r o f i l e contour i n c r e a s e s and t h e curve of t h e p r e s s u r e d i s t r i b u t i o n i s d i s p l a c e d upward. When l o c a l s u p e r s o n i c zones and compression shocks are 25
  • 34. formed on t h e p r o f i l e , i . e . , f o r Mach numbers g r e a t e r than c r i t i c a l , t h e r eis a zone of flow with V > a. "his zone i s enclosed by t h e normal com­p r e s s i o n shock. me formation o f t h e shock causes a decrease i n t h e rare­f a c t i o n on t h e upper p r o f i l e . When t h e r e i s a f u r t h e r i n c r e a s e i n t h e Machnumber, t h e r e g i o n of s u p e r s o n i c speeds broaden and t h e shock g r a d u a l l y i sd i s p l a c e d t o t h e rear. Decreasing t h e r a r e f a c t i o n becomes much mores i g n i f i c a n t . The subsequent i n c r e a s e i n t h e Mach number r e s u l t s i n t h e shockbeing formed on t h e lower s u r f a c e as w e l l , where t h e r a r e f a c t i o n becomesg r e a t e r . With even h i g h e r values f o r t h e Mach number, both shocks reach t h et r a i l i n g edge and t h e e n t i r e p r o f i l e i s surrounded by a s u p e r s o n i c flow. wave j Figure 15. Representative P i c t u r e of the Pressure D i s ­ t r i b u t i o n o n a Symmetrical P r o f i l e ( s o l i d l i n e -- upper s u r f a c e , broken l i n e -- lower s u r f a c e ) . Examination of t h e p i c t u r e of p r e s s u r e d i s t r i b u t i o n gives proof of t h ef a c t t h a t an i n c r e a s e i n t h e Mach number s u b s t a n t i a l l y changes both t h ec h a r a c t e r i s t i c s of t h e curves of p r e s s u r e d i s t r i b u t i o n and t h e momentc h a r a c t e r i s t i c s of t h e wing.26
  • 35. I CHAPTER I I AERODYNAMI C CHARACTER1 STI CS OF THE W l NG AND AI RCRAFT. THE EFFECT OF A I R C O M P R E S S I B I L I T Y . 5 1. T h e Dependence of t h e C o e f f i c i e n t c on t h e A n g l e o f Attack Y The dependence o f t h e l i f t c o e f f i c i e n t c on t h e a n g l e o f a t t a c k a i s Y an important aerodynamic c h a r a c t e r i s t i c of t h e wing and t h e a i r c r a f t . The shape of t h e wing ( f o r a s p e c i f i c number of p r o f i l e s ) i n planform has a s i g n i f i c a n t e f f e c t on t h e c h a r a c t e r of t h e change of t h e c o e f f i c i e n t c f o r Y t h e a i r f o i l a t h i g h angles of a t t a c k a f t e r t h e l o c a l flow s t a r t s t o b r e a k away. Turbojet passenger a i r c r a f t have swept wings, and i t i s t h e s e which we s h a l l d i s c u s s . Figure 16 shows a graph f o r t h e change of t h e c o e f f i c i e n t c as a Y f u n c t i o n of t h e angle a of t h e a i r f o i l w i t h t h e sweep angle x = 35". According t o t h i s graph we may e v a l u a t e t h e l i f t i n g a b i l i t y of t h e a i r f o i l and determine t h e angles of a t t a c k a t which f l i g h t occurs. Depending on t h e f l i g h t speed and a l t i t u d e f o r v a r i o u s f l i g h t w e i g h t s , t h e r e q u i r e d v a l u e s of c are determined f o r h o r i z o n t a l f l i g h t . Y The performace of an a i r c r a f t a t h i g h angles of a t t a c k , t h e causes f o r flow s e p a r a t i o n ( b u r b l e ) and o t h e r c h a r a c t e r i s t i c s a r e a l s o determined and e x p l a i n e d by t h e dependence o f c on a. Y A t h i g h angles of a t t a c k b u r b l i n g begins which d i s t o r t s t h e p i c t u r e of t h e flow and i n t r o d u c e s a c e r t a i n decrease in t h e mean v a l u e o f t h e expansion above t h e a i r f o i l , t h e increa.se i n c slows down, and beyond a Y /33 c e r t a i n angle of a t t a c k c a l l e d t h e c r i t i c a l angle of a t t a c k , t h e r e i s no longer an i n c r e a s e , b u t r a t h e r a d e c r e a s e i n c . Y A t h i g h Mach numbers ( f l i g h t c r u i s i n g s p e e d s ) , a n a l y s i s of t h e dependents c = f (a) must b e c a r r i e d o u t w i t h allowance made f o r t h e a f f e c t of compress­ Y i b i l i t y , which changes t h i s c h a r a c t e r i s t i c t o a c e r t a i n degree. I n swept a i r f o i l s , v a r i a t i o n s i n t h e c o e f f i c i e n t c w i t h r e s p e c t t o t h e Y angle of a t t a c k have t h e i r own c h a r a c t e r i s t i c s . As can b e s e e n from Figure 16, a t angles o f a t t a c k from -1" t o 10 - 12" ( f o r small Mach numbers), there is a linear characteristic of increase i n c . Y However, a t angles o f a t t a c k g r e a t e r t h a n 10 - 12" t h e p r o p o r t i o n a l i t y i s e l i m i n a t e d between t h e increase i n t h e angle of a t t a c k and t h e i n c r e a s e i n c i n addition, Y
  • 36. t h e i n c r e a s e i n c slows down. This i s Y due t o t h e o n s e t o f b u r b l i n g . A t angles o f a t t a c k from 17 t o 20", t h e l i f t c o e f f i c i e n t reaches i t s maximum of c The change i n t h e dependents y ma of c = f (a) a t t h i s p o r t i o n is a Y f u n c t i o n of t h e shape o f t h e leading edge o f t h e a i r f o i l . The wings i n passenger a i r c r a f t have a b l u n t e d leading edge, s o t h a t t h e change i n c Y i n t h e zone c i s smooth. Y m a Swept wings (as compared t o normal wings) have lower values f o r t h e c o e f f i c i e n t c due t o t h e flow around Y t h e wing a t a v e l o c i t y Vef, which by c r e a t i n g l i f t becomes a component of t h e speed V ( s e e Figure 3 3 ) . When POS t h e speed o f the flow around t h e wing does not correspond t o t h e f l i g h t speed, t h e r e a r i s e s a l a t e r a l displacement of t h e a i r p a r t i c l e s i n t h e boundary l a y e r which, f o r t h e c e n t r a l s e c t i o n s of t h e wing, i s e q u i v a l e n t t o t h e e f f e c t which i s obtained when t h e boundary l a y e r i sFigure 16. Graphs f o r t h e blown away o r drawn off ( s e e Chapter V,C o e f f i c i e n t c f o r a Swept § 8). The s e p a r a t i o n of a i r p a r t i c l e s Y from t h e upper s u r f a c e i s p r o t r a c t e dA i r f o i l a t Small MachNumbers ( 1 - w i n g w i t h t o very s u b s t a n t i a l angles of a t t a c k ,geometric t w i s t o f 3 " , 2 ­ and b e f o r e they are reached t h e r e i s aw i thout geomet r i c steady increase i n t h e c o e f f i c i e n t c Yt w i s t j a n d the C o e f f i c i e n t f o r t h e c e n t r a l p o r t i o n of the wing.c f o r the A i r c r a f t as a X Because of t h e g r e a t i n c l i n a t i o n ofFunction of the Angle of t h e curve c = f ( a ) t o the h o r i z o n t a lAttack. Y a x i s i n swept wings (as compared t o normal wings), t h e i n c r e a s e i n c as Ythe angle of a t t a c k i s i n c r e a s e d by l o i t i s l e s s than t h a t f o r a normalwing, i . e . , l e s s than the g r a d i e n t of t h e i n c r e a s e f o r t h e l i f t c o e f f i c i e n t .This a l s o determines t h e lower l i f t i n g a b i l i t y of swept wings as comparedt o normal s t r a i g h t wings. For swept wings, w i t h i n t h e range of angles o f a t t a c k -1.0" - (10-12)"28
  • 37. ( l i n e a r flow of t h e r e l a t i o n c = f (a) on each degree of i n c r e a s e a) t h e Yc o e f f i c i e n t c i n c r e a s e s by approximately 0.09 - 0.11. Y The angle of a t t a c k a t which t h e decreased growth of c i s encountered Yand t h e c h a r a c t e r i s t i c v i b r a t i o n s i n a i r c r a f t a r e observed i s c a l l e d t h ep e r m i s s i b l e angle of a t t a c k aper, while t h e l i f t c o e f f i c i e n t correspondingt o it i s c (Figure 1 7 ) . The v i b r a t i o n i n t h e a i r c r a f t begins a f t e r t h e Y Perb u r b l i n g begins at t h e wing t i p s and the vortex flow s t r i k e s t h e t a i lassembly. On t h e curve (Figure 17) r e f l e c t i n g t h e t o t a l change i n c f o r Y t h e wing as a f u n c t i o n of a, t h e angle ­ /34 of a t t a c k corresponding t o t h e onset of v i b r a t i o n i s determined through t h e s t a r t of l o c a l flow s e p a r a t i o n a t t h e wing t i p ( i n t h e f i g u r e , t h i s c o r r e s ­ ponds t o t h e p o i n t where Curve 2 begins . I I I I t o d e v i a t e from t h e s t r a i g h t l i n e ) . When C Y m a i s reached by t h e wing t i p s , i n s p i t e of t h e subsequent s h a r p decrease i n c a t these t i p s , c f o r t h e e n t i r e Y Y I wing begins t o i n c r e a s e as t h e angle of I a t t a c k does, although slower than a t t h e beginning of s e p a r a t i o n . The i n c r e a s e i n c takes p l a c e due t o t h e Y s e p a r a t i o n - f r e e flow a t t h e c e n t r a l p o r t i o n of t h e wing which occurs a t high angles of a t t a c k . For high Mach numbers , t h e c r i t i c a l angle of a t t a c kFigure 17. The C o e f f i c i e n t c may reach 3 0 - 3 5 . Yf o r Various P a r t s o f a SweptWing as a Function o f the The a i r c r a f t s moving i n t o the v i b r a t i o n zone i n d i c a t e s t h a t lowAngle o f Attack: 1 - c e n t r a l speeds have been a t t a i n e d , and i n t h i sportion; 2 - w i n g t i p ; 3 -w i n g a s a whole. case t h e v i b r a t i o n i s a warning f o r t h e pilot. In t h e zone of high angles o f a t t a c k , t h e r e i s a smooth change i n c Yespecially close to its maximum. As a r e s u l t of t h i s , i n t h e s h i f t t os u p e r c r i t i c a l angles of a t t a c k , swept wings have l e s s o f a tendencytoward a u t o r o t a t i o n than do s t r a i g h t wings. I n g e n e r a l , t h e swept wingson t r a n s p o r t a i r c r a f t have l e s s of a tendency toward s p i n . 29
  • 38. Because of geometric t w i s t , t h e running value of t h e c o e f f i c i e n t c f o r Yt h e c h a r a c t e r i s t i c angles of attack during t a k e o f f , climb, h o r i z o n t a l f l i g h t ,e t c . , decreases. As can b e seen from Figure 16, f o r t h e same angle of attackal, t h e wings l i f t without geometric twist i s b e t t e r , and c > c This i s Y2 Ylwhy f l i g h t i n aircraft with wings having geometric twist i s performed a tg r e a t e r angles o f a t t a c k t h a n with wings without t h i s t w i s t . § 2. T h e E f f e c t of t h e Mach Number on t h e Behavior of the Dependence c = f(c1) Y A i r c o m p r e s s i b i l i t y a f g e c t s t h e dependence o f t h e c o e f f i c i e n t c on t h e Ya n g l e o f a t t a c k . Because of c o m p r e s s i b i l i t y , an i n c r e a s e i n t h e f l i g h t Machnumber of more than 0 . 4 - 0.5 i s accompanied by a q u a l i t a t i v e change i n t h ec h a r a c t e r of flow around t h e wing, because t h e speed o f t h e flow on t h e wingi n c r e a s e s , as a r e s u l t o f which f o r one and t h e same angle of a t t a c k t h e - /3 6c o e f f i c i e n t c increases , i . e . , t h e r e i s an improvement i n t h e l i f t i n g Yc a p a b i l i t y of t h e wing. This i s c l e a r from Figure 18 ( i n which, f o r examplepurposes, t h e angle c1 = 4.5" has been s e l e c t e d ) . The angle of a t t a c k a t whichv i b r a t i o n begins decreases with an i n c r e a s e i n t h e Mach number, because t h ev i b r a t i o n and t h e flow s e p a r a t i o n begins sooner t h a n a t low Mach numbers. Therefore, t h e value c a l s o decreases y vib with an i n c r e a s e i n t h e Mach number. For example, a t M = 0.65, t h e c o e f f i c i e n t C = 0.99, while a t M = 0.85 i t w i l l y vib equal 0.52 (Figure 19). In a d d i t i o n , C a l s o decreases s h a r p l y . If from Y M = 0.65 t h e c o e f f i c i e n t cy v i b d i f f e r s s l i g h t l y from c then a t M = 0.85 y m a t h e value c w i l l be s u b s t a n t i a l l y y vib less than c F l i g h t accompanied by y max v i b r a t i o n u s u a l l y precedes t h e onset of i n s t a b i l i t y i n t h e a i r c r a f t with r e s p e c t t o overload, while a t c e r t a i n values g r e a t e r than c t h e v i b r a t i o n s can l e a d Y IJil iI !5 t o s t a l l i n g a t c e r t a i n Mach numbers. ~~ d l !I !I 1 cf Therefore t h e v a l u e c a t which v i b r a t i o n 0 $54222i&79[ Y per begins i s v i t a l f o r f l i g h t purposes.Figure 18. The Affect of t h e I f f o r M = 0 . 4 - 0 . 5 t h e angle ofMach Number on the Dependence a t t a c k f o r t h e o n s e t of v i b r a t i o n (seec = f ( a ) : - - - wind- t u n n e l Y Figure 19) equals 12-13, then f o r M = tests; - f 1 i g h t tests. = 0 . 8 - 0.9 i t decreases t o 5-7, and C a l s o d e c r e a s e s . This i s e s p e c i a l l y y vib dangerous a t high Mach numbers because a tt h e same time as t h e onset of v i b r a t i o n s , s t a l l i n g may s e t i n .30
  • 39. I Figure 19. T h e Dependence of a v i b and c on t h e y vib Mach Number. In t h e event t h a t t h e s h i f t t o h i g h e r c i s n o t accompanied by t h e Yc h a r a c t e r i s t i c v i b r a t i o n (of i n d i v i d u a l s e c t i o n s of t h e wing) , t o forewarn t h e p i l o t t h a t t h i s s h i f t has occurred, s p e c i a l tubulence s e n s o r s a r e a t t a c h e d t o t h e wings. They t r a p t h e l o c a l flow s e p a r a t i o n s on t h e wing and t r a n s m i t t h e v i b r a t i o n t o t h e c o n t r o l wheel. This, f o r example, i s what was done on t h e B r i t i s h t u r b o j e t Comet, on which t h e sensors a r e s e t symmetrically on t h e leading edge of t h e c e n t e r s e c t i o n of t h e wing (Figure 20). O t h e n p i l o t s instrument panel t h e r e i s a s p e c i a l instrument which s i g n a l s t h e p i l o t ahead of time (before c has been reached) t h a t t h e y vib a i r c r a f t i s s h i f t i n g toward t h i s regime (see Chapter X I , § 15). § 3. The Permissible C o e f f i c i e n t c and Y Per i t s Dependence on the Mach Number F l i g h t s a f e t y i s achieved i n t u r b o j e t a i r c r a f t a t high a l t i t u d e s and Mach numbers through r e s t r i c t i n g the i n c r e a s e i n t h e l i f t c o e f f i c i e n t by t h e determined p e r m i s s i b l e values of c This i s necessary t o - /37Figure 20. Positioning o f Y per maintain l o n g i t u d i n a l s t a b i l i t y i n t h e a i r ­Sensors on the Wing of the c r a f t . Horizontal f l i g h t must be performedComet A i r c r a f t . a t an a l t i t u d e and speed i n which t h e value C does not exceed c f o r a normal­ y hor Y Peri z e d v e r t i c a l wind s e p a r a t i o n . The v a l u e c i s s e l e c t e d such t h a t i t i s Y peralways somewhat l e s s than c o r matches i t (Figure 18). From Figure 2 1 y vibi t can be seen t h a t , f o r example, f o r a Mach number of 0.65 t h e c o e f f i c i e n tC = 0.86, f o r M = 0.80 i t equals 0.635, etc. The less t h e degree of Y Per 31
  • 40. sweep of t h e a i r f o i l , t h e g r e a t e r t h e value C Careful s e l e c t i o n of t h e p r o f i l e s Y per permits improving t h e c o n d i t i o n s f o r flow around t h e wing and y i e l d s h i g h e r values of C Y Per Such s e l e c t i o n of p r o f i l e s i s e s p e c i a l l y c h a r a c t e r i s t i c of second-generation turbo- j e t aircraft. of v i b r a t i o n -1 L - 1 . I 2 4 43 o,b 0,s 0,s 07 . o.a H With high values f o r t h e Mach number, the coefficient c decreases t o almost Y Per h a l f i t s v a l u e , and a t M = 0.85 it reachesFigure 21. The C o e f f i c i e n t as low as 0.54. I n t h e zone of small MachC as a Function of t h e numbers (up t o 0 . 4 6 ) , a v a l u e of c - - Y PerMach Number (angle of sweep Y Per = 1 . 1 2 - 1 . 2 is used, which permits d e t e r ­x = 35"): -.-.-.- first­ mination of t h e lowest p e r m i s s i b l e speed generation a i r c r a f t ; _-----second-gene rat i on a i r c r a f t . f o r an a i r c r a f t with smooth wings (wing flaps retracted). Further, i n examining h o r i z o n t a l f l i g h t and t h e s t a b i l i t y and handinessof t h e a i r c r a f t , we s h a l l r e t u r n t o c and, i n a d d i t i o n , we s h a l l consider Y Perc1 Per and i t s r e p r e s e n t a t i v e Val es .§ 4. Dependence of the C o e f f i c ent c on t h e Mach Number f o r F l i g h t a t a Y Cons tan t Ang le of A t tack In examining t h e e f f e c t of a i r c o m p r e s s i b i l i t y on t h e l i f t i n g p r o p e r t i e sof t h e a i r f o i l i n § 2 , we noted t h a t f o r a constant ( f l i g h t value) angle ofa t t a c k , each Mach number i s matched by a s p e c i f i c v a l u e of c . Y A s can b e seen from Figure 22 ( t h e curve f o r a = 4 . 5 " ) , the c o e f f i c i e n tc i n c r e a s e s c o n s t a n t l y up t o a value of M = 0.83, and then decreases. The Yreason f o r such a change i n c i s due t o t h e e f f e c t of a i r c o m p r e s s i b i l i t y Yon t h e p r e s s u r e d i s t r i b u t i o n along t h e p r o f i l e ( s e e Figure 9 ) . Even with aMach number of 0 . 4 i n t h e v e i n flowing over t h e p r o f i l e , increase i nv e l o c i t y i s accompanied by a marked decrease i n a i r d e n s i t y , which leads t o ­ / 38an a d d i t i o n a l i n c r e a s e i n t h e expansion above t h e upper s u r f a c e ( § 10 ofChapter I ) . O the lower s u r f a c e , t h e a f f e c t of a i r c o m p r e s s i b i l i t y �or nt h e s e Mach numbers has a l e s s e r e f f e c t , s o t h a t i n i t i a l l y t h e r e i s anincrease i n the c o e f f i c i e n t c During t h e formation of a compression Yshock, t h e l i f t i n g c a p a b i l i t y of t h e a i r f o i l d e c r e a s e s . Shock-inductions e p a r a t i o n leads t o a decrease i n expansion on t h e upper p o r t i o n of t h ea i r f o i l p r o f i l e , and c decreases. A t a given Mach number, when t h e r e i s a Yshock on the lower s u r f a c e as w e l l , i t begins moving back, a t f i r s t slowly32
  • 41. and then r a t h e r rapi-dly. As a r e s u l t , on t h e lower s u r f a c e t h e expansion zone w i l l i n c r e a s e as t h e r e s u l t of which t h e l i f t and, consequently, c as w e l l w i l l Y 0: - 2 O s t a r t t o decrease. Later, as a given Mach number, t h e shock on 3 I t h e upper s u r f a c e w i l l a l s o s t a r t03 1 . 1 I I I I t o move back f a s t e r and f a s t e r , 0.4 0.3 48 47 48 49 fl which w i l l e n t a i l an i n c r e a s e i n t h e expansion zone and t h e c o e f f i c i e n t c - ~ . The values ofFigure 22. T h e E f f e c t of Air Compressi- Y t h e Mach number a t which web i l i t y on t h e C o e f f i c i e n t c a t a Y observe t h e i n i t i a l i n c r e a s e i nConstant A n g l e of Attack: 1,2 - s w e p t c-- and i t s subsequent drop andw i n g w i t h geometric t w i s t ; 3 - non- Y renewed i n c r e a s e (ffspoon)swept w i n g . depend on t h e angle o f a t t a c k fo; t h e p r o f i l e and t h e a i r f o i las a whole. A s can be seen from Figure 22, f o r s m a l l e r angles of a t t a c k (2-3O), t h e flow c i s smoother with r e s p e c t t o t h e Mach number and t h e Ylspoonlt i s only s l i g h t l y expressed. This f e a t u r e of the change i n c with r e s p e c t t o t h e Mach number - - t h e Ylspoonll - - explains t h e " i n v e r s e r e a c t i o n " of an a i r c r a f t ( i n banking) t od e c l i n a t i o n i n the c o n t r o l wheel (Chapter X I , § 22).§ 5. The Affect of t h e Mach Number on the C o e f f i c i e n t cx Let us analyze t h e formula f o r dragwhere S i s the wing a r e a . I f the angle of a t t a c k ct i s maintained c o n s t a n t , a t small Mach numbersdrag w i l l vary p r o p o r t i o n a t e l y t o the square of t h e speed, w h i l e t h e drag ­ / 39c o e f f i c i e n t c a t t h e s e Mach numbers w i l l be p r a c t i c a l l y independent of speed Xand w i l l vary only with r e s p e c t t o the angle o f a t t a c k . As we can s e e fromFigure 16, f o r ct = 6-8O t h e c o e f f i c i e n t c = 0.038 - 0.05 ( a t small a l t i t u d e s Xand speeds). However, t h e dependence of cx on only t h e angle of a t t a c k i sobserved a t speeds a t which t h e e f f e c t of a i r c o m p r e s s i b i l i t y may b e ignored.With an i n c r e a s e i n f l i g h t speed, however, when c o m p r e s s i b i l i t y does s t a r tt o have an e f f e c t , t h e c o e f f i c i e n t cx i n c r e a s e s , and more s u b s t a n t i a l l y t h ef a s t e r t h e shock s t a l l on t h e p r o f i l e developes. The r e l a t i o n s h i p between t h e 33
  • 42. development of t h e shock s t a l l and t h e i n c r e a s e i n t h e c o e f f i c i e n t cx may b econsidered from Figure 23. Under Mach = 0.7, t h e c o e f f i c i e n t c is p r a c t i c a l l y X changeless. After t h e i f l i g h t (flow) Mach number exceeds i t s c r i t i c a l I v a l u e , l o c a l compression shocks b e g i n forming on t h e wing, wave drag appears, and a s h a r p i n c r e a s e i n t h e curve c X 1I b e g i n s . This makes i t c l e a r t h a t the g r e a t e r t h e a i r f o i l angle of attack (or the g r e a t e r t h e f l i g h t c ) , t h e lower Y the c r i t i c a l value f o r t h e Mach number. With an i n c r e a s e i n t h e MachFigure 23. Dependence of t h e C o e f f i c i e n t cX number, t h e compressionon t h e Mach Number f o r a S w e p t Wing. shocks a r e d i s p l a c e d toward t h e t r a i l i n g edge and become more powerful.A t Mach = 1.1 - 1.15, a normal shock appears i n f r o n t and shocks appu ar on pboth t h e top and bottom of the t r a i l i n g p o r t i o n of t h e p r o f i l e . I t must b e noted t h a t an understanding of t h e c r i t i c a l Mach number, asr e l a t e d t o t h e appearance of t h e l o c a l speed of sound a t any p o i n t on a sweptwing, has less of a p r a c t i c a l value than i t does f o r a s t r a i g h t wing. Ing e n e r a l , the appearance of the l o c a l speed of sound on s t r a i g h t and sweptwings does not immediately have a s i g n i f i c a n t e f f e c t on t h e aerodynamicp r o p e r t i e s , and w i l l not be n o t i c e d by t h e p i l o t . The c r i t i c a l Mach number f o r a swept wing and t h e a i r c r a f t as a whole /40i s u s u a l l y r e l a t e d t o changes i n the t o t a l aerodynamic c h a r a c t e r i s t i c s and t h i si s understood t o mean t h a t f l i g h t Mach number a t which t h e p i l o t becomes awareof t h e e f f e c t of a i r c o m p r e s s i b i l i t y on the handling q u a l i t i e s of h i s a i r ­c r a f t , i . e . , changes i n t h e s t a b i l i t y and handiness. The c r i t i c a l Mach numberas determined from t h e s e conditions i s M = 0.82 - 0.88. A t such a Mach crnumber, a i r c r a f t i n s t a b i l i t y i n terms of speed developes ( t h e “spoonrt on t h ebalance curve) and t h e r e v e r s e r e a c t i o n ( i n terms of banking) t o d e c l i n a t i o nof t h e rudder a l s o appears. In f l i g h t p r a c t i c e , concepts a r e used such as t h e s o - c a l l e d l i m i t i n g Machnumber, which the p i l o t m u s t know a b s o l u t e l y . I t is u s u a l l y equal t o 0.86 ­0.9. This Mach number can reasonably s a f e l y be s u b s t i t u t e d f o r t h e c r i t i c a lMach numbers d i s c u s s e d e a r l i e r . I t should be p o i n t e d out t h a t i n aerodynamic c a l c u l a t i o n s , the c r i t i c a l34
  • 43. Mach number i s sometimes taken t o b e a f l i g h t Mach number whose i n c r e a s e by0.01 l e a d s t o a 1%increase i n t h e a i r c r a f t s c o e f f i c i e n t cx. .According t ot h e l a t e s t formulas, t h e Mach number M = 0.78 - 0.80 f o r c r u i s i n g v a l u e s crc = 0.25 Y - 0.30. For c Y = 0.35 - 0 . 5 a t c e i l i n g a l t i t u d e s , depending on t h et a k e o f f weight t h e v a l u e Mcr d e c r e a s e s 0.70 - 0.74. As w a s s t a t e d above, when t h e Mach number i s i n c r e a s e d above Mcr, a larges u p e r s o n i c zone of flow appears on t h e p r o f i l e , t h e compression shock i s movedback and expansion i n t h e t a i l p o r t i o n of t h e p r o f i l e i s i n c r e a s e d andi n i t i a t e s an i n c r e a s e i n t h e c o e f f i c i e n t c F o r non-swept wings, f o r example, Xt h i s phenomenon occurs a t Mach numbers 0 . 0 4 = 0 . 1 below Mcr. For a f u r t h e r i n c r e a s e i n t h e Mach number above t h e c r i t i c a l v a l u e , t h ec o e f f i c i e n t c i n c r e a s e s as a r e s u l t of t h e i n c r e a s e i n t h e l o c a l speeds on Xt h e lower p r o f i l e s u r f a c e , where a compression shock i s a l s o formed. A morei n t e n s e i n c r e a s e i n c i n non-swept wings occurs i n t h e range o f Mach numbers Xfrom M to M = 1; with a s h i f t beyond M = 1, however, t h e c o e f f i c i e n t c cr xu s u a l l y decreases. For swept wings, t h e ma-ximun v a l u e of c corresponds t o Xt h e Mach number M = 1.1 - 1.15. I t i s known t h a t wing drag i s compcunded from t h e p r o f i l e dragt h e induced drag Qi; t h e formation of compression shocks on t h e wing2! :list h e wave drag t o these. With r e s p e c t t o t h i s , t h e i n v e r t e d form o f %heformu1.a f o r t h e drag c o e f f i c i e n t w i l l b e t h e f o l l o w i n g : c = c + c + cxw x xp xiwhere c, i s t h e c o e f f i c i e n t of p r o f i l e drag f o r zero lift, and i s cornpiled xp from .the drag of t h e a i r F r i c t i o n on t h e wing s u r f a c e and t h e drag caused by .the d i f f e r e n c e between a i r p r e s s u r e s on t h e leading and t r a i l i n g p o r t i o n s of %he wing. The p r o f i l e drag f o r t h e wing ­ /41 a t small Mach numbers can b e s t b e e s t a b l i s h e d from f r i c t i o n whose v a l u e i s only s l i g h t l y dependent on t h e angle of a t t a c k * ; a t high angles of a t t a c k t h e s e p a r a t i o n drag i s added t o t h e f r i c t i o n drag and t h e c o e f f i c i e n t i n c r e a s e s s h a r p l y : c = c -- c ! xp x fric x pres c i s t h e c o e f f i c i e n t of induced drag, which i s a f u n c t i o n of t h e xi wing l i f t ; i t i s d i r e c t l y p r o p o r t i o n a l t o t h e s q u a r e of t h e l i f t c o e f f i c i e n t and i n v e r s e l y proportional. t o t h e wing a s p e c t r a t i o : 1 CL l2c xi = 2 (here X = ~TX -- S wing a s p e c t r a t i o , 1 - span, and S - Wing a r e a ) ; .__* A. P . Melnikov. High-speed Aerodynamics (Aerodinamika b o l t s h i k h s k o r o s t e y ) , Voyeni z d a t , 1961. 35
  • 44. c i s t h e wave drag c o e f f i c i e n t . xw Induced and wave drag a r e by n a t u r e p r e s s u r e drags. When wave drag developes, t h e c o e f f i c i e n t cx i n c r e a s e s 3-6 times f o r s t r a i g h t wings and 40­ 70% f o r swept wings as compared t o i t s v a l u e s f o r slow speeds. Thus, t h e o n s e t of compression shocks leads t o an i n t e n s e i n c r e a s e i n t h ec o e f f i c i e n t cx because wave drag is added t o t h e normal p r o f i l e drag andinduced drag. § 6. Wing Wave Drag I t w a s e s t a b l i s h e d e a r l i e r t h a t an i n c r e a s e i n t h e f l i g h t speed abovec r i t i c a l leads t o t h e appearance of a new, a d d i t i o n a l form of drag c a l l e dp r o f i l e wave drag. To explain t h e n a t u r e of t h i s drag, l e t us once more examine the p i c t u r eof t h e p r e s s u r e d i s t r i b u t i o n along the upper wing s u r f a c e f o r subsonic flow a tsub- and s u p e r c r i t i c a l f l i g h t speeds (Figure 14 and 24). A s can be s e e n , i n Figure 24 one s e c t i o n of t h e expansion v e c t o r s s o r t of "draw" t h e pro- - /42 f i l e forward, while t h e- +cr - - Y VZ v cr o t h e r draws i t back. To e v a l u a t e what would happen-L--4-d - ­ x=- t o t h e wing under t h e a f f e c t o f t h e s e "pulling" f o r c e s , a l l expansion v e c t o r s must be pro-F i g u r e 24. Examples o f Wave Drag. i ected i n the d i r e c t i o n of f l i g h t . When t h i s i s done we s e e t h a t a t sub-c r i t i c a l speeds t h e f o r c e s "pulling" forward a r e n e g l i g i b l y l e s s than those"pulling" back (Figure 24a). With an i n c r e a s e t o s u p e r c r i t i c a l speeds, t h ep r e s s u r e d i s t r i b u t i o n p i c t u r e changes (Figure 24b), as a r e s u l t of which t h ef o r c e s "pulling" the p r o f i l e forward decrease (expansion becomes l e s s a t t h ebow of t h e p r o f i l e ) while t h e f o r c e s "pulling" back i n c r e a s e (because expansionon the t r a i l i n g s l o p e of t h e p r o f i l e i n c r e a s e s by an a b s o l u t e v a l u e ) . Fromt h e f i g u r e i t i s c l e a r t h a t t h e d i f f e r e n c e i n t h e p r o j e c t i o n s of t h e v e c t o r sof the "pulling" f o r c e s d i r e c t e d t o t h e r e a r i n c r e a s e s , causing an i n c r e a s ei n drag. However, because t h e e x t e n t of t h e s u p e r s o n i c zones over and undert h e wing i n c r e a s e s as f l i g h t speed i n c r e a s e s , t h e r e i s an even g r e a t e rdisplacement of t h e l a r g e s t expansion toward t h e rear and t h e t r a i l i n g edge.The f o r c e s "pulling" t h e p r o f i l e forward i n c r e a s e a t t h e same time t h e p r e s s u r eon the leading edge of t h e p r o f i l e i n c r e a s e s . To sum up, t h e wing dragcontinues t o i n c r e a s e . Thus, t h e wave drag i s by n a t u r e a p r e s s u r e dragbecause i t i s dependent on t h e i n c r e a s e i n t h e p r e s s u r e d i f f e r e n c e i n f r o n tof t h e wing and behind i t . Therefore, i n aerodynamics wave drag has come t o mean t h e a d d i t i o n a l drag36
  • 45. 111 I - caused by an i n c r e a s e i n the p r e s s u r e d i f f e r e n c e s i n f r o n t of t h e wing and behind i t when t h e r e a r e supersonic zones of flow and compression shocks on t h e airf o i 1 p r o f i l e " . This drag i s c a l l e d t h e wave drag because t h e process of t h e development of s u p e r s o n i c zones of flow is accompanied by t h e development of shock waves o r compression shocks. From t h e e n e r g e t i c viewpoint, wave r e s i s t a n c e i s t h e r e s u l t of t h e d e c e l e r a t i o n of a i r flows on t h e compression shocks. When t h i s occurs, t h e k i n e t i c energy of t h e flow i s i r r e v e r s i b l y consumed i n h e a t i n g t h e a i r i n t h e shock . As can b e seen from Figure 25b, i n t h e range o f c r u i s i n g f l i g h t Mach numbers, the v a l u e of t h e wave drag c = 0.004 - 0.012 o r f o r t h e mean value xw c = 0.025, i t w i l l equal 25 - 50% ( f o r a i r c r a f t ) . X A t s u p e r s o n i c f l i g h t speeds (Mach z 1 - 1 . 2 , Figure 25a), a i r d e c e l e r a t i o n on t h e bow a d t a i l compression shocks decreases because t h e angles of i n c l i n a t i o n of t h e s e shocks decrease, which means t h a t t h e wave drag i t s e l f decreases. A t s u p e r c r i t i c a l Mach numbers, a i r c r a f t drag i n c r e a s e s i n t e n s e l y because i t i s a f u n c t i o n of both cx and V 2 . From t h e same f i g u r e we s e e t h a t a t a constant angle of a t t a c k , t h e drag f o r c e below M = 0.5 i n c r e a s e s as a parabola,& while beyond t h i s Mach number t h i s l u l l does n o t hold, and t h e curve d e v i a t e s from t h e square p a r a b o l a , which i s the r e s u l t of t h e e f f e c t of c o m p r e s s i b i l i t y and the development of compression shock. Figure 25. Dependence of t h e C o e f f i c i e n t cx on the Mach Number ( a ) a n d the E f f e c t of t h e Relative P r o f i l e Thick­ ness on Ac f o r the Wing ( b ) . xw * A. P . Melnikov. High-speed Aerodymamics (Aerodinamika b o l s h i k h skorostey) , Voyenizdat, 1961. 37I
  • 46. 9 7. Interference The i n c r e a s e i n . a i r c r a f t f l i g h t speeds has l e d t o an i n c r e a s e i n t h eimportance o f i n t e r f e r e n c e , i. e . , t h e combined e f f e c t of v a r i o u s p a r t s oft h e a i r c r a f t such as t h e wing and t h e f u s e l a g e . Usually i n t e r f e r e n c e leadst o an s u b s t a n t i a l i n c r e a s e i n drag, e s p e c i a l l y i n t h e zone of t r a n s o n i cf l i g h t speeds. I t has been experimentally e s t a b l i s h e d t h a t " p o s i t i v e " i n t e r f e r e n c e canbe achieved. This i s t h e i n t e r f e r e n c e which a i d s in. decreasing t h e a d d i t i o n a ldrag r e s u l t i n g from t h e p o i n t s where t h e v a r i o u s a i r c r a f t components arejoined. Turbojet passenger a i r c r a f t are b a s i c a l l y low-wing a i r c r a f t . Whent h e wing and f u s e l a g e are j o i n e d i n t h i s way, t h e u s e of f a i r i n g s h e l p s t osmooth t h e j u n c t i o n p o i n t of the wing and f u s e l a g e t o a c e r t a i n degree.P o s i t i o n i n g the engines i n t h e b a s e of t h e wing ( s e e Chapter I V , § 8) as w a sdone on t h e Tu-1.04, Tu-124 and Comet a i r c r a f t c r e a t e s an e j e c t o r e f f e c t -- an" a c t i v e f a i r i n g " -- a t t h e j u n c t i o n p o i n t f o r o p e r a t i n g engines. * Another way of decreasing t h e drag i s using t h e " r u l e of area," whichi s a l s o a p p l i c a b l e f o r subsonic a i r c r a f t . With r e s p e c t t o t h i s r u l e , drag i n f l i g h t v e h i c l e s proves t o be minimalwhen t h e law of v a r i a t i o n s i n c r o s s - s e c t i o n s with r e s p e c t t o l e n g t h c o r r e s ­ponds t o the l a w of v a r i a t i o n s i n c r o s s - s e c t i o n s with r e s p e c t t o t h e l e n g t hG� a body of r e v o l u t i o n of l e a s t drag. I t i s w e l l known t h a t drag from t h ecombination of t h e wing and f u s e l a g e (and o t h e r p a r t s of t h e f l i g h t v e h i c l e )will be t h e same as e q u i v a l e n t drag, i . e . , drag having t h e same l a w f o rv a r i a t i o n s i n c r o s s - s e c t i o n with r e s p e c t t o length of a body of r e v o l u t i o n .Therefore vinimal drag may be achieved through decreasing t h e c r o s s - s e c t i o nof t h e f u s e l a g e (ssqueezingtt), a t t h e p o i n t where i t j o i n s t h e wing, by avalue equal t o t h e area of t h e corresponding wing c r o s s - s e c t i o n s (Figure 26) O r i g i n a l body, "r f cr Figure 26. Examples of t h e Use of t h e "Area Law": a - "fuselage - w i n g " combination without a1 lowance f o r t h e area law; b and c - the same combination w i t h allowance f o r t h e "area law." i-- ­* S.M. Yeger. Designing Passenger J e t A i r c r a f t (Proyektirovaniye p a s s a z h i r ­ skikh reaktivnykn samoletov) . Mashinostroyeniye, 1964.38
  • 47. The "area l a w " i s a l s o a p p l i c a b l e t o t h e j u n c t i o n of engine n a c e l l e s ,e x t e r n a l l y suspended f u e l t a n k s and o t h e r a i r c r a f t components. Thus, f o rexample, on t h e Tu-104 and Tu-124 a i r c r a f t having wings with a r e l a t i v e l yhigh wing a s p e c t r a t i o , t h e wing and f u s e l a g e i n t e r f e r e n c e i s somewhatdecreased by t h e s u b s t a n t i a l d i s t a n c e of the wing t i p s from t h e f u s e l a g e ;as a r e s u l t , i n s t e a d of thickening t h e f u s e l a g e behind t h e wing, drop-shapedn a c e l l e s a r e i n s t a l l e d on t h e wing. This y i e l d s a smoother change i n t h evolume of t h e a i r c r a f t along i t s length without modifying t h e f u s e l a g e . On t h e Convair 990, t h e r e are f o u r n a c e l l e s which a r e used t o c a r r y f u e l .A s a r e s u l t t h i s a i r c r a f t has achieved a maximum c r u i s i n g Mach number of0.91. I t is f e l t t h a t allowance f o r t h e "area law! i n designing a i r c r a f t canimprove t h e i r f l i g h t q u a l i t i e s by 20-25%. I n some c a s e s , however, observanceof t h i s law has proven u n s u i t a b l e due t o complications and d i f f i c u l t i e s i ndesigning t h e f u s e l a g e which have r e s u l t e d i n t h e need f o r curvature of i t spower p l a n t s .5 8. T h e A i r c r a f t Polar. The E f f e c t of t h e Landing Gear and W i n g Mechanization on t h e Polar The p o l a r of an a i r c r a f t s e r v e s i n e v a l u a t i n g the a i r c r a f t s aerodynamics.I t o f f e r s a g r a p h i c r e p r e s e n t a t i o n of t h e values of the c o e f f i c i e n t s c and Y& a t various angles of a t t a c k , as w e l l as i n d i c a t i n g t h e i r v a r i a t i o n s when Xt h e s e angles change. Figure 27shows t h e p o l a r s of one a i r c r a f t obtained as t h e r e s u l t o f wind / 45 ­t u n n e l t e s t i n g and r e f i n e d with r e s p e c t t o d a t a from f l i g h t t e s t i n g . Let usdetermine t h e c h a r a c t e r i s t i c angles of attack and t h e i r corresponding aero­dynamic parameters. The p o i n t of i n t e r s e c t i o n of t h e p o l a r a with t h e axisof t h e a b s c i s s a i s determined by t h e z e r o - l i f t angle of a t t a c k a0 = 1 andi t s corresponding c o e f f i c i e n t c = 0.018 ( f o r a r e l a t i v e a i r f o i l p r o f i l e xothickness of c= 10 - 1 2 % ) ; f o r c= 1 2 - 15% t h e c o e f f i c i e n t cxo= 0.021 ­0.023. The small value f o r cxo i s obtained through t h e c r e a t i o n of a wells t r e a m l i n e d shape f o r t h e a i r c r a f t with a small c e n t e r s e c t i o n f o r t h ef u s e l a g e and engine n a c e l l e s . The aerodynamic t e s t s as t o t h e degree of refinement i n t h e a i r c r a f t i si t s e f f i c i e n c y . Modern a i r c r a f t have a maximum e f f i c i e n c y of K = 15 - 18 a tt h e optimum angle of a t t a c k of 5-7" and Mach numbers of M < 0 . 5 . A air­ nc r a f t s l i f t drag r a t i o i n c r e a s e with an i n c r e a s e i n t h e angle of a t t a c k from /46cio t o t h e optimal c1 because a t t h i s p o i n t c i n c r e a s e s f a s t e r than cx. opt YS t a r t i n g with an angle of 5-7", t h e c o e f f i c i e n t cx i n c r e a s e s more r a p i d l y (due to t h e i n c r e a s e i n t h e induced drag) and t h e r e f o r e t h e performance drops. Later i t w i l l b e shown t h a t ci i s t h e d i v i s i o n p o i n t between two f l i g h t opt 39
  • 48. regimes: t h e f i r s t and t h e second. For t h e p o l a r a ( s e e Figure 27), a = 7 at c = O opt Y 0.55, w h i l e K = 17.2. When t h e landing g e a r i s lowered, t h e p o l a r moves t o t h e r i g h t ( p o l a r b i n Figure 27) because t h e c o e f f i c i e n t c increases t o the value X After t h e landing g e a r lg i s r e t r a c t e d , t h e w e l l doors a r e normally c l o s e d s o t h a t AC = 0.015 - 0.020 and t h e x 1g l i f t i n g a b i l i t y of t h e wing does not change. As a r e s u l t t h e s e t t i n g f o r t h e angle of a t t a c k f o r p o l a r b remains t h e same as f o r p o l a r a. The maximum performance f o r an a i r c r a f t with landing g e a r extended decreases i n our case t o 12, while a increases t o 8.5O. optFigure 27. A i r c r a f t P o l a r s : a - landing When t h e landing g e a r andg e a r and w i n g f l a p s withdrawn; b - landing wing f l a p s are extended ( i ng e a r down; c - landing g e a r and w i n g f l a p s 1anding c o n f i g u r a t i o n ) t h eextended i n landing c o n f i g u r a t i o n . p o l a r moves t o t h e r i g h t and upward ( p o l a r c i n Figure 27),and t h e c o e f f i c i e n t ci n c r e a s e s throughout t h e range o f angles of a t t a c k , t h e Yz e r o - l i f t angle of a t t a c k becomes n e g a t i v e (a = - 6 O ) , and t h e maximum p e r ­ 0formance of the a i r c r a f t decreases as a r e s u l t of t h e f a c t t h a t t h e c o e f f i c i e n tc i n c r e a s e s t o a g r e a t e r degree than t h e c o e f f i c i e n t c X . Y When t h e wing f l a p s are i n t h e t a k e o f f c o n f i g u r a t i o n , t h e maximum p e r ­formance (landing g e a r down) decreases t o 10-12 (Figure 65). I n g l i d i n g toward t h e landing with landing g e a r and wing f l a p s down i nt h e landing c o n f i g u r a t i o n , t h e performance decreases t o 7-8. Extending t h ea i r brake moves t h e graph of t h e p o l a r t o t h e r i g h t , as t h e r e s u l t of whicht h e performance decreases s u b s t a n t i a l l y , p a r t i c u l a r l y i n g l i d i n g a t angleso f attack of 2-3, a t which t h e landing run i s made. Displacing t h e hingedf l a p s p o i l e r s causes a s h a r p e r drop i n t h e a i r c r a f t performance (see Figure107).40
  • 49. J § 9. T h e E f f e c t of t h e Mach Number on t h e A i r c r a f t P o l a r For each f l i g h t Mach number w e may c o n s t r u c t a p o l a r by determining f o r t h i s value c and c with an allowance made f o r t h e e f f e c t o f c o m p r e s s i b i l i t y X Y and thereby o b t a i n t h e p o l a r n e t (Figure 2 8 a ) . E a r l i e r it w a s e s t a b l i s h e d t h a t a t s u b c r i t i c a l f l i g h t speeds t h e wing c o e f f i c i e n t cx i s almost i n v a r i a b l e , while t h e l i f t c o e f f i c i e n t c i n c r e a s e s s t a r t i n g a t M = 0.5 - 0.6. Therefore, Y with an i n c r e a s e i n t h e Mach number t o M t h e p o l a r i s p u l l e d forward cr’ because of t h e i n c r e a s e i n cy and i n t h e region of high angles of a t t a c k i s simultaneously s h i f t e d t o t h e r i g h t due t o t h e i n c r e a s e i n cx as a r e s u l t of an i n c r e a s e i n t h e induced drag. This i s c l e a r l y shown i n p o l a r s f o r Mach numbers 0.8 and 0.84 (wing with c= 12 - 15%). As i s w e l l known, aerodynamic performance ­ / 47 A t s u p e r - c r i t i c a l f l i g h t speeds a t which t h e wave drag i n c r e a s e s s u b s t a n t i a l l y , f o r a s p e c i f i c Makh number t h e Dolar moves t o t h e r i g h t and i n c r e a s e s t h e s h i f t t o t h a t s i d e ( i n Figure 2ia, t h i s corresponds i o Mach number of M = 0.84) as a r e s u l t o f a decrease in c I f , however, t h e Y‘ K­ Mach number i s s o g r e a t t h a t t h e r e i s wave drag !J ­ a t almost every angle of a t t a c k , t h i s Mach number ! - 6 /’ / ( f o r any c ) has an Y i n c r e a s e d value o f cx and - i$ t h e p o l a r proves t o be iz ­ only s h i f t e d t o t h e r i g h t ( i n Figure 28a, t h e p o l a r 70 - f o r t h e Mach number 0.9). This b e a r s witness t o t h e decrease i n t h e maximum performance of t h e a i r ­ c r a f t , as can be seen i n Figure 28. A i r c r a f t Polars and Dependence t h e f i g u r e , i n which a r e o f Aerodynamics Performance K on Mach given t h e tangents t o t h e numbers . p o l a r s and t h e angles f o r performance O 2 > O1. I n arranging t h e p o l a r n e t , we may c o n s t r u c t a graph f o r t h e dependence o f performance on c f o r v a r i o u s Mach numbers (Figure 28b). Usually maximum Y performance i s o b t a i n e d f o r v a l u e s of c which a r e 20-30% g r e a t e r than t h e Y 41
  • 50. v a l u e f o r c i n h o r i z o n t a l f l i g h t . If a t M < 0.5 t h e m a x i m u m performance Y K = 15-17, then a t M = 0.8 it w i l l equal approximately 12-14.5. As can b e seen from Figure 29, f o r Mach numbers M = 0 . 8 - 0.84, Kmax = 12-14 and only a t high Mach numbers does i t decrease t o 11-12. High aerodynamic performance i n an a i r c r a f t has a f a v o r a b l e e f f e c t on t h e volume o f f u e l consumed p e r kilometer. ---_ The a f f e c t o f wing sweep i s t h a t with/48 ­ an i n c r e a s e i n t h e angle of sweep, t h e ’ aerodynamic performance decreases a t low f l i g h t speeds and i n c r e a s e s a t high 47 48 n f l i g h t speeds. The parameters f o r second-generation a i r c r a f t wings a t c r u i s i n g Mach numbers of M = 0.8 - 0.85Figure 29. Maximum Aerodynamic have been s e l e c t e d such t h a t K = 13-14Performance as a Function of i s achieved (Figure 29).Mach Number: ----- f i r s t -generation a i r c r a f t ; ~ I t i s w e l l known t h a t f o r each Machvarious second-generation ai r- number, a high-speed a i r c r a f t has i t scraft. own r e l a t i o n between t h e c o e f f i c i e n t cx and c Y . If f o r v a r i o u s Mach numbers wei n t r o d u c e i n t o the p o l a r network values of c f o r h o r i z o n t a l f l i g h t ( f o r Ys p e c i f i c weight and a l t i t u d e ) and then j o i n t h e s e p o i n t s , we o b t a i n t h e p o l a rf o r h o r i z o n t a l f l i g h t regimes ( t h e dot- and dash l i n e i n Figure 28a), whiche s t a b l i s h e s a r e l a t i o n s h i p between c x’ cy’ t h e Mach number and t h e h o r i z o n t a lf l i g h t a l t i t u d e . I t i s c l e a r from t h e p i c t u r e t h a t t h i s p o l a r i n t e r s e c t s a l lt h e working p o l a r s f o r Mach numbers from 0.5 t o 0.84. The h i g h e r t h e Machnumber, t h e lower t h e c a t which t h i s i n t e r s e c t i o n occurs. In o t h e r words, Yt h e h i g h e r t h e f l i g h t Mach number, t h e lower t h e v a l u e of c r e q u i r e d f o rhorizontal f l i g h t . Y42
  • 51. CHAPTER I l l SOME FEATURES OF W I N G C O N S T R U C T I O N§I. Means of Increasing t h e C r i t i c a l Mach Number The i n c r e a s e i n drag a s t h e Mach number Mcr i s r a i s e d i s an unusual b a r r ­i e r which makes i t d i f f i c u l t t o achieve high f l i g h t speeds. Therefore, t e s t shave been run on aerodynamic shapes of a i r c r a f t a t which t h e shock s t a l l wouldbegin a t t h e h i g h e s t p o s s i b l e f l i g h t Mach number and would be maintained a slong as p o s s i b l e smoothly, i . e . , s o t h a t means of i n c r e a s i n g t h e c r i t i c a l Machnumber f o r t h e p r o f i l e could be achieved. The c r i t i c a l Mach number f o r t h e p r o f i l e may be detemhined according t ot h e following empirical formula: M =1-0.71/c-3.2cc,’ - -15 , CTwhere c is t h e r e l a t i v e t h i c k n e s s of t h e p r o f i l e ; c i s t h e l i f t c o e f f i c i e n t f o r t h e angle o f a t t a c k under c o n s i d e r a t i o n . Y Let us b e a r i n mind t h a t t h e c h a r a c t e r i s t i c parameters f o r t h e a i r f o i lp r o f i l e a r e (Figure 30): r e l a t i v e thickness a - t h e r a t i o of t h e maximum p r o f i l e t h i c k n e s s cmaxt o t h e chord b ; t h e p o s i t i o n of t h e maximum p r o f i l e t h i c k n e s s zc% t h e - relative distanceof t h e maximum p r o f i l e t h i c k n e s s x from t h e nose t o t h e chord b; C t h e r e l a t i v e p r o f i l e c u r v a t u r e % - t h e r a t i o of maximum buckle f t o t h echord b ; t h e d i s t a n c e from t h e p r o f i l e nose t o t h e p-i n t o f maximum p r o f i l e curv­ oature x expressed i n u n i t s of t h e chord b , - x f % . j’ Let us examine t h e e f f e c t of each of t h e s e parameters on t h e M number. cr The e f f e c t of c. The p r o f i l e t h i c k n e s s has a d i s t i n c t e f f e c t on t h e v a l u eo f t h e d r a g . The g r e a t e r i t i s , t h e g r e a t e r t h e degree t o which t h e a i r streamsurrounding t h e p r o f i l e i s compressed, and consequently t h e sooner t h e shocks t a l l w i l l occur a t lower Mach numbers. In c o n t r a s t , decreasing t h e p r o f i l et h i c k n e s s d i s p l a c e s t h e moment when t h e shock s t a l l occurs t o a h i g h e r Machnumber. Figure 31 g i v e s a c l e a r example of t h e degree t o which t h e t h i n n e s sof t h e p r o f i l e r e s u l t s i n a g r e a t e r c r i t i c a l Mach number M cr’ 43
  • 52. 4 Figure 30. Geometric Parameters and Shapes of an Air­ f o i 1 Profi le: a - p r o f i le w i t h p o s i t i v e c u r v a t u r e ; b- symmetrical prof i le; c - "inverted" prof i le w i t h nega­ t.ive c u r v a t u r e (Douglas DC-8). A i r c r a f t wings c a r r y f u e l , with t h e r e s u l t t h a t t h e r e l a t i v e p r o f i l e thickness i s 10 t o 15%. This i s necessary t o o b t a i n s u f f i c i e n t volume and maintain wing strength. As an example, l e t us determine t h e /50 - -- c r i t i c a l Mach number f o r p r o f i l e s with r e l a t i v e t h i c k n e s s e s of 10 and 15% i f = 0.3. Calculations show t h a t f o r 3 c = lo%, Mcr = 1 - 0 . 7 4 c - 3.2Fc 1.5 - ­ Y = 1 - 0 . 7 m - 3.2.0.1 - 0 . 3 = 0.722, ~ ~ ~Figure 31. T h e E f f e c t of Air- while f o r c= 15% M = 1 - 0 . 7 m ­ cr f o i 1 P r o f i l e Thickness on t h eC o e f f i c i e n t c f o r Various Mach - 3.20.15 : 0.3l. = 0.651. As w e can numbers. X see from t h i s example, t h e lower t h e r e l a t i v e p r o f i l e thickness, t h e g r e a t e r t h e c r i t i c a l Mach number. When t h e r e i s a change i n t h e angle of a t t a c k , and consequently t h e v a l u ec ( f o r example, l e t us t a k e Y c Y = 0 . 4 and c = l o % ) , we o b t a i n a d i f f e r e n tv a l u e f o r t h e c r i t i c a l Mach number M:Mcr = 1 - 0 . 7 m - 3.2 0.10 - 0.4 1.5 - ­= 0.691. Thus, an i n c r e a s e i n t h e Mach number ( c ) has l e d t o a decrease i n Y from 0.722 t o 0.691. This i s explained by the f a c t t h a t as t h e angle o fa t t a c k i n c r e a s e s , t h e upper a i r stream i s compressed s t r o n g e r by t h e p r o f i l e . The straight-away s e c t i o n s i n t h e stream decrease more i n t e n s e l y , as a r e s u l t t h e v e l o c i t y i n c r e a s e s more s h a r p l y , and t h e speed of sound i s a t t a i n e d a t a lower Mach f l i g h t number. This i s why an i n c r e a s e i n t h e f l i g h t a l t i t u d e (an i n c r e a s e i n c ) decreases t h e c r i t i c a l Mach number. Y Second-generation a i r c r a f t have a i r f o i l p r o f i l e s from c = 10-12%, whichmakes i t p o s s i b l e t o i n c r e a s e t h e c r u i s i n g Mach f l i g h t number t o 0.8 - 0.8544
  • 53. without a s u b s t a n t i a l i n c r e a s e i n drag. Usually t h e optimum c r u i s i n g f l i g h tspeed corresponds t o Mcr o r less. The e f f e c t of a p o s i t i v e maximum thickness and t h e r e l a t i v e p r o f i l ecurvature. I t has been experimentally e s t a b l i s h e d t h a t with i d e n t i c a lwing t h i c k n e s s e s , t h e p r o f i l e which has a h i g h e r c r i t i c a l Mach number Mcr is-eth one i n which t h e maximum t h i c k n e s s i s c l o s e r t o t h e c e n t e r , . i . e . , f o rx = 35-50%. This i s explained by t h e f a c t t h a t with such a v a l u e f o r Fc, Ct h e r e i s a smoother p r o f i l e contour, and consequently a smoother change i np r e s s u r e and v e l o c i t y along i t (Figure 32). A decrease i n t h e p r o f i l e curvature has a favorable e f f e c t on t h e aerodynamic c h a r a c t e r i s t i c s a t high f l i g h t speeds. A symmetrical p r o f i l e (Figure 30,b), i n which T = 0 , o t h e r conditions being t h e same, as a h i g h e r c r i t i c a l Mach number. However, i n such p r o f i l e s t h e v a l u e s f o r c Y max a r e small (by comparison with asymmetric p r o f i l e s ) , s o t h a t t h e i r u s e on t r a n s p o r t a i r c r a f t i sFigure 32. E f f e c t of t h e Position of t h e d i f f i c u l t . Recent y e a r s have shownMaximum A i rfoi 1 P r o f i l e Thickness on t h e a broader u s e of t h e s o - c a l l e dC r i t i c a l Mach Number M c r : a - p r o f i l e "inverted" p r o f i l e , i e. , a .without r a r e f a c t i o n peak; b - p r o f i l e p r o f i l e having n e g a t i v e c u r v a t u r ew i t h r a r e f a c t i o n peak. (Figure 3 0 , c ) . These p r o f i l e s , u s u a l l y used i n t h e b a s i c s e c t i o n of t h e a i r f o i l , s a t i s f a c t o r i l ys o l v e t h e problem of t h e h i g h l y complex i n t e r f e r e n c e between t h e wing and t h ef u s e l a g e , c r e a t i n g smooth flow. The p h y s i c a l n a t u r e of t h e e f f e c t of r e l a t i v ec u r v a t u r e on t h e v a l u e M i s the same as the e f f e c t of t h e t h i c k n e s s . cr Decreasing t h e maximum p r o f i l e t h i c k n e s s , s h i f t i n g i t t o t h e middle of ­ /51t h e chord, and decreasing the p r o f i l e curvature a l l i n c r e a s e t h e v a l u e oft h e c r i t i c a l Mach number by a t o t a l of 0.02 - 0.06. The e f f e c t of wing sweep. The optimum e f f e c t i n i n c r e a s i n g t h e c r i t i c a lMach number i s achieved through t h e use of swept wings. As wing sweep i n c r e a s e s t o 3S0, t h e c r i t i c a l Mach number i n c r e a s e s by0.07 - 0 . 0 8 as compared with t h e c r i t i c a l Mach number f o r a s t r a i g h t wing o rprofile. Let us s e e how t h i s i s achieved. The l i f t of t h e wing and t h e t a i l assembly is determined by t h e v a l u e oft h e aerodynamic f o r c e of the p r e s s u r e s a r i s i n g as a r e s u l t of changes i n t h el o c a l flow v e l o c i t i e s induced by t h e e x t e r n a l contours of t h e p r o f i l e acrosst h e e n t i r e wingspan o r t a i l span. 45
  • 54. L e t us expand t h e f l i g h t speed V over two components: one, perpen- POS d i c u l a r t o t h e leading edge* of t h e wing -- Vef, and t h e o t h e r d i r e c t e d along the leading edge o f t h e wing -- VI (Figure 33,a). The component Vef (effectivespeed) determines t h e v a l u e of t h e l o c a l speeds and expansions along t h e pro­f i l e , and consequently t h e value of t h e l i f t as w e l l . The component V1 i sn o t involved i n t h e c r e a t i o n of t h e aerodynamic p r e s s u r e f o r c e s . I t does havean e f f e c t on t h e boundary l a y e r and, consequently, on t h e flow s e p a r a t i o n .I n conjunction w i t h t h e fact t h a t Vef i s always lower t h a n Vpos, t h e l o c a lspeed of sound w i l l be achieved l a t e r and, consequently, t h e c r i t i c a l Machnumber w i l l be g r e a t e r . The shock s t a l l on t h e p r o f i l e w i l l s e t i n a t ah i g h e r f l i g h t speed. This means t h a t t h e c r i t i c a l Mach number i n swept wingsw i l l always b e g r e a t e r t h a n i n s t r a i g h t wings o r t h e p r o f i l e . The c r i t i c a l Mach number f o r a swept wing, w i t h allowance made f o r t h ee f f e c t of flow c h a r a c t e r i s t i c s on t h e p r e s s u r e d i s t r i b u t i o n along t h e span, - /52may be determined from t h e formula: 2 M crX = *cr.prof 1 + cos x Jwhere x i s t h e angle of sweep f o r t h e wing. F o r wings having a sweep of 35 (cos 35 = 0.821, t h e formula assumes t h efollowing form: M c r X - 3 ~= * 0 Mcr.prof . For example, f o r a r e l a t i v e p r o f i l et h i c k n e s s of lo%, we o b t a i n a Mach number McrX.350 = 0.795. W must b e a r i n emind t h a t t h e e m p i r i c a l formula f o r determining t h e c r i t i c a l Mach numbero f f e r s an e r r o r of 1 5 2 0 % . Along i t s span, t h e a i r c r a f t wing has changing values r e l a t i v e t o t h et h i c k n e s s . Therefore, t h e c r i t i c a l Mach number a l s o has v a r i o u s v a l u e s . The e f f e c t of wing sweep, by i n c r e a s i n g t h e c r i t i c a l Mach number, i sdecreased a t t h e p o i n t where t h e c e n t r a l s e c t i o n of t h e wing j o i n s t h ef u s e l a g e . Here t h e wing i s s u b j e c t e d n o t t o oblique a i r f l o w ( r e s u l t i n g fromdecomposition of t h e i n c i d e n t flow i n t o two components), b u t t o s t r a i g h t a i r ­flow. The c r i t i c a l Mach number i s i n c r e a s e d through i n c r e a s i n g t h e sweep oft h e c e n t r a l p o r t i o n of t h e wing along t h e leading edge. Thus, i f t h e anglex = 30-3S0, i n t h e c e n t r a l s e c t i o n of t h e wing i t reaches 40-45, i . e . , t h ewing i s given a "crescent" shape i n planform. The Tu-104 and Tu-124 a i r - ­ / 53craft have a s l i g h t l y expressed "crescent" shape. .- . . . -. . .. - .... ....* S t r i c t l y speaking, Vef is perpendicular t o t h e aerodynamic c e n t e r l i n e MN, and t h e component V1 i s d i r e c t e d along t h i s l i n e , because t h e wing i s looked upon as t a p e r i n g . Our allowance has been made f o r s i m p l i c i t y i n exp 1anati on.46
  • 55. shock k c) 1 V m Figure 33. Development of F l i g h t Speed on Swept Wing and P o s s i b l e P o s i t i o n s of the Leading Wing d g e Relative t o t h e Mach Cone: 1 - subsonic leading edge -- w i n g located w i t h i n cone (subsonic f l o w ) ; I I - s o n i c leading edge (flow a t t h e speed o f sound); I I I - supersonic leading edge ( s u p e r s o n i c f l o w ) . The c r i t i c a l Mach number f o r t h e wing i n passenger a i r c r a f t i s belowu n i t y . For c l a r i t y i n r e p r e s e n t a t i o n , we w i l l show t h a t f o r a wing witht h i n p r o f i l e s (F = 4-6%) , a t an angle x = 55-60" t h e c r i t i c a l Mach number,determined according t o t h e formula a l r e a d y p r e s e n t e d , may be g r e a t e r thanu n i t y . However, f o r an i s o l a t e d p r o f i l e , as has already been noted, t h i s i simp os s i b l e . The shock s t a l l i n a swept wing occurs l a t e r , and n o t simultaneouslythroughout t h e wingspan, and l e s s i n t e n s e l y than on a s t r a i g h t wing; i na d d i t i o n , i t does n o t l e a d t o a s h a r p change i n the t o t a l aerodynamicc h a r a c t e r i s t i c s of t h e a i r c r a f t . A t various p o i n t s on t h e wing, t h e shock s t a l l developes i n d i f f e r e n tways. Recent s t u d i e s have shown t h a t i n t h e c e n t e r of t h e wing t h e shocks t a l l begins l a t e r than a t t h e t i p s , but because of t h i s i n c r e a s e s morei n t e n s e l y . As a r e s u l t , t h e n e g a t i v e e f f e c t of t h e c e n t r a l p o r t i o n of t h ewing i s f e l t n o t s o much i n t h e s e n s e of a decrease i n t h e c r i t i c a l Machnumbe.r as a more r a p i d i n c r e a s e i n t h e wave drag than a t t h e wing t i p s ,although i t starts t o i n c r e a s e sooner on t h e t i p s . There i s s u b s t a n t i a l l y l e s s wave drag i n a swept wing than i n a s t r a i g h tone, which may be c l a r i f i e d t h u s l y . 47
  • 56. L e t us assume t h a t l o c a l compression shocks a r i s i n g i n p r o f i l e s fromwhich t h e wing i s shaped s t a r t a t t h e l i n e MN (Figure 33,b). I n each p r o f i l e ,t h e l o c a l shock w i l l b e normal, while f o r t h e whole,wing t h e t o t a l shock,a l s o l o c a t e d along t h e l i n e MN, w i l l b e o b l i q u e (with r e s p e c t t o t h e i n c i d e n tflow). As has already been s t a t e d , t h e shock s t a l l developes more weakly whent h e r e i s an oblique shock. The shock f r o n t i s l o c a t e d along t h e l e a d i n g edge of a swept wing a t t h ei n s t a n t when Vef becomes equal t o t h e l o c a l speed of sound. On a wing with asweep angle x = 3S0, t h i s occurs a t a f l i g h t Mach number e q u a l t o 1.22. Letus show t h i s . As can b e seen from Figure 33,a, t h e speed Vef = V cos 35O. L e t us POSequate it t o t h e speed of sound: a = V POS cos 3S0, i . e . , a = 0.821 V pos then - VM = E = a V 0.821 - - 1.22. Thus, a wing with x = 35O may be used a l s o f o r POSs l i g h t s a t low s u p e r s o n i c speeds. As can b e seen from Figure 33,c, a Mach cone forms a t t h e t i p of t h eangle forming t h e leading wing edge when a swept wing encounters s u p e r s o n i cflow. This Mach cone assumes t h e form of an o b l i q u e compression shock. Ift h e leading wing edges l i e w i t h i n t h e Mach cone, they a r e c a l l e d subsonic.With r e s p e c t t o t h e degree t o which t h e s u r f a c e o f t h e Mach cone approachest h e leading edge, t h e wave drag r a t i o i n c r e a s e s and reaches it h i g h e s t value ­ / 54a t t h e i n s t a n t when t h e l e a d i n g edges meet t h e cone s u r f a c e . When t h e r e i sa f u r t h e r i n c r e a s e i n t h e speed, t h e leading edges o f t h e wing go beyond t h eboundary of t h e Mach cone, a f t e r which t h e s u r f a c e s of t h e Mach cone moveaway from t h e edges. In t h i s case, t h e leading edges a r e c a l l e d supersonic. Passenger a i r c r a f t designed i n r e c e n t y e a r s have an optimum anglex = 20-35 and a mean r e l a t i v e thickness of 10-12%. The u s e of a g r e a t e rsweep angle ( p a r t i c u l a r l y one equal t o 45O) i s i n a d v i s a b l e i n terms o f aweight-drag r a t i o f o r t h e wing because of t h e onset o f torque and, a d d i t i o n a l l y ,because of poorer t a k e o f f and landing conditions caused by a lower value f o r Use of a wing with a 35 sweep r e s u l t s i n a 10-25% drop i n wave drag f o rf l i g h t s a t M = 0.80 - 0.85, which s u b s t a n t i a l l y decreases t h e o v e r a l l drag.A t t h e same time it becomes p o s s i b l e t o maintain t h e l i f t - d r a g r a t i o f o r t h ea i r c r a f t w i t h i n l i m i t s of 13-15. The effect o f t h e sweep angle on t h ec o e f f i c i e n t c i s given i n Figure 34. X I n a d d i t i o n t o t h e parameters a l r e a d y d i s c u s s e d , t h e wing a s p e c t r a t i o Xa l s o has a determining e f f e c t on t h e c r i t i c a l Mach number. A s u b s t a n t i a li n c r e a s e i n t h e c r i t i c a l Mach number r e s u l t s f o r A = 1 - 1.5. In wings withsmall aspect r a t i o s ( A = 1 . 5 - 2 . 5 ) , t h e c r i t i c a l Mach number i s g r e a t e r thani n wings with high aspect r a t i o s ( A = 5-8). This i s explained b a s i c a l l y byt h e s o - c a l l e d end e f f e c t .48
  • 57. f ~-without flow /Figure 34. T h e E f f e c t of t h e Figure 35. T h e E f f e c t of Airflow PastSweep A n g l e on t h e Dependence t h e Wing T i p s on Pressure D i s t r i b u t i o ncx = f(M). over t h e Upper Surface. During f l i g h t , p r e s s u r e below t h e wing i s g r e a t e r t h a n above it. There­f o r e , t h e r e i s an overflow of a i r a t t h e wingtip from t h e region of g r e a t e rp r e s s u r e toward t h a t of l e s s e r p r e s s u r e , i . e . , a c e r t a i n p r e s s u r e balancetakes p l a c e , thanks t o which t h e m a x i m u m r a r e f a c t i o n over t h e wing decreases(Figure 3 5 ) . The i n f l u e n c e of t h e end e f f e c t i s s u b s t a n t i a l only c l o s e t o the /55wingtip. If t h e wing aspect r a t i o is decreased, t h e r e l a t i v e length of t h e s es e c t i o n s i n c r e a s e s and t h e end e f f e c t i s spread over a l a r g e s e c t i o n of t h ewing. F o r passenger a i r c r a f t a t an angle x = 3 S 0 , t h e optimum X = 6-8; t h e r e ­f o r e t h e c r i t i c a l Mach number i n t h i s case undergoes no change.§ 2. Features of Flow Around S w e p t Wings I n t h e preceding s e c t i o n , which examined t h e development of t h e speed we s i m p l i f i e d t h e p i c t u r e of t h e flow around a swept wing. Actually,",oshowever, t h i s p i c t u r e assumes a complex s p a t i a l scheme. Let us spend sometime d i s c u s s i n g t h e v a r i o u s b a s i c moments. To t h i s end, l e t us examine a i rstreams flowing around t h e middle and end p o r t i o n s of t h e wing (Figure 36).As a r e s u l t of t h e s p a t i a l c h a r a c t e r of t h e flow of t h e stream as we approacht h e c e n t e r s e c t i o n of t h e wing, i t becomes wider. A s a r e s u l t of t h ec o n s t a n t a i r consumption along t h e stream, t h i s leads t o a decrease i n speedi n t h e c e n t e r s e c t i o n of t h e p r o f i l e , and consequently t o a decrease i n t h er a r e f a c t i o n over t h e r i s i n g p a r t of t h e p r o f i l e i n t h e middle of t h e wing.O t h e descending p a r t t h e r e i s a c o n s t r i c t i o n of t h e stream and a consequent nr i s e i n speed and i n c r e a s e i n r a r e f a c t i o n . Thus, i n t h e middle s e c t i o n oft h e wing t h e r a r e f a c t i o n s d e c r e a s e on t h e r i s i n g s e c t i o n of t h e p r o f i l e , whilethey i n c r e a s e on t h e descending s e c t i o n . A t t h e t i p s of swept wings, t h e p i c t u r e i s reversed. Here t h e streamsapproaching t h e wing a r e f i r s t c o n s t r i c t e d , which leads t o an i n c r e a s e i nv e l o c i t 5 e s on t h e r i s i n g p r o f i l e s e c t i o n . As a r e s u l t , r a r e f a c t i o n s on t h e 49
  • 58. --leading p r o f i l e s e c t i o n s i n c r e a s e . As t h e p r o f i l e descends, t h e stream s t a r t sbroadening, which leads t o a decrease i n v e l o c i t i e s and r a r e f a c t i o n . P r chordsFigure 3 6 . Representative Character Figure 37. Representative P i c t u r e off o r t h e F l o w o f Air Streams i n the Pressure D i s t r i b u t i o n a t VariousMiddle and a t t h e Ends o f a S w e p t Wing. Sections along t h e Win.g: 1 - a t t h e t i p s ; 2 - i n t h e middle of t h e semi- span; 3 - i n the c e n t r a l s e c t i o n . Figure 37 shows t h a t at: the c e n t e r s e c t i o n s of t h e wing, t h e maximum /56r a r e f a c t i o n i s d i s p l a c e d t o the rear, whereas a t t h e t i p s e c t i o n s , i nc o n t r a s t , t h e g r e a t e s t r a r e f a c t i o n i s found a t t h e leading p a r t of t h e pro­f i l e . In a d d i t i o n , t h e v a l u e of t h e r a r e f a c t i o n peak i s h i g h e r a t t h e t i p sthan i n t h e c e n t e r and base s e c t i o n s . Therefore, t h e t i p s e c t i o n s o f t h ewing a r e more loaded (have g r e a t e r l i f t ) than due t h e b a s e s e c t i o n s . The observed f e a t u r e o f p r e s s u r e d i s t r i b u t i o n along t h e chord of t h e wingLeads a l s o t o another d i s t r i b u t i o n of load along t h e span ( i n c o n t r a s t t os t r a i g h t wings). Figure 38 shows t h e load d i s t r i b u t i o n along t h e span of swept and IC,ljec s t r a i g h t wings, as w e l l as changes i n t h e maximum values of the coefficient c y s e c max sec f o r v a r i o u s wing s e c t i o n s * . I - . -. The d i f f e r e n c e i n t h e j f l a t wing I c h a r a c t e r i s t i c f o r t h e change.I in c i n s t r a i g h t and y s e c max swept wings i s explained i n t h e following manner. TheFigure 38. Diagram of Load D i s t r i b u t i o n overflow of air p a s t t h e wingAlong t h e Span of a Swept and a S t r a i g h t t i p from t h e lower t o t h eWing: -..-geometric t w i s t ; -.- aero- upper s u r f a c e i n a s t r a i g h tdynamic t w i s t ; -f l a t w i n g . wing has an e f f e c t only on a* Pashkovskiy, I . M . C h a r a c t e r i s t i c s of S t a b i l i t y and C o n t r o l l a b i l i t y i n High- Speed A i r c r a f t (Osobennosti us t o y c h i v o s t i i upravlyayemos ti skoros tnogo samoleta) . Voyenizdat. 196150
  • 59. small s e c t i o n , as a r e s u l t of which t h e value c i s i d e n t i c a l almost y s e c max everywhere on t h e span and only toward t h e wing t i p s does it s t a r t t o decrease. I n swept wings, however, t h e decrease i n c from t h e base t o t h e t i p y sec max i s r e l a t e d n o t only t o t h e overflow of a i r p a s t t h e t i p b u t a l s o with t h e nonsimultaneous i n c r e a s e i n t h e flow s e p a r a t i o n along t h e span. This s e p a r a t i o n i s h i g h l y dependent on t h e a i r overflow i n t h e boundary l a y e r due t o t h e component V1 ( s e e Figure 3 3 , a ) . Therefore, t h e end s e c t i o n s of the swept wing undergo s e p a r a t i o n b e f o r e a l l t h e o t h e r s , i . e . , they a r e t h e f i r s t t o ­ /57 a t t a i n t h e values c y s e c max As can b e seen from t h e f i g u r e , t h e end s e c t i o n s of the swept wing achieve c f a s t e r than do t h e s e c t i o n s of t h e c e n t e r and b a s e y s e c max p o r t i o n s of t h e wing. In s t r a i g h t wings, on t h e o t h e r hand, cy max i s reached e a r l i e r i n t h e c e n t e r s e c t i o n of t h e wing. Therefore, with an i n c r e a s e i n t h e angle of attack t h e flow s e p a r a t i o n reaches t h e end s e c t i o n s of t h e swept wing and t h e c e n t e r s e c t i o n s of t h e s t r a i g h t wing sooner. In a d d i t i o n , t h e o v e r a l l end flow s e p a r a t i o n on t h e swept wing f a c i l i t a t e s t h e speed V which causes t h e boundary l a y e r t o move 1 Coward t h e wing t i p and causes i t t o thicken. The boundary l a y e r seems t o be i n a sense sucked from t h e c e n t e r s e c t i o n and b u i l t up a t t h e ends of the wing. The "swelling" o f t h e boundary l a y e r and the premature s e p a r a t i o n a t the wing t i p s is one of the b a s i c drawbacks o f swept wings. The end flow s e p a r a t i o n leads t o t h e development of t h e p i t c h i n g moment, which a f f e c t s t h e l o n g i t u d i n a l s t a b i l i t y of t h e a i r c r a f t a d v e r s e l y , e s p e c i a l l y a t slow f l i g h t speeds. Flow s e p a r a t i o n i n t h e a i l e r o n zone leads t o a drop i n t h e l a t e r i a l handiness. Along with end flow s e p a r a t i o n , a t low f l i g h t speeds ( g r e a t e r than t h e angle of a t t a c k ) , such a s e p a r a t i o n i s p o s s i b l e a l s o a t high speeds a t low angles o f a t t a c k , which i s explained by t h e i n t e r a c t i o n of compression shocks with t h e boundary l a y e r during f l i g h t a t high a l t i t u d e s . A s i n well known, a t high a l t i t u d e s f l i g h t i s performed a t high angles o f a t t a c k ( t o o b t a i n t h e necessary v a l u e f o r c ) . With an i n c r e a s e i n t h e angle of a t t a c k , t h e Y hf v a l u e f o r t h e c r i t i c a l Mach number decreases. When t h e angle c1 i n c r e a s e s due t o v e r t i c a l g u s t s , compression shocks may form e a r l i e r (because t h e c r i t i c a l Mach number i s low), which a i d s i n t h e development of flow s e p a r a t i o n . In a l l t h e s e cases , during s e p a r a t i o n t h e r e i s t h e c h a r a c t e r i s t i c v i b r a t i o n , and i n some cases t h e r e i s even p i t c h i n g down. R e d i s t r i b u t i o n of load along the span of a swept ( i n c o n t r a s t t o a s t r a i g h t ) wing always leads t o a displacement o f t h e e q u i v a l e n t aerodynamic f o r c e of t h e wing backward o r forward along t h e chord, and t h e r e f o r e i s accompanied by a change i n i t s l o n g i t u d i n a l moment. As can be seen from Figure 39, when t h e wing i s swept, each s e c t i o n i s 51I
  • 60. d i s p l a c e d r e l a t i v e t o each o t h e r i n such a way t h a t i n t o t o t h e p o i n t s of a p p l i c a t i o n o f t h e i n c r e a s i n g aerodynamic f o r c e s f o r t h e s e s e c t i o n s form a ­ /58 l i n e which i s i n c l i n e d along t h e p e r p e n d i c u l a r t o t h e a x i s o f t h e wing ( t h ea x i s oz) by angle x. The d i s t a n c e from t h e a x i s oz t o t h e p o i n t s of a p p l i c a t i o n of t h e aerodynamic f o r c e s f o r t h e s e s e c t i o n s d i f f e r according t o span. I n s t r a i g h t wings, on t h e c o n t r a r y , t h e p o i n t s of a p p l i ­ c a t i o n of t h e i n c r e a s i n g aerodynamic f o r c e s f o r t h e s e c t i o n s l i e p r a c t i c a l l y on a s t r a i g h t l i n e p a r a l l e l t o t h e a x i s , i.e. , they a r e e q u i d i s t a n t from t h e l a t e r i a l a x i s of t h e wing i n a l l s e c t i o n s a c r o s s t h e span. This f e a t u r e f o r t h e load d i s t r i b u t i o n along t h e span i n swept wings changes s u b s t a n t i a l l y e i t h e r withF i g u r e 39. Example of t h e a change i n t h e angle of attack o r a change i n E f f e c t of Load D i s t r i b u t i o n t h e Mach number. Along t h e Span on t h e Longitudinal Moment of a From Figure 40 we s e e t h a t an i n c r e a s e S w e p t Wing. i n IY, leads t o a g r e a t e r load on t h e c e n t r a l s e c t i o n o f t h e swept wing and a l i g h t e n i n g o f i t s end s e c t i o n s . In t h i s c a s e , t h ep r e s s u r e c e n t e r f o r t h e wing s h i f t s forward along t h e chord, which c r e a t e sa tendency taward p i t c h i n g . The onset of p i t c h i n g corresponds t o t h e momentof t h e onset of s e p a r a t i o n , which s t a r t s a t t h a t s e c t i o n of t h e wing wheret h e a i l e r o n a r e located. I f t h e r e i s a change i n t h e Mach number and a remains c o n s t a n t , t h e r e i sa l s o a r e d i s t r i b u t i o n of load along t h e span. This i s accompanied by anunequal development of shock s t a l l on t h e wing i n t h e process o f reaching ands u r p a s s i n g c r i t i c a l speed. As we can s e e from Figure 40, an i n c r e a s e i n t h ef l i g h t speed up t o c r i t i c a l leads f i r s t t o a c e r t a i n loading o f t h e ends e c t i o n s o f t h e swept wing. Then, w i t h t h e development o f t h e shock s t a l la t a Mach number somewhat g r e a t e r than MCr, t h e end s e c t i o n s s t a r t l o s i n gt h e i r load. The i n i t i a l i n c r e a s e i n t h e loading o f t h e end s e c t i o n leads t ot h e development of a s l i g h t diving moment , i . e . , t o a change i n t h e longi­t u d i n a l s t a b i l i t y * . Subsequent changes i n t h e load d i s t r i b u t i o n a r e broughtabout through t h e propagation of t h e shock s t a l l along t h e upper wing s u r f a c et o t h e base and middle s e c t i o n s of t h e c a n t i l e v e r s , as w e l l as t h e developmentof t h e s t a l l on t h e lower wing s u r f a c e . A l l t h i s leads t o a c e r t a i n d i s ­placement o f t h e wing p r e s s u r e c e n t e r (P.c.) forward along t h e chord and t h eappearance of a p i t c h i n g moment a t Mach numbers g r e a t e r than c r i t i c a l , b u tless than u n i t y ( s o n i c s p e e d s ) . D i s t i n c t changes i n t h e load d i s t r i b u t i o n along t h e span of a sweptwing may a l s o l e a d t o i t s f l e x i b l e deformation (buckling and t w i s t i n g ) . Int h e event of deformation, t h e l o c a l angles of a t t a c k a t various p o i n t s along - ­* Pashkovskiy, I . M . C h a r a c t e r i s t i c s o f S t a b i l i t y and C o n t r o l l a b i l i t y i n High- Speed A i r c r a f t (Osobennosti us t o y c h i v o s t i i upravlyayemosti skorostnogo samoleta). Voyenizdat. 196152 I
  • 61. t h e wing change d i s s i m i l a r l y , because t h e degree of t h e s e changes i s af u n c t i o n of t h e aerodynamic f o r c e s a c t i n g on t h e wing. These l a t t e r , i n t u r n ,are f u n c t i o n s of t h e angle of a t t a c k , f l i g h t speed and Mach number. iv /View along w i n gFigure 40. Change i n t h e Load Figure 41. Decrease i n A n g l e of Attack D i s t r i b u t i o n Along t h e Span o f f o r Bend i n a Swept Wing: a - non­a S w e p t Wing as a Function of deformed f l e x u r a l a x i s ; b - f l e x u r a l the A n g l e o f Attack and t h e a x i s o f cranked w i n g . Mach Number. I n t h e event of buckling o f a swept wing (Figure 41) r e l a t i v e t o t h e 0-0a x i s , t h e p o i n t s 1 ani 3 , lying c l o s e t o t h i s a x i s , w i l l have l e s s of av e r t i c a l displacement than p o i n t s 2 and 4. A s a r e s u l t of t h i s , t h e chords1 - 2 and 3-4 a r e turned r e l a t i v e t o t h e f l e x u r a l axis by a c e r t a i n a n g l e , and ­ / 59t h e e n t i r e wing t u r n s t o t h e s i d e o f t h e decrease i n t h e angle of a t t a c k .Thus, f o r a wing with normal sweep, i n t h e event of t w i s t i n g induced byaerodynamic loads d i r e c t e d upward from below, t h e r e is always a decrease i nt h e angle o f a t t a c k of t h e wing s e c t i o n the c l o s e r t h i s given s e c t i o n i s t othe end of t h e wing. This a l s o aggravates p i t c h i n g , i n t h a t t h e end s e c t i o n shave s m a l l e r angles of a t t a c k and, consequently, lower values f o r cy s e c This f a c t , along with t h e forward displacement of the p r e s s u r e c e n t e r as t h eangle of a t t a c k and speed i n c r e a s e , may a l s o l e a d t o a i r c r a f t i n s t a b i l i t i e sw i t h i n a s p e c i f i c range of Mach numbers.5 3. Wing Construction i n Turbojet Passenger A i r c r a f t I n designing a i r c r a f t f o r c r u i s i n g Mach numbers of 0 . 8 - 0.85, s t r i c ta t t e n t i o n m u s t be given t o t h e s e l e c t i o n of wing parameters. W are a l r e a d y efamiliar with c e r t a i n parameters, and now w e s h a l l continue our examination. I t has been e s t a b l i s h e d t h a t f o r subsonic passenger a i r c r a f t , t h e optimum 53
  • 62. parameters a r e an angle of x = 35 and a wing a s p e c t r a t i o of A = 6 - 8 . Withsuch values f o r A , f l i g h t d i s t a n c e i s s u b s t a n t i a l l y i n c r e a s e d . Narrowing t h e wing i n planform IT = bbas i s decided through t h e s e l e c t i o n ­ / 60 end of conditions y i e l d i n g b e s t s t a b i l i t y c h a r a c t e r i s t i c s and c h a r a c t e r i s t i c s o f l o n g i t u d i n a l s t a b i l i t y , s o as t o e l i m i n a t e s e p a r a t i o n flows a t t h e wing t i p s . For a 3 sweep, t h e optimal s e l e c t i o n i s T = 3 . 5 - 4.5*. 5 I The remaining wing parameters are s e l e c t e d from c a l c u l a t i o n of t h eoptimal l i f t p r o p e r t i e s f o r t h e wing. I t has been e s t a b l i s h e d t h a t t h e dependence of t h e c o e f f i c i e n t c (as Yw e l l as t h e c o e f f i c i e n t f o r t h e l o n g i t u d i n a l moment m Z , Figure 140) on t h eangle a proceeds l i n e a r l y t o avib, a t which p o i n t t h e r e are l o c a l flows e p a r a t i o n s on t h e wing and t h i s r e l a t i o n i s no longer v a l i d . This leads t ot h e f a c t t h a t a t high angles of a t t a c k t h e r e i s a decrease i n l o n g i t u d i n a ls t a b i l i t y ( i n Figure 140, t h i s corresponds t o t h e s o - c a l l e d !balance p o i n t " ) .The d i s r u p t i o n i n l o n g i t u d i n a l s t a b i l i t y i s q u i t e r e p r e s e n t a t i v e of sweptwings. I t i s troublesome n o t only i n t h a t i t a f f e c t s t h e l o n g i t u d i n a ls t a b i l i t y of t h e aircraft a d v e r s e l y , b u t i n a d d i t i o n t h e flow s e p a r a t i o n fromthe wing t i p s decreases t h e e f f e c t i v e n e s s of t h e a i l e r o n s and asymmetrics e p a r a t i o n may r e s u l t i n p i t c h i n g down. Therefore, i n e s t a b l i s h i n g t h e aerodynamic arrangement of t h e swept wingsi n passenger a i r c r a f t , maximum c r u i s i n g f l i g h t speeds and minimum landingspeeds a r e achieved through holding t h e development of t h e flow s e p a r a t i o nt o t h e h i g h e s t p o s s i b l e angles of a t t a c k and t h e h i g h e s t Mach numbers. Thefollowing means a r e used t o achieve t h i s . 1. The aerodynamic t w i s t of t h e wing -- t h e s e l e c t i o n of t h e wingdesign from v a r i o u s p r o f i l e t y p e s , t h e p r o f i l e s o f f e r i n g t h e lowest l i f t beinga t t h e base of t h e wing, while those with t h e g r e a t e s t l i f t a r e a t t h e t i p s .This r e s u l t s from t h e change c h a r a c t e r i s t i c f o r c with r e s p e c t t o t h e y s e c maxwing dimensions (Figure 38). The s e l e c t i o n of p r o f i l e s with g r e a t e r l i f t f o rt h e wing t i p s (with T = 2 . 5 - 3% and g r e a t e r ) w i t h t h e r e v e r s e p o s i t i o n i n gof maximum thickness ( y = 35 - 50%) permits a c e r t a i n i n c r e a s e i n c C y s e c maxa t t h e wing t i p s and, at t h e same time, i n c r e a s i n g t h e angle of a t t a c k andthereby achieving c y sec m a Symmetrical p r o f i l e s (sometimes with s l i g h t curvature) o r p r o f i l e s withn e g a t i v e c u r v a t u r e - - "inverted" p r o f i l e s -- a r e p o s i t i o n e d a t t h e base oft h e wing The DC-8, Convair 880, t h e Boeing-707 and t h e VC-10 have "inverted" . ­* Yeger, S.M. Design of Passenger J e t A i r c r a f t (Proyektirovaniye p a s s a z h i r ­ skikh reaktivnykh samelotov) . Mashinostroyeniye. 1964.54
  • 63. p r o f i l e s i n t h e c e n t e r s e c t i o n s o f t h e wing. This has n o t hindered t h e o v e r a l llift of t h e wing and has made i t p o s s i b l e t o use p r o f i l e s with 7 = 12-15%without a s i g n i f i c a n t i n c r e a s e i n cx a t high f l i g h t Mach numbers. 2. Geometrical t w i s t i s t h e gradual s p i r a l e f f e c t ( p o s i t i o n i n g a t a ­ / 61s m a l l e r angle) of t h e wing t i p s and middle wing s e c t i o n s r e l a t i v e t o t h e b a s ea t an angle of 2-5O ( f o r example, i f t h e angle i s + 3 O a t t h e wing base, whileit i s -1" a t t h e wing t i p , t h e t w i s t angle equals -4). This changes t h el i f t d i s t r i b u t i o n along t h e span toward t h e s i d e of g r e a t e r load f o r t h e wingb a s e and unloading f o r t h e wing t i p s . During f l i g h t , t h i s type wing mayachieve h i g h e r angles of a t t a c k ( c a l c u l a t e d with r e s p e c t t o t h e chord of t h eb a s e p r o f i l e ) b e f o r e t h e wing t i p s reach s e p a r a t i o n . Figure 16 shows t h a t t h egeometrical t w i s t has an affect on t h e extension of t h e r e l a t i o n c = f ( a ) ,moving i t t o t h e r i g h t . Y Having e s t a b l i s h e d t h e geometric t w i s t , w m u s t t a k e i n t o account t h e ebending and warping of t h e wing, as shown i n Figure 41, s o as t o not o b t a i nnegative l i f t a t the t i p s . I t w a s noted e a r l i e r t h a t with geometric t w i s t , t h e r e q u i r e d c is Y 1gachieved a t a s l i g h t l y h i g h e r f l i g h t angle of a t t a c k . 3 . P o s i t i o n i n g aerodynamic b a f f l e s 16-20 cm high (an average of 2-4%of t h e l o c a l wing chord, Figure 42) on t h e upper wing s u r f a c e . The b a f f l e ss e p a r a t e t h e wing i n t o p o r t i o n s and h i n d e r t h e overflow of a i r i n t h e boundaryl a y e r along t h e wing span, r e s u l t i n g i n a decrease i n t h e thickness of t h eboundary l a y e r i n the t i p s e c t i o n s . This leads t o an i n c r e a s e i n the l o c a lvalues f o r c i n t h e end s e c t i o n s (by comparison t o a wing without y s e c mqxb a f f l e s ) , and consequently aids i n holding o f f t h e onset o f flow s e p a r a t i o ni n t h e s e s e c t i o n s u n t i l t h e high angles of a t t a c k . Figure 42, Arrangement o f Aerodynamic Baffles on Upper Wing Surface:1 - l i n e of 1 / 4 chord; 2 - p o i n t of onset of flow s e p a r a t i o n andburbling; 3 - a i l e r o n ; 4 - b a f f l e ; 5 - a i r stream (enlarged s c a l e ) ;6 , - v o r t i c e s s e p a r a t i n g from w i n g w i t h b a f f l e s ; 7 - p o s s i b l e b a f f l eshape. In t h e wing s e c t i o n c l o s e s t t o t h e f u s e l a g e (between t h e b a f f l e s and t h e 55
  • 64. --f u s e l a g e ) t h e r e i s a t h i c k e n i n g of theqboundary l a y e r and a d e c r e a s e i nC Lateral flows arise w i t h i n t h e l i m i t s of only one s e c t i o n , y sec m a v o r t i c e s form a t t h e b a f f l e s , and t h e boundary l a y e r flows o f f w i t h t h e s e . - / 62 Thus, because of t h e l a t e r a l overflow of air i n t h e boundary l a y e r whent h e wing i s equipped with b a f f l e s , t h e i n i t i a l flow s e p a r a t i o n on t h e wings e c t i o n between t h e b a f f l e s and t h e f u s e l a g e i s maintained and s e p a r a t i o nfrom t h e o u t e r s e c t i o n o f t h e b a f f l e s and t h e wing t i p s i s f o r e s t a l l e d .Because the tendency toward s e p a r a t i o n of t h e boundary l a y e r weakens, t h e r ei s an improvement i n t h e l i f t d i s t r i b u t i o n along t h e wing span. Thes e p a r a t i o n zone i s d i s p l a c e d toward the middle s e c t i o n s and, i n some i n d i ­v i d u a l cases, even toward t h e base of t h e wing. Aerodynamic b a f f l e s havebeen i n s t a l l e d on t h e wings of t h e Tu-104, Tu-124, Tu-134 and C a r a v e l l eaircraft . A similar e f f e c t is c r e a t e d by t h e pylons which support t h e engines onsuch a i r c r a f t as t h e Boeing-707, t h e Douglas DC-8 and t h e Convair 880 ( s e eFigure 65). However, pylons behave b a s i c a l l y l i k e b a f f l e s on t h e lowerwing s u r f a c e , where t h e r e i s s u b s t a n t i a l l y l e s s cross c u r r e n t i n t h e boundaryl a y e r . Only t h a t p o r t i o n o f t h e pylon which captures t h e upper wing s u r f a c ea t i t s nose has an e f f e c t on t h e wing. The 11-62 has swept wings with s o - c a l l e d "notches" i n t h e leading edge(Figure 4 3 ) . The "notch" forms a constant vortex cord on t h e wing s u r f a c ewhich acts i n t h e same manner as an aerodynamic b a f f l e , i n c r e a s i n g t h e b u i l dup o f t h e boundary l a y e r behind i t s e l f with t h e r e s u l t t h a t i t does notoverflow t o t h e wing t i p . There are o f course o t h e r means f o r t i g h t e n i n g s e p a r a t i o n s from t h e winga t low speeds, and they w i l l be discussed i n Chapter V, § 8. The Boeing-707, t h e DC-8 and o t h e r a i r c r a f t t i g h t e n t h e flow through t h euse of vortex g e n e r a t o r s . Their b a s i c purpose is t h e c r e a t i o n of a system of - /63v o r t i c e s f o r a c t i v a t i n g the boundary l a y e r (Figure 44). F i g u r e 43. Positioning o f "Notches" on t h e Leading Edge o f a Swept Wing.56
  • 65. I d i r e c t i o n of vortex rotation Figure 44. P o s i t i o n i n g o f F l o w Vortex Generators on t h e Wing o f t h e Boeing-707 (h = 10-12 cm, 01 = I S " , 1 = 15-30 cm, D = 40-60 cm). The p r i n c i p l e behind t h e a c t i o n of v o r t e x generators i s based on t h e f a c t t h a t a system o f v o r t i c e s having a p a r a l l e l i n f l u e n c e on t h e boundary l a y e r flowing around t h e wing s u r f a c e a t t h e upper l i m i t causes an i n c r e a s e d mixing of t h e boundary l a y e r with t h e o u t e r flow. A i r p a r t i c l e s c a r r i e d from t h e o u t e r flow by the v o r t e x d i s p l a c e t h e p a r t i c l e s i n t h e boundary l a y e r and, through mixing with them, a r e entrapped i n t h e o u t e r l a y e r . There is i n t e n s i ­ f i c a t i o n o f t h e boundary l a y e r which r e s t r i c t s i t s breaking away from t h e compression shock. I n those i n s t a n c e s where break away n e v e r t h e l e s s occurs, t h e vortex system e x c i t e d by t h e v o r t e x g e n e r a t o r s c r e a t e s i n intermixing e f f e c t i n t h e s e p a r a t e d flow as w e l l , as a r e s u l t of which t h e flow s e p a r a t i o n region i s l o c a l i z e d and t h e boundaxy l a y e r again "adheres" t o t h e wing surface*. S e t t i n g up v o r t e x g e n e r a t o r s has succeeded i n f o r e s t a l l i n g t h e development of flow s e p a r a t i o n a t high angles of a t t a c k and f l i g h t speeds (an i n c r e a s e i n t h e c r i t i c a l Mach number t o 0 . 0 2 - 0.07). Aileron e f f e c t i v e n e s s i n c r e a s e d because t h e vortex g e n e r a t o r s i n h i b i t s e p a r a t i o n of t h e boundary l a y e r along t h e r u p t u r e l i n e of t h e upper wing s u r f a c e when t h e a i l e r o n i s down. Vortex g e n e r a t o r s s e t i n t h e b a s e s e c t i o n of t h e wing (Boeing-707) decrease l i f t a t high angles of a t t a c k through flow s e p a r a t i o n . In a d d i t i o n , on t h e Comet-4c t h e r e are t h e s o - c a l l e d s e n s o r s ( s p e c i a l p l a t e s , Figure 20) which break up t h e flow a t t h e base s e c t i o n of t h e wing a t high angles o f attack and by s o doing decrease t h e p i t c h i n g moment. I n summary, t h e measures described (including t h o s e l a i d o u t i n Chapter / 64 ­ V, § 8) make it p o s s i b l e t o design a i r c r a f t wings with t h e shape shown i n Figure 45. I t must be noted t h a t i f along t h e 1 / 4 chord l i n e t h e angle x = 3S0, then along t h e leading edge t h e sweep may b e somewhat g r e a t e r ( i n t h e . _- ~ * Yeger, Design of Passenger Jet Aircraft (Proyektirovaniye p a s s a c h i r ­ S.M. skikh reaktivnykh samelotov) . Mashinostroyeniye. 1964. 57
  • 66. lll I I f i g u r e t h i s corresponds t o an angle o f x = 41* i n t h e b a s e s e c t i o n o f t h e wing and x = 38 i n t h e o u t e r wing s e c t i o n ) . Figure 45. Schematic Diagram of A i r c r a f t Wing: 1 - inside s p o i l e r ; 2 - i n s i d e f l a p ; 3 - outside spoiler; 4 o u t s i d e f l a p ; 5 - i n s i d e ai l e r o n ; - 6 outside a i l e r o n ; 7 - f l e t t n e r trim tabs; 8 - intermediate r i b s ; 9 - landing g e a r pod; 10 - secondary c o n t r o l s u r f a c e s ; 1 1 - t i p r i b s ; 1 2 - s p a r a x e s ; 13 - w i n g s t u m p j o i n t ; 1 4 - w i n g joint,axis. Tables 3-5 p r e s e n t t h e values o f parameters ( i n percentage) f o r t h e following v a r i a t i o n s i n wing aerodynamic arrangement : a) f o r a wing without geometric t w i s t ( c r u i s i n g Mach number Mcruise - L = 0.75 - 0.78, $vib = + l o ) : TABLE 3 - - .~ .- . . - . . . ... Section C X C I A t wing stump j o i n t 15* 35 1.0 20 A t wing j o i n t axis 13 35 3.3 A t tip rib 12 37 2.5 50 25 * R e l a t i v e t h i c k n e s s along flow. 58
  • 67. b) f o r a wing with geometric twist (engines i n t a i l s e c t i o n of f u s e l a g e , /65c r u i s i n g Mach number M c r u i se = 0.8 - 0.82, and 4 vib = +lo, vib = -130): otip TABLE 4 -- - .-. . .- . . S e c t i on . -- . . - - C X 1 - - - -f - - - - . .. . -- - -C Xf . [ . - . - . - - -.. .. -A t wing stump j o i n tA t wing j o i n t axisA t tip rib 9.75* 13 11.0 :: 35 ;:: 2.2 30 35 35* R e l a t i v e thickness along flow.c r u i s i n g Mach number Mcruise = 0.82 - 0.85, +, c) f o r wing with geometric t w i s t (engines i n t a i l s e c t i o n of f u s e l a g e , ase vib = + 3 0 J inter. r i b ­ -= o", = -1"): tip vib TABLE 5 Secti o nA t wing stump j o i n t 12 56 -0.7 30Intermediate 40A t tip rib§ 4. Drag Propagation Between S e p a r a t e P a r t s o f A i r c r a f t T o t a l a i r c r a f t drag i s known t o be t h e composite of drag i n t h e i n d i v i d u a ls e c t i o n s . F o r various f l i g h t speeds (Mach numbers) diverging drag propagationsr e s u l t between t h e s e p a r t s mainly due t o t h e onset of wave drag a t t h er e s p e c t i v e Mach numbers. I n subsonic a i r c r a f t , around h a l f o f t h e t o t a l dragi s c r e a t e d by t h e wing. Table 6 shows r e p r e s e n t a t i v e v a l u e s Acx f o r t h e b a s i ca i r c r a f t components with t h e engines s e t i n t h e t a i l s e c t i o n of t h e f u s e l a g e( t h e d a t a p e r t a i n t o h o r i z o n t a l f l i g h t a t a Mach number of M = 0.8, a t whichc f o r t h e e n t i r e a i r c r a f t equals 0.0305, while c = 0 . 4 ) . X Y I t should be noted t h a t t h e p o r t i o n of wave drag f o r M = 0 . 8 a t c = 0 . 4 Y(corresponding roughly t o t h e high angle of attack c1 5.5) i s approximately20% (Actail = 0.006). Having t h e landing g e a r down (Acx = 0.015 - 0.020) a tlow f l i g h t speeds c r e a t e s approximately h a l f of t h e e n t i r e a i r c r a f t drag. 59 I
  • 68. TABLE 6 Averaged In % of for A i r craf t compon ent total remaining aircraft aircraft (%IWing 0.015 49.5 45-50 Elevator u n i t 0.001.7 5.57 5- 6 Rudder-fin u n i t 0.001 3.28 3- 4 Fus e 1age 0.008 26.2 25-30 Landing g e a r pods 0.00116 3.8 3- 5 Side engine pods 0.0027 8.83 8- 10 Center engine i n t a k e 0.001 3.28 Entire aircraft c =O. 0305 100 100 X 60
  • 69. CHAPTER I V CHARACTER1 STI CS OF THE POWER SYSTEM J e t engines and, i n p a r t i c u l a r , t u r b o j e t engines g e n e r a t e high i n - f l i g h t ­ / 66t h r u s t and, consequently, high t h r u s t horsepower (30,000 - 60,000 hp)necessary f o r p r o p e l l i n g a i r c r a f t weighing 40 - 160 tons a t a speed o f 850 ­900 km/hr. P i s t o n and turboprop engines u s e up a l l o r almost a l l t h e energy from t h ef u e l i n r o t a t i n g t h e p r o p e l l e r . I t i s t h e p r o p e l l e r which, driven i n i t sr o t a t i o n by t h e engine, c r e a t e s t h e t h r u s t . Therefore t h e p r o p e l l e r i s c a l l e dt h e prime mover of t h e a i r c r a f t . The power system f o r p i s t o n and turbopropengines comprises b o t h t h e engine and t h e prime mover, which c r e a t e t h e t h r u s t . In t h e o p e r a t i o n of a j e t engine, however, t h e t h r u s t i s achieved in­d i r e c t l y as t h e i n t e r a c t i o n of a l l the f o r c e s a c t i n g on t h e s u r f a c e of t h eengine components. The j e t engine o r g a n i c a l l y combines w i t h i n i t s e l f t h eengine i n the normal .concept of t h e word and t h e prime mover. During t e s t - s t a n d o p e r a t i o n of modern t u r b o j e t engines , t h e p r e s s u r e a tt h e compressor exhaust equals 5-10 atm o r more. The gas temperature a t t h e combustion chamber exhaust i s 1 , O O - 1,200"abs. The power generated by t h e gas t u r b i n e i s 60,000 - 90,000 hp f o r engineswith a t h r u s t from 5,000 t o 10,000 kG. As i t e x i s t s from t h e t u r b i n e , t h e g a s s t i l l has a high amount of h e a tenergy, i t s p r e s s u r e i s g r e a t e r than atmospheric, and i t s temperature equals800 - 1,000" abs. Through t h e process of expansion, t h e thermal energy oft h e gas a t the- exhaust nozzle is transformed i n t o k i n e t i c energy, and as ar e s u l t of the high speed of t h e g a s exhaust, t h e exhaust t h r u s t i s generated.5 1. Two-Ci rcui t a n d Turbofan Engines ­ 1 67 Attempts by a e r o n a u t i c a l engineers t o i n c r e a s e engine t h r u s t and decreasef u e l consumption l e d t o t h e c r e a t i o n of t h e t w o - c i r c u i t and turbofan engines(Figure 46). Fuel consumption i n p a r t i c u l a r decreased by 1 5 2 0 %by comparisonwith consumption i n normal t u r b o j e t engines. The t w o - c i r c u i t (turbofan) engine i s a gas t u r b i n e engine i n which t h eexcess t u r b i n e horsepower, i n c o n t r a s t t o t h e turboprop engine, i s t r a n s m i t t e dt o a compressor o r f a n enclosed i n t h e c i r c u l a r cowling. The t w o - c i r c u i t t u r b o j e t engine may assume one of s e v e r a l s t r u c t u r a ldesigns (Figure 46a and b ) which are c h a r a c t e r i z e d by t h e e x i s t e n c e of an 61
  • 70. a d d i t i o n a l a i r c i r c u i t through which, a f t e r compression, p a r t o f t h e a i r whichhas been sucked i n i s fed t o t h e combustion chamber and t u r b i n e bypass d i r e c t l yt o t h e o u t l e t , thereby i n c r e a s i n g t h e m a s s and decreasing t h e speed o f t h ej e t s tream. Two-contour engines i n which t h e volume of a i r passing through t h esupplementary c i r c u i t i s r e l a t i v e l y g r e a t while t h e degree of compression oft h i s air i s small a r e u s u a l l y c a l l e d turbofan engines. A t p r e s e n t t h e r e arei n use t w o - c i r c u i t engines of t h i s type and turbofan engines, which are derived/68 ­through t h e i n s t a l l a t i o n of a f a n i n a d d i t i o n t o t h e normal t u r b o j e t engine(Figure 46c and d ) . The expediency of c r e a t i n g turbofan engines based ons e r i e s t u r b o j e t engines f o r c i v i l i a n a i r c r a f t i s j u s t i f i e d through t h e i rg r e a t economy and high r e l i a b i l i t y during use. Figure 46. Various Types of Two-Circuit and Turbofan Engines: a - normal scheme (Rolls Royce "Conway" engine) ; b - t w o - c i r c u i t engine w i t h a i r displacement from o u t e r contour w i t h gases from t h e inner contour (Rolls Royce JT8D "Spey"); c - turbofan scheme w i t h forward fan (Pratt-Whi tney JT3D) ; d - turbofan with r e a r fan (General E l e c t r i c CJ-805-23). When a t u r b o j e t engine i s being designed s t r i c t l y along t h e t w o - c i r c u i tp l a n , optimal parameters a r e obtained i f t h e design and the parameters of t h eturbofan engine a r e t o a g r e a t degree determined and l i m i t e d by t h e parametersof t h e i n i t i a l t u r b o j e t engine. Figure 47 shows a s i m p l i f i e d schematic of a t w o - c i r c u i t engine. Atmos­p h e r i c a i r e n t e r s t h e a i r scoop through t h e two l a y e r s of blades which formt h e fan B. From t h i s f a n , which i s i n e f f e c t a low-pressure compressor, t h ea i r moves on i n two s e p a r a t e p a t h s . One p a r t of the a i r moves along t h e o u t e rbody of t h e b a s i c engine contour through t h e second contour C , while the o t h e rp a r t moves through t h e high-pressure compressor D. From t h e r e i t moves throughthe combustion chamber E , i n t o which f u e l i s i n j e c t e d through f e e d l i n e F and,62
  • 71. f i n a l l y , a f t e r expanding, passes through t h e high-pressure t u r b i n e K and low- p r e s s u r e t u r b i n e H. Then t h e high-temperature gas e x i t s through t h e exhaust nozzle, which surrounds t h e o u t e r r i n g nozzle with a cold c u r r e n t of a i r . Figure 47. Simplified Schematic Diagram o f t h e Operation of a Two-Circuit J e t Engine. The a i r which has been speeded up through t h e fan of a turbofan engine i s exhausted with a slower speed than i n t h e normal t u r b o j e t engine o r t h e normal t w o - c i r c u i t engine. The slower t h e speed o f t h e flow behind t h e engine, t h e lower t h e energy l o s s e s w i l l be and t h e g r e a t e r t h e engines e f f i c i e n c y . From j e t - e n g i n e theory we know t h a t t h e o v e r a l l e f f i c i e n c y ( o v e r a l l Q­ f a c t o r ) f o r t h e power system of any a i r c r a f t i s determined as t h e product of the two b a s i c f i g u r e s : t h a t of t h e i n t e r n a l ( e f f e c t i v e ) and exhaust ( f l i g h t ) factors. The e f f e c t i v e Q-factor i n c r e a s e s with an i n c r e a s e i n t h e a i r p r e s s u r e i n~ the engine and with an i n c r e a s e i n t h e gas temperature. This leads t o a s u b s t a n t i a l decrease i n t h e s p e c i f i c f u e l consumption. Because only p a r t of the a i r passes through t h e t u r b i n e i n a two-system turbo­ j e t engine, the t u r b i n e blades may be s h o r t e r than i n a t u r b o j e t engine with t h e same o v e r a l l f u e l consumption. F o r i d e n t i c a l b l a d e s a f e t y f a c t o r s , t h i s i n /69 t u r n permits a 100 - 150° temperature i n c r e a s e i n t h e g a s i n f r o n t of t h e t u r b i n e , which gives a decided advantage over t h e t u r b o j e t engine i n terms of f u e l economy. This i s one of t h e reasons t h a t t h e t w o - c i r c u i t and turbofan engines have lower s p e c i f i c f u e l consumptions. For p r o p u l s i v e f l i g h t e f f i c i e n c y , from t h e theory of j e t engines we a r e familiar with t h e following formula: 2 ?f=- w fv where W i s t h e speed of t h e j e t s t r e a m ; and V i s t h e f l i g h t speed. 63
  • 72. When t h e d i f f e r e n c e between t h e speed of t h e j e t s t r e a m and t h e f l i g h tspeed i s decreased, i . e . , when t h e r e i s l e s s of an unused p o r t i o n of t h ek i n e t i c energy, t h e p r o p u l s i v e e f f i c i e n c y i n c r e a s e s and reaches i t s maximumv a l u e (11 - 1) a t a f l i g h t speed equal t o t h e speed o f t h e exhaust j e t s t r e a m . f -When t h i s i s t r u e , t h e unused p o r t i o n of t h e k i n e t i c energy i s zero. A c l e a rexample i s t h e turboprop engine, i n which t h e speed a t which t h e a i r i s t h r u s tback by t h e b l a d e i s c l o s e t o t h e f l i g h t speed. However, i n turboprop a i r ­c r a f t t h e f l i g h t e f f i c i e n c y drops as t h e f l i g h t speed i n c r e a s e s due t o a dropi n t h e blade e f f i c i e n c y , and reaches low values a t high s u b s o n i c speeds. In t w o - c i r c u i t and turbofan engines, t h e r e i s an i n c r e a s e i n t h e a r e a o fhigh e f f i c i e n c y , which t h e turboprop engine has a t low f l i g h t speeds, up t ohigh subsonic speeds a t which t h e f l i g h t e f f i c i e n c y i s s t i l l t o o low. To achieve t h i s , i n t w o - c i r c u i t and turbofan engines t h e r e i s a secondc i r c u i t from which g r e a t masses of a i r flow a t speeds c l o s e t o t h e f l i g h tspeed, which a i d s i n achieving a high f l i g h t e f f i c i e n c y as w e l l as a lows p e c i f i c f u e l consumption. The s p e c i f i c f u e l consumption f o r a t w o - c i r c u i t j e tengine and a t u r b o f a n engine i s 0.52 = 0.65 kG fuel/kG t h r u s t - hr for H = 0and V = 0 and 0.75 - 0.85 kG fuel/kG t h r u s t - h r f o r H = 10-11 km a t V = 750 ­880 km/hr. I n designing t w o - c i r c u i t engines, t h e s e l e c t i o n of t h e two c h i e f v a r i a b l e si s v i t a l : t h e forward o r r e a r p o s i t i o n i n g of t h e f a n and t h e r a t i o o f t h e massflow of cold a i r p a s s i n g through c i r c u i t C t o t h e mass flow of h o t a i r passingthrough c i r c u i t D, t h e s o - c a l l e d t w o - c i r c u i t l e v e l m = G C/G D’ whose v a l u e maybe from 0.23 t o 3.5. The t w o - c i r c u i t l e v e l i s a v i t a l engine parameter and determines i t se f f i c i e n c y , weight and t h r u s t c h a r a c t e r i s t i c s . The g r e a t e r t h e l e v e l m , t h e ­ / 70lower the s p e c i f i c f u e l consumption; however, t h i s e n t a i l s an i n c r e a s e i n t h eengine dimensions and weight. A t p r e s e n t the optimum degree i s m = 0.6 - 0.7f o r c i v i l i a n a i r c r a f t a t a f l i g h t Mach number of 0 . 8 - 0 . 9 . F i r s t - g e n e r a t i o n (Boeing-707-420, and Douglas DC-8) and second-generation(Vickers VC-10 and o t h e r s ) t r a n s p o r t a i r c r a f t a r e equipped with t h e RollsRoyce Conway t w o - c i r c u i t engine i n which m = 0.7 - 0.8. The engine t h r u s tf o r t h e Conway-509 i s 10,200 kG, while t h e s p e c i f i c f u e l consumption a t topconditions i s 0.725 kG/kG - hr. Even g r e a t e r economy may be obtained through mixing flows o f highp r e s s u r e ( a f t e r t h e t u r b i n e ) and low p r e s s u r e ( a f t e r t h e f a n ) ( i n t h e JT8Dengine) o r a f t e r t h e f i r s t compressor s t a g e ( t h e Spey engine) i n t h e exhaustnozzle. When t h i s i s done, a r e l a t i v e l y low speed of flow i s achieved andt h e r e i s a correspondingly high e f f i c i e n c y . The combination of high thermo­dynamic and t h r u s t e f f y c i e n c i e s has a l s o made it p o s s i b l e t o c r e a t e engineswith low s p e c i f i c f u e l consumptions. As an example, Table 7 p r e s e n t s somed a t a on t h e JT8D and Spey engines.64
  • 73. TABLE 7 - Flight conditions -_ 1 Engine type 1 Thrust kG Specific I o ? Y kGj&e%r ­ I 1 c n L ffm. v*km/hr Takeoff I JT8D flspeyf I I 6350 5150 0,585 0,611 I_ X 1 0 0 Maxi" (climbin?) I JTSD "Speyfl I I % 7iI I I 0 Cruising I l ~ ~ 1 ~ ~ 2140 1680 y l I l 0,838 0.77 1 7500 7600 I 730 870 T r . Note: Commas i n d i c a t e decimal p o i n t s There are t h r e e JT8D engines on t h e Boeing-727 and two on t h e DC-9, andt h e r e a r e two Spey engines on t h e Bak-1-11-200 and t h r e e on t h e Trident a i r ­c r a f t . S o v i e t t w o - c i r c u i t engines were f i r s t i n s t a l l e d on t h e Tu-124. Replacing normal t u r b o j e t engines with t w o - c i r c u i t engines o f f e r s ani n c r e a s e i n payload and a decrease i n t h e s p e c i f i c f u e l consumption and t h enoise level. As has already been s t a t e d , t u r b o f a n engines have t h e fans placed e i t h e rforward or behind. When t h e f a n i s placed behind, as w a s done by GeneralE l e c t r i c (Figure 46d), t h e design o f t h e forward p a r t of the engine d i f f e r si n no way from a normal t u r b o j e t engine: t h e compressor, t h e combustionchamber and t h e g a s t u r b i n e a r e i d e n t i c a l . However, with t u r b o f a n engines,a f t e r t h e gases have passed through t h e main t u r b i n e they run i n t o one more,t h e s o - c a l l e d fan t u r b i n e , which i s mechanically t i e d i n t o t h e main t u r b i n e . ­ /71The b l a d e t i p s i n t h e f a n t u r b i n e f u n c t i o n as they would i n a normal f a n and,i n t h e annular gap between t h e n o z z l e and t h e a d d i t i o n a l t u r b i n e , they t h r u s tback a s t r o n g flow of a i r running p a r a l l e l t o t h e b a s i c g a s j e t . The American Convair 990A has f o u r CJ-805-23B turbofan engines ( b u i l t byGeneral E l e c t r i c ) with t h e r e a r f a n , each g e n e r a t i n g a t h r u s t of 7,300 kG.The same engines a r e used on t h e French Caravelle-XA i n replacement f o r t h eo b s o l e t e Avon t u r b o j e t engines. The P r a t t and Whitney JT3D engine, with m = 1.5, has t h e f a n p o s i t i o n e dforward. This t y p e of engine i s used on t h e Boeing-720B and DC-8. Table 8o f f e r s some d a t a on t h e JT3D engine. Thus, u s e of t w o - c i r c u i t and f a n engines makes i t p o s s i b l e t o c r e a t ea i r c r a f t with optimal f l i g h t c h a r a c t e r i s t i c s f o r various purposes. Thei n c r e a s e d t h r u s t makes i t p o s s i b l e t o decrease t h e t a k e o f f d i s t a n c e f o r anys p e c i f i c a i r c r a f t weight o r , i n maintaining t h e t a k e o f f d i s t a n c e , i t becomesp o s s i b l e t o i n c r e a s e t h e payload o r t h e f u e l r e s e r v e . 65
  • 74. TABLE 8 Takeoff . . . . .. 8160 0,538 0 0 Aaximum (climbing). Cruising * -- . - 1 7400 1700 0,515 0,79 0 9100 0 865 1 Tr. Note: Commas i n d i c a t e decimal p o i n t s .9 2. Basic C h a r a c t e r i s t i c s o f Turbojet E n g i n e s In examining t h e f l i g h t conditions f o r t u r b o j e t passenger a i r c r a f t wemust know t h e following b a s i c engine c h a r a c t e r i s t i c s : t h r u s t , s p e c i f i c t h r u s t ,s p e c i f i c f u e l consumption, s p e c i f i c weight and maximum-power a l t i t u d e . Thrust i n t u r b o j e t engines is determined i n accordance with t h e followingformula : p = - G s e c (W - V) kG, gwhere i s t h e per-second r a t e of a i r f l o w through t h e engine, Gsec (kG/sec) ; g = 9.81 m/sec2 is t h e a c c e l e r a t i o n ; W i s the speed of t h e r a t e of gas flow from t h e exhaust nozzle (m/sec) ; V i s t h e a i r c r a f t f l i g h t speed (m/sec) . Turbojet engines designed i n the last two decades have Gsec = 18 - 260 ­ /72kG/sec, which corresponds t o a t h r u s t of from 800 - 900 t o 10,000 - 13,000 kG,W = 550 - 600 m/sec ( s t a n d - s t i l l o p e r a t i o n ) , while i n f l i g h t i t reaches highvalues. Two-circuit engines have a discharge v e l o c i t y of 520 - 550 m/sec,whereas t u r b o f a n engines have only 350 - 370 m/sec. S p e c i f i c t h r u s t -- t h i s is t h e t h r u s t obtained from 1 kG of a i r passingthrough t h e engine per-second: - W - V --- kG s pe f g kG/sec * S p e c i f i c t h r u s t c h a r a c t e r i z e s t h e economy of an engine. I n modern turbo­j e t engines , = 40 - 70 kG/kG/sec. S p e c i f i c t h r u s t depends s t r o n g l y on speft h e compressor k f f i c i e n c y and t u r b i n e e f f i c i e n c y , as w e l l as t h e degree t o66
  • 75. which t h e air has been pre-heated. I t determines t h e r e l a t i v e dimensions andweight of t h e engine: t h e g r e a t e r t h e s p e c i f i c t h r u s t , t h e lower t h e enginedimensions and weight f o r a given t h r u s t . S p e c i f i c f u e l consumption -- t h i s i s t h e r e l a t i v e hourly f u e l consumed i ngenerating engine t h r u s t : c = -GG * P P k t fuel/kG - thrust - hr,where G t i s t h e hourly f u e l consumption (kG f u e l / h r ) . The s p e c i f i c consumption i n d i c a t e how many k of f u e l have been expended Gi n c r e a t i n g 1 kG of t h r u s t i n an hour, and a l s o , c h a r a c t e r i z e s t h e enginee f f i c i e n c y . The lower t h e c t h e more e f f i c i e n t t h e engine and t h e g r e a t e r Pt h e a i r c r a f t f l i g h t range and duration. S p e c i f i c weight of the engine i s t h e r a t i o of the dry weight of t h e enginet o its thrust: In modern t u r b o j e t engines, = 0.19 - 0.35 kG/kG t h r u s t . For example, gtjf o r the 5-58 engine, t h e v a l u e of t h e s p e c i f i c weight i s g = 0.25 kG/kG tjt h r u s t . This means t h a t f o r a t h r u s t o f 13,600 kG, the engine weight i sG = 3,400 kG. A s can b e seen from t h e s e f i g u r e s , t u r b o j e t engines do n o t tjoverload t h e a i r c r a f t by v i r t u e of t h e i r weight. Whereas t h e weight of t h epower system f o r a piston-engine a i r c r a f t may sometimes amount t o 2 2 - 25% oft h e takeoff weight, f o r t u r b o j e t a i r c r a f t t h i s value equals only 10 - 1 2 % .§ 3. Throttle Characteristics Depending on how i t i s used and on i t s r a t e d s e r v i c e l i f e , each enginehas s e v e r a l b a s i c modes of o p e r a t i o n which d i f f e r by t h e number of rpms, t h e /73 ­temperature regimes, e t c . Usually t h e following o p e r a t i o n conditions a r ed i s t i n g u i s h e d : t a k e o f f , nominal, c r u i s i n g , and i d l i n g . P r a c t i c e i n a i r c r a f t and engine u s e has r e s u l t e d i n t h e need f o r ana d d i t i o n a l condition which, f o r t h e Tu-104 f o r example,has come t o be c a l l e dt h e "extreme" condition. As can be seen from t h e very name i t s e l f , t h i s i sused i n only c e r t a i n c a s e s , s p e c i f i c a l l y i n t h e event of f a i l u r e of one ofthe engines. In t h i s event, because of t h e engine f o r c i n g with r e s p e c t t ot h e temperature of t h e supply of a d d i t i o n a l f u e l and t h e i n c r e a s e d r e v o l u t i o n s ,t h e t h r u s t i n c r e a s e s by 8 t o 10%by comparison t o t a k e o f f . However, t h i semergency condition p u t s an overload on t h e engine which i n t u r n means t h a tt h e engine must be overhauled f a s t e r than normally. 67
  • 76. The t a k e o f f c o n d i t i o n corresponds t o t h e maximum p e r m i s s i b l e number ofrpms and t h e m a x i m u m t h r u s t . Under t h i s c o n d i t i o n , t h e engine components ares u b j e c t e d t o t h e g r e a t e s t mechanical and thermal s t r e s s e s , as a r e s u l t o f whicht h e i r p e r i o d of continuous u s e i s l i m i t e d and normally does n o t exceed 5 - 10minutes. Takeoff c o n d i t i o n s are a p p l i e d t o decrease t h e t a k e o f f run throughi n c r e a s i n g t h e h o r i z o n t a l f l i g h t speed, decreasing t h e a i r c r a f t a c c e l e r a t i o nt i m e and a c c e l e r a t i n g t h e breaking clouds i n g a i n i n g a l t i t u d e . The normal r a t i n g corresponds t o somewhat decreased (by 3-8%) r o t a t i o nwith r e s p e c t t o t h e takeoff r a t i n g . The t h r u s t i s approximately 90% of t h et a k e o f f t h r u s t . The o p e r a t i o n time a t a normal r a t i n g i s s u b s t a n t i a l l y longer:i t i s used i n gaining a l t i t u d e and f o r n e a r - c e i l i n g f l i g h t . During sucho p e r a t i o n t h e engine components are s u b j e c t e d t o s u b s t a n t i a l l y l i g h t e r loads. Cruising performance d i f f e r s from t h e two preceding conditions throughdecreased rpms (by 10-15%) and t h r u s t (by 25-50%) as opposed t o maximum. The i d l i n g p e r i o d corresponds t o t h e lowest number o f rpms a t which t h eengine can o p e r a t e s t a b l y . Under t h e s e c o n d i t i o n s , t h e r e i s l i t t l e t h r u s tand t h e r e f o r e i t i s used i n landing runs, dropping from high a l t i t u d e s , e t c .The amount o f t h r u s t i s 300-600 kG a t low f l i g h t a l t i t u d e s and 150-300 kG a ta l t i t u d e s of 8,000 - 10,000 m. The c h a r a c t e r of t h e change i n engine t h r u s t with r e s p e c t t o rpms i sshown i n Figure 48, from which we can s e e t h a t an i n c r e a s e i n t h e number of rpms causes an i n c r e a s e i n t h r u s t . A t low rpms, t h e amount o f a i r p a s s i n g through t h e engine i s a l s o low and as a consequence, t h e f u e l consumption, too, i s low. The amount o f gases formed i s small and develop a n e g l i g i b l e exhaust v e l o c i t y , so t h a t t h e t h r u s t g e n e r a t e d by t h e engines with t h i s v a l u e o f rpms i s low, u s u a l l y 300 - 600 kG. A i n c r e a s e i n t h e n 1 - -- - - -- - - Pt-0 r p m s leads t o a s h a r p i n c r e a s e f&q i n t h e a i r exhaust, t h e f u e l d e l i v e r y i n c r e a s e s , t h e temperature o f gases i n f r o n t of t h e t u r b i n e i n c r e a s e s and, as a r e s u l t -- t h r u s t i n c r e a s e s . The h i g h e s t t h r u s t may be obtained a t t h e maximum p e r m i s s i b l e rpms , i . e . , during t a k e o f f o r emergency con­ ditions. n , rpm(%) Figure 48. Engine T h r u s t , S p e c i f i c Thrust Figure 48 a l s o shows t h e /74 and S p e c i f i c Fuel Consumption a s Functions of t h e s p e c i f i c f u e l of t h e rpms. n = n consumption on t h e number of rpms. t-o take o f f The change i n cp i s a f u n c t i o n o f 68
  • 77. I t h e degree of compression o f t h e air i n t h e combusion chamber. The more h i g h l y compressed the a i r i s , t h e more f u l l y t h e h e a t is used during t h e process of f u e l consumption and t h e lower t h e s p e c i f i c f u e l consumption w i l l be. P r e ­ compression of t h e air depends b a s i c a l l y on t h e compressor (engine rpms) and on t h e f l i g h t speed. Therefore, when t h e rpms a r e i n c r e a s e d , t h e s p e c i f i c f u e l consumption decreases. During normal and t a k e o f f c o n d i t i o n s , t h e s p e c i f i c consumption i s c l o s e t o minimum. Engine u s e during c r u i s i n g rpm conditions y i e l d optimum economy. 5 4. High-speed Characteristics The high-speed c h a r a c t e r i st i c s of t u r b o j e t engines a r e t h e dependence of t h e engine t h r u s t , s p e c i f i c t h r u s t and s p e c i f i c f u e l consumption on f l i g h t speed a t a given a l t i t u d e f o r a s e l e c t e d r u l e of c o n t r o l . Let us examine t h e high-speed c h a r a c t e r i s t i c s f o r c o n s t a n t rpm, gas temperature i n f r o n t of t h e t u r b i n e and f l i g h t a l t i t u d e (Figures 49 and 50). Normally t h e c h a r a c t e r i s t i c s are examined f o r a nominal number o f rpms. bs e c From t h e formula P = - (W - V) we can s e e t h a t t h e exhaust t h r u s t w i l l /75 g be g r e a t e r , t h e g r e a t e r t h e amount of a i r which passes through t h e engine p e r second and t h e g r e a t e r t h e d i f f e r e n c e between t h e g a s exhaust speed and t h e f l i g h t speed. I n i n c r e a s i n g t h e f l i g h t speed from 0 t o 700 - 800 W h r , t h r u s t de creas e s somewhat , becaus e i n c r e a s e s more s lowly Gsec than t h e d i f f e r e n c e W -V drops. With an a d d i t i o n a l i n c r e a s e i n speed, on t h e o t h e r hand, t h e i n c r e a s e i n a i r exhaust begins t o surpass t h e decrease i n t h e d i f f e r e n c e s between t h e speeds W and V. This is explained by t h e c h a r a c t e r of t h e change i n t h r u s t with r e s p e c t t o speed. When t h e f l i g h t speed i s i n c r e a s e d from 0 t o 700 - 800 km/hr, t h r u s t decreases by no 0,Z 0.3 04 . 0,5 OP Q7 0,8 0.0 fl more than 10-15%. This per­ m i t s us t o consider t h e avai l a b l e t h r u s t generated by Figure 49. E n g i n e Thrust as a Function of a subsonic t u r b o j e t engine t o Mach Number ( f l i g h t speed) f o r Various b e p r a c t i c a l l y independent of A1 t i t u d e s (standard c o n d i t i o n s , t h e broken f l i g h t speed. 1 i n e representing a temperature 10" above standard) . T-0 = Take-off.
  • 78. W - The s p e c i f i c t h r u s t (Pspef - - ) drops as t h e speed i n c r e a s e s , because g t h e d i f f e r e n c e between speeds (W -V) decreases (Figure 50a). The s p e c i f i c f u e l consumption i n c r e a s e s with h i n c r e a s e i n f l i g h t speed (Figure 50b). When t h e r e i s a change i n t h e f l i g h t speed from zero t o 750 ­ 850 km/hr, t h e s p e c i f i c f u e l consumption i n c r e a s e s by 15-30%. Thus, i f f o r V = 0 t h e consumption i s cp = 0.89 kG/kG -h r , then a t a speed of 850 km/hr i t w i l l i n c r e a s e t o 1.15 ( f o r t h e RD-3M engine). For t h e JTSD turbofan engine, f o r V = 0 , t h e consumption i s c = 0.61, whereas f o r a speed o f 880 km/hr i t /76 - i s 0.781 kG/kG - h r (at ~ F I a l t i f u d e of 11 km). 1st , Figure 5 0 . Change i n S p e c i f i c Fuel Consumption ( b ) and S p e c i f i c Thrust ( a ) w i t h Respect t o F1 i g h t Speed. P,kG" kG on the ground, which i s increased t o 7,200 kG through t h r u s t augmentation by afterburning. I n f l i g h t 5000 a t a l t i t u d e , t h e drop i n0 0 7 I t h r u s t i s compensated by I I 3000 ~. v e l o c i t y head. During 70
  • 79. § 5. High-Altitude Characteristics The dependence of t h r u s t , s p e c i f i c t h r u s t and s p e c i f i c f u e l consumptionon f l i g h t a l t i t u d e f o r a c o n s t a n t number of engine rpms and c o n s t a n t f l i g h t ­ / 77speed i s c a l l e d t h e h i g h - a l t i t u d e c h a r a c t e r i s t i c s . The t h r u s t o f a t u r b o j e t engine decreases s h a r p l y with an i n c r e a s e i nf l i g h t a l t i t u d e because t h r u s t i s d i r e c t l y p r o p o r t i o n a l t o t h e weight r a t e ofa i r f l o w , while t h e r a t e decreases with a l t i t u d e due t o a drop i n a i r d e n s i t y .The decrease i n t h r u s t with a l t i t u d e occurs i n s p i t e of t h e f a c t t h a t t h es p e c i f i c t h r u s t , i . e . , t h e t h r u s t c r e a t e d by each kilogram of a i r passingthrough t h e engine, i n c r e a s e s by approximately h a l f again as much as comparedt o t h e ground l e v e l . U t o an a l t i t u d e of 11,000 meters, because of precompression i n t h e pcompressor, t h e weight r a t e of a i r f l o w decreases more slowly than t h e aird e n s i t y , whereas above 11,000 meters, where t h e temperature remains c o n s t a n t ,i t drops more r a p i d l y . The change i n engine t h r u s t with a l t i t u d e may b ec a l c u l a t e d with r e s e c t t o the following formula: f o r a l t i t u d e s up t o 11,000meters: P = P * f o r a l t i t u d e s g r e a t e r than 11,000 meters: PH = 1.44 A g a 7 ; H OA * Po (here PH i s t h e t h r u s t a t a l t i t u d e ; P is t h e ground engine t h r u s t ) ; 0 PHA = -is t h e r a t i o of d e n s i t i e s ( A < 1 ) . If we t a k e P 0 as loo%, then a t an a l t i t u d e of 10,000 meters the t h r u s ti s approximately 45-50% of t h e ground t h r u s t , while a t an a l t i t u d e of 20,000meters i t i s only 10%. This comments on t h e lack of maximum-power a l t i t u d ei n t u r b o j e t engines. However, modified t u r b o j e t engines developing a groundt h r u s t of 10,000 - 13,000 kG have high f l i g h t speeds a t a l t i t u d e s of 10,000 ­12,000 meters. Figure 52 shows t h e v a r i a t i o n i n engine t h r u s t i n terms o f a l t i t u d e f o rvarious rpms. I t should b e noted t h a t above t h e maximum-power a l t i t u d eboundary t h e power of p i s t o n engines drops more r a p i d l y than does t h e t h r u s tof j e t engines. Up t o an a l t i t u d e of 11,000 meters t h e s p e c i f i c f u e l consumption c Pdecreases, a f t e r which i t holds c o n s t a n t (Figure 53). The b a s i c p r i n c i p l e i n ­ /78t h e drop i n c (and t h e i n c r e a s e i n s p e c i f i c t h r u s t ) l i e s i n t h e f a c t t h a t Pwith a drop i n t h e temperature of t h e surrounding a i r t h e degree of com­p r e s s i o n i n the compressor and t h e degree of precompression a r e i n c r e a s e d . The hourly f u e l consumption, which i s equal t o t h e product o f c P , Pdecreases with an i n c r e a s e i n f l i g h t a l t i t u d e by approximately t h e samei n t e n s i t y as does t h e a i r consumption and t h r u s t . The hourly f u e l consumption a t an a l t i t u d e of 11,000 meters i s l e s s t h a none h a l f t h e ground consumption f o r t h e same engine rpm conditions. 71
  • 80. I I I 5 io H,iKmFigure 52. Variation i n E n g i n e Figure 53. Dependence o f S p e c i f i cThrust i n Terms o f F l i g h t A l t i t u d e Fuel Consumption on F l i g h t A l t i t u d e .(Mach = 0 . 7 5 ) . Thus, t h e s e engines a r e more e f f e c t i v e i n operation a t high a l t i t u d e s .5 6. The Effect o f Air Temperature on Turbojet Engine Thrust Air temperature, l i k e a l t i t u d e ( p r e s s u r e ) , has a s i g n i f i c a n t e f f e c t ont h r u s t and s p e c i f i c f u e l consumption. During t e s t - s t a n d t r i a l runs of the engine t h e measured t h r u s t i sreduced t o standard conditions, i . e . , t h e s o - c a l l e d reduced t h r u s t i s d e t e r ­mined f o r p = 760 mm H and t = 15°C. Depending on t h e c o n t r o l system, the ge f f e c t of temperature changes on t h r u s t i s manifested i n d i f f e r e n t ways. Thus,f o r example, f o r t u r b o j e t engine with o p e r a t i o n a l rpms of 4,000 - 5,000, aone-percent temperature i n c r e a s e decreases t h r u s t by approximately 2%. Fortwo-circuit and turbofan engines with 6,700 - 11,000 rpm, a one-percenttemperature change v a r i e s t h e t h r u s t by 1 - 1.5%. For example, t h e t h r u s ti n a t u r b o j e t engine equals 7,000 kG f o r t = 15OC and p = 760 mm Hg. Atemperature i n c r e a s e of up t o t = 25°C has occurred. Let us determine t h ev a r i a t i o n i n engine t h r u s t . To do s o , l e t us express t h e temperature changei n a percentage r a t i o : T = t " C + 273" = 15" + 273" = 288O; T = 25" + 273" = 1 2= 298"; 298 : 288 = 1.03, i . e . , the temperature increased by 3 % . Consequently,t h r u s t decreased by 6 % , amounting t o 420 kG. Thus, f o r t = 25"C, the engine w i l l generate around 6,600 kG of t h r u s t .If the temperature i n c r e a s e s t o 35"C, the t h r u s t decreases by 13.6%, i . e . ,the engine w i l l generate only about 6,000 kG of t h r u s t . When the a i r temperature i n c r e a s e s , t h r u s t i n c r e a s e s , This comes aboutbecause of t h e c o n t r o l system on the fuel-supply arrangement i n t u r b o j e tengines, which i n c r e a s e s the f u e l supply when temperature drops. An i n c r e a s ei n t h r u s t u s u a l l y occurs when t h e temperature decreases t o + 3 - -15"C,72
  • 81. IIdepending on t h e engine c o n d i t i o n s and t h e c o n t r o l o f t h e f u e l pump andregul a t or. L e t us determine t h e i n c r e a s e i n t h r u s t f o r a temperature of -15OC i ff o r t = 15OC t h r u s t P = 7,000 kG: T 1 - 288OC, T2 = 258°C and 288 : 258 = 1.115, -i . e . , t h e temperature i n c r e a s e s by 11.5%, consequently, t h e t h r u s t i n c r e a s e s ­ / 79 1by 2 3 % , amounting t o 1,600 kG (Figure 54). To maintain t h e s e engineP,M- 8600 kG t h r u s t v a l u e s a t high a l t i t u d e s , water i n j e c t i o n i n t o t h e compressor 8000 t rbojet i s used. Figure 55 shows t h e change i n 7000 t h r u s t i n a JT3D turbofan engine with and without water i n j e c t i o n . A s can b e seen from t h e figure, 6000 --- "ZEYL -- --- - water i n j e c t i o n a i d s i n maintaining t h e c a l c u l a t e d takeoff t h r u s t up I I t o and i n t a k e temperature of +3SoC. While t h i s h o l d s , t h e high-tempera­ ture flight characteristics for t h e a i r c r a f t change n e g l i g i b l y . I nFigure 54. E f f e c t o f External Air t h e case of t h e "Spey" engine, waterTemperature on Thrust of Turbojet injection aids i n f o r e s t a l l i n g aEngines . drop i n i t s t h r u s t a t temperatures g r e a t e r than 2OoC. 5 7. Thrust Horsepower / 80 - Thrust horsepower i s t h e a v a i l a b l e engine power: where V i s t h e f l i g h t speed i n m/sec.Figure 5 5 . Test-Stand Thrust i n t h e JT3DTurbofan E n g i n e and t h e ISpey - type Two- Let us determine t h e t h r u s tC i r c u i t Turbojet E n g i n e as a Function o f horsepower f o r t h e engines ofthe A m b i e n t A i r Temperature. an a i r c r a f t f l y i n g a t an a l t i ­ tude o f 10,000 meters and aspeed of 900 km/hr, if t h e a v a i l a b l e engine t h r u s t is 6,000 kG: However, a t f l i g h t w i t h t h e maximum speed o f 1,000 km/hr a t an a l t i t u d eof 6,000 m and with an a v a i l a b l e t h r u s t o f 9,000 kG, t h e t h r u s t horsepower i s 73
  • 82. The t h r u s t horsepower i n c r e a s e s d i r e c t l y p r o p o r t i o n a t e l y t o t h e speed.When r a c i n g t h e engines on t h e ground without t h e a i r c r a f t s moving, N = 0,because t h e r e i s no work being done, i . e . , PV = 0. A change i n t h e a v a i l a b l ehorsepower with r e s p e c t t o a l t i t u d e (rpms being constant) i s shown i n Figure56. In contrast t o piston aircraft, i n which t h e a v a i l a b l e horsepower decreases with an i n c r e a s e i n speed above maximum32000 - due t o a drop i n t h e p r o p e l l e r e f f i c i e n c y , i n j e t a i r c r a f t i t i n c r e a s e s with an i n c r e a s e i n f l i g h t speed. Therefore, r a p i d f l i g h t speeds may b e obtained only i n a i r c r a f t with t u r b o j e t engines o r o t h e r types of j e t engines. Like t h r u s t , t h e a v a i l a b l e horse­ power is a f u n c t i o n of t h e engine rpms: - . t h e g r e a t e r t h e number of engine rpms ( f o r a s p e c i f i c a l t i t u d e and f l i g h t speed), t h e higher the available horse-Figure 5 6 . Thrust Horsepower as power.a Function o f Mach Number f o rVarious F l i g h t A l t i t u d e s ( c o n s t a n trpms). § 8. P o s i t i o n i n g the Engines on t h e A i rcraft ­ / 81 The absence of p r o p e l l e r s , t h e r e l a t i v e l y low weight f o r high s t r e s s , andt h e i r s i m p l i c i t y with r e s p e c t t o design and s e r v i c i n g make i t p o s s i b l e t oi n s t a l l t u r b o j e t and turbofan engines i n such a way t h a t t h e i r optimal opera­t i o n a l conditions and those of t h e a i r c r a f t a r e achieved. A t p r e s e n t , f i r s t - and second-generation t u r b o j e t passenger a i r c r a f t havet h e i r engines mounted on t h e wing, on pylons below t h e wing, o r i n t h e t a i ls e c t i o n of the f u s e l a g e . Engine I n s t a l l a t i o n i n wings. When t h e engines are i n s t a l l e d i n t h e wing (between t h e upper and lower p l a n k i n g s ) , t h e t o t a l drag i s reduced. I np r a c t i c e , however, the engine i s f a s t e n e d t o t h e f u s e l a g e ( i n double-enginea i r c r a f t ) , while t h e a i r duct extends along t h e chord i n t h e wing. This leadst o a decrease i n t h r u s t as a r e s u l t of a p r e s s u r e l o s s i n t h e d u c t , b u t i nc o n t r a s t an advantage i s t h e almost " c l e a r " wing (without secondary s t r u c t u r e s )which r e s u l t s . Engines arranged i n t h i s manner ( c l o s e t o t h e a i r c r a f t a x i s ) ,if one of them f a i l s t h i s c r e a t e s only a s l i g h t t u r n i n g moment. Of t h e disadvantages which r e s u l t from t h i s arrangement, l e t us p o i n to u t t h e f a c t t h a t i t becomes impossible t o make u s e o f t h e t h r u s t r e v e r s a l74
  • 83. due t o t h e h e a t e f f e c t s of t h e gas j e t on t h e f u s e l a g e ( f o r a double-enginea i r c r a f t ) and t h e p a r t i a l use of t h r u s t r e v e r s a l ( f o r a four-engine arrangement)(see Chapter I X ) . The stream of exhaust gases c r e a t e s s u b s t a n t i a l n o i s e i n t h et a i l s e c t i o n of t h e f u s e l a g e and causes discomfort t o t h e passengers s e a t e d i nt h e r e a r . On t h e Tu-104 and t h e Tu-124 (Figure 57) , t h e engines a r e l o c a t e di n t h e base of t h e wing, so t h a t t h e g r e a t e r p a r t o f the engine pod is hiddenbehind t h e wing. In t h e De Havilland Comet, however, t h e engines a r e f u l l yhidden i n the wing (Figure 58). The e n g i n e s small s i z e makes it p o s s i b l e t odesign i t s pods with q u i t e small maximum c r o s s - s e c t i o n s . Figure 57. The Tu-124. Figure 58. T h e Comet Engines l o c a t e d a t the base of t h e wing c r e a t e p o s i t i v e i n t e r f e r e n c e a tt h e most complex aerodynamic p o i n t - - t h e j o i n t between t h e low-hung wing andt h e f u s e l a g e . The e f f e c t of t h e j e t s t r e a m causes the formation of an " a c t i v e ­ / 82f a i r i n g " h e r e , i . e . , an i n c r e a s e i n t h e "regeneration" o f t h e surrounding flow.This leads t o a decrease i n drag f o r t h e a i r c r a f t as a whole*. However, t h i s engine arrangement r e q u i r e s an i n c r e a s e i n t h e r e l a t i v ethickness of the a i r f o i l p r o f i l e , which causes a decrease i n t h e a i r c r a f t s __ __ . --- - . . ­* Yeger, S .M. Design of Passenger J e t A i r c r a f t (Proyektirovaniye p a s s a c h i r ­ s k i k h reaktivnykh samelotov) . Mashinostroyeniye. 1964. 75
  • 84. high-speed c h a r a c t e r i s t i c s . The angle a t which t h e engines a r e i n s t a l l e dr e l a t i v e t o t h e l o n g i t u d i n a l axis i s 3-So i n t h i s arrangement. This i n c l i n a ­t i o n i s necessary t o guarantee t h a t t h e engine exhaust flow does not h i t t h eelevator unit. In planform, t h e engines are turned outward by an angle of2-4, i n o r d e r t h a t t h e exhaust gas j e t have less of an e f f e c t on t h e f u s e l a g e . P o s i t i o n i n g t h e engines on pylons beneath t h e wings. This is done on t h eAmerican J e t s t h e Boeing-707 and 720, t h e Douglas DC-8 (Figure 5 9 ) , and t h eConvair 880 and 990. Even t h e newly c r e a t e d Boeing-737 shows a r e t u r n t o t h epylon arrangement. In t h i s s e t u p , t h e p o s i t i o n i n g of t h e engines i n c r e a s e s a i r c r a f t drag s l i g h t l y , p a r t i c u l a r l y due t o negative i n t e r f e r e n c e from t h e wing and pylons. However, t h e s h o r t length of t h e e n g i n e s i n t a k e duct when t h e a i r admission i s we1 1 designed minimi zes t h r u s t l o s s e s and thereby improve t h e a i r c r a f t s t a k e o f f performance. Suspending t h e engine from a t h i n swept wing Figure 59. A i r c r a f t w i t h Pylon Suspension substantially lightens theof E n g i n e s . wing and decreases i t s s t r u c t u r a l weight. How­ever, such a suspension r e q u i r e s i n c r e a s e d reinforcement of t h e engine andi t s pylon (due t o g r e a t e r i n e r t i a l loads during a i r c r a f t maneuvering) and asa r e s u l t t h e wing weight i s n e g l i g i b l y decreased. A i r c r a f t with pylon s u s ­pension of engines should be used only on concrete runways which haves u b s t a n t i a l l y c l e a n e r s u r f a c e s , because t h e engines a r e only 40-70 c above m / 83 -t h e ground. If f o r e i g n m a t t e r i s drawn i n t o t h e i n t a k e d u c t , t h e enginecompressor may f a i l . Although p o s i t i o n i n g t h e engines t o t h e s i d e of t h ef u s e l a g e makes i t p o s s i b l e t o e f f e c t i v e l y u s e t h r u s t r e v e r s a l from a l l f o u rengines, the f a i l u r e of t h e o u t s i d e engine c r e a t e s a s u b s t a n t i a l t u r n i n gmoment, which g r e a t l y impedes handling t h e a i r c r a f t . This moment, a c t i n g i nt h e h o r i z o n t a l p l a n e , causes an i n t e n s e r o l l i n g motion around t h e l o n g i t u d i n a la x i s , which (with allowance made f o r t h e a i r c r a f t s s u b s t a n t i a l moment o fi n e r t i a r e l a t i v e t o t h e l o n g i t u d i n a l a x i s ) leads t o an emergency s i t u a t i o n . The b a s i c advantage of pylon engine suspension i s t h e decreased n o i s ew i t h i n t h e passengers compartment. P o s i t i o n i n g of engines i n the f u s e l a g e t a i l s e c t i o n . This arrangementwas f i r s t used i n the French Caravelle passenger a i r c r a f t (Figure 60). Thefollowing a i r c r a f t have a l s o been designed along t h e s e l i n e s : t h e 11-62, t h e76
  • 85. - .. ..... ..I I , , Tu-134, t h e DC-9, t h e BAC-1 11, t h e Boeing-727, t h e De Havilland D H . 1 2 1 T r i d e n t and t h e Vickers VC-10 (Figure 6 1 ) . Such an engine arrangement y i e l d s t h e I f c l e a r wing" and o f f e r s maximum mechanization of t h e wing. J e t passenger a i r l i n e s w i t h such engine arrange­ ments have s e v e r a l ad­ vantages. The b a s i c advantage i s t h e i r i n c r e a s e d ,aerodynamic c h a r a c t e r i s t i c s and i n ­ creased comfort w i t h i n t h e passenger cabin (decreased n o i s e l e v e l ) . The absence of engine pods on t h e wing Figure 60. T h e C a r a v e l l e . r e s u l t s i n n e. a t i v e i n t e r - g , f e r e n c e being a f a c t o r only a t the j u n c t u r e of the wing and f u s e l a g e . I n a d d i t i o n , conditions a r e c r e a t e d f o r designing a wing with an i n c r e a s e d c r i t i c a l Mach number and a more e f f e c t i v e mechanical h i g h - l i f t device on t h e wing. The lack of secondary s t r u c t u r e s on t h e wing improves t h e wings l i f t , which i n t u r n permits a drop i n t h e wing a r e a . a c­ _ e . Figure 61. T h e Vickers VC-10 ( a ) and t h e D Havilland DH.121 (b). e 77
  • 86. Conditions are a l s o c r e a t e d f o r t h e o p e r a t i o n of t h e engine a i r scoops a t /84high angles of a t t a c k as a r e s u l t of downwash, which i n a sense " c o r r e c t s " t h e -flow toward t h e s i d e engine. During g u s t s , t h e e n t r a n c e angle of t h e a i r f l o wi n t o t h e a i r scopp decreases almost t o h a l f t h e a i r f o i l angle o f a t t a c k , i . e . , /85when t h e a i r f o i l angle of attack changes by 4 O , f o r example, t h e d i r e c t i o n of -the a i r f l o w around t h e a i r scoop varies by approximately. 2 O . The a i r w i l le n t e r the engine a t less of an angle, which s u b s t a n t i a l l y decreases t h e p r e s s u r el o s s a t t h e i n t a k e . When t h e engine is i n s t a l l e d i n t h e wing o r suspended froma pylon, however, t h e e n t r a n c e angle corresponds t o t h e angle o f attack atwhich t h e a i r c r a f t i s f l y i n g . Here t h e a i r c i r c u l a t i o n around t h e wingi n c r e a s e s t h e flow i n t a k e angle. A s is well known, t h i s causes a d d i t i o n a llosses. * One of t h e s t r u c t u r a l c h a r a c t e r i s t i c s of t h i s arrangement i s t h e T-shapedt a i l assembly with i t s a d j u s t a b l e s t a b i l i z e r . The e l e v a t o r assembly, l o c a t e don t h e upper s e c t i o n of t h e v e r t i c a l f i n , is f r e e from t h e d e s t r u c t i v e e f f e c tof sound-waves c r e a t e d by t h e sound f i e l d s of t h e engine exhaust (Figure 62).This, t o o , has a s p e c i f i c e f f e c t i n decreasing v i b r a t i o n . datum l i n e Figure 62. Diagram of the E f f e c t of Eng.ine Exhaust J e t s on the S t a b i l i z e r and V e r t i c a l F i n . The aerodynamic advantage of t h e T-shaped t a i l assembly i s t h a t t h e flowbpyond the wing and i t s r e s u l t a n t s e p a r a t i o n s have l i t t l e e f f e c t on i t duringhorizontal f l i g h t . The engine pods form h o r i z o n t a l s u r f a c e s which i n c r e a s e t h e a i r c r a f t sl o n g i t u d i n a l s t a b i l i t y , i n view of which t h e a i r c r a f t s l o n g i t u d i n a l s t a b i l i t yc h a r a c t e r i s t i c progress l i n e a r l y up t o high angles of a t t a c k . A t the p o i n t of i n t e r s e c t i o n of t h e h o r i z o n t a l t a i l s u r f a c e s and t h ee l e v a t o r f o r t h e T-shaped arrangement a t high f l i g h t speeds, t h e i n c r e a s e i ndrag drops as compared t o t h e normal arrangement. This i s an example of so-c a l l e d p o s i t i v e i n t e r f e r e n c e , and t h e e f f e c t i v e n e s s of t h e v e r t i c a l t a i lsurface increases. The engine pods have a h o r i z o n t a l pylon. The angle a t which t h e pod i ss e t r e l a t i v e t o t h e a x i s of t h e f u s e l a g e v a r i e s from zero t o + 2 O , while i nt h e h o r i z o n t a l p l a n e t h e pods may b e turned o u t from t h e f u s e l a g e by an angleof 2-4" (Figure 62). .- - .- -- - .--.- -- - . ­* Yeger, S .M. Design of Passenger J e t A i r c r a f t (Proyektirovaniye p a s s a c h i r ­ . skikh reaktivnykh samelotov) Mashinos t r o y e n i y e . 1964.78
  • 87. When t h e pod a x i s i s h i g h e r than t h e s t r u c t u r a l a x i s of t h e f u s e l a g e andconsequently h i g h e r than t h e a i r c r a f t s c e n t e r of g r a v i t y , a n e g a t i v e p i t c h i n gmoment i s c r e a t e d from t h e engine t h r u s t . Moving t h e engines t o t h e t a i l s e c t i o n of t h e f u s e l a g e c r e a t e s t h e / 86following o p e r a t i o n a l advantages. As can be seen from Figure 6 3 , only a s l i g h tp o r t i o n of t h e a i r f l o w t h r u s t back by t h e nose wheels i s covered by t h e engine.The j e t s from t h e main wheels a r e covered by t h e wing b o t h during t a k e o f f andlanding. This decreases t h e p o s s i b i l i t y t h a t f o r e i g n m a t t e r w i l l e n t e r t h eengines o f f the runway. Ground maintenance of t h e engine is made s i m p l e rthrough t h e e a s e w i t h which t h e pods can b e reached. Figure 6 3 . Diagram o f the E f f e c t o f Airstream Thrown Back from t h e Landi ng Gear Wheels : a - engines mounted i n wing; b - engines i n tail s e c t i o n o f f u s e l a g e ; c - engines on pylons. When t h e engines a r e suspended from pylons, as was s t a t e d above, t h e r e i sno need f o r long a i r scoops. However, when t h e engines a r e mounted i n t h ewing, as w a s done i n t h e Tu-104 and Tu-124 and t h e Comet, t h e length of t h ea i r i n t a k e i s 4-5 m e t e r s , as a r e s u l t of which l o s s e s i n a i r p r e s s u r e a t thei n t a k e decrease engine t h r u s t by 3 - 6 % . Moving t h e engines t o t h e t a i l ,however, decreases l o s s e s a t t h e i n t a k e and t h e t h r u s t drop i s only 1 - 2 % ,which improves t h e a i r c r a f t s t a k e o f f performance. In conclusion i t should be noted t h a t i n s p i t e of t h e numerous advantagesderived from i n s t a l l i n g t h e engines i n t h e t a i l s e c t i o n o f t h e f u s e l a g e , t h i sarrangement a l s o has i t s drawbacks. Thus, f o r example, t h e engine performancedecreases a t high angles of s i d e s l i p . The diving moment from engine t h r u s ti n c r e a s e s both t h e speed of r a i s i n g t h e landing g e a r nose wheels s t r u t duringt h e takeoff run and t h e c o n d i t i o n s f o r t h e c o n t r o l wheel. The need a r i s e sf o r an a d j u s t a b l e s t a b i l i z e r . There i s an i n c r e a s e i n t h e weight of t h erudder u n i t , which supports t h e e l e v a t o r u n i t . The s t r u c t u r e o f t h e a i r c r a f t 79
  • 88. becomes h e a v i e r as a r e s u l t of t h e reinforcement f o r t h e c o n s t r u c t i o n o f t h ef u s e l a g e t a i l s e c t i o n due t o t h e a d d i t i o n a l m a s s and i n e r t i a l loads from t h eengines as w e l l as t h e need t o i n c r e a s e reinforcement f o r t h e engines t o /87prevent i t s breakaway during emergency landing. During charging and f u e l i n g -up, t h e a i r c r a f t c e n t e r of g r a v i t y i s s h i f t e d s u b s t a n t i a l l y f a r t h e r forward,which makes t a k e o f f h a r d e r , and during f l i g h t r e q u i r e s p r e c i s e f u n c t i o n i n g oft h e automatic equipment which c o n t r o l s t h e f u e l output. Grouping t h e engines t o g e t h e r i n t h e t a i l s e c t i o n of t h e f u s e l a g ef a c i l i t a t e s using them f o r c o n t r o l l i n g t h e boundary l a y e r ( s e e Chapter I V )and, f i n a l l y , with t h e power p l a n t arranged i n t h i s manner, t h e d i s t a n c efrom the engines t o t h e ground i s determined only by t h e a i r c r a f t s landingc o n f i g u r a t i o n and the h e i g h t o f the landing gear. This makes i t p o s s i b l e t odecrease t h e landing g e a r h e i g h t and r e t a i n t h e p e r m i s s i b l e d i s t a n c e fromt h e ground t o t h e edges of t h e a i r scoops.80
  • 89. CHAPTER V TAKE0 FF§ 1. Taxiing A i r c r a f t with engines i n t h e t a i l s e c t i o n o f t h e f u s e l a g e o r i n t h e wing(along t h e s i d e s of t h e f u s e l a g e ) have s a t i s f a c t o r y t a x i i n g p r o p e r t i e s . Thesmall t h r u s t arm has no adverse e f f e c t s on t h e a i r c r a f t s maneuvering pro­p e r t i e s . In f a c t , a l l modern j e t a i r c r a f t have a p e d a l - c o n t r o l l e d leadingstrut, which makes i t easy t o perform t u r n s and maintain d i r e c t i o n duringtake o f f runs and landing runs. The angle of r o t a t i o n of the leading strut i s 35-45", w h i l e during takeo f f runs and landing runs (with f l a p s down) i t i s decreased t o 5-6". Thet a x i i n g speed along the ground, during t u r n s and c l o s e t o o b s t a c l e s reachesno more than 10 km/hr, while i n c l e a r and s t r a i g h t runway s e c t i o n s , i t isno more than 50 km/hr. Landing gears with nose wheels o f f e r good runway s t a b i l i t y during t a x i i n gon runways and taxiways. Turns a r e manipulated through t h e use of the leadings t r u t s , a s w e l l as the c r e a t i o n of asymmetrical t h r u s t and p a r t i a l braking,of t h e r i g h t o r l e f t landing gear t r o l l e y wheel. Turning an a i r c r a f t 180"r e q u i r e s a runway 50-60 meters wide, depending on t h e width o f t h e landingg e a r wheels. T u r b o j e t a i r c r a f t can a l s o t a x i over wet grass cover and overunsmoothed snow cover a t an a i r f i e l d . The f o u r t o s i x wheels on each mainstrut of t h e landing g e a r causes an even d i s t r i b u t i o n of load over t h e a i r ­f i e l d s u r f a c e , and reduced p r e s s u r e i n t h e pneumatic wheels (up t o 4.5 - 6kG/cm2) i n c r e a s e s a b i l i t y t o t r a v e l over d i r t a i r f i e l d s . Modern a i r c r a f tusing concrete landing s t r i p s maintain a t i r e p r e s s u r e of 6.5 - 9 . 5 kG/cm2. One drawback i n the use o f a i r c r a f t on d i r t a i r f i e l d s i s t h e damage t othe s u r f a c e caused by t h e wheels during t a x i i n g , t a k e o f f and landing, t h e - /88formation of r u t s , and the g r e a t amount. of d u s t thrown up from t h e exhaustof the j e t engines, which reduces v i s i b i l i t y on t h e landing s t r i p f o r p i l o t sof a i r c r a f t approaching f o r a landing.5 2. Stages of Takeoff Takeoff i s t h e a i r c r a f t s motion from t h e moment of s t a r t i n g u n t i l i treaches an a l t i t u d e of 10.7 meters* and has a t t a i n e d a s a f e f l i g h t speed. . .* This i s t h e p r e s e n t l y accepted a l t i t u d e f o r complete t a k e o f f according t o t h e ICAO and norms f o r f l i g h t worthiness f o r c i v i l a i r c r a f t i n t h e USSR. 81
  • 90. The d i s t a n c e covered by t h e a i r c r a f t from t h e moment o f s t a r t i n g u n t i lt h e a l t i t u d e of 10.7 meters has been reached i s c a l l e d t h e t a k e o f f d i s t a n c e . Aircraft t a k e o f f (Figure 64) c o n s i s t s of two s t a g e s : a) t a x i i n g u n t i l t h espeed o f l i f t - o f f and l i f t - o f f i t s e l f , b) a c c e l e r a t i o n from t h e l i f t - o f f speedt o a safe speed, w i t h simultaneous climbing. Figure 64. Diagram of A i r c r a f t Takeoff and t h e Calculated Takeoff T r a j e c t o r y According t o t h e I C A O : 1 - beginning o f run; 2 - takeoff run; 3 - a c c e l e r a t i o n and climbing; 4 - p o i n t of a i r c r a f t l i f t - o f f ; 5 - takeoff d i s t a n c e ; 6 - climbing t r a j e c t o r y f o r 100% e n g i n e t h r u s t ; 7 - l e n g t h of calculated takeoff t ra j ec t o r y ; 8 - permissible inclina­ t i o n s i n t r a j e c t o r y f o r extended takeoff d u e t o e n g i n e f a i l u r e ; 9 - a c t u a l t r a j e c t o r y of extended t a k e o f f . Immediately a f t e r l i f t - o f f , t h e a i r c r a f t s high t h r u s t - w e i g h t r a t i opermits i t t o g a i n a l t i t u d e and a c c e l e r a t e up t o i t s r a t e of climb along aninclined trajectory. In t h i s case, t h e gain i n a l t i t u d e i s c u r v i l i n e a r ,because i t s angle of i n c l i n a t i o n c o n s t a n t l y i n c r e a s e s . The holding a f t e r l i f t - o f f , which i s used i n t h e a c c e l e r a t i o n o f p i s t o na i r c r a f t p r i o r t o beginning g a i n i n g a l t i t u d e , i s n o t a p p l i e d i n t u r b o j e taircraft. The take-off run up t o l i f t - o f f speed. A s a r u l e , t a k e o f f is performedw i t h f l a p d e f l e c t i o n , from t h e b r a k e s when t h e t a k e o f f regime f o r t h e engines /89 -i s used. To t h i s end, t h e engines are f i r s t p u t i n t o t a k e o f f rpms and t h e nt h e brakes are slowly r e l e a s e d . Figure 65 shows a graph of t h e c o e f f i c i e n tc as a f u n c t i o n of t h e angle of a t t a c k and t h e a i r c r a f t p o l a r f o r t a k e o f f& s i t i o n of t h e wing f l a p s and s l a t s . An a i r c r a f t having t r i p l e - s l o t t e d f l a p s(high v a l u e f o r c ) was used as an example. y 1-082
  • 91. A t t h e beginning of t h e take- /90 o f f r u n , d i r e c t i o n i s maintained by t h e brakes and d i r e c t i n g t h e nose wheel, and a t a speed of 150-170 km/hr, when t h e rudder becomes e f f e c t i v e , i t i s maintained through t h e a p p r o p r i a t e i n c l i n a t i o n of t h e rudder t o t h e s i d e as r e q u i r e d . When t h e p r o p e r t a k e o f f a n g l e of a t t a c k (9-10") i s maintained, l i f t - o f f of t h e a i r c r a f t from t h e ground occurs without a d d i t i o n a l movement of t h e c o n t r o l wheel when l i f t - o f f speed i s a t t a i n e d . With a l i f t - o f f a n g l e o f a t t a c k of 9-10", the t a i l section of the fuselage must be s u f f i c i e n t l y f a r o f f t h e runway and a s p e c i f i c s u b - c r i t i c a l angle of a t t a c k must b e maintained. If the p i l o t unintentionally i n c r e a s e s t h e angle of a t t a c k t o 11-12", c o n t a c t of t h e t a i l p o r t i o n of t h e f u s e l a g e with t h e c o n c r e t e must be avoided. An improperly chosen angle of a t t a c k during l i f t - o f f may e i t h e r extend t h e l e n g t h of t h e t a k e o f f r u n , o r , on t h e c o n t r a r y , l e a d t o premature l i f t - o f f a t a low speed. Thus, i f t h e p i l o t achieves l i f t -Figure 65. T h e D e p e n d e n c e of c on c1 Y o f f a t a lower angle of a t t a c kand t h e P o l a r s of an A i r c r a f t having ( f o r example, w i t h M = 6" i n s t e a dT r i p l e - S l o t t e d W i n g Flaps and S l a t s : o f 9-10">, i . e . , below ca - p o l a r f o r a i r c r a f t w i t h landing y 1-0 which corresponds t o a high speed,g e a r down and w i n g f l a p s d e f l e c t e d a t t h e length of t h e t a k e o f f run2 5 " ; b - t h e same ai r c r a f t w i t h increases. In calculating t h eallowance made f o r t h e e f f e c t of a i r c r a f t 1 - i f t - o f f during t a k e o f f ,s c r e e n i n g by t h e e a r t h during t h e t h e v a l u e s normally accepted a r etakeoff run ( K = 1.6 : 0.134 = 1 2 ) .Note: T-0 = Take Off c1 = 8-11" and cy l-o = 1 . 3 - 1 . 7 (depending on t h e design andarrangement o f t h e f l a p s ) . For t h e example shown i n Figure 65, w e have c1 = 1-0= 11" and c = 1.6. y 1-0 A c c e l e r a t i o n from t h e l i f t - o f f speed t o a safe speed w i t h simultaneousclimbing. P i l o t i n g an a i r c r a f t during t h i s s t a g e of f l i g h t i n v o l v e s t h efollowing. A f t e r l i f t - o f f , maintaining t h e t a k e o f f a n g l e , t h e a i r c r a f tsmoothly s h i f t s i n t o g a i n i n g a l t i t u d e w i t h a subsequent d e c r e a s e i n t h e angle 83
  • 92. of a t t a c k . The main wheels a r e braked, t h e time f o r complete braking averaging0.2 - 0 . 3 s e c . To decrease drag a g a i n s t t h e a i r c r a f t during climbing ( a f t e rl i f t - o f f ) , t h e landing g e a r must be r e t r a c t e d without delay. The a i r c r a f t sh y d r a u l i c system r e t r a c t s t h e landing g e a r , with opening and c l o s i n g o f t h emain landing g e a r doors, i n 5-15 s e c . The landing g e a r i s r e t r a c t e d a t aspeed of 20-30 km/hr above t h e l i f t - o f f speed, and a t a h e i g h t n o t below5-7 meters. During t h e process of r e t r a c t i o n , t h e a i r c r a f t s speed i n c r e a s e s .After t h e landing g e a r i s r e t r a c t e d , t h e f l a p s are i n t u r n r e t r a c t e d a t ah e i g h t not l e s s t h a n 50-80 meters, and t h e a i r c r a f t a c c e l e r a t e s t o a speedf o r g a i n i n g a l t i t u d e . The p i l o t must f l y t h e a i r c r a f t during t h i s i n t e r v a li n such a way t h a t b e f o r e t h e f l a p s a r e r e t r a c t e d , t h e speed does not exceedt h e p e r m i s s i b l e with r e s p e c t t o s t a b i l i t y c o n d i t i o n s . The time r e q u i r e d f o rr e t r a c t i n g f l a p s d e f l e c t e d a t a t a k e o f f angle i s 8-12 s e c . As t h e f l a p s a r er e t r a c t e d , a p i t c h i n g moment i s c r e a t e d , s o t h a t p r e s s i n g f o r c e s a r e c r e a t e don t h e c o n t r o l wheel which a r e e a s i l y r e l i e v e d by t h e e l e v a t o r t r i m t a b s .This i s a case i n which t h e e l e c t r i c a l c o n t r o l of t h e e l e v a t o r t r i m t a b s i sconvenient t o use. A f t e r t h e f l a p s a r e r e t r a c t e d , t h e engine rpms decreaset o normal and t h e r e i s a f u r t h e r a c c e l e r a t i o n up t o t h e climbing c r u i s i n gspeed o r t o t h e f l i g h t speed along a r e c t a n g u l a r r o o t .§ 3. Forces Acting on t h e A i r c r a f t During t h e Takeoff Run and Takeoff /91 Let us examine t h e f o r c e s a c t i n g on t h e a i r c r a f t during t h e takeoff run(Figure 66). The t o t a l f o r c e of t h e engine t h r u s t a c t s i n t h e d i r e c t i o n oft h e a i r c r a f t motion. The o v e r a l l f o r c e of wheel f r i c t i o n a g a i n s t t h e groundF = F + F and t h e a i r c r a f t drag Q a c t a g a i n s t t h e a i r c r a f t s motion, 1 2braking i t . The d i f f e r e n c e i n the f o r c e s P -Q - F = R is called the acca c c e l e r a t i o n f o r c e . The following f o r c e s a c t p e r p e n d i c u l a r t o t h e t r a j e c t o r yof motion: l i f t f o r c e Y , f o r c e N of t h e r e a c t i o n o f t h e ground on t h e landingg e a r wheels, and t h e f o r c e of weight G. The f o r c e Racc communicates t o t h eaircraft the accelerationwhere m i s t h e a i r c r a f t mass. The g r e a t e r t h e a c c e l e r a t i o n f o r c e and t h e lower t h e a i r c r a f t weight,the h i g h e r t h e a c c e l e r a t i o n w i l l be. If i n s t e a d o f Racc we s u b s t i t u t e i t sv a l u e i n t o t h e formula, we o b t a i n j,=9.81 ( -$-+). As t h e landing g e a r wheels r o l l along t h e ground, f r i c t i o n f o r c e s a r i s ewhose v a l u e i s a f u n c t i o n of t h e condition of t h e runway (type o f s u r f a c e ) and84
  • 93. .. - - ., . .. ....-... .-,.., ...,, ,.. , , I , I I ,111 111.11 1 11 .1 1 11.11 I I1I t h e degree o f deformation i n t h e t i r e s . The amount of t h e f o r c e of f r i c t i o n i s determined as t h e product of t h e loads on t h e wheels on t h e f r i c t i o n coefficient f. a) moment o f f r i c t i o n f o r c e +--l F i g u r e 6 6 . Diagram of Forces Acting on t h e A i r c r a f t During Takeoff Run ( a ) and A f t e r L i f t - o f f During C 1 i m b i ng ( b ) . During t h e t a k e o f f run, t h e a i r c r a f t wing begins c r e a t i n g a l i f t i n g f o r c e which r a p i d l y i n c r e a s e s and removes t h e l o a d from t h e landing g e a r wheels. The v a l u e of t h e f r i c t i o n f o r c e f o r each moment may b e determined according t o t h e following formula: F = f (G - Y ) . The f r i c t i o n c o e f f i c i e n t ( o r c o e f f i c i e n t of adhesion) f o r dry c o n c r e t e i s f = 0.03 - 0 . 0 4 , and f o r w e t c o n c r e t e i t is 0.05; f o r dry ground cover and f o r a c l e a r e d snow cover i t i s 0.07; f o r a w e t g r a s s s u r f a c e it i s 0.10. The v a l u e P/G i s t h e a i r c r a f t t h r u s t - w e i g h t r a t i o during t a k e o f f . The g r e a t e r t h e t h n i s t - w e i g h t r a t i o , t h e g r e a t e r t h e t a k e o f f run a c c e l e r a t i o n and ­ /91 t h e s h o r t e r t h e l e n g t h of t h e t a k e o f f run. I n c r e a s i n g t h e t h r u s t - w e i g h t r a t i o i s an e f f e c t i v e means of improving t a k e o f f c h a r a c t e r i s t i c s . For example, when t h e Conway 550 d o u b l e - c i r c u i t engines w i t h t h e i r 7,500 k G t h r u s t were i n s t a l l e d on t h e Boeing-707, t h e t h r u s t - w e i g h t r a t i o i n c r e a s e d from 0.2 t o 0.26. A g r e a t e r t h r u s t - w e i g h t r a t i o i s enjoyed by a i r c r a f t w i t h two engines (0.28 ­ 0.33 kG t h r u s t / k g w e i g h t ) , and t h e l e a s t is t h a t of a i r c r a f t with f o u r engines (0.22 - 0.26 kG t h r u s t / k g w e i g h t ) . A s can b e s e e n from t h e formula above, t h e maximum a c c e l e r a t i o n i s during t h e f i r s t s t a g e of t h e t a k e o f f run ( t h e a i r c r a f t drag f o r c e i s low). With an i n c r e a s e i n speed t h e t h r u s t of j e t engines d e c r e a s e s , although during t h e t a k e o f f run i t may b e considered c o n s t a n t . B comparison w i t h y p i s t o n e n g i n e s , t h e t h r u s t of j e t engines d u r i n g t a k e o f f decreases l e s s s i g n i f i c a n t l y and a t t h e end of t h e t a k e o f f run amounts t o 87 - 92% of t h e s t a t i c thrust P . The drag f o r c e during t h e t a k e o f f run i n c r e a s e s from 0 t o Ql-0 ( a i r c r a f t grag a t t h e i n s t a n t of l i f t - o f f ) . A t l i f t - o f f , Y = G , s o t h a t t h e f r i c t i o n f o r c e w i l l equal zero. Thus, a t t h e end of t h e t a k e o f f p o r t i o n , when t h e a i r c r a f t s e p a r a t e s from t h e ground, t h e a c c e l e r a t i o n f o r c e ( r e s e r v e t h r u s t ) equals t h e d i f f e r e n c e between t h e t o t a l engine t h r u s t and t h e a i r c r a f t drag: Racc = P -Q. 85
  • 94. A i r c r a f t drag a t t h e i n s t a n t of l i f t - o f f (1-0) may be determined accordingt o formula:where c X i s t h e drag c o e f f i c i e n t f o r an a i r c r a f t w i t h landing g e a r down and f l a p s extended i n takeoff p o s i t i o n a t an angle of a t t a c k a t t h e i n s t a n t of l i f t - o f f . For example, f o r an a i r c r a f t with a t a k e o f f weight of 76 tons and a wingarea of S = 180 m2, t h e t h r u s t during t a k e o f f c o n f i g u r a t i o n f o r a l i f t - o f fspeed of 300 km/hr (83.3 m/sec) i s approximately 17,000 kG. If we assumethat at lift-off c = 0.07 - 0.075, then x 1-0 Q1-o= C.po PS V -83 0.071 *0.125*180 3 2 -5500 I - kG, 2Then t h e a c c e l e r a t i o n f o r c e R = 17,000 -5,500 = 11,500 kG. The mean acca c c e l e r a t i o n a t t h i s i n s t a n t w i l l be The lower t h e v a l u e c (due t o t h e p r o p e r s e l e c t i o n of t h e f l a p and x 1-0s l a t systems), t h e lower Ql-o w i l l b e and t h e g r e a t e r t h e a c c e l e r a t i o n f o r c ew i l l be f o r the same assumed engi?e t h r u s t . For example, f o r an a i r c r a f t witha low takeoff weight (two e n g i n e s ) , during t h e t a k e o f f run below t h e l i f t - o f fspeed Racc = 9,000 -5,800 kG, while t h e mean a c c e l e r a t i o n j x = 2.5 - 2 . 0 m/sec2J93 -I n such an a i r c r a f t , t h e t a k e o f f time decreases. During the climbing p o r t i o n of f l i g h t , under t h e e f f e c t of t h e f o r c e (Figure 66) t h e r e w i l l be a f u r t h e r i n c r e a s e i n f l i g h t speed. For t h i sRacecase we may w r i t e the following equation of motion Race = P - Q - G sin 0 = mj,where G s i n 0 i s t h e a i r c r a f t component weight a c t i n g along t h e l i n e of flight; m i s t h e a i r c r a f t mass. Decreasing t h e t o t a l engine t h r u s t with an i n c r e a s e i n f l i g h t speed doesn o t decrease the v a l u e of t h e a c c e l e r a t i o n f o r c e , because as a r e s u l t o f adecrease i n t h e angle of a t t a c k , t h e induced drag f o r t h e a i r c r a f t d e c r e a s e s .This allows an i n c r e a s e i n t h e speed during t h e t a k e o f f run p o r t i o n (achievingt h e r e q u i r e d climbing speed o r f l i g h t speed along a r e c t a n g u l a r r o o t ) .86
  • 95. The l e n g t h of t h e climbing p o r t i o n with a c c e l e r a t i o n i s a f u n c t i o n of t h es p e c i f i c load, thrust-weight r a t i o , and o t h e r parameters. The component G s i n 0 i n i t i a l l y has a low v a l u e , because t h e angle ofi n c l i n a t i o n of the t r a j e c t o r y during climbing i s small (0 = 6 - l o o ; s i n 0 == 0.105 - 0.175).§ 4. Length of Takeoff Run. Lift-off Speed The length of t h e a i r c r a f t takeoff run i s a f u n c t i o n of t h e l i f t - o f fspeed and a c c e l e r a t i o n : L = v21-o ace 2 j x ave where jx ave i s the average a c c e l e r a t i o n value. The l i f t - o f f speed i s determined according t o formula: /-G S ~ km/hr , cYl-O. Gwhere - i s t h e u n i t load p e r 1 m2 of wing area. S The g r e a t e s t u n i t load i s i n four-engined a i r c r a f t ( t h e Super VickersVC-10, 570 kG/m2; DC-8-3C, 560 kG/m2) and somewhat lower i n two-engineda i r c r a f t (BAC-111-200, 370 k G / m 2 , t h e Caravelle-XB, 350 kG/m2) ; f o r t h r e e ­engined a i r c r a f t ( t h e Boeing-727 and t h e De Havilland Trident-1E) i t i s 450kG/m2. For an average c = 1.6 ( t r i p l e - s l o t f l a p s and s l a t s ) , t h e l i f t - o f f y 1-0speed f o r G/S = 450 - 500 kG/m2 i s 220 - 240 km/hr. For an average a c c e l e r a t i o nof j x = 2 m/sec2, t h e length of t h e t a k e o f f - r u n i s 1 , 1 0 0 - 1,300 m . A s has already been noted, t h e swept wing has a lower v a l u e f o r t h e ­ /94coefficient c then does t h e s t r a i g h t wing. This r e s u l t s i n a lower v a l u e Y Inaxfor c A l l i n a l l , t h i s leads t o a s u b s t a n t i a l i n c r e a s e i n Vlm0, and y 1-0consequently i n the length of t h e t a k e o f f run. Therefore, t h e f l a p s and s l a t sa r e used t o i n c r e a s e cy m a Deflecting them t o t h e i r maximum angle a t take­o f f may, of course, s u b s t a n t i a l l y decrease t h e l i f t - o f f speed, b u t i n t h i sevent t h e r e i s a l s o an i n c r e a s e i n drag, a decrease i n a c c e l e r a t i o n and, lastly,an i n c r e a s e i n t h e length of t h e t a k e o f f run. This r e q u i r e s s e l e c t i o n of t h eoptimum angle of i n c l i n a t i o n f o r t h e f l a p s , a t which c i n c r e a s e s and, Y 87
  • 96. consequently, s o does c while t h e a i r c r a f t drag i n c r e a s e s n e g l i g i b l y . y 1-0Designers are s t r i v i n g t o achieve b o t h t h e g r e a t e s t v a l u e f o r cy 1-0 and highaerodynamic performance i n a i r c r a f t . If during t a k e o f f t h e a i r c r a f t has af i n e n e s s r a t i o of 14-15, t h i s makes i t p o s s i b l e t o s o l v e many problems suchas, f o r example, achieving t h e c o n t i n u a t i o n o f t a k e o f f i n t h e event o f t h ef a i l u r e of an engine, decreasing n o i s e i n t h e area through a s h a r p e r climbingt r a j e c t o r y , t h e s e l e c t i o n of engines with optimal t h r u s t values f o r a givena i r c r a f t , e t c . C a l c u l a t i o n s and f l i g h t t e s t s have shown t h a t t h e optimumangle of d e f l e c t i o n f o r f l a p s during t a k e o f f i s 10-25". This angle y i e l d st h e optimum r a t i o between c and cx, which leads t o a marked decrease i n y 1-0t h e length of t h e t a k e o f f run. W must once more t a k e n o t e t h a t cy l-o i s es e l e c t e d from t h e c o n d i t i o n of a s u f f i c i e n t r e s e r v e with r e s p e c t t o t h e angleof attack p r i o r t o l i f t - o f f ( c ) , s o as t o e l i m i n a t e s i d e s l i p . According Y m at o norms of a i r w o r t h i n e s s , t h e a i r c r a f t l i f t - o f f speed must b e no l e s s than20% g r e a t e r than t h e brakeaway speed ( s e e how i t is determined i n Chapter X I ,5 14).§ 5. Methods of Takeoff E a r l i e r w e e s t a b l i s h e d t h a t a c c e l e r a t i o n during t h e t a k e o f f run andconsequently t h e length of the t a k e o f f run a r e f u n c t i o n s of t h e d i f f e r e n c e i nt h e a v a i l a b l e t h r u s t and t h e o v e r a l l a i r c r a f t drag. The engine t h r u s t duringthe t a k e o f f run up t o t h e l i f t - o f f speed of 220-240 km/hr v a r i e s i n s i g n i f i ­c a n t l y (by 6-8%). The o v e r a l l a i r c r a f t drag during t h i s p o r t i o n o f t a k e o f fi s t h e s m of t h e aerodynamic drag (which i n c r e a s e s as t h e angle of a t t a c k ui n c r e a s e s ) and t h e f r i c t i o n f o r c e of t h e wheels (on t h e runway s u r f a c e ) , which.decreases as a r e s u l t of a l e s s e n i n g of t h e load on t h e wheels then i n c r e a s ei n wing l i f t . Therefore, t h e p i l o t must s e l e c t an angle a ( d i f f e r e n t f o r eacha i r c r a f t ) a t which t h e t o t a l drag w i l l be minimal and, consequently, t h e t a k e ­o f f run w i l l be s h o r t e s t . Due t o t h e lack of a i r f l o w o f t h e s l i p s t r e a m fromthe p r o p e l l e r s , t h e e f f e c t i v e n e s s of t h e p i t c h c o n t r o l a t t h e beginning o f t h etakeoff run i s below t h a t of a prop-driven a i r c r a f t . The r e q u i r e d l o n g i t u d i ­n a l moment f o r l i f t - o f f o f the nose wheel i s c r e a t e d by t h e e l e v a t o r only a ta r a t h e r high speed, c l o s e t o t h e take-off speed. A s a r e s u l t of t h i s , t h eg r e a t e r p a r t of the take-off run f o r a t u r b o j e t a i r c r a f t i s achieved i n stand- - /95ing configuration. The angle of attack during t h e t a k e o f f run i s a f u n c t i o nof t h e angle I$ of t h e wing s e t t i n g ; i f , f o r example, t h e s e t t i n g angle I$ = l o ,then c1 = 1" a l s o . However, t h e wings of modern a i r c r a f t have geometric t w i s t (Chapter 11, § l ) , which c r e a t e s an angle c1 which v a r i e s along t h i s span. I nthe graph shown i n Figure 65, t h e v a l u e c corresponds t o t h e average f o r y t-0a t a k e o f f run of c1 = 1 - 3". B t h e l o n g i t u d i n a l p o s i t i o n of t h e a i r c r a f t ( t h e angle of t h e a i r c r a f t s yl o n g i t u d i n a l a x i s ) , i . e . , t h e angle of a t t a c k , t h e p i l o t may c o n t r o l i nachieving a speed a t which the e f f e c t i v e n e s s of t h e e l e v a t o r i s s u f f i c i e n tt o i n i t i a t e l i f t i n g t h e a i r c r a f t s nose ( f r o n t landing g e a r s t r u t ) . Often88
  • 97. I - I - .I --- t h i s speed i s s e l e c t e d from t h e condition of achieving rudder e f f i c i e n c y i n o r d e r t o prevent t h e a i r c r a f t from turning on t h e main landing g e a r struts with nose r a i s e d i n t h e event of engine f a i l u r e during t h e t a k e o f f run. I n t h i s event, t h e rudder should p a r r y t h e t u r n i n g moment from t h e asymmetric t h r u s t o f the o p e r a t i n g engines. Usually, a f t e r l i f t - o f f of t h e f r o n t s t r u t , t h e a i r c r a f t tends t o p r o g r e s s i v e l y i n c r e a s e t h e p i t c h angle under t h e e f f e c t of t h e i n c r e a s i n g wing l i f t . Therefore, i n i t i a l l y t h e c o n t r o l wheel i s brought back toward o n e s e l f , and then commensurably moved away, i n an attempt t o maintain t h e a i r c r a f t a t an angle of a t t a c k of 3 - 4 O . The length of t h e takeoff run i s a f u n c t i o n b a s i c a l l y of t h e a c c u r a t e s e t t i n g of t h e angle of a t t a c k . During t h e t a k e o f f run, minor d e v i a t i o n s from t h e optimum a, a t which drag i s minimal, do n o t l e a d t o a s u b s t a n t i a l i n c r e a s e i n t h e length of takeoff run. There are two ways of p u t t i n g t h e a i r c r a f t i n t o t h e t a k e o f f angle of a t t a c k . The f i r s t c o n s i s t s of t h e nose struts l i f t i n g o f f a t t h e i n s t a n t when e l e v a t o r e f f i c i e n c y i s achieved. The a i r c r a f t achieves an angle o f at%ack of 3-4" and t h e r e s t of t h e run t a k e s p l a c e on t h e main landing g e a r s . Smoothly operating t h e e l e v a t o r , t h e p i l o t maintains t h e angle of a t t a c k during t h e t a k e o f f run and a t t h e i n s t a n t of l i f t - o f f he c r e a t e s t h e takeoff angle of a t t a c k . In the second way, which has only r e c e n t l y gained acceptance, t h e e n t i r e takeoff run i s performed i n t h e s t a n d i n g c o n f i g u r a t i o n , and when a speed c l o s e t o t h e l i f t - o f f speed (Vl-o - 15 - 20 km/hr) i s achieved, t h e c o n t r o l wheel i s smoothly b u t vigorously p u l l e d toward oneself ( i n 4-5 s e c ) , by which motion t h e p i l o t l i f t s t h e f r o n t strut o f f and, without maintaining t h e a i r ­ c r a f t i n a two-point c o n f i g u r a t i o n , p u t s i t i n t o t h e t a k e o f f angle of a t t a c k . Separation occurs p r a c t i c a l l y from t h r e e p o i n t s without any p e r c e p t i b l e over­ load during t h e process of r o t a t i n g the a i r c r a f t r e l a t i v e t o t h e l a t e r a l a x i s and i n c r e a s i n g t h e p i t c h i n g angle. In t h i s way t h e p i l o t maintains complete c o n t r o l of t h e t a k e o f f r u n , t h e speed and t h e o p e r a t i o n of the engines. Usually during t h e t a k e o f f run, t h e n a v i g a t o r s t a t e s t h e a i r c r a f t speed over the intercom a t each 10 km/hr, s t a r t i n g a t a speed of 150 km/hr, while t h e p i l o t d i r e c t s a l l h i s a t t e n t i o n s t r a i g h t ahead. A c o n t r o l l a b l e leading s t r u t s i m p l i f i e s maintaining the d i r e c t i o n during t h e f i r s t s t a g e of ­ / 96 the takeoff run, b e f o r e t h e rudder becomes responsive, which almost e l i m i n a t e s t h e use of the brakes i n t h e main landing g e a r t r o l l e y . In t h e second method of p i l o t i n g , the t a k e o f f d i s t a n c e remains p r a c t i c a l l y t h e same as i n the f i r s t , but t h e takeoff run i s somewhat s h o r t e r due t o t h e h i g h e r speed. Also, t a k e o f f with. a s i d e wind i s f a c i l i t a t e d , s i n c e t h e c o n t r o l l a b l e nose wheel i n combination with t h e rudder makes it p o s s i b l e t o hold a f i x e d d i r e c t i o n up t o t h e moment of s e p a r a t i o n without i n c r e a s i n g t h e t a k e o f f run length ( i n a i r c r a f t with u n c o n t r o l l e d nose wheel, t h e run length i s u s u a l l y i n c r e a s e d due t o t h e asymmetrical braking of main landing gear t r u c k s ) . A f t e r t h e a i r c r a f t breaks away, t h e s i d e wind causes it t o t u r n a g a i n s t t h e wind; f o r example, with a wind speed of 18-20 m/sec, t h e r o t a t i o n angle i s 18-20". 89
  • 98. F l y i n g i n v e s t i g a t i o n s have shown t h a t t h e r e q u i r e d r o t a t i o n of t h e f r o n t wheel does n o t exceed 4-5" with a s i d e wind up t o 20 m/sec. This allows t h e maximum p e r m i s s i b l e s i d e wind d u r i n g t a k e o f f t o b e i n c r e a s e d , f o r example,a wind a t 90" t o t h e runway can be up t o 15-18 m/sec, and a l s o s i m p l i f i e s t h e t a k e o f f maneuver. Up t o t h e p r e s e n t time, no s i n g l e o p i n i o n h a s developed among p i l o t s ast o t h e way i n which t h e c o n t r o l system o f t h e f r o n t g e a r should bec o n s t r u c t e d . The predominant opinion i s t h a t t h e r o t a t i o n o f t h e wheelsshould b e c o n t r o l l e d by t h e rudder p e d a l s ( a s on t h e TU-124 a i r c r a f t ) ,f r e e i n g t h e p i l o t s hands f o r o p e r a t i o n of t h e e l e v a t o r c o n t r o l l e v e r , motort h r o t t l e s , e t c . However, i t i s known t h a t when t h e t a k e o f f speed reaches150-200 km/hr and t h e rudder begins t o be e f f e c t i v e , i t i s more expedient t ou s e t h e rudder alone t o m a i n t a i n t h e t a k e o f f d i r e c t i o n , d i s c o n n e c t i n g t h ef r o n t l a n d i n g g e a r , which i s n o t always t e c h n i c a l l y p o s s i b l e i f t h e g e a r i sc o n t r o l l e d by t h e p e d a l s . Therefore, t h e wear r a t e of t h e rubber t i r e s ont h e f r o n t landing g e a r may be i n c r e a s e d . A second p l a n i s t h a t o findependent c o n t r o l o f r o t a t i o n of t h e f r o n t l a n d i n g g e a r , n o t connected t ot h e o p e r a t i o n o f t h e r u d d e r (TU-104 a i r c r a f t ) . Let us analyze t h e technique of performing a t a k e o f f u s i n g t h e secondmethod ( s e p a r a t i o n from t h r e e p o i n t s ) . I t i s recommended t h a t t h e e l e v a t o rtrimmer l e v e r be s e t a t 0 . 5 - 0 . 8 d i v i s i o n s forward i n advance, i n o r d e r t oi n c r e a s e t h e load on t h e s t i c k from t h e e l e v a t o r a t t h e moment o f s e p a r ­a t i o n . Thus, t h e s e a c t i o n s a r e i n o p p o s i t i o n t o t h e e s t a b l i s h e d t r a d i t i o n ,according t o which t h e trimmer c o n t r o l i s moved 0.5-1 d i v i s i o n s back i no r d e r t o d e c r e a s e l o a d s a t t h e moment o f l i f t i n g o f t h e f r o n t g e a r ands e p a r a t i o n o f t h e a i r c r a f t . Before beginning t h e t a k e o f f r u n , t h e s t i c k i spushed forward approximately t o t h e n e u t r a l p o s i t i o n . Holding t h e a i r c r a f twith t h e b r a k e s , t h e engines are s e t a t t a k e o f f regime. A f t e r making s u r et h a t t h e o p e r a t i n g regime of t h e engines corresponds t o t h e norm, t h e b r a k e sa r e r e l e a s e d and t h e t a k e o f f run i s begun, d u r i n g which t h e r e q u i r e dd i r e c t i o n i s maintained by c o n t r o l l i n g t h e f r o n t landing g e a r . Thee f f e c t i v e n e s s o f c o n t r o l of t h e f r o n t l a n d i n g g e a r i s h i g h e r , t h e mores t r o n g l y t h e wheels a r e f o r c e d down t o t h e runway. When s u f f i c i e n t e f f e c t ­ /% i v e n e s s o f t h e r u d d e r has been achieved t o m a i n t a i n t h e t a k e o f f c o u r s e ,g e n e r a l l y 60-70% of t h e maximum speed, c o n t r o l of t h e f r o n t wheels can bedisconnected ( i f t h i s i s p o s s i b l e i n t h e a i r c r a f t ) . When t h e t a k e o f f i sb e i n g performed with a s i d e wind, i n o r d e r t o p r e v e n t wind banking a t t h emoment o f s e p a r a t i o n , t h e a i l e r o n c o n t r o l must be t u r n e d " a g a i n s t t h e wind"by 30-80" with a wind speed of 8-18 m/sec b e f o r e s e p a r a t i o n . A f t e rs e p a r a t i o n , t h e r a t e of i n c r e a s e i n t h e p i t c h a n g l e must be s l i g h t l ydecreased and t h e s t i c k smoothly moved t o t h e n e u t r a l p o s i t i o n .86. F a i l u r e o f E n g i n e D u r i n g Takeoff Main t a k e o f f c h a r a c t e r i s t i c s of a i r c r a f t with one engine i n o p e r a t i v e .A s we know, one of t h e main requirements p l a c e d on passenger a i r c r a f t i s t h ep o s s i b i l i t y of c o n t i n u i n g t a k e o f f and climb i n c a s e o f engine f a i l u r e . A90
  • 99. knowledge o f t h e t a k e o f f c h a r a c t e r i s t i c s of an a i r c r a f t and t i m e l y usage o ft h e p i l o t i n g recommendations i n c a s e o f engine f a i l u r e w i l l guarantee a .s u c c e s s f u l c o n t i n u a t i o n o f t h e f 1i g h t The t a k e o f f c h a r a c t e r i s t i c s o f an a i r c r a f t with one i n o p e r a t i v e enginei n c l u d e t h e following: a ) t h e l e n g t h of t h e t a k e o f f run from t h e s t a r t i n gp o i n t t o t h e moment of engine f a i l u r e ; b) t h e l e n g t h of t h e t a k e o f f run fromt h e moment o f engine f a i l u r e t o t h e moment o f s e p a r a t i o n ; c ) t h e i n c l i n a t i o nof t h e t r a j e c t o r y during t h e climbing s e c t o r with a c c e l e r a t i o n ; d) t h ei n c l i n a t i o n of t h e t r a j e c t o r y during t h e climbing s e c t o r with landing g e a rup; e ) t h e c r i t i c a l engine f a i l u r e speed ( t h e speed o f i n t e r r u p t i o n oft a k e o f f ) Vcr; f ) t h e s a f e t a k e o f f speed Vsto. I f we know t h e l e n g t h of t h e t a k e o f f run o f t h e a i r c r a f t from t h es t a r t p o s i t i o n t o t h e moment o f engine f a i l u r e and t h e l e n g t h of t h e runfrom t h e moment of f a i l u r e t o complete a i r c r a f t h a l t , which make up t h ed i s t a n c e f o r i n t e r r u p t i o n of t a k e o f f , we can determine which a i r f i e l d s a r es a f e f o r o p e r a t i o n of a given a i r c r a f t , which t y p e of approaches t o t h erunway should b e used, how t h e a i r c r a f t should b e p i l o t e d with an inoper­a t i v e engine, e t c . I n o r d e r t o a s s u r e s a f e t y during c o n t i n u a t i o n of t h e t a k e o f f and climbwith one motor i n o p e r a t i v e , i t i s necessary t h a t t h e angle of i n c l i n a t i o n oft h e t a k e o f f t r a j e c t o r y and climb t o a l t i t u d e measured during t e s t s beg r e a t e r than t h e minimum p e r m i s s i b l e angle (Figure 6 4 ) . A s we can s e e fromt h e f i g u r e , a f t e r t h e landing gear are r a i s e d t h e i n c l i n a t i o n of t h et r a j e c t o r y should be no less than 2 . 5 % , corresponding t o an angle0 = 1 30 min ( s i n 0 = V /V = 0 . 0 2 5 and 0 = 1 30 min) . The end of t h e Yo p e r a t i o n of r a i s i n g t h e landing g e a r should correspond approximately t o t h emoment of passage of t h e t a k e o f f d i s t a n c e (H = 10.7 m p l u s 300 m . ) I n case of an engine f a i l u r e during t a k e o f f , t h e a v a i l a b l e t h r u s td e c r e a s e s , t h e f l y i n g q u a l i t y of t h e a i r c r a f t becomes w o r s e and p i l o t i n gbecomes more d i f f i c u l t due t o t h e asymmetrical n a t u r e of t h e t h r u s t and t h e /98 low f l i g h t speeds, decrease i n c o n t r o l l a b i l i t y and decrease i n r a t e ofclimb. The decrease i n a v a i l a b l e t h r u s t l e a d s t o an i n c r e a s e i n t h e dependenceof t h e f l y i n g c h a r a c t e r i s t i c s of t h e a i r c r a f t on temperature and a i rp r e s s u r e . Therefore, t h e v e r t i c a l speed of t h e a i r c r a f t with one enginei n o p e r a t i v e , c h a r a c t e r i z i n g . t h e p o s s i b i l i t y of continuing t h e t a k e o f f andclimb under design c o n d i t i o n s (p = 730 mm Hg and t = +3OoC) a r e s l i g h t l yl e s s than under s t a n d a r d c o n d i t i o n s (p = 760 mm H and t = +15C). g The following speeds a r e c h a r a c t e r i s t i c f o r continued and i n t e r r u p t e dt a k e o f f s : a ) t h e c r i t i c a l speed o f engine f a i l u r e , V i s t h e speed c o r r e ­ cr Jsponding t o t h e " c r i t i c a l p o i n t " during t h e t a k e o f f r u n , a t which f a i l u r e ofone of t h e engines i s p o s s i b l e . I n c a s e of f a i l u r e of one engine a t t h i sp o i n t , t h e p i l o t can e i t h e r end t h e t a k e o f f run w i t h i n t h e d i s t a n c e 91
  • 100. a v a i l a b l e , s e p a r a t e and c o n t i n u e h i s f l i g h t , o r end h i s t a k e o f f run and s t o p w i t h i n t h e i n t e r r u p t e d t a k e o f f d i s t a n c e ; b ) t h e s a f e t a k e o f f speed i s t h e speed a t which t h e a i r c r a f t begins"to climb a f t e r s e p a r a t i o n and VstoJa c c e l e r a t i o n with one engine i n o p e r a t i v e . According t o t h e norms of t h eICAO, t h i s should be 15-20% (depending on t h e number o f engines on t h ea i r c r a f t ) g r e a t e r t h a n t h e s e p a r a t i o n speed f o r t h e t a k e o f f c o n f i g u r a t i o n oft h e a i r c r a f t : V s t o - (1.15-1.2) Vs > ( s e e Chapter X I , 514). 1 If t h e speed o f s e p a r a t i o n i s l e s s t h a n t h e s a f e speed o f t h e a i r c r a f t ,t h e a i r c r a f t i s h e l d a f t e r s e p a r a t i o n with a c c e l e r a t i o n t o V s t o t h e n t h eclimb : o a l t i t u d e i s begun. The main c h a r a c t e r i s t i c i n d i c a t i n g t o t h e p i l o t t h a t an engine hasf a i l e d i s t h e appearance of a tendency of t h e a i r c r a f t t o t u r n and banktoward t h e engine which has f a i l e d . Also, f a i l u r e o f an engine can b edetermined from t h e d r o p i n o i l p r e s s u r e and f u e l p r e s s u r e , d e c r e a s e i nengine r o t a t i n g speed i n d i c a t e d by t h e tachometer, e t c . I n o r d e r t o make i t p o s s i b l e f o r t h e p i l o t t o d e c i d e t o c o n t i n u e t h et a k e o f f o r i n t e r r u p t t h e t a k e o f f , t h e p i l o t should know t h e c r i t i c a l speedf o r engine f a i l u r e and f o r i n t e r r u p t i o n of t h e t a k e o f f . During t h e p r o c e s s of a i r c r a f t t e s t i n g , i n t e r r u p t e d and continuedt a k e o f f s a r e u s u a l l y performed w i t h one engine switched o f f d u r i n g v a r i o u ss t a g e s o f t h e t a k e o f f . When t h i s i s done, t h e l e n g t h of t h e t a k e o f f run t os e p a r a t i o n o f t h e a i r c r a f t and t h e l e n g t h of t h e t r a j e c t o r y t o a l t i t u d e1 0 . 7 m a r e measured i f t h e t a k e o f f i s continued, a s well a s t h e l e n g t h oft h e run t o h a l t i f it i s i n t e r r u p t e d . When an i n t e r r u p t e d t a k e o f f i sperformed, f i r s t t h e engine i s turned o f f , t h e n a f t e r 3 s e c ( r e a c t i o nof p i l o t t o f a i l u r e ) t h e o p e r a t i n g engines a r e reduced t o t h e i d l e ,t h e s p o i l e r s a r e extended and t h e b r a k i n g p a r a c h u t e i s r e l e a s e d andi n t e n s i v e b r a k i n g i s begun. The t r a n s i t i o n t o t h e i d l e i s made due t o t h en e c e s s i t y of maintaining p r e s s u r e i n t h e h y d r a u l i c system c o n t r o l l i n g t h es p o i l e r s and landing g e a r . When a continued t a k e o f f i s performed, t h e p i l o t , a f t e r t h e engine i s /Eturned o f f , c o n t i n u e s h i s a c c e l e r a t i o n t o t h e s e p a r a t i o n speed and a c c e l ­e r a t i o n t o t h e s a f e f l y i n g speed. The d a t a produced by t h e s e t e s t s a r e usedt o c o n s t r u c t graphs o f t h e dependence of t a k e o f f r u n , d i s t a n c e of continuedf l i g h t t o H = 10.7 m and d i s t a n c e of i n t e r r u p t e d t a k e o f f on speed(Figure 6 7 ) . The c r i t i c a l speed f o r engine f a i l u r e ( p o i n t B) corresponds t op o i n t A of t h e i n t e r s e c t i o n of t h e curves f o r i n t e r r u p t e d and continuedt a k e o f f s . Here a l s o t h e s o - c a l l e d runway b a l a n c e l i n e i n t h e d i r e c t i o n oft h e t a k e o f f c o u r s e ( p o i n t C) i s determined, which i n c a s e of an enginef a i l u r e d u r i n g t a k e o f f provides f o r c o n t i n u a t i o n of t h e t a k e o f f o r s t o p p i n g92
  • 101. I111 of t h e a i r c r a f t (by braking) w i t h i n t h e l e n g t h o f t h e runway a f t e r t h e /- loo takeoff i s interrupted. I L I Figure 67. Diagram f o r Determination o f Balance Runway L e n g t h and C r i t i c a l S p e e d o f E n g i n e Failure I f t h e t a k e o f f i s continued, a c c e l e r a t i o n o f t h e a i r c r a f t t o t h e s a f e t a k e o f f speed should b e performed a t an a l t i t u d e of 5-7 m (above t h e runway), a t which p o i n t t h e l a n d i n g g e a r should begin t o b e r a i s e d . A t 1 0 . 7 m , t h e landing g e a r should be almost a l l t h e way up [ t a k e o f f d i s t a n c e ) . The complete r a i s i n g of t h e landing g e a r should be completed a f t e r t h e . t a k e o f f d i s t a n c e p l u s 300 m ( r e s e r v e ) have been covered. I n c a s e o f i n t e r r u p t i o n of t h e t a k e o f f , t h e run should b e completed on t h e runway. 93
  • 102. The c r i t i c a l speed f o r engine f a i l u r e is t h e maximum speed, upon r e a c h i n g which t h e p i l o t can i n t e r r u p t t h e t a k e o f f o r c o n t i n u e i t with equal s a f e t y . If t h e t a k e o f f i s continued a t VM < cr (F.igure 68), t h e continued t a k e o f f d i s t a n c e LM t o a l t i t u d e 1 0 . 7 m i s g r e a t e r t h a n t h e balanced runway l e n g t h ; t h i s i s p a r t i c u l a r l y dangerous i f t h i s l e n g t h i n c l u d e s t h e 400-m t e r m i n a l s a f e t y s t r i p . This i s a paved c o n c r e t e s t r i p ( i n case t h e a i r c r a f t r o l l s beyond t h e a c t u a l runway d u r i n g an i n t e r r u p t e d t a k e o f f ) . 240 260 280 300 320 340 34 35 36 37 E.. �on zKM/hr r.0: Figure 68. V e r t i c a l S p e e d of Figure 69. V e r t i c a l S p e e d A i r c r a f t During C 1 imb w i t h O n e A s a Funct ion of Takeoff I n o p e r a t i v e Engine A s a Func­ Weight of Passenger Air­ t i o n of F l i g h t S p e e d ( A i r c r a f t c r a f t ( A i r c r a f t w i t h Two w i t h Two E n g i n e s , G t o = 35 t , E n g i n e s , S p e c i f i c Loading 360 kg/m2, O n e E n g i n e Landing Gear Up, H = 900 m) lnoperat i v e , A v a i l a b l e Power 0.14 kg t h r u s t / k g W i gh t ) e I n c a s e o f an i n t e r r u p t e d t a k e o f f a t t h e s e p a r a t i o n speed V s e p cr,t h e braking d i s t a n c e w i l l a l s o be i n c r e a s e d ( p o i n t P ) and t h e a i r c r a f t w i l lr o l l beyond t h e end o f t h e a i r f i e l d . The b e s t c a s e i s e q u a l i t y of c r i t i c a l speed and s e p a r a t i o n speed, s i n c et h i s f a c i l i t a t e s p i l o t i n g o f t h e a i r c r a f t c o n s i d e r a b l y and makes i t p o s s i b l et o i n t e r r u p t t h e t a k e o f f s a f e l y r i g h t up t o t h e moment of s e p a r a t i o n o f t h eaircraft. Let u s now analyze t h e s e l e c t i o n o f a safe speed f o r c o n t i n u i n g o f t h et a k e o f f (Figure 6 8 ) . Usually a t speeds of 280-320 km/hr, t h e maximumv e r t i c a l speed i s achieved with t h e f l a p s i n t h e t a k e o f f p o s i t i o n .However, a c c e l e r a t i o n o f t h e a i r c r a f t from V = 220-260 km/hr t o a speed sePo f 280-320 km/hr r e q u i r e s a g r e a t d e a l o f time and l e n g t h e n s t h e t a k e o f fd i s t a n c e . Therefore, i n o r d e r t o avoid i n c r e a s i n g t h e t a k e o f f run l e n g t hu n n e c e s s a r i l y , l e a v i n g it w i t h i n l i m i t s o f 600-800 m , t h e s a f e t a k e o f f speedi s s e l e c t e d a s 10-15 km/hr g r e a t e r than t h e s e p a r a t i o n speed, i f t h i s w i l lprovide a climb t r a j e c t o r y angle of no l e s s t h a n 2.5% f o r an a i r c r a f t withl a n d i n g g e a r up. With an average a c c e l e r a t i o n o f 1 m/sec2, 3-4 s e c a r e94
  • 103. r e q u i r e d t o i n c r e a s e t h e speed o f t h e a i r c r a f t by 10-15 km/hr (2.8­4 . 2 m/sec). During t h i s t i m e , t h e a i r c r a f t can climb 5-7 m . The c r i t i c a l ­ /lo1speed of engine f a i l u r e f o r an a i r c r a f t with a given weight under given c o n c r e t e atmospheric c o n d i t i o n s f o r t h e balanced runway length h a s a unique value. However, i t i s known t h a t t h e engine t h r u s t depends s t r o n g l y on temperature of t h e surrounding a i r and atmospheric p r e s s u r e , and, f o r example, decreases below t h e s t a n d a r d t h r u s t with i n c r e a s i n g temperature, s o t h a t t h e excess a v a i l a b l e t h r u s t d e c r e a s e s . T h i s means t h a t t h e t a k e o f f run l e n g t h and t a k e o f f d i s t a n c e i n c r e a s e , t h e v e r t i c a l speed d e c r e a s e s (Figure 69), t h e angle of i n c l i n a t i o n o f t h e a i r c r a f t t r a j e c t o r y with a continued t a k e o f f w i t h one engine i n o p e r a t i v e d e c r e a s e s . I n o r d e r t o go beyond t h e l i m i t a t i o n with r e s p e c t t o t r a j e c t o r y i n c l i n ­a t i o n , t h e angle o f i n c l i n a t i o n of t h e f l a p s must be decreased, o r i f t h i si s i n s u f f i c i e n t , t h e t a k e o f f weight must b e decreased. The o p e r a t i n g i n s t r u c t i o n s of every a i r c r a f t include graphs andnomograms which can be used t o determine t h e t a k e o f f c h a r a c t e r i s t i c s i n caseo f engine f a i l u r e during t h e t a k e o f f run. For t h i s purpose, f i r s t of a l l ont h e b a s i s of t h e f a c t t h a t t h e t r a j e c t o r y i n c l i n a t i o n of a continued t a k e o f fshould b e no l e s s t h a n 2 . 5 % , t h e p e r m i s s i b l e t a k e o f f weight i s determinedf o r each s e l e c t e d f l a p angle and a c t u a l a i r temperature (Figure 7 0 ) . . Then,u s i n g t h e nomogram (Figure 71) f o r t h e same atmospheric c o n d i t i o n s and t h eweight which h a s been determined, t h e balanced runway length i s found(point K ) . Then, u s i n g t h e nonogram (of Figure 72), t h e c r i t i c a l enginef a i l u r e speed ( t a k e o f f i n t e r r u p t i o n ) i s found, a s w e l l a s t h e s a f e speed f o rcontinued t a k e o f f . Figure 72 shows a nomogram f o r determination o f t h ec r i t i c a l speed. The same form of nomogram as on Figure 72 i s c o n s t r u c t e d i no r d e r t o determine t h e s a f e speed f o r continued t a k e o f f , t a k e o f f run l e n g t h ,s e p a r a t i o n speed, e t c . The nomograms on Figures 70-72 correspond t o t h e norms of t h e ICAO.The arrows on t h e nomograms show t h e p a t h f o r determining d e s i r e d q u a n t i ­ties. P i l o t i n g of an a i r c r a f t with one engine i n o p e r a t i v e a f t e r s e p a r a t i o n .S e p a r a t i o n of an a i r c r a f t with one engine i n o p e r a t i v e occurs a t t h e samespeeds as with a l l engines o p e r a t i n g . The e f f e c t i v e n e s s of t h e a i l e r o n s i sdecreased. Therefore, t h e p i l o t should a c c e l e r a t e t h e a i r c r a f t t o a s a f espeed, exceeding t h e s e p a r a t i o n speed by 10-15 km/hr. This speed i s a l s o / l­ o2c a l l e d t h e b e s t t a k e o f f speed, s i n c e i t provides s u f f i c i e n t t r a n s v e r s ec o n t r o l l a b i l i t y and allows a climb t o b e performed a t V :V = 2 . 5 % . Y A c c e l e r a t i o n a f t e r s e p a r a t i o n should b e performed n e a r t h e ground,s i n c e t h e aerodynamic i n f l u e n c e of t h e s u r f a c e i s f a v o r a b l e and t h ei n d u c t i v e drag of t h e a i r c r a f t i s decreased. A t V + 10-15 km/hr with SePf l a p s d e f l e c t e d by 10-25", c1 = 7-9" and t h e aerodynamic q u a l i t y i s 12-13;t h e i n d u c t i v e d r a g ( c = 1.15-1.3) i s approximately equal t o one-half of t h e Y 95
  • 104. e n t i r e d r a g o f t h e a i r c r a f t . With q u a l i t y v a l u e s o f 12-13, t h e t h r u s t consumption of t h e a i r c r a f t i s always c o n s i d e r a b l y less t h a n t h e a v a i l a b l e t h r u s t and t h e a i r c r a f t can be e i t h e r a c c e l e r a t e d o r t r a n s ­ f e r r e d i n t o a climb. W can see from Figure 65 t h a t e f o r an a n g l e ci = l l " , t h e aero- SeP dynamic q u a l i t y of t h e a i r c r a f t K = 9 , while c o n s i d e r i n g t h e i n f l u ­ ence of t h e e a r t h it i s i n c r e a s e d t o 1 2 . A t 10-15 m , t h e i n f l u e n c e o f t h e e a r t h d e c r e a s e s s h a r p l y , and b y t h i s time t h e a i r c r a f t i s a l r e a d y f l y i n g a t t h e s a f e speed ( i n our example t h i s corresponds t o c1 = 8" and K = 9 ) . The a i r b o r n e s e c t o r of a i r c r a f t a c c e l e r a t i o n d u r i n g which it climbs t o 5-7 m, i s 600-800 m , and t h e v e r t i c a l speed V = 1.5- Y 2.5 m/sec (depending on atmospheric c o n d i t i o n s ) . Upon a c h i e v i n g t h e f i e l d temp., O C safe a l t i t u d e a f t e r acceleration, t h e l a n d i n g g e a r must be r a i s e d , i n order t o decrease t h e drag. Figure 70. Nomogram f o r 6-8 s e c a f t e r t h e landing Determination o f P e r m i s s i b l e g e a r b e g i n t o come up, t h e d r a g of Takeoff W e i g h t from Cond i t ion t h e a i r c r a f t i s decreased s i g n i f ­ of Product ion of T r a j e c t o r y i c a n t l y and t h e excess t h r u s t can I n c l i n a t i o n of 2.5% i n Con­ s u p p o r t a climb with h i g h e r v e r t i c a l t i n u e d Takeoff speed, i n c r e a s i n g t h e s a f e t y o f continuation of the f l i g h t . Therefore, i f t h e landing g e a r a r er a i s e d q u i c k l y , t h i s should be done d u r i n g t h e a c c e l e r a t i o n s e c t o r , althought h e f l y i n g a l t i t u d e will s t i l l b e q u i t e low. Raising t h e landing g e a r /lo3i n c r e a s e s t h e v e r t i c a l speed by 0.5-1.0 m/sec, i . e . , t h e climb w i l l occur a t ­V = 2-2.7 m/sec (depending on t h e a i r c r a f t w e i g h t ) . Y Climbing up t o 100 m a l t i t u d e should b e continued a t c o n s t a n t speed.A t t h i s a l t i t u d e , t h e a i r c r a f t can b e a c c e l e r a t e d t o t h e p e r m i s s i b l e f l i g h tspeed with mechanical d e v i c e s r e t r a c t e d , and t h e f l a p s can b e r a i s e d . I no r d e r t o avoid a l o s s i n a l t i t u d e , it i s recommended t h a t t h e f l a p s b er a i s e d i n two t o t h r e e p a r t i a l movements. A f t e r t h e f l a p s a r e r a i s e d , t h eengines should b e s e t i n t h e nominal regime. The d i r e c t i o n of f l i g h t can bemaintained with one engine i n o p e r a t i v e by d e f l e c t i o n of t h e p e d a l s andc r e a t i o n of a 2-3-degree bank toward t h e engine s t i l l o p e r a t i n g .96
  • 105. E Figure 71. Nomogram f o r Determination of Balanced Runway Length Field TemD.9 OC Takeoff w t . , T Flgure 7 2 . Nomogram f o r Determination o f C r i t i c a l E n g i n e Failure Speed F l i g h t t r a j e c t o r y with one engine i n o p e r a t i v e . A s we noted above, t h e /lo4 ­angle of i n c l i n a t i o n of t h e t r a j e c t o r y during t h e f l i g h t s e c t o r a f t e r t h elanding gear a r e r a i s e d should be no l e s s t h a n 1 30 min, i . e . , 2 . 5 % .However, depending on t h e c o n c r e t e c o n d i t i o n s i n which t h e a i r c r a f t i s beingo p e r a t e d , t h i s t r a j e c t o r y i n c l i n a t i o n may vary. Under s t a n d a r d c o n d i t i o n s , t h e a i r c r a f t h a s g r e a t v e r t i c a l speed, s ot h a t it i s not d i f f i c u l t t o p r o v i d e t h e necessary t r a j e c t o r y a n g l e . Theproblem i s somewhat more d i f f i c u l t under design c o n d i t i o n s , and p a r t i c u l a r l ya t high a i r temperatures, a t which t h e v e r t i c a l speed d u r i n g t a k e o f f withone engine i n o p e r a t i v e i s s h a r p l y decreased. Usually, t h e f i r s t marker beacon i s l o c a t e d 900-1000 m from t h e runway,and has a tower 10-12 m h i g h . I f t h e takeoff i s continued, t h e a i r c r a f t
  • 106. w i l l f l y over thTs p o i n t w i t h l a n d i n g g e a r almost up a t 90-25 m. E r r o r s i np i l o t i n g t e c h n i q u e s and i n s t r u m e n t a l e r r o r s , as w e l l a s f a i l u r e t o f o l l o wt h e f l y i n g i n s t r u c t i o n s may r e s u l t i n reduced a l t i t u d e of f l i g h t over t h i sbeacon. I t i s t h e r e f o r e r e q u i r e d t h a t t h e approach t o t h e runway b e open i no r d e r t o avoid c o l l i s i o n of a i r c r a f t w i t h o b s t a c l e s i n c a s e o f a continuedtakeoff . S7. Influence of Various Factors on Takeoff Run L e n g t h During t h e p r o c e s s o f f l y i n g o p e r a t i o n s , t h e l e n g t h o f t h e t a k e o f f r u nmay d i f f e r from t h e v a l u e s c a l c u l a t e d f o r s t a n d a r d c o n d i t i o n s under t h ei n f l u e n c e of changes i n engine t h r u s t , a i r c r a f t weight, temperature,d e n s i t y and p r e s s u r e of t h e a i r , p o s i t i o n of t h e f l a p s , speed and d i r e c t i o nof t h e wind. Engine t h r u s t h a s a c l e a r l y expressed dependence on engine r o t a t i o nspeed. For example, i f t h e r o t a t i n g speed i s decreased from t h e t a k e o f f t ot h e nominal speed, t h e t h r u s t i s decreased by 5-7% ( s e e F i g u r e 5 2 ) .T h e r e f o r e , a d e c r e a s e i n r o t a t i n g speed may i n c r e a s e t h e t a k e o f f r u n l e n g t hc o n s i d e r a b l y . During t a k e o f f a t t h e nominal regime, t h e t a k e o f f run l e n g t his i n c r e a s e d by 10-12%, and f l i g h t s a f e t y i n c a s e of an engine f a i l u r e i sdecreased. The t a k e o f f weight i n f l u e n c e s t h e t a k e o f f r u n l e n g t h as f o l l o w s :1) with an i n c r e a s e i n weight, t h e s e p a r a t i o n speed i n c r e a s e s ; 2) w i t h t h esame engine t h r u s t , an i n c r e a s e i n weight l e a d s t o a d e c r e a s e i n perform­ance, and consequently t o a d e c r e a s e i n a c c e l e r a t i o n d u r i n g t h e takeoff run.As a r e s u l t , t h e l e n g t h o f t h e r u n i s i n c r e a s e d . The a i r temperature i n f l u e n c e s t h e t a k e o f f run l e n g t h i n two d i r e c ­t i o n s . F i r s t of a l l , t h e a i r temperature i n f l u e n c e s t h e t h r u s t of t h eengine, and, secondly, i t i n f l u e n c e s t h e t r u e s e p a r a t i o n speed. I n c r e a s i n gt h e temperature aauses a d e c r e a s e i n t h r u s t , and consequently o fa c c e l e r a t i o n d u r i n g t h e t a k e o f f r u n , which i n c r e a s e s t h e t a k e o f f run l e n g t h .Also, i n c r e a s i n g t h e temperature causes a d e c r e a s e i n d e n s i t y a n d ,consequently, an i n c r e a s e i n t h e s e p a r a t i o n speed. For. example, an i n c r e a s e /lo5i n a i r temperature of 10" i n c r e a s e s t h e t a k e o f f run l e n g t h by 6 - 7 % . - P r e s s u r e and d e n s i t y of t h e a i r . I f t h e a i r temperature i s c o n s t a n t ,b u t t h e p r e s s u r e changes, t h e d e n s i t y of t h e a i r w i l l a l s o change; a s t h ep r e s s u r e changes, t h e d e n s i t y changes by t h e same f a c t o r , s i n c e p = o 0473 f,98
  • 107. I where p i s t h e a i r p r e s s u r e , mm Hg; T = 273 + t i s t h e a b s o l u t e temperature; t i s t h e temperature of t h e surrounding a i r i n degrees Centigrade. This formula allows us t o determine t h e d e n s i t y i n case o f a simul­ taneous change of t e m p e r a t u r e and a i r p r e s s u r e . A d e c r e a s e i n d e n s i t y l e a d s t o an i n c r e a s e i n t h e s e p a r a t i o n speeds and a d e c r e a s e i n t h e t h r u s t o f t h e engine due t o t h e d e c r e a s e i n t h e a i r flow by weight through t h e engine. With d e c r e a s i n g t h r u s t , t h e mean a c c e l e r a t i o n j d e c r e a s e s and, i n t h e x av f i n a l a n a l y s i s , t h e t a k e o f f run l e n g t h i n c r e a s e s . A d e c r e a s e i n p r e s s u r e of 10 mm Hg l e a d s t o an i n c r e a s e i n t a k e o f f run l e n g t h o f 3-4%. Thus, d u r i n g t a k e o f f under nonstandard c o n d i t i o n s ( t = +3OoC and p = 730 mm Hg) t h e t a k e o f f r u n l e n g t h i s i n c r e a s e d by 30-32%. Wind speed and d i r e c t i o n . The l e n g t h of t h e t a k e o f f run with a wind i s determined by t h e f o l l o w i n g formula: where W i s t h e head wind component o f t h e wind ( t h e "plus s i g n i s taken with a t a i l wind, "minus" - - with a head wind). The t a k e o f f , a s a r u l e , i s performed a g a i n s t t h e wind, s o t h a t t h e run l e n g t h and t a k e o f f d i s t a n c e a r e minimal. S e p a r a t i o n occurs a t a given a i r speed V SeP . With a head wind, t h e s e p a r a t i o n speed of t h e a i r c r a f t r e l a t i v e t o t h e ground i s decreased by t h e v a l u e of t h e wind speed. T h e r e f o r e , l e s s time i s r e q u i r e d f o r a t a k e o f f run with a head wind t h a n i n calm a i r , and t h e t a k e o f f run l e n g t h i s decreased; whileewith a t a i l wind i t i s i n c r e a s e d . F o r example, i f t h e head wind speed i s 5 m/sec (18 km/hr), t h e a i r c r a f t need b e a c c e l e r a t e d t o only 2 2 2 km/hr ground speed, a t which time t h e a i r speed w i l l be 240 km/hr, i . e . , t h e s e p a r a t i o n speed i s reached, and t h e t a k e o f f run i s s h o r t e n e d . A headwind o f 5 m/sec decreases t h e t a k e o f f run length by an average of 15-17%, while a t a i l wind of t h i s same speed i n c r e a s e s t h e l e n g t h by 18-20%. When t a k i n g o f f w i t h a s i d e wind, t h e a i r c r a f t t e n d s t o t u r n i n t o t h e wind, p a r t i c u l a r l y during a c c e l e r a t i o n with t h e f r o n t landing g e a r up. The reason f o r t h i s r o t a t i o n is t h e f a c t t h a t a i r c r a f t with t u r b o j e t engines have l a r g e v e r t i c a l t a i l s u r f a c e a r e a , l o c a t e d a t a c o n s i d e r a b l e d i s t a n c e from t h e main landing g e a r . A q u a n t i t a t i v e e s t i m a t e of t h e i n f l u e n c e o f v a r i o u s f a c t o r s on t h e ­ /lo6 l e n g t h o f t h e t a k e o f f run can be made u s i n g nomograms, w i t h which t h e p i l o t can determine t h e t a k e o f f r u n l e n g t h under t h e c o n c r e t e t a k e o f f c o n d i t i o n s involved.
  • 108. 98. Methods of Improving Takeoff C h a r a c t e r i s t i c s As we analyzed above, t h e l e n g t h .of t h e t a k e o f f r u n depends on t h es e p a r a t i o n speed and a c c e l e r a t i o n d u r i n g t h e t a k e o f f run. I n t u r n , t h es e p a r a t i o n speed depends on t h e s p e c i f i c loading p e r 1 m2 o f wing a r e a andC while t h e a c c e l e r a t i o n depends on t h e excess t h r u s t a v a i l a b l e . Y sep’ A decrease i n s p e c i f i c loading on t h e wing i s t h e most e f f e c t i v e methodo f decreasing V and Ltor. However, t h i s always i n v o l v e s a d e c r e a s e i n sePt h e u s e f u l weight c a r r i e d , s i n c e with t h e s u r f a c e area of t h e wing c o n s t a n t ,a decrease i n t a k e o f f weight can b e achieved only by d e c r e a s i n g t h e u s e f u lload. A decrease i n t h e weight c a r r i e d i n a passenger a i r c r a f t means ad e c r e a s e i n o p e r a t i o n a l economy. Therefore, t h i s means o f decreasing t h et a k e o f f run length i s used t o a l i m i t e d e x t e n t , p a r t i c u l a r l y s i n c e t h etendency t o u s e t h e maximum p o s s i b l e f l i g h t range r e q u i r e s an i n c r e a s e i ns p e c i f i c loading on t h e wing. The most a c c e p t a b l e method of d e c r e a s i n g t h e t a k e o f f run length i s ani n c r e a s e i n t h e l i f t i n g f o r c e of t h e wing u s i n g t h e wing mechanisms. A s w e know, t h e main means of mechanization o f t h e wing c o n s i s t s of t h ef l a p s . A l l modern j e t passenger a i r c r a f t have extendable ( s l i d i n g ) s l i tt y p e wing f l a p s 1 . The ef?�ectiveness o f t h e f l a p s (magnitude o f i n c r e a s e i nA c ) i n c r e a s e s as t h e s l i d e (outward movement) of t h e f l a p s and angle o f Yf l a p d e f l e c t i o n a r e i n c r e a s e d . With low angles o f f l a p d e f l e c t i o n , t h el i f t i n g f o r c e i s p r i m a r i l y i n c r e a s e d without any e s s e n t i a l i n c r e a s e i n drag,and t h e aerodynamic q u a l i t y i s decreased o n l y i n s i g n i f i c a n t l y . These anglescan be used f o r t a k e o f f d u r i n g high temperature c o n d i t i o n s , when t h e lengtho f t h e t a k e o f f run can b e r e t a i n e d w i t h i n t h e r e q u i r e d l i m i t s i n s p i t e oft h e decrease i n q u a l i t y . The lower drag during t h e t a k e o f f run allows aconsiderable a c c e l e r a t i o n t o b e achieved. Usually, attempts a r e made t o produce t h e maximum a i r c r a f t aerodynamicq u a l i t y with t h e f l a p s d e f l e c t e d t o t h e t a k e o f f p o s i t i o n , s i n c e t h e q u a l i t ydetermines t h e t h r u s t consumed and t h e excess t h r u s t which a c c e l e r a t e s t h ea i r c r a f t during t h e t a k e o f f run. For a i r c r a f t with t a k e o f f weights of55-80 and aerodynamic q u a l i t y o f 12-14, a t h r u s t o f consumption of 5000­6000 kg i s r e q u i r e d , and with a t o t a l a v a i l a b l e t h r u s t o f 13,000-28,000 kg,t h e excess t h r u s t provides r a p i d (25-30 sec) a c c e l e r a t i o n of t h e a i r c r a f t t o /= t h e s e p a r a t i o n speed; t h e t a k e o f f run l e n g t h i s 1000-1200 m . Long experience of passenger a i r c r a f t o p e r a t i o n h a s proven t h e u s e f u l ­ness of t h e method o f d e c r e a s i n g t a k e o f f run l e n g t h by i n c r e a s i n g t h ea v a i l a b l e power ( g r e a t e r excess t h r u s t ) . The Boeing 727 a i r c r a f t c a r r i e s a . .I S M Yege r-, Proyektirovaniye Passazhirskikh Reaktivnikh SumoZetov[Design of Passenger J e t A i r c r a f t ] , Mashinostroyeniye P r e s s , 1964.100
  • 109. t h r e e - s l i t f l a p (Figure 73) which, t o g e t h e r with t h e s l i t t y p e s l a t andKruger s l a t ( f r o n t f l a p ) makes i t p o s s i b l e t o produce c = 2 . 7 with t h e Y m amaximum angle o f f l a p d e f l e c t i o n . T h i s i n t u r n allows r a t h e r high v a l u e s ofc t o b e achieved with lesser a n g l e s of d e f l e c t i o n , corresponding t o t h e Yt a k e o f f p o s i t i o n of t h e f l a p s ( c = 1.6-1.8). Y sep aJ - . =% - ti . % Figure 73. Diagram of Extendable Flaps: a , S i n g l e - s l i t (flow s e p a r a t i o n b e g i n s a t 6 3 = 35­ 4 0 " ) ; b , c , M u l t i - s l i t (flow s e p a r a t i o n delayed t o 6 3 - 50-60") Th.e m u l t i - s l i t f l a p , due t o t h e i n c r e a s e i n c u r v a t u r e of t h e p r o f i l eand t h e pumping e f f e c t of t h e s l i t s , delays flow s e p a r a t i o n t o l a r g e r anglesof a t t a c k , which allows r a t h e r high values of c t o be produced duringt a k e o f f and landing. The i n c r e a s e i n t h e l i f t i x g f o r c e of t h e wing withf l a p s down r e s u l t s from a change i n c i r c u l a t i o n around t h e wing withi n c r e a s i n g flow speed over t h e upper s u r f a c e of t h e wing. However, a t l a r g e angles of a t t a c k , flow s e p a r a t i o n a t t h e uppers u r f a c e begins a t t h e f r o n t of t h e wing p r o f i l e , which i s combatted u s i n gf r o n t s l a t s o r d e f l e c t a b l e leading edges of t h e wing. S l i t t y p e s l a t s (Figure 7 4 , a ) , which allow a i r t o flow through t h e f r o n t s l i t , i n t e n s i f yt h e boundary l a y e r behind t h e peak of r a r e f a c t i o n on t h e wing p r o f i l e andi n c r e a s e t h e energy of t h e flow, s o t h a t s e p a r a t i o n of t h e flow i s delayeda t high angles o f a t t a c k . When Kruger s l a t s a r e opened (Figure 74, c ) t h e e f f e c t i v e aerodynamicc u r v a t u r e of t h e p r o v i l e i s increased i n t h e f r o n t p o r t i o n , as a r e s u l t o fwhich t h e load-bearing c h a r a c t e r i s t i c s of t h e p r o f i l e a r e improved. Since / l­ o8t h i s i n c r e a s e s t h e s u c t i o n f o r c e p u l l i n g forward, t h e drag of t h e wing witht h e f r o n t s l a t open i n c r e a s e s only s l i g h t l y , and t h e aerodynamic q u a l i t yof t h e wing remains e s s e n t i a l l y unchanged. 10 1
  • 110. The same effect can a l s o b e achieved by t i l t i n g t h e forward edge o f t h e wing downward (Figure 74, b ) . Thus, t h e r e i s a r a t h e r l a r g e number o f methods o f i n c r e a s i n g c and, Y consequently, d e c r e a s i n g t h e s e p a r a t i o n speed and l e n g t h o f t h e a i r c r a f t takeoff run. One promising method i s t h e usage o f t h e g a s streams from t h e j e te n g i n e s . Experiments have shown t h a t i f t h e gas stream i s d i r e c t e d down­ward, i t can supplement t h e l i f t i n g f o r c e of t h e wings. As a r e s u l t , t h ea i r c r a f t can be s e p a r a t e d from t h e e a r t h almost without a t a k e o f f r u n .During t h e l a n d i n g , t h i s same gas stream c a r r i e s a p o r t i o n of t h e f l y i n gweight o f t h e a i r c r a f t and allows t h e a i r c r a f t t o be landed a t low speeds PI , Slat UP Slat out 1 - Figure 7 4 . Diagram of S l i t T y p e Front S l a t ( a ) , D e f l e c t a b l e Front P o r t i o n of A i r c r a f t Wing of "Trident" A i r c r a f t ( b ) and Kruger Front S l a t ( c ) The r e a c t i o n f l a p (Figure 7 5 ) , a device c o n s i s t i n g o f a s l i t along t h er e a r edge o f t h e wing through which a stream o f a i r flows a t a c e r t a i n angle 6 t o t h e chord, d r i v e n by t h e compressor of t h e j e t e n g i n e , i s q u i t e important f o r heavy t r a n s p o r t a i r c r a f t . This d e v i c e changes t h e n a t u r e offlow around t h e wing, causing a s i g n i f i c a n t i n c r e a s e i n l i f t i n g f o r c e . Thev a l u e o f c i n c r e a s e s due t o t h e pumping o f gas j e t s i n t h e boundary l a y e r Yfrom t h e upper s u r f a c e of t h e wing and t h e r e a c t i o n o f t h e outflowing gasstream. The f o r c e o f t h e r e a c t i o n of t h e s t r e a m i s d i v i d e d i n t o componentsN and N x . The component N i n c r e a s e s t h e l i f t o f t h e wing, while N Y Y Xproduces a d d i t i o n a l t h r u s t . The l i f t i n g f a c t o r o f a wing with a r e a c t i v ef l a p i s equal t o t h e sum of t h e l i f t f a c t o r s of t h e aerodynamic e f f e c t o f /- 109t h e flow o v e r t h e wing and from t h e r e a c t i o n of t h e outflowing g a s e s .102
  • 111. The usage o f t h e r e a c t i v e f l a p allows a broad range o f f l i g h t speeds t ob e used and s i m p l i f i e s t h e problem o f t a k e o f f and l a n d i n g . Systems a r e known f o r c o n t r o l l i n g t h e boundary l a y e r , which e i t h e rremove o r i n j e c t a i r . A s w e know, flow s e p a r a t i o n o f t h e wing due t o ani n c r e a s e d boundary l a y e r t h i c k n e s s d e c r e a s e s c o e f f i c i e n t c By u s i n g Yremoval o r i n j e c t i o n i n t h e boundary l a y e r , t h e beginning of s e p a r a t i o n canb e delayed t o h i g h e r a n g l e s of a t t a c k , which makes it p o s s i b l e t o i n c r e a s et h e l i f t of t h e wing, d e c r e a s e t h e t a k e o f f and l a n d i n g speed o f t h e a i r c r a f tand reduce t h e t a k e o f f and landing r u n l e n g t h (and consequently t h e l e n g t hof t h e runway). F o r example, a boundary l a y e r blowing d e v i c e decreases t h elanding speed by 20 - 25%. This t y p e of boundary l a y e r c o n t r o l system (BLAC)was used on t h e C-130C "Hercules" heavy turboprop t r a n s p o r t . With t h i ssystem, t h e l i f t i n g f o r c e o f t h e wing i s i n c r e a s e d more t h a n when t h eboundary l a y e r is drawn o f f b y s u c t i o n . Four gas t u r b i n e r e a c t i o n enginesl o c a t e d i n two gondolas beneath t h e wing were used t o supply compressed a i rt o t h e system. The a i r i s c o l l e c t e d i n t h e r e a r p o r t i o n s of t h e gondolaand f e d by f o u r c e n t r i f u g a l compressors t o a network o f a i r l i n e s (commonsystem f o r wing and t a i l s u r f a c e ) . Many small l i n e s connect t h e maind i s t r i b u t i n g l i n e with a common c o l l e c t i n g chamber, from which t h e a i r i se j e c t e d on t h e upper s u r f a c e s of t h e f l a p s and a i l e r o n s through s l i t s . Thelanding speed of- t h e a i r c r a f t was decreased from 170 t o 110 km/hr, while t h et a k e o f f d i s t a n c e was reduced from 1280 t o 853 m , and t h e l a n d i n g d i s t a n c ewas reduced from 427 t o 250 m . D i s t r i b u t i ng Figure 75. Reactive Flap on Wing ( a ) and Air F e e d System f o r Boundary Layer I n j e c t i o n a t Wing Surface ( b ) A BLAC system i s a l s o i n s t a l l e d on t h e English Blackburn NA39"Buckaneer" m i l i t a r y t u r b o j e t a i r c r a f t . The experimental Boeing 707a i r c r a f t used a system f o r boundary l a y e r i n j e c t i o n i n t h e a r e a of t h e f l a p su s i n g a i r taken from t h e engine compressors. During t h e t e s t s , a d e c r e a s ei n l a n d i n g speed from 220-240 t o 150-160 km/hr was achieved, i . e . , by ­ /110approximately 30%. 103 I
  • 112. Turbofan engines expand t h e p o s s i b i l i t y f o r u s i n g BLAC i n passenger j e ta i r c r a f t , s i n c e t h e removal of c o n s i d e r a b l e masses of a i r from t h e o u t e rchannel does not d i s r u p t t h e o p e r a t i o n o f t h e engine. The placement of a s l a t on t h e f r o n t edge of t h e wing and i n j e c t i o n o ft h e boundary l a y e r a t t h e f l a p s and a i l e r o n s can produce a c o n s i d e r a b l edecrease i n landing and t a k e o f f speeds and allow t h e l e n g t h of runways t o bedecreased by 30-40%. The placement of a s l a t on t h e wing o f a j e t a i r c r a f t ,i n a d d i t i o n t o decreasing t a k e o f f and landing speeds, a l s o improves i t smaneuverability a t high speeds, s i n c e i t d e l a y s t h e p o i n t o f flow s e p a r a t i o nt o higher angles o f a t t a c k . P r a c t i c e has shown t h a t s l a t s can be used up t oM = 0.9. A laminar flow c o n t r o l system i s i n t h e s t a g e of development. I t hasbeen experimentally e s t a b l i s h e d t h a t t h e t r a n s i t i o n o f laminar flow t ot u r b u l e n t flow can be prevented by sucking t h e slow, t u r b u l i z a t i o n - i n c l i n e dboundary l a y e r away from t h e wing s u r f a c e through a l a r g e number of t h i ns l o t s c u t i n t h e wing covering. This i s c a l l e d laminar flow c o n t r o l .I n v e s t i g a t i o n s performed i n t h e USA have shown t h a t t h i s method can.i n c r e a s e t h e p r o f i l e d r a g c o e f f i c i e n t of a swept wing t o a v a l u e n e a r t h edrag c o e f f i c i e n t of a p l a t e with laminar flow, i . e . , decrease i t by approx­imately s i x t i m e s . Laminar flow c o n t r o l by sucking away t h e boundary l a y e r , n a t u r a l l y ,i n c r e a s e s t h e load-carrying c a p a c i t y of t h e wing. However, t h e usage o f l f ct o i n c r e a s e c alone i s not expedient, s i n c e t h i s problem can be more Ysimply solved by i n j e c t i o n i n t o t h e boundary l a y e r . The production of highaerodynamic q u a l i t y ( i n c r e a s e d by a f a c t o r of 1 . 5 times) b o t h during t a k e o f fand during f l i g h t , allows t h e t a k e o f f and o t h e r c h a r a c t e r i s t i c s of t h ea i r c r a f t t o be improved. C a l c u l a t i o n s have shown t h a t f o r an a i r c r a f t l i k et h e Lockheed C-141 with a t a k e o f f weight of about 120 t and a c r u i s i n g speedo f 850 km/hr, laminar flow c o n t r o l can i n c r e a s e t h e f l i g h t range by 30-33%.With t h i s f l i g h t range, t h e t a k e o f f weight of t h e a i r c r a f t can be decreasedby 18-20% by decreasing t h e f u e l r e s e r v e s c a r r i e d . In conclusion f o r t h i s c h a p t e r , we n o t e t h a t an improvement of t a k e o f f( a s well as landing) c h a r a c t e r i s t i c s of passenger j e t a i r c r a f t - - decreasedt a k e o f f run l e n g t h and s e p a r a t i o n speed -- makes i t p o s s i b l e t o expand t h enetwork of a i r f i e l d s and connect a r e a and a d m i n i s t r a t i v e c e n t e r s . I t i salways e a s i e r t o f i n d a r e a s f o r small a i r f i e l d s t h a n f o r l a r g e a i r f i e l d s . /111 -B e t t e r t a k e o f f and landing c h a r a c t e r i s t i c s of a i r c r a f t w i l l a l s o provide alower "minimum weather" (see Chapter I X , S8). A t t h e p r e s e n t time, c o n s i d e r a b l e a t t e n t i o n i s being turned t o t h ec r e a t i o n of s p e c i a l passenger j e t a i r c r a f t with s h o r t t a k e o f f and landingcharacteristics. ~ _ -_ S. M. Yeger , Proyektirovaniye Passazhirskikh Reaktivnykh ShoZetov[Design of Passenger J e t A i r c r a f t ] , Mashinostroyeniye P r e s s , 1964.104
  • 113. I I Chapter V I . Climbing§l. Forces A c t i n g on A i r c r a f t Climbing refers t o s t r a i g h t and even (constant v e l o c i t y ) f l i g h t of ana i r c r a f t i n an ascending t r a j e c t o r y . During t h e climb, t h e f o r c e s a c t i n g ont h e a i r c r a f t i n c l u d e t h e f o r c e o f g r a v i t y G , t h e f o r c e of t h e t h r u s t P,l i f t i n g f o r c e Y and drag Q (Figure 7 6 ) . Forces Y and Q a r e a r b i t r a r i l y considered t o be a p p l i e d t o t h ec e n t e r of g r a v i t y o f t h e a i r c r a f t , although t h e y a r e a c t u a l l y a p p l i e d a t t h ec e n t e r of p r e s s u r e . This a r b i t r a r i n e s s i s p e r m i t t e d f o r f o r c e s Y and Q,s i n c e t h e a i r c r a f t i s balanced by d e f l e c t i o n of t h e e l e v a t o r . Force P f o rs i m p l i c i t y of d i s c u s s i o n w i l l b e considered t o b e a p p l i e d through t h ec e n t e r of g r a v i t y . The d i r e c t i o n o f t h e e f f e c t of t h e f o r c e s i s as follows:f o r c e G a c t s v e r t i c a l l y downward, f o r c e P - - forward a t a c e r t a i n angle f3t o t h e d i r e c t i o n of f l i g h t , f o r c e Y - - p e r p e n d i c u l a r t o t h e d i r e c t i o n off l i g h t and f o r c e Q - - o p p o s i t e t o t h e d i r e c t i o n of f l i g h t . Figure 76. Diagram of Forces Acting on A i r c r a f t i n S t a b l e C 1 i m b : 1 , C l i m b t r a j e c t o r y ; 2 , Longitudinal a x i s of a i r c r a f t ; 3 , Chord o f w i n g The f l i g h t t r a j e c t o r y o f t h e a i r c r a f t is i n c l i n e d t o t h e h o r i z o n t a l a ta c e r t a i n angle 0 , c a l l e d t h e climbing angle. The following dependencee x i s t s between t h e p i t c h a n g l e 9, t h e climbing a n g l e 0, angle o f a t t a c k aand a n g l e of wing s e t t i n g ( a n g l e i n c l u d e d between l o n g i t u d i n a l a x i s of /112a i r c r a f t and wing chord) : 9 + 4 = 0 + a. For modern a i r c r a f t , a n g l e4 = 1-3", angle a = 2 . 5 - 5 " , t h e p i t c h angle ( t h e angle included between t h ea x i s of t h e f u s e l a g e and t h e h o r i z o n t a l ) i n f l i g h t can b e determined u s i n gt h e gyrohorizon. During a climb, t h e climbing angle i s less t h a n t h e p i t c hangle. 105
  • 114. Force P does n o t correspond t o t h e f l i g h t t r a j e c t o r y , forming with it ac e r t a i n angle 8 . The magnitude o f t h i s a n g l e i s i n f l u e n c e d .by t h e angle ofmotor s e t t i n g r e l a t i v e t o t h e l o n g i t u d i n a l a x i s o f t h e a i r c r a f t . As w ee x p l a i n e d e a r l i e r ( c h a p t e r 4, 58) t h e a n g l e of motor s e t t i n g may b e fromzero t o f i v e d e g r e e s . Angle B can b e determined as f o l l o w s . L e t us a n a l y z et h e climb d u r i n g t h e f i r s t moments a f t e r t a k e o f f . Let us assume t h a t f o r c eP forms an a n g l e o f 5" w i t h t h e l o n g i t u d i n a l axis o f t h e a i r c r a f t ,t h e v e l o c i t y i n t h e climb i s 520 km/hr, and t h e v e r t i c a l speed i s 16 m/sec.The climbing a n g l e can be determined as f o l l o w s (Figure 76):i . e . , 0 = 6.5". Then p i t c h a n g l e 4 = 0 .t ci - 4 = 6.5" + 3" - 1" = 8.5" (weassume ci = 3" f o r Vr = 520 km/hr, and t h e a n g l e of wing s e t t i n g $ = 1").S i n c e t h e d i f f e r e n c e between angles 4 and 0 f o r t h i s c a s e i s 2 " , f o r c e Pcorresponds t o t h e climbing t r a j e c t o r y , a n g l e B = 7". I n t h i s c a s e , t h ecomponent P s i n B i s added t o t h e l i f t i n g f o r c e . The magnitude o f t h i scomponent may b e r a t h e r high. For t h e q u a n t i t i e s h e r e b e i n g analyzed i n ana i r c r a f t with f o u r motors with a t h r u s t of each motor o f 8,000 kg, w eproduce P s i n B = 32,000*0.122 = 3900 kg. This f o r c e i s added t o t h e l i f tY = 80-85 t . As t h e a l t i t u d e i n c r e a s e s , t h e v e r t i c a l speed d e c r e a s e s , b u t t h e t r u ev e l o c i t y i n t h e climb i n c r e a s e s . Therefore, t h e l i f t a n g l e i s c o n t i n u a l l ydecreased. W can t h e r e f o r e w r i t e t h e f o l l o w i n g two e q u a t i o n s f o r a s t a b l e eclimb : Y=G COS 9; P=Qf G sin 0.W can see from t h e f i r s t e q u a t i o n t h a t t h e l i f t d u r i n g a climb e q u a l i z e s eonly a p o r t i o n o f t h e weight of t h e a i r c r a f t . The o t h e r p o r t i o n of t h ea i r c r a f t weight (G s i n 0) i s balanced by t h e motor t h r u s t . For example,f o r an a i r c r a f t weighing 38 t with a climbing angle 0 = 7 " , componentG s i n 0 = 38,000-0.122 = 4630 kg, and f o r an a i r c r a f t weighing 80 t t h i sf i g u r e i s 9770 kg. If t h e a v a i l a b l e engine t h r u s t f o r an a i r c r a f t with a t a k e o f f weight of38 t i s 6700-7000 kg i n t h e nominal o p e r a t i n g mode ( n e a r t h e e a r t h ) , moret h a n one h a l f o f t h i s t h r u s t i s expended t o b a l a n c e t h e weight o f t h ea i r c r a f t , while t h e remaining t h r u s t is expended i n overcoming drag. Theclimbing a n g l e 0 can a l s o b e determined from t h e second f o r c e equation:106
  • 115. I /113 c _ - where P - Q = AP is t h e excess t h r u s t ; P is t h e t h r u s t f a c t o r of t h e a i r c r a f t :t h e r a t i o o f engine t h r u s t t o a i r c r a f t weight; Q/G i s a q u a n t i t y i n v e r s e toquality. A t climbing angles of 6-8, t h e v a l u e o f cos 0 1, and t h e f i r s t equation can b e w r i t t e n as follows: In o r d e r t o determine a n g l e 0, w e must u s e t h e Zhukovskiy curves f o r consumed and a v a i l a b l e t h r u s t . Figure 77 shows t h e d e f i n i t i o n of APmax, a t which t h e maximum climbing angle i s achieved. The maximum excess t h r u s t is produced a t t h e m o s t f a v o r a b l e f l i g h t v e l o c i t y , corresponding t o t h e maximum aerodynamic q u a l i t y of t h e a i r c r a f t and t h e s t e e p e s t climbing angle. For a i r c r a f t with s p e c i f i c loads of 350-370 kg/m2, t h e most s u i t a b l e speed i s 360-370 km/hr, f o r s p e c i f i c loads of 500-550 kg/m2 - - 400-450 km/hr. The excess t h r u s t produced under t h e s e c o n d i t i o n s a t nominal engine o p e r a t i o n w i l l provide a climbing angle 0 = 6-8. 52. Determination o f Most S u i t a b l e C1 imbing Speed The v e r t i c a l speed i n a climb i s determined by t h e formula V = V s i n 0. Y Replacing s i n 0 with t h e excess t h r u s t and weight (we know from aerodynamics t h a t AP/G = s i n 0, we produce VAP V Y = 7 m/sec F i g u r e 77. Determination o f Maximum Excess Thrust U s i n g Zhukovskiy Curves I n o r d e r t o produce t h e maximum r a t e of a l t i t u d e i n c r e a s e ( s i n c e it i s t h i s q u a n t i t y , not t h e climbing angle which i s of t h e g r e a t e s t p r a c t i c a l i n t e r e s t ) , w e must know t h e maximum value of t h e product APV, which r e p r e s e n t s t h e excess power: AN = APV. 107
  • 116. For t u r b o j e t a i r c r a f t , t h e maximum v a l u e s of t h e product APV kg*m/sec i sdetermined, and t h e v e r t i c a l v e l o c i t i e s are c a l c u l a t e d (Figure 78). I f we have t h e maximum v a l u e s of t h e product APV/3.6(kg-m/sec), we can /114determine t h e maximum V f o r v a r i o u s weights. Y The v e l o c i t y along t h e t r a j e c t o r y a t which t h e maximum r a t e o f a l t i t u d ei n c r e a s e is achieved i s c a l l e d t h e climbing speed V I t i s higher than t h e clspeed a t s t e e p e s t climb which, as w e showed i n t h e preceding paragraph, c o r r e ­sponds t o t h e most s u i t a b l e a i r c r a f t v e l o c i t y (maximum q u a l i t y ) . The climbing speed can be e a s i l y determined a l s o u s i n g Zhukovskiy curvesf o r power consumed and a v a i l a b l e (Figure 79) ( t h e a v a i l a b l e t h r u s t power wasanalyzed i n Chapter IV,§7, and t h e graph of power consumption f o r v a r i o u sf l i g h t a l t i t u d e s i s c o n s t r u c t e d l i k e t h e graph f o r t h r u s t consumed). I n o r d e rt o do t h i s , we must draw a tangent p a r a l l e l t o l i n e N o f power t o t h e curve Pf o r power consumed. A t t h e p o i n t of c o n t a c t , t h e excess AN = PAV and maxv e l o c i t y corresponding t o t h i s excess power are determined. k g , m/se_c f 885000 825000 Figure 78. Excess Power Figure 79. Zhukovskiy As a Function of F l i g h t Curves f o r Power Velocity ( G t L = 52 T , spec i f i c 1 oad 390 kg/m2) F o r a i r c r a f t with wings swept a t 30-35", t h e maximum r a t e o f a l t i t u d ei n c r e a s e i s produced f o r p r a c t i c a l l y a l l t a k e o f f weights ( f r o m t h e maximump e r m i s s i b l e t o t h e minimum with small commercial load) i s produced a ti n d i c a t e d speeds o f 480-550 km/hr a t t h e e a r t h . This speed must be maintainedup t o 5000-6000 m . I f t h i s i s done, t h e maximum r a t e o f a l t i t u d e i n c r e a s ew i l l be achieved a t a l l a l t i t u d e s . A s t h e a l t i t u d e i n c r e a s e s , t h e t r u e f l i g h tspeed w i l l i n c r e a s e ( f o r example a t H = 6000 m and V = 520 km/hr, indVtr = 700 km/hr).108
  • 117. Many f l y i n g i n v e s t i g a t i o n s have shown t h a t i n order t o r e t a i n maximumv e r t i c a l speed, t h e i n d i c a t e d speed must be decreased beginning a t 6000-7000 m /1 15by an average of 15-20 km/hr p e r 1000 m. Figure 78 shows t h a t t h e product APVhas a smoothly s l o p i n g upper p o r t i o n i n t h e zone of maximum v a l u e s , s o t h a t ad e v i a t i o n of t h e i n d i c a t e d climbing speed o f * 2 0 km/hr from t h e most f a v o r a b l ev a l u e ( p i l o t e r r o r ) changes t h e v e r t i c a l speed i n s i g n i f i c a n t l y , and t h e timet o climb and f u e l expenditure over t h e climb remain p r a c t i c a l l y unchanged fromt h e most f a v o r a b l e v a l u e s . The maximum v e r t i c a l speeds of a i r c r a f t with two and t h r e e motors a r e17-25 m/sec ( a t t h e e a r t h ) , decreasing with i n c r e a s i n g a l t i t u d e t o 8-10 m/seca t 8000-9000 m. For a i r c r a f t with f o u r motors, t h e v e r t i c a l speeds a r e12-15 m/sec a t low a l t i t u d e and 5-8 m/sec a t high a l t i t u d e s . The g r e a t e s tdecrease i n v e r t i c a l speeds i s observed a t a l t i t u d e s of over 10,000 m. Thef l i g h t a l t i t u d e a t which t h e v e r t i c a l speeds equal 0 . 5 m/sec co.rresponds t ot h e p r a c t i c a l c e i l i n g of t h e a i r c r a f t . The height of t h e p r a c t i c a l c e i l i n g ofa passenger a i r c r a f t i s 12,000-13,500 m. The h e i g h t of t h e p r a c t i c a l c e i l i n g (without c o n s i d e r a t i o n of maneuvering i n t h e a r e a of t h e a i r f i e l d a f t e rt a k e o f f ) can be reached by an a i r c r a f t i n 43-45 min. Figure 80. Vertical Speed and Time o f C l i m b f o r An A i r c r a f t w i t h Two Motors (nominal mode, power f a c t o r P = 0.3) Climbing a t t h e nominal engine mode i s t h e most economical (Figure SO),s i n c e t h e maximum d i f f e r e n c e between a v a i l a b l e and consumed power i s produced, - / 116and t h e s p e c i f i c f u e l consumption w i l l be near minimal. A decrease i n t h eo p e r a t i n g mode o f t h e engines i n a climb leads t o an i n c r e a s e i n s p e c i f i c f u e lconsumption, a decrease i n a v a i l a b l e power and r a t e o f a l t i t u d e i n c r e a s e oft h e a i r c r a f t , an i n c r e a s e i n climbing time, and as a r e s u l t an i n c r e a s e i n t h et o t a l f u e l expenditure r e q u i r e d t o perform t h e climb. A modern passenger 109
  • 118. I a i r c r a f t reaches an a l t i t u d e o f 10,000-11,000 m i n 18-25 min, covering 200-250 km and expending 2000-4000 kg of f u e l ( t h e h i g h e r . v a l u e s correspond t o t h r e e - and four-motor a i r c r a f t ) . S3. Velocity Regime o f C l i m b Climbing a t t h e maximum r a t e o f a l t i t u d e i n c r e a s e i s most economical. Int h i s case, up t o 10,000-11,000 m t h e climb occurs a t an i n d i c a t e d speed of460-440 km/hr (with corresponding lower t r u e v e l o c i t y ) , and upon reaching t h ei n d i c a t e d a l t i t u d e t h e p i l o t a c c e l e r a t e s t h e a i r c r a f t a t t h e nominal regime t oan i n d i c a t e d speed o f 500-550 km/hr i n 4-5 min f o r subsequent h o r i z o n t a lf l i g h t a t t h e maximum c r u i s i n g regime. Thus, a c c e l e r a t i o n of t h e a i r c r a f t a tt h e s e a l t i t u d e s , where t h e excess t h r u s t is s l i g h t , r e q u i r e s a d d i t i o n a l time.Operational t e s t s of many t u r b o j e t passenger a i r c r a f t have shown t h a t a t timesit i s more expedient (from t h e p o i n t o f view o f c o s t ) t o climb t o a l t i t u d e i nt h e s o - c a l l e d h i g h speed regime. To do t h i s , t h e a i r c r a f t i s turned i n i t s f i n a l f l i g h t d i r e c t i o n , t h e na c c e l e r a t e d t o an i n d i c a t e d speed of 600-670 km/hr and t h e climb i s performeda t t h i s speed u n t i l t h e a i r speed reaches 800-880 km/hr (according t o t h e t h i nneedle). A t t h i s p o i n t , t h e r a t e of a l t i t u d e i n c r e a s e o f t h e a i r c r a f t i s .de­creased t o 12-14 m/sec, while t h e i n d i c a t e d speeds a r e considerably h i g h e rthan t h e most f a v o r a b l e speed. When an a i r speed of 800-880 km/hr i s reached, f u r t h e r climb i s continueda t t h i s speed. The r a t e o f a l t i t u d e i n c r e a s e decreases t o 2 - 3 m/sec asa l t i t u d e s of 10,000-11,000 m a r e reached. The a i r c r a f t a r r i v e s a t i t sassigned a l t i t u d e with s u f f i c i e n t t r u e v e l o c i t y , so t h a t almost no a d d i t i o n a lacceleration is required. After t h e t r a n s i t i o n t o horizontal f l i g h t , t h ec r u i s i n g o p e r a t i n g regime of t h e motors i s i n s t i t u t e d . Climbing a t t h e high speed regime d e c r e a s e s t h e d u r a t i o n of t h e f l i g h t ,b u t i n c r e a s e s s l i g h t l y t h e f u e l expenditure. The problem i s t h a t a5 speeds o f600-880 km/hr are maintained, t h e v e r t i c a l speed i s decreased a t a l l a l t i t u d e sand t h e time which t h e a i r c r a f t spends a t low a l t i t u d e s i s i n c r e a s e d , l e a d i n gt o an i n c r e a s e i n f u e l expenditure i n t h e climb. Therefore, t h e high speedclimb method is g e n e r a l l y recommended f o r f l i g h t s over s h o r t d i s t a n c e s , SO-60%of t h e maximum range of t h e a i r c r a f t with f u l l f u e l load. The a d d i t i o n a l /I17f u e l expenditure i n t h e s e f l i g h t s r e q u i r e s no d e c r e a s e i n commercial l o a d , The d i s t a n c e which t h e a i r c r a f t t r a v e l s i n t h e h o r i z o n t a l d i r e c t i o nd u r i n g t h e climb i n t h e high speed regime i s 50-100 km g r e a t e r t h a n d u r i n g t h eclimb a t maximum r a t e o f a l t i t u d e i n c r e a s e . The p o l a r curve on Figure 81c h a r a c t e r i z e s t h e s e two climbing methods. A s w e can s e e from t h e f i g u r e , t h ev e c t o r corresponding t o t h e speed of 500 km/hr is d i r e c t e d more s t e e p l y upward,corresponding t o v e r t i c a l speeds o f 15-17 m/sec, while a t 650 km/hr t h ev e r t i c a l speeds produced a r e l e s s , but t h e h o r i z o n t a l range i s g r e a t e r .110
  • 119. S4. Noise R e d u c t ion Methods The n o i s e of t u r b o j e t passenger a i r c r a f t i s caused by: o s c i l l a t i o n s o f -- 0 $KN/h; c o l d a i r flowing around t h e a i r c r a f t and mixing o f t h e cold a i r w i t h t h e - p u l s a t i n g , h o t gas j e t s from t h e engines and o s c i l l a t i o n s of a i r com- F i g u r e 81. Polar Curve o f p r e s s e d i n t h e compressors of t h e C 1 imb i ng S p e e d s engines. The frequency spectrum o f t h i s n o i s e i s s i g n i f i c a n t l y d i f f e r e n t fromt h e n o i s e c r e a t e d by p i s t o n and turboprop motors. Whereas t h e n o i s e spectrumof turboprop engines i s c h a r a c t e r i z e d by high sound p r e s s u r e s i n t h e lowf r e q u e n c i e s , t h e n o i s e spectrum o f t u r b o j e t engines c o n t a i n s predominantlyhigh frequency sound. This makes t h e n o i s e c r e a t e d by a t u r b o j e t engine moreunpleasant t o human h e a r i n g . The n o i s e c r e a t e d by an o r d i n a r y t u r b o j e t a tover 35% t h r u s t i s g r e a t e r t h a n t h e n o i s e r e s u l t i n g from t h e e f f l u x o f t h ejets. The usage of two c i r c u i t t u r b o j e t motors allows t h e n o i s e l e v e l t o bedecreased during t a k e o f f by 8-10 db ( d e c i b e l s ) , although t h e n o i s e l e v e l i ss t i l l q u i t e high. E x i s t i n g engineering methods of n o i s e r e d u c t i o n - - dampersa t t h e i n p u t p i p e s (JT8D engine) and exhaust nozzles (JTSD and Conway engines,e t c . ) are n o t e f f e c t i v e , and d e c r e a s e t h e n o i s e very s l i g h t l y . F o r example, am u f f l e r on t h e output nozzle c o n s i s t i n g of n i n e t u b e s d e c r e a s e s t h e n o i s el e v e l by 5 . 5 db, b u t a l s o d e c r e a s e s t h e e f f i c i e n c y o f t h e engine. I n s t a l l ­a t i o n o f p e r f o r a t e d s h e e t s and a s c r e e n around t h e a i r i n t a k e a l s o providesome decrease i n n o i s e l e v e l a t t h e i n p u t t o t h e compressor o r f a n . Therefore, i n o r d e r t o decrease t h e n o i s e t o t h e r e q u i r e d l e v e l ( a t high /118power, t h e n o i s e from t h e t u r b i n e and exhaust j e t , a t low power - - from t h ecompressor), s p e c i a l methods of p i l o t i n g a f t e r s e p a r a t i o n and d u r i n g landingmust b e used. A s we know, f o r e i g n a i r c r a f t ( t h e Boing 7 0 7 , C a r a v e l l e ,e t c . ) employ t h e s o - c a l l e d low n o i s e t a k e o f f and landing method ( t a k e o f f andlanding u s i n g t h e s t e e p e s t t r a j e c t o r i e s with engines t h r o t t l e d overl i s t e n i n g check p o i n t s ) , i . e . , t h e d e c r e a s e of n o i s e a t ground l e v e l is basedon r a p i d removal o f t h e n o i s e source from ground l e v e l . The i n i t i a l climb i sachieved on s t e e p t r a j e c t o r i e s a t s a f e speed with decreased engine power.This i s aided by improved engine design and high mechanization o f t h e wing. I n o r d e r t o determine t h e i n f l u e n c e of t h e n o i s e of an a i r c r a f t t a k i n go f f on t h e population i n t h e r e g i o n of an a i r p o r t , t h e q u a n t i t y known asperceived n o i s e l e v e l i s o f t e n used. I t has been e s t a b l i s h e d t h a t t h emaximum p e r m i s s i b l e perceived n o i s e l e v e l a c t i n g on t h e organs of h e a r i n g f o rs e v e r a l seconds P = 1 1 2 PN db (here PN db i s t h e u n i t o f measurement of "axt h e n o i s e ) . Noise l e v e l s over 1 1 2 PN db i s s a i d t o b e above t h e " t o l e r a n c el i m i t " f o r man. 111
  • 120. A t many l a r g e a i r p o r t s i n Europe and t h e USA, l i m i t a t i o n s have beenp l a c e d on t h e n o i s e c r e a t e d by a i r c r a f t t a k i n g o f f and landing!. The a p p a r a t u smeasuring t h e n o i s e l e v e l i s p l a c e d d i r e c t l y beneath t h e f l i g h t p a t h o f t h ea i r c r a f t . I f t h e maximum p e r m i s s i b l e n o i s e l e v e l i s exceeded, t h e a i r l i n ecompanies are f o r b i d d e n t o c o n t i n u e o p e r a t i n g t h e a i r c r a f t . L e t u s a n a l y z e t h e s p e c i f i c s o f a i r c r a f t f l i g h t along a s t e e p t r a j e c t o r y .As w can s e e from t h e formula s i n 0 = V /V, e i n o r d e r t o produce t h e maximum Ya n g l e 0, w e must p r o v i d e a combination of v e r t i c a l speed and speed alongt r a j e c t o r y such t h a t t h e v a l u e of s i n 0 is maximal. F l i g h t t e s t s are u s u a l l yperformed t o determine t h e s t e e p climbing speed, d u r i n g which t h e f l a p s arel e f t down a t low speeds a f t e r t a k e o f f i n o r d e r t o i n c r e a s e f l i g h t s a f e t y .T h e r e f o r e , t h e s t e e p climbing speed i s g e n e r a l l y 40-50 km/hr h i g h e r t h a n t h es e p a r a t i o n speed and p r a c t i c a l l y corresponds t o maximum a i r c r a f t aerodynamicq u a l i t y f o r t h e t a k e o f f wing s e t t i n g angle. As i s known, t h e f l i g h t regime with maximum t r a j e c t o r y i n c l i n a t i o n 0corresponds t o t h e maximum excess t h r u s t AP and, consequently, t h e maximumv a l u e of s i n 0: sin8,,,=-- ARnax- . G Therefore, i f t h e most f a v o r a b l e a i r c r a f t speed (K ) i s about max 9 Omax350-360 km/hr f o r f l a p s up, due t o t h e placement of t h e f l a p s i n t h e i r landing ­ / 119p o s i t i o n , t h i s speed i s decreased t o 300-310 km/hr. The climb a f t e r t a k e o f fon t h e s t e e p t r a j e c t o r y i s performed a t t h e most f a v o r a b l e speed w i t h f l a p sdown. During t e s t i n g o f one a i r c r a f t , t h e following method was developed f o rs t e e p climbing (Figure 8 2 ) . With f l a p s down i n t h e t a k e o f f p o s i t i o n ( l o " ) ,V = 260 km/hr. A f t e r s e p a r a t i o n , a t an a l t i t u d e of 5-10 m , t h e landing S ePg e a r was r a i s e d and t h e speed i n c r e a s e d t o 300 km/hr ( a t 50-60 m ) . Theclimb was continued t o 300 m a t t h i s speed with t h e motor o p e r a t i n g i n t h et a k e o f f mode, a f t e r which t h e motor was s h i f t e d t o t h e nominal regime.Whereas t h e climbing a n g l e o f t h e t r a j e c t o r y a t t h e t a k e o f f regime 0 =a t t h e nominal regime i t i s decreased t o 6.5-7". A t an a l t i t u d e of 500 m, t h ea i r c r a f t was d e c e l e r a t e d by d e c r e a s i n g t h e v e r t i c a l speed and t h e f l a p s werer a i s e d . The f l i g h t was performed a t a p i t c h angle o f 14-16". During t h e l a n d i n g , i t i.s impossible t o reduce n o i s e by i n c r e a s i n g t h es t e e p n e s s o f t h e g l i d i n g t b a j e c t o r y , s i n c e t h e r a t e o f descent i s f i x e d by t h eo p e r a t i n g c o n d i t i o n s of t h e l a n d i n g system. However, s i n c e t h e engines a r eo p e r a t i n g a t reduced power, t h e i n i t i a l n o i s e l e v e l i s decreased.112 I
  • 121. 500 --- H,fl ­ 450 - 300 - 1.50 - 0 - Figure 82. Optimal C l i m b i n g Tra e c t o r i e s f o r Noise Reduction a t Ground L e v e l : a , S e p a r a t i o n , V = 260 km/hr; b, B e g i n n i n g of 1 f t i n g of landing g e a r ; c , Landing g e a r u p ; d , Accelera­ t i o n t o V = 300 km/hr; e , F1 i g h t s e c t o r a t V = 300 km/hr; 6 3 = 10"; f , B e g i n n i n g o f a c c e l ­ e r a t i o n f o r r a i s i n g of f l a p s ; g , L i s t e n i n g p o i n t ; h , F l i g h t t r a j e c t o r y w i t h continuous a c c e l e r a t i o n ; i , Point o f b e g i n n i n g of l i f t i n g f l a p s ; j , End o f l i f t i n g of f l a p s The i n f l u e n c e of noise from an a i r c r a f t t a k i n g o f f i s p a r t i c u l a r l yn o t i c e a b l e i f t h e r e i s a populated p o i n t along t h e f l i g h t p a t h a t l e s s t h a n4-5 km from t h e s t a r t i n g p o i n t of t h e a i r c r a f t . I n such c a s e s , t e s t s must b emade t o determine under which c o n d i t i o n s and o p e r a t i n g modes o f t h e enginesp e r m i s s i b l e n o i s e l e v e l s can be provided ( i n p a r t i c u l a r , 110-112 PN db f o rt a k e o f f d u r i n g t h e day and 102 PN db a t n i g h t , t h e " t o l e r a n c e l i m i t " f o rn o i s e being c o n s i d e r a b l y lower a t n i g h t ) . The nomogram on Figure 83 i s /120c o n s t r u c t e d from t h e r e s u l t s of f l y i n g t e s t s on a i r c r a f t with two engines withmaximum t a k e o f f weight under s t a n d a r d c o n d i t i o n s of 38 T . The s l o p i n g l i n e sof t h e nomogram a r e t h e t r a j e c t o r i e s i n s t e e p climb s i t u a t i o n s . The z e r o p o i n t on t h e nomogram corresponds t o t h e beginning of t h ea i r c r a f t t a k e o f f r u n . O t h e r i g h t we have a t a b l e of o p e r a t i n g regimes of nt h e engines and t h e corresponding n o i s e l e v e l s perceived on t h e ground. Thed o t t e d l i n e shows an example of d e t e r m i n a t i o n o f t h e a l t i t u d e of change i nengine o p e r a t i n g regime and t h e necessary regime d u r i n g t a k e o f f o f ana i r c r a f t weighing 38 T when t h e edge of a populated p o i n t i s l o c a t e d3 . 3 km from t h e beginning o f t h e t a k e o f f r u n ( t h e t a k e o f f is performed d u r i n gt h e day, s t a n d a r d c o n d i t i o n s , no wind). To do t h i s , w e draw a l i n e fromp o i n t A, corresponding t o a d i s t a n c e o f 3 . 3 km, upward t o t h e p o i n t o f i n t e r ­s e c t i o n with t h e 38 T weight l i n e ( p o i n t B ) , t h e n draw a h o r i z o n t a l l i n e .Point C determines t h e a l t i t u d e (230-240 m) a t whichlhe o p e r a t i n g regime of 113
  • 122. t h e engines must b e reduced t o 88-89% ( p o i n t D), corresponding t o t h e maximump e r m i s s i b l e n o i s e l e v e l f o r daytime, 1 1 2 PN db. If t h e regime i s n o t changed,t h e n o i s e l e v e l i s 117 PN db ( p o i n t D). After f l y i n g over t h e populated p o i n t o r an i n c r e a s e i n a l t i t u d e of500 m , t h e engines must be s h i f t e d t o t h e nominal o p e r a t i n g regime. % U 1 2 3 4 5 6 7 8 9 Distance from s t a r t o f rup, KM Figure 83. Nomogram f o r Determination of A l t i ­ t u d e of Change i n Operating Regime o f Motor (con­ ditions of i n i t i a l c l i m b : V = 300 km/hr, i nd n = 97%, 63 = IOo) A s we can s e e from t h e same nomogram, with t h e same a i r c r a f t , b u t with a /I21s e p a r a t i o n d i s t a n c e t o t h e populated p o i n t o f 3 . 8 km ( p o i n t E ) , i t i s s u f f i ­c i e n t t o e s t a b l i s h t h e nominal regime ( p o i n t I ) and maintain an a l t i t u d e o f300 m ( p o i n t F) i n o r d e r t o produce a n o i s e l e v e l o f 1 1 2 PN db i n t h e daytime. When t h e a i r temperature and p r e s s u r e are changed o r when t h e r e is awind, s p e c i a l graphs must b e used t o determine t h e c o r r e c t e d a i r c r a f t weight,s i n c e t h e f l y i n g d a t a change. These graphs change f o r each a i r c r a f t i n t h ehandbook on f l y i n g o p e r a t i o n s . For example, f o r t h e example above a tt = +25"C, p = 760 mm H with a head wind component o f 2 m/sec, t h e c o r r e c t e d gweight Gcor = 40 t w i t h an a c t u a l weight of 38 t . The i n c r e a s e d c o r r e c t e dweight r e q u i r e s a lower a l t i t u d e f o r t h e beginning of motor t h r o t t l i n g .However, t h e decreased o p e r a t i n g regime o f t h e engines a f t e r r a i s i n g t h elanding g e a r is not p e r m i t t e d a t an a l t i t u d e o f l e s s t h a n 150 m. I n c o n c l u s i o n , we n o t e t h a t t h e f l i g h t speed d u r i n g a s t e e p climb t oa l t i t u d e w i t h f l a p s down should provide a s u f f i c i e n t r e s e r v e a g a i n s t114
  • 123. s e p a r a t i o n . The a k r c r a f t speeds a t which h o r i z o n t a l f l i g h t with s u f f i c i e n t c o n t r o l l a b i l i t y i s p o s s i b l e i s c a l l e d t h e maneuvering speed; it must b e1.15 times t h e minimum speed corresponding t o s e p a r a t i o n . F o r example, f l y i n gt e s t s i n d i c a t e a minimum speed of 200 km/hr, s o t h a t t h e maneuvering speed i s230 km/hr. The r e s e r v e a g a i n s t s e p a r a t i o n with a s t e e p climb speed o f300 km/hr i s 70 km/hr, and t h e r e s e r v e t o s t a l l i s about 100 km/hr.S5. C l i m b i n g w i t h O n e Motor Not Operating If t h e s i t u a t i o n r e q u i r e s a p i l o t t o f l y t o a r e s e r v e a i r f i e l d a f t e r amotor f a i l u r e on t a k e o f f , with t h e r e s e r v e a i r f i e l d l o c a t e d 350-400 k md i s t a n c e , a climb must b e performed. I t w i l l b e shown i n Chapter V I 1 t h a tt h e most f a v o r a b l e a l t i t u d e f o r ranges of 300-400 k i s 5700-6000 m; mhowever, f o r f l i g h t w i t h one motor n o t o p e r a t i n g , t h e most f a v o r a b l e a l t i t u d ei s 2500-3000 m. An a i r c r a f t w i t h a motor o u t , when climbing a t t h e nominalregime, can a t t a i n a v e r t i c a l v e l o c i t y component o f 3-6.5 m/sec a t groundl e v e l . This speed d e c r e a s e s with a l t i t u d e and a t 4500-7000 m , t h e r a t e ofa l t i t u d e i n c r e a s e i s about 0 . 5 m/sec. I t i s considered t h a t a t t h i s p o i n t t h ea i r c r a f t reaches i t s p r a c t i c a l f l i g h t c e i l i n g w i t h one motor n o t o p e r a t i n g .F o r a i r c r a f t with t h r e e motors, t h e f l i g h t a l t i t u d e with one nonoperatingmotor, n a t u r a l l y , i s g r e a t e r t h a n f o r a i r c r a f t with two motors. The time t oclimb t o t h i s a l t i t u d e i s 45-50 min and depends s t r o n g l y on t h e a c t u a ltemperature of t h e surrounding a i r . The climbing speed i n such c a s e s i s70-100 km/hr l e s s , explained by t h e d e c r e a s e i n a v a i l a b l e t h r u s t of 30-SO%,s o t h a t t h e maximum of product APY is d i s p l a c e d toward lower v a l u e s ofi n d i c a t e d ( a s w e l l as t r u e ) speed. I t i s recommended t h a t as t h e a l t i t u d e i si n c r e a s e d , t h e i n d i c a t e d speed be decreased by 5 km/hr p e r 1000 m a l t i t u d e .T r a n s i t i o n of engines from nominal t o t a k e o f f regime i n c r e a s e s t h e excesst h r u s t and allows t h e r a t e of a l t i t u d e i n c r e a s e o f t h e a i r c r a f t t o b ei n c r e a s e d t e m p o r a r i l y , although t h e time of o p e r a t i o n i n t a k e o f f regime i s1i m i t e d . 115
  • 124. Chapter V I I . Horizontal F1 i g h t /122 91. Diagram of Forces A c t i n g on A i r c r a f t H o r i z o n t a l f l i g h t means s t r a i g h t l i n e , s t a b l e a i r c r a f t f l i g h t withouti n c r e a s e o r d e c r e a s e of a l t i t u d e . The f o r c e s a c t i n g on t h e a i r c r a f t were shown i n c h a p t e r V I . W add t h a t et h e t o t a l aerodynamic f o r c e R ( e q u a l i z i n g f o r c e s Y and Q) i s a p p l i e d a t t h ec e n t e r of p r e s s u r e , and i s d e f l e c t e d from f o r c e Y by c e r t a i n angle 0 (Figure 8 4 ) . I n c l i n a t i o n of f o r c e R i s changed by t h e p i l o t by u s i n g t h ee l e v a t o r , d e f l e c t i n g it enough so t h a t f o r c e R p a s s e s through t h e c e n t e r o fg r a v i t y . T h e r e f o r e , we w i l l c o n s i d e r f o r h o r i z o n t a l f l i g h t , as f o r climbing,t h a t a l l f o r c e s a r e a p p l i e d t o t h e c e n t e r of g r a v i t y o f t h e a i r c r a f t . Figure 84. Diagram of Forces Acting on A i r c r a f t i n Horizontal F l i g h t : 1 , Longitudinal a x i s of a i r c r a f t ; 2 , Chord l i n e ; 3 , D i r e c t i o n of a i r ­ c r a f t ; 4 , Direction of t h r u s t As we know, i n o r d e r t o achieve s t a b l e h o r i z o n t a l f l i g h t , i t i s n e c e s s a r yt h a t t h e following e q u a t i o n b e f u l f i l l e d : G=Y+Psinp; Q=Pcosp.These e q u a l i t i e s show t h e c o n d i t i o n s o f h o r i z o n t a l f l i g h t . The f i r s t e q u a l i t yshows t h a t t h e movement o f t h e a i r c r a f t i s l i n e a r and occurs i n t h e h o r i z o n t a lp l a n e . The second i s t h e c o n d i t i o n of evenness of motion, i . e . , f l i g h t a tc o n s t a n t v e l o c i t y . If t h i s c o n d i t i o n were n o t f u l f i l l e d , t h e f l i g h t would be /123u n s t a b l e (with a c c e l e r a t i o n o r d e c e l e r a t i o n ) .116
  • 125. I t w a s s t a t e d above t h a t f o r c e P may make a c e r t a i n angle w i t h t h e chordo f t h e wing. If w e assume as an average a = 3", t h e wing s e t t i n g a n g l e $I = 1"and t h e motor s e t t i n g a n g l e ( i n t h e t a i l p o r t i o n of t h e f u s e l a g e ) i s z e r o , a sw e see from F i g u r e 84 a n g l e B = 2O. T h e r e f o r e , t h e force, P cos B w i l l b e lesst h a n f o r c e P . I n p r a c t i c e , w i t h angle B = 2-7", t h e v a l u e of cos B d i f f e r sl i t t l e from u n i t y , s o t h a t it can b e considered t h a t Q = P. W can a l s o ec o n s i d e r t h a t Y = G , s i n c e w e can i g n o r e t h e component P s i n 6 , which f o rc r u i s i n g t h r u s t v a l u e s w i l l b e less t h a n one p e r c e n t of t h e mean f l y i n gweight. For example, w i t h an average f l y i n g weight o f 70 t and a q u a l i t y of14, t h e r e q u i r e d t h r u s t Pr = 5000 kg, and P s i n 2" = 5000*0.035 = 175 kg,i . e . , 0.25% of t h e average weight. Even i f $Ien = 5" (with engines i n t h e rearp o r t i o n o f t h e wing) and a = 3" and B = 7", = 5000 kg w e w i t h t h e same P rproduce P s i n 7" = 5000-0.122 = 610 kg. T h i s i s 0.87% of t h e weight o f 70 t .52. Required T h r u s t f o r H o r i z o n t a l F1 i g h t An a i r c r a f t i s capable of performing f l i g h t a t v a r i o u s angles of a t t a c kw i t h i n t h e speed range from t h e minimum t o t h e maximum, i . e . , a t v a r i o u sregimes. Each o f t h e s e regimes corresponds t o a c e r t a i n a i r speed (angle ofa t t a c k ) , providing t h e l i f t i n g f o r c e equal t o t h e weight of t h e a i r c r a f t .This v e l o c i t y has come t o be c a l l e d t h e r e q u i r e d v e l o c i t y f o r h o r i z o n t a lf l i g h t , and t h e t h r u s t n e c e s s a r y f o r t h e performance of h o r i z o n t a l f l i g h t a tt h i s angle o f a t t a c k i s t h e r e q u i r e d t h r u s t f o r h o r i z o n t a l f l i g h t . Thus, i nh o r i z o n t a l f l i g h t a given angle of a t t a c k corresponds t o a d e f i n i t e r e q u i r e dv e l o c i t y and t h r u s t . I n o r d e r t o c a l c u l a t e t h e graphs o f r e q u i r e d t h r u s t onFigure 85, a graph o f t h e dependence c = f ( a ) and t h e p o l a r curve o f t h ea i r c r a f t with a wing without geometricYtwist i s used. The c a l c u l a t i o n wasperformed i n t h e f o l l o w i n g o r d e r : t h e r e q u i r e d t h r u s t i n h o r i z o n t a l f l i g h t i ss e t equal t o t h e d r a g : Pr = Q. S e t t i n g v a r i o u s f l i g h t speeds, we determinef o r each of them t h e impact p r e s s u r e and c Y - u s i n g t h e p o l a r curve ( f o rv a r i o u s M numbers) w e f i n d t h e v a l u e o f c corresponding t o t h e s e speeds. XUsing t h e formula Pr = Q = cxSp(V2/2) = cxSq, w e determine t h e r e q u i r e dthrust . As w e can s e e from F i g u r e 85, with t h e most f a v o r a b l e angle o f a t t a c kOL = 6" and H = 0 , we produce t h e minimum r e q u i r e d t h r u s t , corresponding t o hvt h e most f a v o r a b l e speed of 360 km/hr and q u a l i t y K = 15 (from t h e formula = G / K w e produce K = G/Pr = 35,000/2330 = 1 5 ) . An i n c r e a s e o r d e c r e a s e i nrspeed l e a d s t o an i n c r e a s e i n r e q u i r e d t h r u s t , s i n c e w i t h angles of a t t a c kg r e a t e r t h a n o r l e s s t h a n 6", t h e aerodynamic q u a l i t y d e c r e a s e s . /124 For f l i g h t a t 360 km/hr n e a r t h e e a r t h t h e motors must b e t h r o t t l e d backso as t o achieve e q u a l i t y P = Pr. I n t h i s c a s e , t h e curve o f a v a i l a b l e P 117
  • 126. t h r u s t touches t h e curve o f r e q u i r e d t h r u s t a t p o i n t B , corresponding t o a = 6. As w e can see from F i g u r e 85, f o r f l i g h t with lower speed (V = 300 km/hr) as w e l l as f o r f l i g h t w i t h h i g h e r speed (600 km/hr), an i n c r e a s e i n engine t h r u s t i s r e q u i r e d ( p o i n t s C and A ) . --- i.g. 3000 2500 Figure 85. Required T:lrust As a Function of F l i g h t S p e e d ( f l y i n g w e i g h t 35 T I : 1 , Thrust f o r f l i g h t w i t h = 360 km/hr; 2 , Thrust f o r f l i g h t w i t h hv 1 . g . = landing g e a r V = 600 km/hr W know t h a t f o r a i r c r a f t with t u r b o j e t engines, t h e maximum excess et h r u s t corresponds t o t h e most f a v o r a b l e speed and, i n t h e example h e r eanalyzed Vhv = 360 km/hr. I n o r d e r t o achieve APmax a t t h e t a k e o f f o rnominal regime, an i n d i c a t e d f l i g h t speed of 360 km/hr must be maintained. As t h e f l y i n g a l t i t u d e i s i n c r e a s e d ( f o r t h e same weight, i n o u r example.35 t ) , t h e r e q u i r e d t h r u s t remains unchanged i f t h e q u a l i t y i s t h e same. I np r a c t i c e , however, as t h e i n d i c a t e d speed i s r e t a i n e d , Kmax d e c r e a s e s s l i g h t l ywith i n c r e a s i n g a l t i t u d e (by 0 . 4 - 0 . 6 ) , s o t h a t Pr i s somewhat h i g h e r . I n ourexample (Figure 85), t h e i n d i c a t e d speed o f 360 km/hr a t 10,000 m correspondst o a t r u e speed of 592 km/hr (M = 0.5) and a maximum q u a l i t y of 1 4 . 5 , i . e . ,t h e q u a l i t y i s decreased by 0.5. The angles of a t t a c k corresponding t o Kmaxare a l s o d i f f e r e n t f o r d i f f e r e n t a l t i t u d e s due t o t h e i n f l u e n c e of t h eM number on t h e p o l a r curve of t h e a i r c r a f t . F o r example, f o r H = 0 , t h e /125angle of a t t a c k corresponding t o t h e minimum r e q u i r e d t h r u s t i s 6 " , and f o rH = 10,000 m -- 4.8".118
  • 127. A d e c r e a s e i n f l y i n g weight r e s u l t s i n a d e c r e a s e i n r e q u i r e d t h r u s t f o rt h e same angles of a t t a c k (and t h e r e f o r e , f o r t h e same a l t i t u d e s ) . As w e cansee on Figure 85, a t H = 10,000 m f o r G = 30 t , t h e minimum Pr i s less t h a nt h e minimum P f o r G = 35 t , and a l s o t h e speed corresponding t o t h e minimum rr e q u i r e d t h r u s t i s less - - 575 km/hr (Vind = 350 km/hr). 9000 C I I Figure 86. Required Thrust As a Function of F l i g h t Speed ( a i r c r a f t w i t h three e n g i n e s ) If w e c o n s t r u c t curves of r e q u i r e d t h r u s t s f o r a i r c r a f t with h i g h weightand s p e c i f i c load ( f o r example with G = 80 t and G/S = 432 kg/m2), t h e mostf a v o r a b l e speed is i n c r e a s e d t o 400 km/hr a t H = 0 and 625 km/hr a tH = 10,000 m (Figure 8 6 ) . I n o r d e r t o c a l c u l a t e t h e curves on Figure 86, w e used t h e dependencec = f ( a ) and t h e p o l a r curve of t h e a i r c r a f t shown on F i g u r e s 16 and 27. The Yi n c r e a s e d ah,, i s explained by t h e geometric t w i s t of t h e wing, about 3". F o r /126 c l a r i t y , Figure 86 shows t h e r e q u i r e d t h r u s t as a f u n c t i o n of f l i g h t speed f o r an a i r c r a f t w i t h landing g e a r and f l a p s down, when t h e r e q u i r e d t h r u s t i s i n c r e a s e d due t o t h e decreased q u a l i t y . 119
  • 128. S3. Two Horizontal F l i g h t Regimes The p o i n t s o f i n t e r s e c t i o n of t h e curves o f r e q u i r e d and a v a i l a b l e t h r u s tcorrespond t o t h e e q u a l i t y P = P a consequently, f o r c e s P and Q, as w e l l as r P’Y and G w i l l a l s o b e e q u a l . On Figure 85 f o r H = 0, t h e s e p o i n t s are markedby t h e l e t t e r s a , b and c. Due t o t h e s p e c i f i c f d a t u r e s of p i l o t i n g d u r i n gt r a n s i t i o n from one v e l o c i t y t o a n o t h e r , t h e s e p o i n t s d i f f e r considerably.For example, a t p o i n t a t h e t r a n s i t i o n t o a d i f f e r e n t speed r e q u i r e s s i m p l e rc o n t r o l t h a n a t p o i n t c. Thus, i n o r d e r t o i n c r e a s e t h e speed t o over600 km/hr, a c c e l e r a t i o n must b e performed by i n c r e a s i n g t h e t h r u s t (P > Q ) .I n o r d e r t o decreas.e t h e speed, t h e a v a i l a b l e t h r u s t should be decreased,s i n c e t h e r e q u i r e d t h r u s t i n h o r i z o n t a l f l i g h t i n t h i s case i s l e s s t h a n f o r600 km/hr. However, i n o r d e r t o move t o a d i f f e r e n t speed a t p o i n t c, f o rexample, i n o r d e r t o i n c r e a s e t h r u s t over 300 km/hr, t h e c o n t r o l s t i c k must b epushed forward t o t r a n s f e r t h e a i r c r a f t t o a lower angle of a t t a c k and, i no r d e r t o maintain t h e same f l i g h t a l t i t u d e , t h e t h r u s t must b e i n i t i a l l ydecreased, t h e n t h e n e c e s s a r y regime s e t when t h e speed begins t o i n c r e a s e .The same t h i n g must b e done t o d e c r e a s e t h e f l i g h t speed: t h e t h r u s t must b et e m p o r a r i l y decreased, t h e n once more i n c r e a s e d , s i n c e a d e c r e a s e i n speedcauses an i n c r e a s e i n r e q u i r e d t h r u s t . Point a corresponds t o t h e f i r s t f l i g h t regime, p o i n t c t o t h e second.The main p e c u l i a r i t y o f t h e second regime i s t h e n e c e s s i t y o f double a c t i o nwith t h e c o n t r o l l e v e r o f t h e motor when f l i g h t speed i s changed. Therefore,f l i g h t should n o t be performed i n t h e second regime. s i n c e i t decreases c o n t r o l l a b i l i t y and makes flow s e p a r a t i o n on t h e a i r c r a f t wing p o s s i b l e . The boundary between t h e f i r s t and second f l i g h t regimes i s t h e mostf a v o r a b l e angle o f a t t a c k f o r a t u r b o j e t a i r c r a f t ( f o r a p i s t o n powereda i r c r a f t it i s t h e most economical). Whereas f l i g h t s i n t h e second regime hadno p r a c t i c a l s i g n i f i c a n c e f o r p i s t o n powered c r a f t , s i n c e f l i g h t s a t angles ofa t t a c k g r e a t e r t h a n t h e economical angle of a t t a c k were almost never performedsince a was n e a r t h e maximum p e r m i s s i b l e a n g l e o f a t t a c k , f l i g h t s of j e t eca i r c r a f t ( p a r t i c u l a r l y a t a l t i t u d e s n e a r t h e p r a c t i c a l c e i l i n g ) may occur a tregimes n e a r t h e most f a v o r a b l e . The e s t a b l i s h e d minimum p e r m i s s i b l e o p e r a t i n g speed on t h e b a s i s of t h evalues c i s u s u a l l y 50-70 km/hr less t h a n t h e most f a v o r a b l e speed. W e Y Pershould n o t e t h a t i n t h e f o l l o w i n g i n our a n a l y s i s o f examples w e w i l l n o tc o n s i d e r a l t i t u d e l i m i t a t i o n s r e l a t e d t o t h e f l y i n g weight of t h e a i r c r a f t( s e e 58 of t h i s c h a p t e r ) . I n t h e examples on F i g u r e s 85 and 86, t h e d i v i s i o n between t h e two f l i g h t /127regimes a t low a l t i t u d e c o n s i s t s o f t h e most f a v o r a b l e speeds of 360 km/hr and400 km/hr. I n h o r i z o n t a l f l i g h t with Vhv t h e motors must b e t h r o t t l e d back s ot h a t f l i g h t occurs a t speeds corresponding t o t h e p o i n t of c o n t a c t of t h ecurves of a v a i l a b l e and r e q u i r e d t h r u s t (on F i g u r e 85, p o i n t b ) . As t h ef l y i n g weight i s d e c r e a s e d , t h e most f a v o r a b l e speed d e c r e a s e s ; f o r example,120
  • 129. a t 30 t , Vmf = 350 km/hr i n d i c a t e d (Figure 85). Lowering t h e landing g e a r and f l a p s d i s p l a c e s t h e boundary between f i r s tand second regimes c o n s i d e r a b l y toward lower speeds (Figure 8 6 ) . For example,with f l a p s down t h e speed d e c r e a s e s t o 325 km/hr ( a = 8.5") and with f l a p s mfdown 25", t o 265 km/hr (amf = 7 . 8 " ) . A s a r u l e , t h e a i r c r a f t i s brought i nf o r a l a n d i n g i n t h e f i r s t regime. I n o r d e r t o avoid t r a n s f e r r i n g t o t h e second regime with t h e a i r c r a f twing mechanics i n t h e t a k e o f f and l a n d i n g p o s i t i o n , t h e p i l o t must r e c a l l t h ei n d i c a t e d speed corresponding t o t h e boundary between t h e two f l i g h t regimes.94. Influence o f External Air Temperature on Required Thrust A s was noted, a change i n t h e temperature of t h e surrounding a i r l e a d s t oa change i n engine t h r u s t ( c h a p t e r V I , § 6 ) . Also, temperature o f t h e s u r ­rounding a i r i n f l u e n c e s t h e n a t u r e of t h e dependence of r e q u i r e d t h r u s t onf l i g h t speed, which appears a s a displacement of t h e curve t o t h e l e f t (withd e c r e a s i n g t ) o r t o t h e r i g h t (with i n c r e a s i n g t ) and i n f l u e n c e s t h e v a l u e ofr e q u i r e d speed f o r h o r i z o n t a l f l i g h t . The e x t e r n a l a i r temperature does n o ti n f l u e n c e t h e r e q u i r e d t h r u s t , s i n c e P = G / K , and K = c / c depends only on r Y Xt h e angle of a t t a c k . Let US analyze t h e reason why t h e curve P = (V,t") i s rd i s p l a c e d . W know t h a t i n h o r i z o n t a l f l i g h t with unchanging a n g l e o f a t t a c k e( o r c ) a t d i f f e r e n t temperatures t h e following c o n d i t i o n should be f u l f i l l e d : YA s t h e temperature i s decreased with c o n s t a n t p r e s s u r e , t h e d e n s i t y of t h e a i ri s i n c r e a s e d . I n t h i s c a s e , i n o r d e r f o r e q u a l i t y Y = G t o be f u l f i l l e d , t h er e q u i r e d h o r i z o n t a l f l i g h t speed must be decreased ( c unchanged). As t h e Yv e l o c i t i e s a r e decreased, t h e curves of r e q u i r e d t h r u s t w i l l be s h i f t e d t o t h el e f t . A s t h e temperature i s i n c r e a s e d , on t h e o t h e r hand, t h e curves o frequired t h r u s t a r e displaced t o t h e r i g h t , s i n c e t h e required v e l o c i t i e si n c r e a s e (Figure 8 7 ) . A s w e can s e e from t h e f i g u r e , t h e same Prl corresponds t o a g r e a t e rr e q u i r e d t h r u s t f o r a temperature 10" h i g h e r t h a n t h e s t a n d a r d t e m p e r a t u r e , /128 __.since f o r t we have Vcrl, and f o r tst + 10" v e l o c i t y V st Vcrl. The curves of r e q u i r e d t h r u s t f o r c o n d i t i o n s o t h e r t h a n s t a n d a r d a r ec a l c u l a t e d as f o l l o w s . A t f i r s t we f i n d t h e a i r d e n s i t y under t h e new condi­t i o n s . For example, when t h e o u t s i d e a i r temperature i s i n c r e a s e d by 10" withp r e s s u r e unchanged f o r H = 10,000 m y T = 223°K and p = 198 mm Hg, w e produce 1 21
  • 130. T = 223 + 10 = 233, p = 0.0473 p/T = 0.0473*198/233 = 0.0403 kg*sec2/m4.This v a l u e o f p , according t o t h e s t a n d a r d t a b l e , i s e q u i v a l e n t t o a f l i g h ta l t i t u d e o f 10,300 m. Then, f i x i n g t h e f l i g h t speed, w e determine c then take c from t h e YY Xp o l a r curve o f t h e a i r c r a f t w i t h v a r i o u s M (Figure 28). Using t h e formulaPr = cxSq, w e determine t h e r e q u i r e d t h r u s t . I n d e t e r m i n i n g t h e M number, w eb a s e o u r c a l c u l a t i o n s on t h e f a c t t h a t a t T = 233K, t h e speed o f sounda = 306 m/sec. W must n o t e t h a t as t h e e t e m p e r a t u r e is i n c r e a s e d by more . -­ t h a n lo, t h e d e c r e a s e i n d e n s i t y ( i n c r e a s e i n speed) w i l l b e g r e a t e r . For example, w i t h A t = +30° a t H = 10,000 m y t h e tS decrease i n d e n s i t y i s e q u i v a l e n t t o an i n c r e a s e i n f l y i n g a l t i t u d e t o approximately 11,000 m. Let u s now a n a l y z e t h e graphs o f r e q u i r e d t h r u s t (Figure 87). f i g u r e 87. Influence o f Surrounding Air Temperature o n Required and With s t a n d a r d t e m p e r a t u r e , Ava i 1 ab le A i r c r a f t Thrust ( s p e c i f i c i n o r d e r t o produce t h e v e l o c i t y 1 oad i ng 340 kg/m2) a t H = 10,000 m , we must crl u s e engine speed n O At this 1"speed, t h e a v a i l a b l e t h r u s t w i l l be equal t o t h e r e q u i r e d t h r u s t ( p o i n t A ) .A s t h e temperature i s i n c r e a s e d by 10 (by 4.2% o f 233K) , t h e curve o fr e q u i r e d t h r u s t i s d i s p l a c e d t o t h e r i g h t , and t h e curve of P i s d i s p l a c e ddownward. The a v a i l a b l e t h r u s t , depending on t h e t y p e and d e s i g n o f t h e motor, maybe decreased by 5-8% (curve 2 ) . The i n t e r s e c t i o n o f t h e curves of a v a i l a b l eand r e q u i r e d t h r u s t d e f i n e s t h e speed Vcr2 w i t h unchanged engine o p e r a t i n g - /129regime. As we can see from t h e f i g u r e , t h e t r u e f l i g h t speed has decreased,s o t h a t t h e M number i s a l s o decreased, s i n c e t h e speed o f sound i s n o t 300,b u t r a t h e r 306 m/sec (M = Vcr2/306). Thus, as t h e a i r temperature i s i n c r e a s e d by lo, t h e f l y i n g regimechanges s i g n i f i c a n t l y . If we must maintain t h e previous M number ( i . e . ,corresponding t o t s t ) w e must i n c r e a s e t h e o p e r a t i n g speed of t h e enginesand, as w can see on Figure 87, s e t i n engine speed n3% ( p o i n t B ) . e The t r u ef l i g h t speed i n c r e a s e s and becomes V cr3 = aM = 306 M.122
  • 131. . . a,, , , I , 0 ! I: ,.;(, , : . If t h e p i l o t does not change t h e o p e r a t i n g regime of t h e engines, as t h e. 1 , , f l i g h t speed i s decreased from Vcrl t o Vcr2, t h e angle o f a t t a c k and c , , .II ,, * Y . . , , .I <; , i n c r e a s e . Allowing t h e aircraft t o f l y a t h i g h e r angles of a t t a c k i s danger- I ,*,x.:. ,.. .., ous due t o t h e approach toward c and t h e s e p a r a t i o n l i m i t . Also, under .., Y Per:.,$,,,.-.e. . -. r e l a t i v e l y h i g h temperature c o n d i t i o n s , t h e v e r t i c a l gust reserve i s r , I: 3 , . -.< . _.. ;,,:, : ,: decreased. Therefore, i n case such c o n d i t i o n s are encountered, t h e r o t a t i n g . _ I . speed o f t h e engine should b e i n c r e a s e d by .an -avecage of 5% f o r each 5-10" k - .,I,:, .:. , , 8. , , -. : /. -. < ,I. ; o f i n c r e a s e i n temperature, o r if t h i s i s impossible, a lower f l y i n g a l t i t u d e s ­ ),, .. ~ should be requested. I ,.I .1. ? I . As t h e temperature d e c r e a s e s , t h e a v a i l a b l e t h r u s t i n c r e a s e s (curve 4) I ad; and t h e curve of r e q u i r e d t h r u s t i s d i s p l a c e d t o t h e l e f t . The p o i n t of t h e i r.;. , , ,,,x. ., . . > 1 i n t e r s e c t i o n c d e f i n e s t h e new f l i g h t . s p e e d .:~,, I ; .>, .I, . .. I : 95. Most Favorable Horizontal F l i g h t Regimes. Influence of A l t i t u d e and .. ! .,_ , ) " .r :- ,. . > ..> . . . The f l i g h t range i s t h e d i s t a n c e t r a v e l e d by t h e a i r c r a f t during t h e , h o r i z o n t a l f l i g h t and descent. If f l i g h t i s performed u n t i l t h e f u e l i s completely exhausted, t h e d i s t a n c e t r a v e l e d i s c a l l e d t h e t e c h n i c a l range. F o r . p a s s e n g e r a i r c r a f t , t h e f l i g h t range given i s u s u a l l y t h a t with one hours f u e l reserve i f t h e f l i g h t schedule i s maintained. (recommended regimes). t h e r e are v a r i o u s ways w h i c h - t h e aircraft can l e a v e t h e area of t h e e l d and climb after t a k e o f f , t h e range o f f l i g h t covered during t h e climb t o assigned a l t i t u d e changes s i g n i f i c a n t l y . However, t h e range covered during t o a l t i t u d e i s r e l a t i v e l y . s l i g h t , s o t h a t i n t h e following w e w i l l d i s c u s s t h e range of h o r i z o n t a l f l i g h t . The range of t h e h o r i z o n t a l f l i g h t s e c t o r depends on t h e f u e l r e s e r v e f o r h o r i z o n t a l f l i g h t and on t h e rate a t which it i s expended, i . e . , t h e kilometer expenditure c -- t h e expenditure of f u e l p e r kilometer of f l i g h t path. k ,:,;* Before going over t o h o r i z o n t a l f l i g h t , t h e a i r c r a f t must t a k e o f f and climb. , The f u e l expenditure during t h e time of t a k e o f f and climb t o 9-11 k f o r two- m : ! and three-engine aircraft is 1600-4000 kg. The f u e l expended d u r i n g t a k e o f f and establishment of nominal f l i g h t , . j regime (without c o n s i d e r a t i o n o f climb) i s 250-350 kg, t h e f u e l expended - /130 , , . : during t h e descent and landing i s 700-1000 kg. I n o r d e r t o determine t h e ! q u a n t i t y o f f u e l t o be used i n t h e h o r i z o n t a l f l i g h t s e c t o r Gf her, w e must ,- !{ s u b t r a c t from t h e q u a n t i t y of f u e l t a k e n on board a l l supplementary expend- ,,,,: i t u r e s and t h e n a v i g a t i o n a l reserve. For example, with a t a k e o f f weight o f . . - ... . .. ,,; t h e aircraft o r 44,000 kg and an i n i t i a l f u e l weight of 13,000 kg, 7000­ >, 7700 kg o f f u e l remain f o r h o r i z o n t a l f l i g h t a t H = 10,000 m, s i n c e about " 2000 kg are expended i n t a k e o f f and climbing, 800-1000 kg f o r descent and I , , ! landing and 2500 kg are h e l d as n a v i g a t i o n a l reserve. 123
  • 132. For s h o r t e r range f l i g h t s a t t h e same a l t i t u d e , t h e o n l y change i s i nt h e q u a n t i t y of f u e l r e q u i r e d f o r t h e h o r i z o n t a l s e c t o r , while t h e remainingf u e l expenditure norms remain approximately unchanged. The d u r a t i o n of h o r i z o n t a l f l i g h t i s determined from t h e r e l a t i o n s h i pwhere 5 is t h e hourly f u e l expenditure. The hourly f u e l e x p e n d i t u r e i s t h e q u a n t i t y of f u e l expended by t h ea i r c r a f t i n one hour of h o r i z o n t a l f l i g h t . For example, f o r an a i r c r a f t witht h r e e engines with a r e q u i r e d t h r u s t o f 6000 kg and a s p e c i f i c expenditure of0 , 8 kg/kg.hr, t h e h o u r l y r a t e i s 4800 kg/hr. The r e l a t i o n s h i p between h o u r l y and kilometer e x p e n d i t u r e s i s e s t a b l i s h e dfrom t h e f o l l o w i n g c o n s i d e r a t i o n s : i n one hour of f l i g h t , t h e engines burn kg o f f u e l . However, d u r i n g t h i s same time t h e a i r c r a f t covers a d i s t a n c enumerically e q u a l t o t h e f l i g h t speed V ( i n calm a i r ) . Therefore, t h e f u e lexpenditure p e r k i s mwhere V i s t a k e n i n km/hr. If V i s taken i n m/sec, ch cK=- * 3.6V For V = 880 km/hr and ch = 4800 kg/hr, w produce ck = 5.46 kg/km. e Both t h e hourly and k i l o m e t e r e x p e n d i t u r e s depend g r e a t l y on t h es p e c i f i c e x p e n d i t u r e o f t h e engines c The r e l a t i o n s h i p between t h e P‘s p e c i f i c and h o u r l y e x p e n d i t u r e s i s e s t a b l i s h e d as f o l l o w s : f o r each1 kg of t h r u s t and one hour of engine o p e r a t i o n , cp kg of f u e l are expended,while a t h r u s t o f P kg r e q u i r e s t h e e x p e n d i t u r e o f P times more f u e l .Therefore,124
  • 133. I n Chzpter I V w e s t a b l i s h e d t h a t t h e s p e c i f i c fuel expenditure depends eon t h e r o t a t i n g speed o f t h e engine, a l t i t u d e and v e l o c i t y of f l i g h t . - /131 L e t u s now go over t o an a n a l y s i s o f f l i g h t range. With i d e n t i c a l f u e lreserve w i t h i n t h e l i m i t s of p o s s i b l e speeds, v a r i o u s ranges w i l l b e produced.For example, i n t h e example o u t l i n e d above with a f u e l load of 13,000 kg, at a k e o f f weight o f 44,000 kg, f l i g h t a t 10,000 m with a t r u e speed of810 km/hr (M = 0.75-0.76) and an hourly fue1,expenditure of 2500 kg/hr, i ncalm a i r a range on t h e or-der of 2800-3000 k can be produced. With f l i g h t a t ma high M number (V > 810 km/hr), t h e range is decreased t o 2200-2500 km.Figure 88 shows. a f l i g h t p r o f i l e f o r , an a i r c r a f t c a l c u l a t e d f o r varioush o r i z o n t a l f l i g h t speeds, which a l s o i l l u s t r a t e s t h e above. A head wind o r t a i l wind changes t h e f l i g h t range. Let u s analyze t h e i n f l u e n c e of f l i g h t speed on t h e hourly and kilometer f u e l expenditures. W can explain t h i s e f o r f l i g h t a t one and t h e same a l t i t u d e , using t h e Zhukovskiy curves f o r r e q u i r e d and a v a i l a b l e t h r u s t (Figure 89). F i g u r e 88. C h a r a c t e r i s t i c I n order t o achieve h o r i z o n t a l f l i g h t F l i g h t P r o f i l e of A i r c r a f t a t any given speed (Vmax 1, 2 and vmf) to Range a t Fixed A l t i t u d e it i s r e q u i r e d t h a t P = P,. This means P t h a t i n o r d e r t o f l y a t less than Vma,t h e engine must b e t h r o t t l e d back s o t h a t t h e curve o f P passes through Pp0int.s AI, A and A r e s p e c t i v e l y (Figure 89 a ) . 2 3 The hourly f u e l expenditure 5= cpP P b u t s i n c e a t any v e l o c i t y o f - /132h o r i z o n t a l f l i g h t Pr = Pp > Ch 5 cppr. I n order t o decrease t h e f l y i n g speed, t h e r o t a t i n g speed of t h e enginemust be decreased. This r e s u l t s i n an i n c r e a s e i n s p e c i f i c consumption.However, as t h e f l y i n g speed i s decreased, t h e value of Pr = G/K i s a l s odecreased. Thus, as t h e engine is t h r o t t l e d back, cp i n c r e a s e s , b u t Prdecreases. The hourly expenditure w i l l depend on t h e way i n which cp and Pchange. W f i n d t h a t as t h e f l i g h t speed i s decreased, t h r u s t P decreases e .more i n t e n s i v e l y than cp i n c r e a s e s . Therefore, c a l s o decreases; t h e minimum h 125
  • 134. "h min w i l l correspond t o Vmf, a t which Pr min - G/Kma. With V < Vmf, 5begins t o i n c r e a s e , s i n c e P increases. Consequently, t h e g r e a t e s t f l i g h t rd u r a t i o n a t any a l t i t u d e w i l l occur when f l y i n g at t h e most f a v o r a b l e speed. F i g u r e 89. Explanation of Influence of F l i g h t Speed on Hourly and Kilometer F u e l Expenditures Let us e x p l a i n how t h e f l y i n g a l t i t u d e i n f l u e n c e s t h e hourly expenditure.I n 92 of t h i s chapter we showed t h a t t h e r e q u i r e d t h r u s t i s almost i d e n t i c a lfor t h e same weight a t a l l f l y i n g a l t i t u d e s up t o 10,000 m. However, t h er e q u i r e d speed i n c r e a s e s with a l t i t u d e . Therefore, t h e curves of r e q u i r e dt h r u s t a r e d i s p l a c e d toward t h e a r e a of h i g h e r speeds with i n c r e a s i n g a l t i t u d e( s e e Figure 85). Since t h e a v a i l a b l e t h r u s t of t h e engine decreases with a l t i t u d e , t h ecurves o f t h e change i n t h r u s t with v e l o c i t y are displaced downward with ani n c r e a s e i n a l t i t u d e . Therefore, whereas a t low a l t i t u d e t h e engines must bet h r o t t l e d back, t h u s considerably i n c r e a s i n g t h e s p e c i f i c expenditure, a t10,000 m l e s s t h r o t t l i n g i s r e q u i r e d and t h e s p e c i f i c expenditure i n c r e a s e sonly s l i g h t l y . When f l y i n g a t t h e c e i l i n g , t h e engines need not be t h r o t t l e dback a t a l l . Therefore, as t h e f l y i n g a l t i t u d e i n c r e a s e s t h e product cpPr mindecreases, which e x p l a i n s t h e decrease i n hourly expenditure. Also, t h edecrease i n with a l t i t u d e f a c i l i t a t e s a decrease i n s p e c i f i c expenditure a tconstant o p e r a t i n g speed. Therefore, t h e l o n g e s t f l i g h t d u r a t i o n f o r ana i r c r a f t with a t u r b o j e t engine i s produced n e a r t h e c e i l i n g . F l i g h t d u r a t i o na t high a l t i t u d e i s 2-2.5 times g r e a t e r than a t low a l t i t u d e . The regimeof lowest hourly expenditure i s used when f l y i n g i n a holding p a t t e r n o r witha s t r o n g t a i l wind (150-200 km/hr) i n o r d e r t o maintain t h e scheduled time ofarrival. Let u s now analyze t h e way i n which t h e s e l e c t i o n o f f l i g h t speedi n f l u e n c e s t h e kilometer expenditure. I t was shown above t h a t ck = eh//3.6 V.S u b s t i t u t i n g t h e value = cpPr i n t h i s formula, we produce126
  • 135. If t h e p i l o t does n o t change t h e o p e r a t i n g regime of t h e engines, as t h e f l i g h t speed i s decreased from Vcrl t o Vcr2, t h e angle of a t t a c k and c ch=L Y i n c r e a s e . Allowing t h e a i r c r a f t t o f l y a t h i g h e r angles of a t t a c k is danger­ cI(=Ch= ous due t o t h e approach toward c and t h e s e p a r a t i o n l i m i t . Also, under Y Per r e l a t i v e l y h i g h temperature c o n d i t i o n s , t h e v e r t i c a l g u s t r e s e r v e i s decreased. T h e r e f o r e , i n c a s e such c o n d i t i o n s a r e encountered, t h e r o t a t i n g speed of t h e engine should b e i n c r e a s e d by an average of 5% f o r each 5-10 In C h W e r I V w e established t h a t t h of i n c r e a s e i n temperature, o r i f t h i s i s impossible, a lower f l y i n g a l t i t u d eon t h e r o t a t i n g speed o f t h e engine, a l t should b e r e q u e s t e d . L e t u s now go over t o an a n a l y s i s o A s t h e temperature d e c r e a s e s , t h e a v a i l a b l e t h r u s t i n c r e a s e s (curve 4)r e s e r v e w i t h i n t h e l i m i t s of p o s s i b l e s p and t h e curve of r e q u i r e d t h r u s t i s d i s p l a c e d t o t h e l e f t . The p o i n t of t h e i rFor example, i n t h e example o u t l i n e d abo: i n t e r s e c t i o n c d e f i n e s t h e new f l i g h t speed.t a k e o f f weight o f 44,000 kg, f . l i g h t a t 1 810 km/hr (M = 0.75-0.76) and an h o u r l y calm a i r a range on t h e o r d e r o f 2800-30 95. M o s t Favorable Horizontal F l i g h t Regimes. Influence o f A l t i t u d e and a high M number (V > 810 km/hr), t h e r a n S p e e d Figure 88 shows a f l i g h t p r o f i l e f o r an h o r i z o n t a l f l i g h t speeds, which a l s o i l l The f l i g h t range i s t h e d i s t a n c e t r a v e l e d by t h e a i r c r a f t d u r i n g t h e climb, h o r i z o n t a l f l i g h t and d e s c e n t . I f f l i g h t i s performed u n t i l t h e f u e l i s completely exhausted, t h e d i s t a n c e t r a v e l e d i s c a l l e d t h e t e c h n i c a l range. f l i g For passenger a i r c r a f t , t h e f l i g h t range given i s u s u a l l y t h a t with one h o u r s V= 75-OK+, f u e l r e s e r v e if t h e f l i g h t schedule i s maintained. (recommended regimes). S i n c e t h e r e a r e v a r i o u s ways which t h e a i r c r a f t can l e a v e t h e a r e a of t h e f l i g a i r f i e l d and climb a f t e r t a k e o f f , t h e range of f l i g h t covered d u r i n g t h e climb f u e l t o assigned a l t i t u d e changes s i g n i f i c a n t l y , However, t h e range covered d u r i n g f o r climb t o a l t i t u d e i s r e l a t i v e l y s l i g h t , s o t h a t i n t h e following w e w i l l u s i n d i s c u s s t h e range of h o r i z o n t a l f l i g h t . U 2800 L m and The range of t h e h o r i z o n t a l f l i g h t s e c t o r depends on t h e f u e l r e s e r v e f o r Figure 88. C h a r a c t e r i s t i c h o r i z o n t a l f l i g h t and on t h e r a t e a t which it i s expended, i . e . , t h e k i l o m e t e r F l i g h t P r o f i l e of A i r c r a f t at a e x p e n d i t u r e c - - t h e e x p e n d i t u r e of f u e l p e r k i l o m e t e r of f l i g h t p a t h . t o Range a t Fixed A l t i t u d e k it Before going over t o h o r i z o n t a l f l i g h t , t h e a i r c r a f t must t a k e o f f and climb. t h a t The f u e l e x p e n d i t u r e d u r i n g t h e t i m e of t a k e o f f and climb t o 9-11 km f o r two- and t h r e e - e n g i n e a i r c r a f t i s 1600-4000 kg.t h e engine must b e t h r o t t l e d back s o tha -p o i n t s A1, A and A3 r e s p e c t i v e l y (Figur 2 The f u e l expended d u r i n g t a k e o f f and e s t a b l i s h m e n t of nominal f l i g h t regime (without c o n s i d e r a t i o n o f climb) i s 250-350 kg, t h e f u e l expended - /130 The h o u r l y f u e l e x p e n d i t u r e ch = E d u r i n g t h e d e s c e n t and l a n d i n g i s 700-1000 kg. I n o r d e r t o determine t h e i q u a n t i t y of f u e l t o be used i n t h e h o r i z o n t a l f l i g h t s e c t o r Gf her, w e musth o r i z o n t a l f l i g h t Pr = P p , ch = c p P r . s u b t r a c t from t h e q u a n t i t y of f u e l t a k e n on board a l l supplementary expend- 1 I n o r d e r t o d e c r e a s e t h e f l y i n g s p i t u r e s and t h e n a v i g a t i o n a l r e s e r v e . F o r example, with a t a k e o f f weight ofmust be decreased. This r e s u l t s i n an , t h e a i r c r a f t o r 44,000 kg and an i n i t i a l f u e l weight of 13,000 kg, 7000­However, as t h e f l y i n g speed i s decreasc 7700 kg of f u e l remain f o r h o r i z o n t a l f l i g h t a t H = 10,000 m , s i n c e about 2000 kg a r e expended i n t a k e o f f and climbing, 800-1000 kg f o r descent anddecreased. Thus, a s t h e engine is t h r o ; l a n d i n g and 2500 kg are h e l d as n a v i g a t i o n a l r e s e r v e .d e c r e a s e s . The hourly expenditure w i l l 1 c 1change. W f i n d t h a t a s t h e f l i g h t spef emore i n t e n s i v e l y t h a n c P i n c r e a s e s . Thl I I 123
  • 136. For s h o r t e r range f l i g h t st h e q u a n t i t y of f u e l r e q u i r e d f w i l l correspond t o Vmf, a t which Pr min - G/Kmm. With V < Vmf, chf u e l expenditure norms remain ch min b e g i n s t o i n c r e a s e , s i n c e Pr i n c r e a s e s . Consequently, t h e g r e a t e s t f l i g h t The d u r a t i o n of h o r i z o n t a l d u r a t i o n a t any a l t i t u d e w i l l occur when f l y i n g a t t h e most f a v o r a b l e speed.where % i s t h e h o u r l y f u e l expc The h o u r l y f u e l expenditurca i r c r a f t i n one hour of horizon:t h r e e engines with a r e q u i r e d t l0 , 8 kg/kg-hr, t h e h o u r l y r a t e i t The r e l a t i o n s h i p between hcfrom t h e f o l l o w i n g c o n s i d e r a t i o r Figure 89. Explanation o f I n f l u e n c e o f F l i g h t% kg of f u e l . However, d u r i n g S p e e d o n Hourly and K i lometer F u e l Expend i t u r e snumerically e q u a l t o t h e f l i g h texpenditure p e r km i s Let u s e x p l a i n how t h e f l y i n g a l t i t u d e i n f l u e n c e s t h e h o u r l y e x p e n d i t u r e . I n 9 2 o f t h i s c h a p t e r w e showed t h a t t h e r e q u i r e d t h r u s t i s almost i d e n t i c a l f o r t h e same weight a t a l l f l y i n g a l t i t u d e s up t o 10,000 m. However, t h e r e q u i r e d speed i n c r e a s e s w i t h a l t i t u d e . T h e r e f o r e , t h e curves of r e q u i r e d t h r u s t a r e d i s p l a c e d toward t h e area of h i g h e r speeds w i t h i n c r e a s i n g a l t i t u d e ( s e e Figure 8 5 ) .where V i s taken i n km/hr. If L S i n c e t h e a v a i l a b l e t h r u s t of t h e engine d e c r e a s e s with a l t i t u d e , t h e curves o f t h e change i n t h r u s t w i t h v e l o c i t y a r e d i s p l a c e d downward w i t h an i n c r e a s e i n a l t i t u d e . T h e r e f o r e , whereas a t low a l t i t u d e t h e engines must b e t h r o t t l e d back, t h u s c o n s i d e r a b l y i n c r e a s i n g t h e s p e c i f i c e x p e n d i t u r e , a t 10,000 m l e s s t h r o t t l i n g i s r e q u i r e d and t h e s p e c i f i c e x p e n d i t u r e i n c r e a s e s only s l i g h t l y . When f l y i n g a t t h e c e i l i n g , t h e engines need n o t be t h r o t t l e d back a t a l l . T h e r e f o r e , as t h e f l y i n g a l t i t u d e i n c r e a s e s t h e product cpPr min F o r V = 880 km/hr and ch = d e c r e a s e s , which e x p l a i n s t h e d e c r e a s e i n h o u r l y e x p e n d i t u r e . Also, t h e Both t h e hourly and kilomet d e c r e a s e i n w i t h a l t i t u d e f a c i l i t a t e s a d e c r e a s e i n s p e c i f i c expenditure a ts p e c i f i c expenditure o f t h e engi c o n s t a n t o p e r a t i n g speed. T h e r e f o r e , t h e l o n g e s t f l i g h t d u r a t i o n f o r ans p e c i f i c and h o u r l y e x p e n d i t u r e s a i r c r a f t with a t u r b o j e t engine i s produced n e a r t h e c e i l i n g . F l i g h t d u r a t i o n1 kg of t h r u s t and one hour of e a t high a l t i t u d e i s 2-2.5 times g r e a t e r t h a n a t low a l t i t u d e . The regime of lowest h o u r l y e x p e n d i t u r e i s used when f l y i n g i n a h o l d i n g p a t t e r n o r w i t hwhile a t h r u s t o f P kg r e q u i r e s a s t r o n g t a i l wind (150-200 km/hr) i n o r d e r t o m a i n t a i n t h e scheduled time ofTherefore , arr i v a 1. Let u s now analyze t h e way i n which t h e s e l e c t i o n o f f l i g h t speed i n f l u e n c e s t h e k i l o m e t e r e x p e n d i t u r e . I t was shown above t h a t ck = ch/3.6 V. S u b s t i t u t i n g t h e v a l u e ch = cpPr i n t h i s formula, we produce124 126
  • 137. I n o r d e r t o s i m p l i f y o u r d i s c u s s i o n s , l e t u s assume t h a t c remains Pc o n s t a n t with changing f l i g h t speed, i . e . , c o n s i d e r t h a t n e i t h e r a d e c r e a s e i nengine t h r u s t n o r a d e c r e a s e i n t h e v e l o c i t y i t s e l f i n f l u e n c e s c Then i t Pf o l l o w s from t h e l a s t e x p r e s s i o n f o r c t h a t t h e minimum k i l o m e t e r e x p e n d i t u r e - ,133 kw i l l occur a t t h e speed f o r which t h e q u a n t i t y P / V i s minimal. In order t o rdetermine t h i s speed, we u s e t h e graph on Figure 89 b . The q u a n t i t yP / V = t a n $ ( a n g l e $ i s formed by t h e h o r i z o n t a l a x i s and a r a y from t h e rc o o r d i n a t e o r i g i n t o any p o i n t on curve P ) . When f l y i n g a t Vmf, rtan $ = P and when f l y i n g a t Vmm, t a n $ = P / V r minlVmf r max W can s e e from t h e f i g u r e t h a t w i t h d e c r e a s i n g f l i g h t speed, a n g l e 4 ed e c r e a s e s and reaches a minimum a t a speed corresponding t o t h e p o i n t ofc o n t a c t o f t h e r a y t o t h e curve o f r e q u i r e d t h r u s t . This speed, a t which Pr/Vi s minimal, w i l l be c a l l e d speed V With a f u r t h e r d e c r e a s e i n speed, angle 3$ b e g i n s t o i n c r e a s e , i . e . , P / V i s i n c r e a s e d . Thus, i f we c o n s i d e r t h e rs p e c i f i c e x p e n d i t u r e c o n s t a n t a s t h e speed i s changed, (Pr/V)min and conse­q u e n t l y a l s o t h e minimal k i l o m e t e r expenditure w i l l be produced a t speed V 3A s we can s e e , V i s always g r e a t e r t h a n Vmf. 3 Let us now c o n s i d e r t h a t t h e s p e c i f i c expenditure i s n o t c o n s t a n t withchanging speed and c o n s i d e r t h e i n f l u e n c e of t h r o t t l i n g of t h e motor onc I f f l i g h t i s performed a t V w e have high P / V and nominal motor P max ro p e r a t i n g speed, s o t h a t c h e r e i s minimal. When we d e c r e a s e t h e speed P ( d e c r e a s e motor o p e r a t i n g s p e e d ) , we d e c r e a s e P / V , but due t o t h e t h r o t t l i n g ro f t h e motors, c i n c r e a s e s . A t V3, t h e v a l u e of P / V i s minimal, b u t h e r e P rc i s i n c r e a s e d , s i n c e t h e engines are c o n s i d e r a b l y t h r o t t l e d . Comparing Pt h e s e two extreme p o s i t i o n s , we might conclude t h a t somewhere between Vmax andV t h e r e should be a speed a t which c P / V i s minimal. This speed i s s l i g h t l y 3 P r g r e a t e r t h a n V3 and i s c a l l e d t h e speed of minimal k i l o m e t e r e x p e n d i t u r e . For H = 0 w i t h a s p e c i f i c l o a d i n g o f 350-420 kg/m2, t h i s speed i s approximately450- 52 0 km/hr . W can see from Figure 90 t h a t as t h e a l t i t u d e i n c r e a s e s , t h e t r u e speed ecorresponding t o t h e minimal k i l o m e t e r e x p e n d i t u r e a l s o i n c r e a s e s . W can see efrom F i g u r e 91 t h a t t h e minimal k i l o m e t e r expenditure d e c r e a s e s up t o10,800 m , t h e n b e g i n s t o i n c r e a s e . The d e c r e a s e i n k i l o m e t e r e x p e n d i t u r e of 127
  • 138. , f u e l with i n c r e a s i n g a l t i t u d e i s f a c i l i t a t e d by t h e d e c r e a s e i n t h e q u a n t i t y P /V r e s u l t i n g from t h e i n c r e a s e d f l i g h t speed and decreased s p e c i f i c f u e l /134 r expenditure. I n t h i s example, t h e a l t i t u d e of 10,800 m a t which t h e minimum k i l o m e t e re x p e n d i t u r e i s produced i s c a l l e d t h e most f a v o r a b l e a l t i t u d e . For t u r b o j e ta i r c r a f t it i s 1000-1200 m below t h e p r a c t i c a l c e i l i n g , a t which a c o n s i d e r ­a b l e wave d r a g i s c r e a t e d due t o t h e high a n g l e s o f a t t a c k . T r a n s i t i o n t olower a l t i t u d e , i . e . , t o lower angles o f a t t a c k , d e c r e a s e s t h i s drag components i g n i f i c a n t l y and i n c r e a s e s t h e aerodynamic q u a l i t y . Let u s show t h a t t h ek i l o m e t e r e x p e n d i t u r e depends on q u a l i t y : Figure 90. S p e e d of M i n ­ Figure 91. Influe.nce of imal Kilometer Expend­ F l i g h t A l t i t u d e on M i n ­ i t u r e o f F u e l As a imal Kilometer F u e l Function of F l y i n g Expend i t u r e Altitude (aircraft w i t h two e n g i n e s ) W can see from t h e formula t h a t t h e k i l o m e t e r e x p e n d i t u r e i s i n v e r s e l y ep r o p o r t i o n a l t o t h e q u a l i t y . Now w e can f o r m u l a t e a d e f i n i t i o n of mostfavorable f l i g h t a l t i t u d e : t h e a l t i t u d e corresponding t o (KV) called t h e max ’most f a v o r a b l e a l t i t u d e o r t h e a l t i t u d e o f l e a s t k i l o m e t e r e x p e n d i t u r e . The dependence o f t h e a l t i t u d e of t h e p r a c t i c a l c e i l i n g and t h e a l t i t u d eof minimal k i l o m e t e r e x p e n d i t u r e on f l y i n g weight of a TU-124 a i r c r a f t i sshown on Figure 9 2 , w h i l e F i g u r e 93 shows t h e dependence o f t h e minimalk i l o m e t e r e x p e n d i t u r e f o r t h i s a i r c r a f t on f l i g h t speed. W can s e e from t h i s el a s t graph t h a t t h e minimal k i l o m e t e r e x p e n d i t u r e i s produced a t128
  • 139. V = 752 km/hr. T h i s i s t h e speed V a t t h e most f a v o r a b l e a l t i t u d e . C k minF l i g h t s a t lower and h i g h e r speeds and a t o t h e r a l t i t u d e s cause i n c r e a s e s i nk i l o m e t e r expenditure. I t has been e s t a b l i s h e d t h a t a t speeds 5-8% (30-50 km/hr) h i g h e r t h a n , t h e k i l o m e t e r e x p e n d i t u r e i s i n c r e a s e d by an average of 1%( f o r"k minexample, i f ck min = 3 kg/km, i t w i l l be i n c r e a s e d t o 3.03 kg/lcm), and t h a tt h i s i s t h e optimal regime f o r l o n g - d i s t a n c e f l i g h t s . T h i s c r u i s i n g regimei s t h e most economical as concerns t o t a l t r a n s p o r t a t i o n c o s t , s i n c e i t - / 135consumes l i t t l e f u e l , allowing h i g h e r commercial load t o b e c a r r i e d . For medium range f l i g h t s (1300-1500 km), t h e h i g h e s t c r u i s i n g regime i srecommended, i n which t h e k i l o m e t e r e x p e n d i t u r e s a r e h i g h e r b u t t h e i n c r e a s e df u e l load does n o t r e q u i r e a d e c r e a s e i n commercial l o a d , b u t t h e i n c r e a s e i nspeed does d e c r e a s e t h e f l y i n g t i m e , as a r e s u l t of which t h e c o s t o f t r a n s ­p o r t a t i o n i s decreased. These regimes correspond t o f l y i n g a l t i t u d e s o f7000-9000 m and maximal i n d i c a t e d speeds, o r maximum p e r m i s s i b l e M number a thigher a l t i t u d e s . rre 700 752 800 K M / ~r Figure 9 2 . Height of Figure 93. Minimal Kilo­ P r a c t i c a l C e i l i n g and meter Expenditure of F u e l H e i g h t of Minimal Kilometer As a Function of F l i g h t Expenditure o f F u e l As a S p e e d ( a i r c r a f t w i t h two Function of F l y i n g W e i g h t eng i nes) (TU-124 a i r c r a f t )56. D e f i n i t i o n of Required Q u a n t i t y of F u e l I n o r d e r t o determine t h e f u e l expenditure i n f l i g h t s t o v a r i o u sd i s t a n c e s a t v a r i o u s a l t i t u d e s w i t h v a r i o u s winds, a s p e c i a l graph must beused (Figure 9 4 ) . I n c a l c u l a t i n g t h i s graph, we assume t h e mean c r u i s i n gregime of engine o p e r a t i o n , with a k i l o m e t e r expenditure of one p e r c e n t 129
  • 140. I1 I I 1 g r e a t e r than t h e minimal. This i s s u f f i c i e n t t o provide a f u e l r e s e r v e i n case t h e f l i g h t i s performed a t h i g h e r o r lower speed t h a n t h e minimal expenditure speed. The climbing and descending regimes f o r t h e a i r c r a f t a r e i d e n t i c a l i n p r a c t i c a l l y a l l c a s e s . Therefore, t h e expenditures o f time and f u e l f o r t h e s e p o r t i o n s of t h e f l i g h t can be considered c o n s t a n t , dependent only on t h e f l y i n g a l t i t u d e . The d i s t a n c e t r a v e l e d by t h e a i r c r a f t during t h e climb and descent a l s o depends only on a l t i t u d e . When it i s necessary t o determine t h e f l i g h t range o r f u e l r e s e r v e p r e c i s e l y under s p e c i a l c o n d i t i o n s ( s p e c i a l f l i g h t s ) , a graph of t h i s t y p e must be c o n s t r u c t e d f o r t h e regime s e l e c t e d . Figure 94 allows us t o determine - /136 without c a l c u l a t i o n s t h e range of an a i r c r a f t f o r a given q u a n t i t y of f u e l f o r any p o i n t . For example, p o i n t 4 corresponds t o a f u e l r e s e r v e of 7750 kg and a f l i g h t range (calm wind) of 2220 km a t H = 10,000 m. The lower p o r t i o n o f t h e graph p r e s e n t s c o r r e c t i o n s c o n s i d e r i n g t h e i n f l u e n c e of wind. Distance between a i r p o r t s (S), Figure 94. Total Fuel Expenditure As a Function o f Distance, A l t i t u d e and Wind I f we must determine t h e f u e l expenditure f o r f l i g h t o f 1700 km a t 8000 m with a t a i l wind of 175 km/hr, we move from p o i n t 1, corresponding t o s = 1700 km along t h e i n c l i n e d l i n e s f o r wind t o p o i n t 2 corresponding t o a t a i l wind of 175 km/hr. Then we move v e r t i c a l l y upward t o t h e assigned a l t i t u d e of 8000 m ( p o i n t 3 ) and h e r e read t h e f u e l expenditure: 5500 kg. Adding t h e n a v i g a t i o n a l r e s e r v e , we produce t h e q u a n t i t y o f f u e l which must be placed i n t o t h e f u e l t a n k s of t h e a i r c r a f t . For a f l i g h t of t h e same range with a head wind o f 80 km/hr (point 2) a t 7000 m, 8000 kg w i l l be required (point 3 ) . 130
  • 141. I n p r o c e s s i n g t h e m a t e r i a l o f f l y i n g t e s t s with r e s p e c t t o f u e l r e s e r v e s ,w e u s u a l l y determine t h e f l y i n g a l t i t u d e most s u i t a b l e as concerns t o t a lf l i g h t Cost. Table 9 p r e s e n t s t h e s e a l t i t u d e s f o r one passenger a i r c r a f t . A s w e can see from t h e t a b l e , even a t 200-400 km range, t h e f l i g h t shouldb e performed at 4500-7000 m, s i n c e t h i s w i l l produce minimum f u e l e x p e n d i t u r e . /137F l i g h t s o v e r t h e s e ranges a t 1200-1500 m ( t h e a l t i t u d e of t h e IL-14 a i r c r a f t ) -are i n e f f i c i e n t , s i n c e due t o t h e comparatively low t r u e f l y i n g speeds ( 5 7 0 ­600 km/hr, i n d i c a t e d speed 480-550 km/hr) t h e k i l o m e t e r expenditure i s r a t h e rhigh. TABLE 9 - . .. ~~ . . ~ * &-- __ - ­ Distance, km Most favor­ able a l t i t u d e , m57. F l i g h t a t t h e "Ceilings" With d e c r e a s i n g f l y i n g weight of t h e a i r c r a f t , t h e h e i g h t of minimalk i l o m e t e r e x p e n d i t u r e (most f a v o r a b l e a l t i t u d e ) i n c r e a s e s (Figure 9 2 ) . Thisdependence i s used when f l y i n g a t t h e " c e i l i n g s . " The weight o f t h e a i r c r a f twhen f l y i n g t o maximum range can be reduced by 10-25 t (by 10-30% of i n i t i a lw e i g h t ) . I n o r d e r t o keep t h e a i r c r a f t f l y i n g a t a l l times a t ck min, t h ea l t i t u d e must be g r a d u a l l y i n c r e a s e d as t h e f u e l i s consumed. The d e n s i t yshould b e decreased i n p r o p o r t i o n t o t h e d e c r e a s i n g f l y i n g weight. This t y p eof f l i g h t i s c a l l e d f l i g h t a t t h e c e i l i n g s . This i s t h e way i n which maximumrange can b e a t t a i n e d . During t h e p r o c e s s o f such a f l i g h t , t h e a i r c r a f t w i l lremain c o n t i n u o u s l y a t 1000-1200 m below i t s c u r r e n t p r a c t i c a l c e i l i n g . W should n o t e t h a t c i v i l a i r c r a f t perform f l i g h t s a t assigned a l t i t u d e s . eHowever, it i s of i n t e r e s t t o t h e p i l o t t o know t h e s p e c i f i c n a t u r e of f l i g h ta t t h e c e i l i n g s , s i n c e he may f i n d t h i s f l i g h t n e c e s s a r y , f o r example, whenf l y i n g along o t h e r t h a n e s t a b l i s h e d a i r l a n e s and i n o t h e r cases when maximumrange must be a t t a i n e d . Let us analyze t h e performance of a f l i g h t a t t h e c e i l i n g s ( F i g u r e 95)u s i n g a TU- 1_24 a i r c r a f t . The i n i t i a l a l t i t u d e f o r t h i s t y p e o f f l i g h t w i l l b e10,500 m. This a l t i t u d e ( p e r m i s s i b l e on t h e b a s i s o f t h e c o n d i t i o n o f t h ee f f e c t on t h e a i r c r a f t o f a 1 0 - s / s e c v e r t i c a l g u s t ) w i l l correspond t o ana c t u a l a i r c r a f t weight a t t h e i n n i n g of t h e f l i g h t o f 36 t (we w i l lc o n s i d e r t h a t t h e f l i g h t i s nc- along an e s t a b l i s h e d a i r l a n e ) . A t t h i s a l t i t u d e ( p = 0.0395 kg*sec2/m4, f u e l weight 8400 k g ) , t h e p i l o t 131
  • 142. should e s t a b l i s h a h o r i z o n t a l f l i g h t speed of Vc , which i n t h i s c a s e k min *corresponds t o M = 0.7. T h i s a i r speed w i l l b e maintained throughout t h ee n t i r e f l i g h t . A f t e r approximately 2 h r 36 min, t h e p i l o t h a s expendedabout 5200-5400 kg f u e l , i . e . , 15.5% of t h e i n i t i a l weight. The a i r d e n s i t yshould b e decreased by t h e same f a c t o r : 0.0395.84.5 = 0.0334 kg.sec2/m4 (84.5% d e n s i t y a t H = 10,500 m), meaning t h a t t h e a i r c r a f t w i l l a c t u a l l y haver i s e n t o an a l t i t u d e o f 11,800 m ( s e e s t a n d a r d atmosphere t a b l e ) , i . e . , w i l lhave climbed by 1300 m, w i t h a v e r t i c a l v e l o c i t y component o f 1300/156-60 == 0.139 m/sec. I t i s d i f f i c u l t t o m a i n t a i n t h i s speed u s i n g t h e v a r i o m e t e r ,p i l o t i n g t h e a i r c r a f t by r e f e r r i n g t o t h e t h i n . n e e d l e o f t h e KUS-1200 speedi n d i c a t o r . In p r a c t i c e , i t i s e a s i e r t o maintain t h e M number s t e a d y u s i n gt h e M number i n d i c a t o r , s i n c e t h e v a l u e of a scale d i v i s i o n of t h i s instrumenti s 0.01. A t 10,000-12,000 M, t h e a i r temperature, and consequently t h e speedof sound, remains p r a c t i c a l l y unchanged, so t h a t with c o n s t a n t M number, t h et r u e speed w i l l a l s o remain c o n s t a n t . I n t h i s example as t h e weight i s changed f o r each 1000 kg t h e flying altitude is i n c r e a s e d by 200-220 m. For a i r c r a f t with h o u r l y f u e l expend­ i t u r e s of 4000-5000 kg, t h e increase i n a l t i t u d e w i l l be 50-70 m . In f l i g h t a t the ceilings, the r o t a t i n g speed of t h e engines and t h e M 36 min+28min = 3 h r 29 m i n number must b e kept c o n s t a n t . If t h e a i r Figure 95. P r o f i l e of F l i g h t a t t h e temperature changes, c e i l i n g s : a , A t most f a v o r a b l e a l t i t u d e s ; t h e engine r o t a t i n g b, C e i l i n g ; c , W i t h a l t i t u d e l i m i t e d speed should be changed according t o f l y i n g w e i g h t by one p e r c e n t f o r each So ( d e c r e a s i n g w i t h d e c r e a s i n g temperatureand i n c r e a s i n g with i n c r e a s i n g t e m p e r a t u r e ) . Flying t e s t s have e s t a b l i s h e d t h a t f l i g h t a t t h e c e i l i n g s can i n c r e a s et h e range by 3-8%. F l i g h t a t t h e c e i l i n g s can b e p r i m a r i l y used i n c a s e o fengine f a i l u r e , when it i s necessary t o c o n t i n u e f l y i n g t o t h e assignedd e s t i n a t i o n . I t i s h e r e t h a t t h e advantages o f t h i s t y p e o f f l y i n g a r e mostnotable.132
  • 143. 98. P e r m i s s i b l e F l y i n g A l t i t u d e s . Influence o f A i r c r a f t W e i g h t / 139 The o p e r a t i o n of j e t a i r c r a f t with high p r a c t i c a l c e i l i n g s (11,500­13,000 m h a s shown t h a t i t i s n o t always p o s s i b l e t o f l y a t t h e s e a l t i t u d e s , )o r even a t t h e a l t i t u d e o f minimal kilometer expenditure (most f a v o r a b l ea l t i t u d e , Figure 92). The problem i s t h a t t h e f l y i n g a l t i t u d e of a highspeed a i r c r a f t is s e l e c t e d on t h e b a s i s o f t h e c o n d i t i o n o f maintenance of areserve f o r overloads i n case a v e r t i c a l wind gust is encountered. ChapterXIw i l l p r e s e n t an a n a l y s i s o f t h e e f f e c t o f a v e r t i c a l g u s t on an a i r c r a f t , andnow l e t u s analyze t h e i n f l u e n c e o f a i r c r a f t weight on t h e s e l e c t i o n ofp e r m i s s i b l e f l i g h t a l t i t u d e , u s i n g t h e combined graphs c = f(M) and Y PerC = f(M). Yhf Let u s analyze t h e f l i g h t o f a TU-124 weighing 34 t a t 10,000 m a t aspeed corresponding t o M = 0.75, and e x p l a i n t h e p e r m i s s i b l e overload i n caseo f a v e r t i c a l maneuver from t h e s t a n d p o i n t of s a f e t y . As we can see from t h e CY hF f i g u r e , f o r t h e s e a l t i t u d e s and M numbers t h e a i r c r a f t will have = 0.3 and c = 0.715. yh f Y Per Consequently, t h e r e s e r v e with r e s p e c t t o c will be AC = c y- = 0.715 ­ Y Y Per CYhf - 0 . 3 = 0.415. I n case a v e r t i c a l gust i s encountered o r i n case of maneuver, t h i s r e s e r v e may be expended and t h e a i r c r a f t w i l l find i t s e l f a t c . This Y Per r e q u i r e s t h a t t h e overload C per 0.715 N per = Y = - 2.4. Y C h.f. 0 .. 3 Y Figure 96. Combined Graphs o f Dependences o f Coef f i c i e n t s c Yhf This w i l l be t h e value of and c on M Number of F l i g h t p e r m i s s i b l e overload. Each Y Per M number (with unchanged weight) corresponds t o a d e f i n i t e B j o i n i n g t h e p o i n t s corresponding t o t h e s e v a l u e s , we y Of CYhfproduce t h e dependence c = f(M) (Figure 9 6 ) . A s w e can s e e from Figure 96, Y f hi n t h e range of numbers M = 0.7-0.75, t h e r e s e r v e with r e s p e c t t o c i s Ymaximal. With high M numbers, p a r t i c u l a r l y a t M > 0 . 8 , t h e r e s e r v e of c i s Ydecreased. This r e s e r v e i s a l s o decreased with i n c r e a s i n g f l i g h t a l t i t u d e(with unchanged weight) and i n c r e a s i n g a i r c r a f t weight ( a t constant a l t i t u d e ) . 133
  • 144. The r e s e r v e of c i s e q u i v a l e n t t o r e s e r v e a g a i n s t a v e r t i c a l g u s t . I n Y - /140p a r t i c u l a r , it i s r e q u i r e d f o r a passenger a i r c r a f t t h a t i f an e f f e c t i v ei n d i c a t o r g u s t o f 10 m/sec i s encountered, t h e a i r c r a f t w i l l r e a c h onlyC n o t encountering s t a l l ( s e e d e f i n i t i o n i n C h a p t e r X I ) . Therefore; i n Y Pero r d e r t o avoid exceeding c and c a u s i n g t h e a i r c r a f t t o s t a l l , p e r m i s s i b l e Y Perf l y i n g a l t i t u d e s are e s t a b l i s h e d as a f u n c t i o n o f f l y i n g weight (Figure 9 7 ) .I f t h e s e l i m i t a t i o n s are n o t observed, a v e r t i c a l g u s t o f lower magnitude w i l lbring t h e aircraft t o c or stall. Y Per The d e c r e a s e i n weight r e s u l t i n g from consumption o f f u e l i n c r e a s e s t h er e s e r v e w i t h r e s p e c t t o c and, t h e r e f o r e , t h e r e s e r v e f o r v e r t i c a l g u s t s ; Yt h e r e f o r e , t h e f l y i n g a l t i t u d e can b e i n c r e a s e d . I n t h e same way as t h ea l t i t u d e i s decreased ( f o r example t o 5000 m), t h e r e s e r v e with r e s p e c t t o c Yand gusts i n c r e a s e s . For M = 0.6 (V = aM = 32000.6 = 198 m/sec) , c - yhf ­= 0.24 and c = 0.92 (Figure 96). I n t h i s case, t h e overload p e r m i s s i b l e Y Perwith r e s p e c t t o c w i l l b e n = 0.92/0.24 = 3.83. Y Y Per Figure 97 shows a graph o f p e r m i s s i b l e f l y i n g a l t i t u d e ( f o r t h i sexample) as a f u n c t i o n of f l y i n g weight. The s t a n d a r d p r a c t i c e of assigning a l t i t u d e intervals of I f 500 1000 m a t a l t i t u d e s above 6000 m rmu -r - - - reduces t h e " r e s o l v i n g capacity" o f ----I- -- - 3- a i r c r a f t as t o p e r m i s s i b l e a l t i t u d e ; fUz0D tom -1- -I- - - 4 -- t h e r e f o r e , i t would b e more d e s i r a b l e t o u s e s e p a r a t i o n s o f 600 m a l t i t u d e . 29 32 354 The h e i g h t s o f f l i g h t a t t h e c e i l i n g s correspond t o p e r m i s s i b l e f l y i n g Figure 97. P e r m i s s i b l e F l y i n g altitudes. A l t i t u d e A s a Function o f Air­ c r a f t Weight The l i m i t a t i o n on f l y i n g a l t i t u d e i s n o t t h e only l i m i t a t i o n f o r a high speed passenger a i r c r a f t .The second l i - m i t a t i o n i s t h e p e r m i s s i b l e M number f o r f l i g h t s a t higha l t i t u d e s (Chapter X$ 512). AS f l y i n g o p e r a t i o n s have shown, t h e mostf a v o r a b l e c r u i s i n g f l i g h t regimes as t o M number and a l t i t u d e f o r t h e f i r s tg e n e r a t i o n of a i r c r a f t d i f f e r s l i g h t l y from safe regimes as concerns t h ec o n d i t i o n s of encountering powerful ascending g u s t s .59. E n g i n e F a i l u r e During Horizontal F1 i g h t I n c a s e of engine f a i l u r e , i f c a n a i r c r a f t cannot c o n t i n u e f l y i n g a ta l t i t u d e s o r d i n a r i l y used (8000-11,000 m). As we know, i n f l i g h t s a t a l t i ­t u d e s below t h e c e i l i n g a t speeds lower t h a n t h e maximal, t h e engines a r e134
  • 145. t h r o t t l e d t o some e x t e n t . This i s a l s o t r u e of c r u i s i n g f l i g h t regimes a t 8000-11,000 m . The n e c e s s i t y of reducing engine speed i n t h e s e regimes causes /141 an i n c r e a s e i n t h e s p e c i f i c f u e l e x p e n d i t u r e . I n case of f a i l u r e of one engine, t h e p i l o t w i l l b e forced t o s e t t h e remaining engines a t t h e nominal regime (which i s permitted f o r long term o p e r a t i o n ) , which should reduce t h e s p e c i f i c e x p e n d i t u r e . However, i n t h i s case t h e d r a g i s increased due t o a u t o r o t a t i o n of t h e compressor and t u r b i n e o f t h e engine which has f a i l e d ( f o r example, a t V = 600-620 km/hr a t 4000-5000 m a l t i t u d e , t h e a u t o r o t a t i o n drag i s 150-300 kg), l e a d i n g t o an i n c r e a s e i n t h e k i l o m e t e r and h o u r l y e x p e n d i t u r e s . I n c a s e o f an engine f a i l u r e , h o r i z o n t a l f l i g h t a t a l t i t u d e s above 6000-7000 m i s impossible, and t h e a i r c r a f t w i l l descend t o 5500-6000 m (two-engine a i r c r a f t , Figure 9 8 ) . For a i r c r a f t with t h r e e and f o u r engines i n c a s e of f a i l u r e o f one engine, t h e d e c r e a s e i n a l t i t u d e i s not s o g r e a t . The a l t i t u d e a t which a t h e a i r c r a f t can f l y without f u r t h e r descent w i l l be e s s e n t i a l l y t h e i n i t i a l a l t i t u d e of f l i g h t a t t h e c e i l i n g s with one nonoperating motor, i f long range f l i g h t must be Derformed and a landing " 0 500 I0 00 m-0 L, KM cannot be made immediately a f t e r t h e motor f a i l s . Figure 98. P r o f i l e of F l i g h t of A i r c r a f t . w i t h Two E n g i n e s i n Case of F a i l u r e of O n e I n case of a motor E n g i n e A f t e r 45 m i n F l y i n g Time: a , Point f a i l u r e , i t i s necessary of f a i l u r e ; b , Descending t r a j e c t o r y ( t i m e f i r s t of a l l t o achieve 37 m i n , L = 400 km); c , F l i g h t w i t h t h e l e a s t p o s s i b l e r a t e of increasing a l t i t u d e v e r t i c a l descent and secondly t o decrease t h e weight of t h e a i r c r a f tr a p i d l y (using up f u e l ) i n o r d e r t o make i t p o s s i b l e t o continue h o r i z o n t a lf l i g h t with one nonoperating engine a t high a l t i t u d e . Therefore, t h e descentshould be made a t t h e nominal regime, g r a d u a l l y decreasing t h e v e r t i c a lv e l o c i t y component, which a t t h e beginning of t h e descent w i l l beV = 3-5.5 m/sec. The i n d i c a t e d speed f o r each a i r c r a f t depends on t h e Ys p e c i f i c loading on t h e wing and t h e power f a c t o r . For exam l e , f o r an 8a i r c r a f t with two engines and a s p e c i f i c loading of 350 kg/m , an i n d i c a t e d speed of 430 km/hr was produced. The descent from 10,000-11,000 m t o t h e /142 p r a c t i c a l c e i l i n g of t h e a i r c r a f t with one nonoperating engine occurs i n 35-45 min. Over t h i s time, t h e a i r c r a f t covers 350-500 km. I f i t i s necessary t o continue t h e f l i g h t , t h e p i l o t should s h i f t t h ea i r c r a f t t o t h e regime o f f l y i n g a t t h e c e i l i n g s ; then i n 60-70 min t h ea i r c r a f t w i l l cover another 650-750 km, with an i n c r e a s e i n a l t i t u d e of800-1000 m and an average r a t e of a l t i t u d e i n c r e a s e of 0.15-0.2 m/sec. F l i g h t 135 , .., . . I
  • 146. should b e performed a t M = 0.50-0.55, corresponding a t 5500-6500 m a l t i t u d e t oa t r u e speed o f 600-650 km/hr. The mean k i l o m e t e r f u e l e x p e n d i t u r e f o r ana i r c r a f t with two engines a t t h i s s t a g e w i l l b e about 3 . 5 kg/km, which i sapproximately 0 . 5 kg/km g r e a t e r t h a n a t 10,000 m with two engines o p e r a t i n g .Thus, t h e f l i g h t range with one engine n o t o p e r a t i n g i s always l e s s . A g a i n i n f l y i n g range with one engine n o t o p e r a t i n g can be produced onlyif t h e i n i t i a l f l y i n g weight was planned (due t o u n a v a i l a b i l i t y o f h i g h e ra l t i t u d e s o r o t h e r reasons) f o r a low a l t i t u d e , f o r example 6000-7000 m. F o rexample, f o r t h e TU-104 a i r c r a f t a t t h i s a l t i t u d e a t 800 km/hr, t h e h o u r l yf u e l e x p e n d i t u r e i s 3100 kg/hr, and t h e k i l o m e t e r e x p e n d i t u r e i s 3100/800 == 3.88 kg/km. I n case one engine f a i l s , it i s p o s s i b l e t o f l y a t 5000 m and620 km/hr, t h e second engine o p e r a t i n g a t t h e nominal regime w i t h an h o u r l ye x p e n d i t u r e of 2200-2300 kg/hr. I n t h i s c a s e t h e k i l o m e t e r expenditure w i l lbe about 3.6 kg/km, i . e . , l e s s t h a n i n f l i g h t w i t h both engines ( f o r t h i sa l t i t u d e ) and t h e p o s s i b l e f l y i n g range i n c r e a s e s . In a l l c a s e s i n case of f a i l u r e o f one engine, t h e crew should r e t u r nt o t h e a i r f i e l d o f o r i g i n i f p o s s i b l e o r land a t t h e n e a r e s t a v a i l a b l ea i r f i e 1d .010. M i n i m u m P e r m i s s i b l e Horizontal F1 i g h t S p e e d The most f a v o r a b l e h o r i z o n t a l f l i g h t speed i s t h e d i v i s i o n between t h etwo f l i g h t regimes. However, i n e s t a b l i s h i n g t h e minimum p e r m i s s i b l e speed,t h e most f a v o r a b l e speed i s not t a k e n i n t o c o n s i d e r a t i o n , b u t c a l c u l a t i o n sa r e based on c produced ?or low M numbers. The v a l u e of c which Y per’ y max’i s used t o determine t h e s t a l l speed, i s a l s o n o t used i n t h i s c a s e . Let u s determine t h e minimum speed o f h o r i z o n t a l f l i g h t , i . e . , t h e speedcorresponding t o c assuming t h a t t h e wing a r e a i s 120 m 2 , t h e a i r c r a f t Y per’weight i s 50 t , and c = 1 . 2 (from t h e graph on F i g u r e 9 6 ) : Y Per When v a l u e s o f c > c are achieved, t h e s t a b i l i t y o f an a i r c r a f t /143 Y Y Perwith a smooth wing ( f l a p s up) may be d i s r u p t e d . I n o r d e r t o prevent a l o s s ofspeed and a s t a l l , t h e minimum p e r m i s s i b l e h o r i z o n t a l f l i g h t speed should be.50-60 km/hr g r e a t e r t h a n t h e a b s o l u t e l y minimal speed. I n o u r example, t h i sw i l l be 320 km/hr. A f t e r 10 t of f u e l have been expended (Ginst = 40 t ) w eproduce (according t o t h e l a s t formula) t h e minimal p o s s i b l e speed of240 km/hr, s o t h a t t h e minimal p e r m i s s i b l e speed w i l l b e 300 km/hr.136
  • 147. Frequently, i n o r d e r t o avoid t h e n e c e s s i t y o f memorizing many v a l u e s o fminimal p e r m i s s i b l e speed, f l y i n g handbooks show o n l y t h e v a l u e f o r m a x i m u mweight. I n our example, t h i s w i l l b e 320 km/hr. When f l y i n g a t t h i s speed,an a i r c r a f t weighing 40-50 t o r l e s s w i l l have c < c by 30-40%. With Y Y Pernormal o p e r a t i o n o f t h e a i r c r a f t , f l y i n g a t 320 km/hr is n o t p e r m i s s i b l e ,s i n c e even f o r c i r c l e f l i g h t s t h e speed a t t h i s weight (S = 120 m2) should be350-370 km/hr. T h i s l i m i t a t i o n w i l l provide f l i g h t s a f e t y . 137
  • 148. Chapter V I I I . Descent / 143 91. General Statements. Forces Acting on A i r c r a f t During Descent Descent refers t o s t e a d y , s t r a i g h t l i n e f l i g h t o f t h e a i r c r a f t on adescending t r a j e c t o r y . Descent a t low power, when t h e t h r u s t a t 8000­10,000 m i s f l i g h t , w i l l b e c a l l e d g l i d i n g . Usually, passenger a i r c r a f tdescend with t h e engines o p e r a t i n g a t 80-86% r e v o l u t i o n s , a t which t h e t h r u s tis g r e a t e r t h a n a t t h e i d l e ( f o r example, t h e i d l e a t H = 10,000 m mightcorrespond t o 72-74% r e v o l u t i o n ) . The p r e s e n c e o f motor t h r u s t i n c r e a s e s t h edescent range and d e c r e a s e s t h e a n g l e of i n c l i n a t i o n o f t h e t r a j e c t o r y . Following h i s a s s i g n e d a l t i t u d e (9000-11,000 m) t h e p i l o t begins h i sdescent a t 250-300 km from t h e a i r f i e l d a t a h i g h i n d i c a t e d speed(550-650 km/hr). The time f o r t h e beginning o f t h e d e s c e n t i s c a l c u l a t e d bythe navigator. I n t h o s e c a s e s when t h e f l i g h t range i s n o t over 1000-1200 km and f u e leconomy i s of l e s s s i g n i f i c a n c e t h a n f l y i n g time economy, t h e descent i sperformed a t t h e g r e a t e s t p e r m i s s i b l e i n d i c a t e d speed o r M number. Figure 99 shows t h e f o r c e s a c t i n g on an a i r c r a f t d u r i n g t h e descent withengines o p e r a t i n g . The angle of i n c l i n a t i o n of t h e t r a j e c t o r y of t h e d e s c e n tfrom 9000-11,000 m w i l l be 0 = 2.5-3, t h e p i t c h a n g l e = 2-2.5. I t must b e /144b e noted t h a t a n g l e 0 does n o t remain c o n s t a n t , b u t r a t h e r changes as af u n c t i o n of t h e v e r t i c a l component of t h e d e s c e n t , which i s maintained by t h ep i l o t by s e t t i n g t h e corresponding engine o p e r a t i n g regime. Operational e x p e r i e n c e has shown t h a t d u r i n g a descent from 9000­1 1 , 0 0 0 m with t r u e speeds o f 850-900 km/hr, a t f i r s t a v e r t i c a l speed o f8-10 m/sec must be maintained, t h e n g r a d u a l l y decreased s o t h a t by5000-6500 m , when t h e p r e s s u r e i n t h e c a b i n i s c o n s t a n t (Figure 100) t h ev e r t i c a l speed i s n o t over 5-6 m/sec. A t a l t i t u d e s o f l e s s t h a n 5000 m , t h ev e r t i c a l speed can b e i n c r e a s e d t o 10 m/sec. W w i l l consider t h a t t h e et h r u s t of t h e engines P a c t s i n t h e d i r e c t i o n o f movement o f t h e a i r c r a f t ,although as was s t a t e d above t h e r e i s a c e r t a i n angle B between f o r c e P andt h e d i r e c t i o n of movement of t h e a i r c r a f t . The l i f t i n g f o r c e Y i s perpen­d i c u l a r t o t h e d i r e c t i o n of movement of t h e a i r c r a f t , and t h e drag 0 a c t s i nt h e d i r e c t i o n o p p o s i t e t o a i r c r a f t movement. For a s t a b l e d e s c e n t , it i s necessary t h a t t h e a i r c r a f t weight componentG cos 0 b e balanced by f o r c e Y , and t h a t f o r c e Q be balanced by t h e weightcomponent G s i n 0 and f o r c e P , i . e . , t h a t t h e f o l l o w i n g e q u a l i t y be f u l f i l l e d :138
  • 149. Y=G cos 0 ; Q . = P f G sin 8. rd Horizon L i n e Figure 99. Diagram o f Forces Acting on A i r c r a f t During Descent: 1 , Longitudinal a x i s o f a i r ­ c r a f t ; 2 , Descent t r a j e c t o r y ; 6 , P i t c h a n g l e ; 0, , F l i g h t - p a t h a n g l e ; 4 , R i g g i n g a n g l e of . incidence; a, Angle o f attack The f i r s t e q u a l i t y i s t h e c o n d i t i o n f o r s t r a i g h t l i n e movement, while t h e /145 -second i s t h e c o n d i t i o n f o r c o n s t a n t v e l o c i t y on t h e t r a j e c t o r y .92. Most Favorable Descent Regimes I n o r d e r t o analyze t h e most f a v o r a b l e descent regimes from t h e s t a n d ­p o i n t of f u e l economy, l e t us use t h e formula Q = P + G s i n @, which char­a c t e r i z e s t h e c o n d i t i o n of c o n s t a n t v e l o c i t y . Let u s analyze a t f i r s t descentwith engines t h r o t t l e d . W w i l l c o n s i d e r t h a t when t h e engines o p e r a t e a t t h e i d l e , t h e descent eoccurs only under t h e i n f l u e n c e of t h e component G s i n 0, when Q = G s i n 0. Let u s assume t h a t t h e f l y i n g weight of t h e a i r c r a f t G = 33,000 kg, f o r c eQ = 3000 kg with a q u a l i t y of 11 and t h e f l i g h t speed i s 810 km/hr. Thens i n 0 = Q/G = 3000/33,000 = 0.091 and t h e a n g l e of i n c l i n a t i o n o f t h etrajectory 0 So. I n o r d e r t o m a i n t a i n t h i s angle 0, w i t h a forward speed ofV = 810 km/hr ( 2 2 5 m/sec) it i s n e c e s s a r y t o m a i n t a i n a v e r t i c a l speed 139
  • 150. As t h e f l y i n g a l t i t u d e is decreased, t h e t r u e speed o f t h e a i r c r a f t w i l ld e c r e a s e and, consequently, i n o r d e r t o r e t a i n t h e c o n s t a n t t r a j e c t o r y a n g l e ,t h e v e r t i c a l v e l o c i t y component must be i n c r e a s e d t o 15-17 m/sec. With t h i s s o r t o f v e r t i c a l speed, t h e t o t a l d e s c e n t time t o t h e h o l d i n ga l t i t u d e w i l l b e 10-12 min, and t h e t o t a l f u e l e x p e n d i t u r e 300-400 kg, t h edescent range 120-170 k ( c o n s i d e r i n g t h e c o n s i d e r a b l e d e c r e a s e i n v e r t i c a l mspeed involved a t low a l t i t u d e s ) . T h i s method of d e s c e n t i s used when t h e c a b i n a i r p r e s s u r e r e g u l a t i o n canprovide normal c o n d i t i o n s f o r crew and p a s s e n g e r s . Another descent regimei s t h a t i n which t h e engine speed i s maintained o v e r t h e i d l e ( i n p r a c t i c e i npassenger a i r c r a f t t h e d e s c e n t a t i d l i n g regime i s j u s t b e i n g i n t r o d u c e d ) .When t h i s regime i s used f o r t h e d e s c e n t , t h e f u e l expended i s 400-500 kgg r e a t e r t h a n i n t h e regime d e s c r i b e d above, b u t Z a t i s f a c t o r y c o n d i t i o n s a r emaintained f o r passenger and crew. Table 1 0 shows t h e c h a r a c t e r i s t i c s of t h edescent regime with l e a s t e x p e n d i t u r e of f u e l f o r a TU-124 a i r c r a f t . In comparison with t h e descent regime a t t h e i d l e , t h e d e s c e n t t i m e isalmost doubled, and t h e range i s i n c r e a s e d by 50-100 km. The v e r t i c a lv e l o c i t y components are s e l e c t e d from t h e c o n d i t i o n o f maintenance o f aconstant p r e s s u r e drop i n t h e passenger c a b i n . The d u r a t i o n o f t h e l a n d i n g - /146maneuver (approximately from t h e r e g i o n of t h e t h i r d t u r n , see Chapter IX) i staken as 6 min (according t o s t a t i s t i c a l d a t a from scheduled f l i g h t s ) . The next method i s d e s c e n t a t t h e h i g h e s t speed, i n which p i l o t i n g i sperformed a t t h e c r u i s i n g (maximum p e r m i s s i b l e ) M number o r maximum i n d i c a t e dspeed. I n t h i s regime, t h e descent must be begun 270-300 km from t h e landingp o i n t . The f u e l e x p e n d i t u r e during t h e descent i s i n c r e a s e d , s i n c e t h eengines o p e r a t e a t a regime n e a r t h e c r u i s i n g regime f o r h o r i z o n t a l f l i g h t . /147 -Table 11 shows t h e c h a r a c t e r i s t i c s of t h e regime o f descent a t g r e a t e s t speed(TU-124 a i r c r a f t ) .53. Provision o f Normal Conditions i n Cabin During H i g h A l t i t u d e F l y i n g The c a b i n o f a passenger t u r b o j e t a i r c r a f t i s s e a l e d . I n t h e c a b i n , t h etemperature (20-22°C) , r e l a t i v e humidity and a i r p r e s s u r e a r e maintained s o a st o support normal v i t a l a c t i v i t y o f t h e crew and passengers d u r i n g highaltitude flight.140
  • 151. TABLE 10 V m/sec Eng i n e Des cen t Range, k m F u e l expend­ Y "ind speed, % and i t u r e , kg km/h r landing time, min 1 440 so 31 -1 1 1 000 8.0 10 OOO 7,5 450 80 28,s 9000 . 70 455 80 26,1 8 000 6,s 460 73 23,s 7 OCO 6,O 460 75 . 21,l 6000 5,5 465 75 1. 82 5 000 5-10 470 60 15,l 4 000 10 475 60 13,4 3 000 10 480 60 11,s 2 000 10 490 60 10,2 500 60 S.3 1000 landing 10 - - 6.0maneuverfrom H=500m A excess p r e s s u r e over t h e atmospheric p r e s s u r e i s i a i n t a i n e d i n t h e n cabin (Figure 100). A t . a l t i t u d e s between zero and 12,000 m , two p r e s s u r e r e g u l a t i o n regimes a r e g e n e r a l l y used: a) The regime of c o n s t a n t a b s o l u t e p r e s s u r e , during which from ground l e v e l t o 4500-6500 m y a p r e s s u r e of 760 mm H i s maintained; g b) A regime o f c o n s t a n t p r e s s u r e drop ( d i f f e r e n c e between p r e s s u r e i n cabin and atmosphere), i n which a t a l t i t u d e s over 4500-6500 m , t h e p r e s s u r e i n t h e cabin i s 0.5-0.65 kg/cm2 h i g h e r t h a n t h e atmospheric p r e s s u r e . With Ap = 0.5 kg/cm2 a t 8000 m, t h e cabin a l t i t u d e i s 1493 m, a t 10,000 m - - 2417 m ; with Ap = 0.6, t h e cabin a l t i t u d e a t t h e s e a l t i t u d e s w i l l be 500-600 m lower. Each of t h e s e regimes h a s a c h a r a c t e r i s t i c r a t e of change o f p r e s s u r e as a f u n c t i o n of a l t i t u d e . I n t h e c o n s t a n t a b s o l u t e p r e s s u r e regime, t h e a l t i t u d e i n t h e c a b i n remains unchanged d u r i n g a s c e n t and d e s c e n t , equal t o zero. T h e r e f o r e , a t a l t i t u d e s from z e r o t o 4500-6500 m a t any v e r t i c a l speeds p r a c t i c a l l y p o s s i b l e (climb o r d e s c e n t ) t h e r a t e of change o f a l t i t u d e i n t h e c a b i n i s equal t o z e r o . I n t h e c o n s t a n t excess and v a r i a b l e a b s o l u t e p r e s s u r e regime, t h e r a t e of change of p r e s s u r e i n t h e c a b i n i s of e s s e n t i a l s i g n i f i c a n c e f o r high a l t i t u d e passenger a i r c r a f t d u r i n g a climb and p a r t i c u l a r l y d u r i n g a d e s c e n t , d u r i n g which v e r t i c a l speeds may r e a c h 45-70 m/sec ( i n an emergency s i t u a t i o n ) . 141
  • 152. A t a l t i t u d e s Over 5000-6000 m, t h e v e r t i c a l climbing speeds are u s u a l l y huch less t h a n descending speeds, 10-15 m/sec. /14 TABLE 1 1 - . _I_- .- ~ -~ H ,m V m/sec Eng i n e Descent Range, km F u e l expend­ Y ind speed, % and i t u r e , kg km/hr landing time, min 11 000 8,O 480 84 31 270 960 10 OGO 7.5 520 83 28,8 240 900 9 cm 7.0 555 83 26,4 210 830 8 oco 6.5 595 82 23.8 175 760 7 000 690 600 82 21,l I0 4 680 6 GOO 5,5 600 81 18,2 105 600 5 000 5-10 600 80 15,1 65 500 4 000 10 600 79 13.4 45 460 3 000 10 600 77 11,8 30 400 2000 10 600 76 10,2 20 340 1 000 10 600 75 8,O 10 2801 and i ng - - ­ 6,O 0 250m neuve r afrom H-500m The comfort o f most passengers v a r i e s s t r o n g l y w i t h t h e r a t e o f change i n b a r o m e t r i c p r e s s u r e . During r a p i d p r e s s u r e changes ( p a r t i c u l a r l y during descent) t h e passengers experience unpleasant and p a i n f u l s e n s a t i o n s i n t h e i r e a r s . Therefore, t h e r a t e of change of c a b i n p r e s s u r e W should be cab = 0.18-0.20 mm Hg/sec, according t o medical requirements. Maintenance cab o f Wcab w i t h i n t h e s e l i m i t s a t a l l a l t i t u d e s o v e r which p r e s s u r e changes w i l l a s s u r e an even r a t e o f p r e s s u r e i n c r e a s e . The r a t e o f change of cabin p r e s s u r e i s equal t o W cab = V y - A p H , where V i s t h e v e r t i c a l r a t e of descent (climb); Y A H i s t h e v e r t i c a l p r e s s u r e g r a d i e n t o f t h e atmosphere, mm Hg/m. p For H = 0, t h e g r a d i e n t Ap = 0.09, f o r H = 8000 m - - 0.038 and f o r H H = 10,000 m -- 0 . 0 3 mm Hg/m.142
  • 153. T h i s dependence can b e used t o d e t e r ­ mine t h e v e r t i c a l r a t e o f descent o r climb f o r any h e i g h t , on t h e b a s i s of t h e c o n d i t i o n o f maintenance of normal s e n s a t i o n s of t h e passengers. For example , l e t u s determine t h e v e r t i c a l r a t e of d e s c e n t o f an a i r c r a f t f o r W = cab = 0.18 mm Hg/sec: F i g u r e 100. P r e s s u r e i n Sealed Cabin A s a F u n c ­ For H = 0 tion o f F l y i n g Altitude ( p r e s s u r e drop Ap = = 0.5k0.02 kg/cm2) : 1 , Pressure i n cabin; 2 , Atmospheric p r e s s u r e For H = 10,000 m v 0,18 =-- - 6 0,03 mlsec Let u s now determine t h e p e r m i s s i b l e " v e r t i c a l speed" o f t h e descent i n apassenger a i r c r a f t with s e a l e d c a b i n a t H = 10,000 m, i f t h e c a b i n a l t i t u d e i s2417 m and t h e v e r t i c a l p r e s s u r e g r a d i e n t f o r t h i s a l t i t u d e Ap = H= 0.07 mm Hg/m: V = 0.18/0.07 = 2 . 5 m/sec. However, f l y i n g t e s t s have shown Yt h a t an i n c r e a s e i n t h e v e r t i c a l v e l o c i t y component a t 10-12 km t o 8-9 m/secand a corresponding i n c r e a s e i n t h e v e r t i c a l i r e l o c i t y o f c a b i n a l t i t u d e t o3-3.2 m/sec has almost no i n f l u e n c e on t h e f e e l i n g s o f t h e p a s s e n g e r s .Therefore, t h e descent can be begun a t 250-300 k from t h e a i r f i e l d , i n o r d e r mt o provide normal landing maneuver. A improvement i n t h e v a l v e s o f t h e cabin a l t i t u d e system allows V n t o be Yi n c r e a s e d and t h e r e f o r e allows t h e descent t o be i n i t i a t e d 100-120 km from t h elanding p o i n t with t h e engines o p e r a t i n g a t t h e i d l e , which w i l l provide as a v i n g s o f 350-600 kg f u e l ( t h e descent a t t h e l e a s t f u e l e x p e n d i t u r e regime,t h e i d l i n g regime, analyzed above). The p e r m i s s i b l e " v e r t i c a l v e l o c i t i e s " i n t h e s e a l e d passenger cabin o f at u r b o j e t a i r c r a f t a r e p r e s e n t e d i n Table 1 2 . 143
  • 154. TABLE 12Flyingaltitude, kmV i n cab i n , Y m/sec I t f o l l o w s from t h e above t h a t descent from high a l t i t u d e s should b eperformed a t a v e r t i c a l r a t e o f 8-9 m/sec down t o 4500-6500 m, t h e n w i t h anyv e r t i c a l r a t e r e q u i r e d , a s long a s t h e p e r m i s s i b l e i n d i c a t e d speed i s n o texceeded, s i n c e t h e p r e s s u r e i n t h e cabin w i l l be made c o n s t a n t a t 760 mm Hg.S4. Emergency Descent W have n o t e d t h a t i n s e a l e d cabins of t u r b o j e t a i r c r a f t t h e a i r p r e s s u r e ei s 640-540 mm H w i t h a p r e s s u r e drop Ap = 0.50-0.62 kg/cm2 ( c o n s t a n t excess gp r e s s u r e r e g u l a t i o n regime). The change i n t h e primary a i r parameters ( p r e s s u r e , weight d e n s i t y ,temperature and humidity) a s a f u n c t i o n of " a l t i t u d e t t i n a s e a l e d c a b i n i s ofc o n s i d e r a b l e s i g n i f i c a n c e f o r l i f e support o f man i n f l i g h t . O f primarys i g n i f i c a n c e i s any change i n p a r t i a l oxygen p r e s s u r e (p ) and i t s p e r c e n t O2content . The p a r t i a l p r e s s u r e o f a gas included i n t h e composition of any gasmixture i s t h a t p o r t i o n o f t h e t o t a l p r e s s u r e o f t h e mixture produced by t h es h a r e o f t h e gas i n q u e s t i o n . Oxygen e n t e r s t h e human organism, as w e know,through t h e lungs, t h e a l v e o l i o f which are covered by a network o f bloodv e s s e l s . The p e n e t r a t i o n ( d i f f u s i o n ) of oxygen through t h e walls o f t h e bloodv e s s e l s i n t o t h e blood can occur o n l y i f t h e p a r t i a l p r e s s u r e exceeds t h ep r e s s u r e o f t h e oxygen i n t h e blood. S i m i l a r l y , removal o f carbon d i o x i d efrom t h e organism r e q u i r e s t h a t t h e p a r t i a l p r e s s u r e of carbon d i o x i d e i n t h eblood b e h i g h e r t h a n i n t h e a i r i n t h e a l v e o l i o f t h e l u n g s . Thus, whereast h e p a r t i a l oxygen p r e s s u r e a t which normal gas exchange i s a s s u r e d unders u r f a c e c o n d i t i o n s f o r t h e a i r i n h a l e d i s 159 mm Hg, t h i s f i g u r e f o r a l v e o l a ra i r i s 105-110 mm Hg. The minimum p e r m i s s i b l e p a r t i a l p r e s s u r e o f oxygen i na l v e o l a r a i r , a t which blood s a t u r a t i o n of 80-85% w i l l occur i s 37-50 mm Hg.T h i s p r e s s u r e corresponds t o an a l t i t u d e o f 4 . 5 km, and t h i s a l t i t u d e cannotb e exceeded without s p e c i a l d e v i c e s t o i n c r e a s e t h e p a r t i a l p r e s s u r e /150without oxygen s t a r v a t i o n . This a l t i t u d e i s t h e p h y s i o l o g i c a l l i m i t f o r144
  • 155. f l i g h t i n nonpressurized c a b i n s without oxygen d e v i c e s . Oxygen s t a r v a t i o n ,which causes s o - c a l l e d a l t i t u d e s i c k n e s s , may occur b e f o r e t h i s a l t i t u d e ,s i n c e it depends t o a g r e a t e x t e n t on t h e work performed by man. Thesymptoms of a l t i t u d e s i c k n e s s a r e headache, s l e e p i n e s s , decreased a c u i t y o fv i s i o n and h e a r i n g , d i s r u p t i o n of d i g e s t i o n and metabolism. These symptomsb e g i n t o appear q u i t e a c u t e l y beginning a t 4 . 5 km due t o t h e d e c r e a s e i noxygen supply t o t h e c e r e b r a l c o r t e x . I t i s d i f f i c u l t f o r t h e organism t ocompensate f o r a d e c r e a s e i n t h e q u a n t i t y o f oxygen i n t h e blood. T h e r e f o r e ,t h e a l t i t u d e zone from 4 t o 6 k i s c a l l e d t h e zone of incomplete compensa­ mt i o n . Above 6 km t h e c r i t i c a l zone b e g i n s , i n which t h e d i s r u p t i o n of mentala c t i v i t y , and f u n c t i o n s of t h e organism becomes q u i t e dangerous f o r s u r v i v a l .I n t h i s zone, man l o s e s consciousness and can only b e saved by immediatedescent o r supplementary oxygen supply. The c r i t i c a l zone ends a t an a l t i t u d eo f 8 km. I n c a s e of a sudden s h a r p drop o f p r e s s u r e i n t h e cabin ( l o s s of cabinp r e s s u r e ) , oxygen s t a r v a t i o n may occur. The t i m e from t h e beginning of oxygens t a r v a t i o n t o l o s s of consciousness i s c a l l e d t h e r e s e r v e t i m e . I t must b eused t o descend t o an a l t i t u d e p r o v i d i n g s u f f i c i e n t oxygen c o n c e n t r a t i o n . I n c a s e of a l o s s of c a b i n p r e s s u r i z a t i o n o r i n o t h e r cases ( i np a r t i c u l a r i n case of f i r e on t h e a i r c r a f t ) r e q u i r i n g a r a p i d d e s c e n t , t h ea i r c r a f t commander should d e c r e a s e t h e f l y i n g a l t i t u d e t o 5000 m ( s a f ea l t i t u d e ) i n 2.5-3 min o r should perform an emergency l a n d i n g . An emergency descent should be performed a t t h e maximum p o s s i b l e v e r t i c a lspeed. This can b e achieved by i n c r e a s i n g t h e forward speed and t h e angle ofi n c l i n a t i o n o f t h e t r a j e c t o r y . The g r e a t e r t h e forward speed and t h e g r e a t e rt h e a n g l e o f i n c l i n a t i o n , of t h e t r a j e c t o r y , t h e g r e a t e r w i l l b e t h e v e r t i c a lspeed. However, t h e speed of an a i r c r a f t i s u s u a l l y l i m i t e d a t high a l t i t u d e sby t h e p e r m i s s i b l e M number, and a t a l t i t u d e s below 6000-7000 m by t h ep e r m i s s i b l e i n d i c a t e d speed. T h e r e f o r e , u n l i m i t e d i n c r e a s e s i n forwardspeed cannot be used, and t h e forward speed must be maintained w i t h i npermissible l i m i t s . The next p o s s i b i l i t y f o r i n c r e a s i n g t h e v e r t i c a l speed i s t o i n c r e a s e t h eangle o f t h e t r a j e c t o r y 0 . The l o n g i t u d i n a l f o r c e s must be equal d u r i n gdescent a t c o n s t a n t speed. I t should be kept i n mind t h a t i n a t u r b o j e ta i r c r a f t d u r i n g an emergency d e s c e n t , t h e engines o p e r a t e a t t h e i d l e ,c r e a t i n g i n s i g n i f i c a n t t h r u s t . W can s e e from t h e e q u a t i o n P + G s i n 0 = Q et h a t s i n 0 = (Q - P ) / G , i . e . , t h e a n g l e of i n c l i n a t i o n of t h e descent t r a j e c ­t o r y (with c o n s t a n t a i r c r a f t weight) i s g r e a t e r , t h e g r e a t e r t h e drag of t h e ­ / 151a i r c r a f t . A i n c r e a s e i n t h e d r a g of a t u r b o j e t a i r c r a f t can be achieved by nlowering t h e l a n d i n g g e a r and s p o i l e r s . F o r example, during an emergencyd e s c e n t , c o f t h e a i r c r a f t i s 0.024-0.026 f o r M = 0.84-0.86. Lowering t h e Xl a n d i n g g e a r i n c r e a s e s c o f t h e a i r c r a f t by 0.015-0.020. Lowering t h e Xs p o i l e r s can i n c r e a s e cX s t i l l more. I n s p i t e of t h e high f l y i n g a l t i t u d e s(9000-11,000 m), t h e impact p r e s s u r e r e a c h e s h i g h v a l u e s ( f o r example, f o r 145
  • 156. v = 900 km/hr a t H = 10,000 m y q = 1300 k /m2, while a t 6000-7000 m w i t hind 5 = 650-700 km/hr it i s over 2000 kg/m ) , which makes it d i f f i c u l t t o lowerand lock t h e l a n d i n g - g e a r if t h e y are r a i s e d w i t h t h e flow, o r t o lower them if t h e y are r a i s e d a g a i n s t t h e flow. Therefore, i n o r d e r t o lower t h e l a n d i n g g e a r t h e i n d i c a t e d speed must b e decreased by 40-60 km/hr. The l o s s o f t i m e t o a c h i e v e t h i s i s compensated f o r by t h e c o n s i d e r a b l e i n c r e a s e i n a n g l e of i n c l i n a t i o n o f t h e descent t r a j e c t o r y and, t h e r e f o r e , t h e d e c r e a s e i n time r e q u i r e d f o r t h e emergency d e s c e n t . A t t h e same time, r a i s i n g t h e s p o i l e r i s p r a c t i c a l l y independent o f t h e impact p r e s s u r e . Emergency d e s c e n t o f an a i r c r a f t can b e d i v i d e d i n t o t h r e e main stageso!1) t r a n s i t i o n t o descent with a t t a i n m e n t o f t h e maximum v e r t i c a l v e l o c i t y of35-40 m/sec with l a n d i n g g e a r up o r 65-70 m/sec w i t h l a n d i n g g e a r down;2) s t a b l e descent w i t h t h e s e v e r t i c a l v e l o c i t i e s without exceeding t h e maximump e r m i s s i b l e M number a t h i g h a l t i t u d e s o r p e r m i s s i b l e i n d i c a t e d speed a t lowa l t i t u d e s ; 3) b r i n g i n g t h e a i r c r a f t out o f t h e d e s c e n t . E n e r g e t i c t r a n s i t i o n from i n i t i a l c r u i s i n g regime t o t h e descent a tM = 0.78-0.80 i s performed with an overload n = 0.6-0.55, and t h e c o n t r o l Yshould b e performed u s i n g t h e overload i n d i c a t o r of t h e AUAP d e v i c e (Chapter X I , 915). During t h i s t r a n s i t i o n , V = 35-40 m/sec can b e achievedr Yi n 12-15 sec, with t h e M number i n c r e a s i n g only t o 0.82-0.84 (with landingg e a r u p ) . With a smooth t r a n s i t i o n with an overload o f 0.9-0.8, t h e v e r t i c a lspeed w i l l o n l y reach 25-28 m/sec a f t e r 35-40 s e c , and t h e M number w i l l beapproximately 0.85-0.86, i . e . , t h e r a t e of i n c r e a s e i n M number exceeds t h er a t e of i n c r e a s e i n v e r t i c a l v e l o c i t y . If t h i s mode of t r a n s i t i o n i s used,t h e a i r c r a f t may q u i c k l y reach t h e maximum p e r m i s s i b l e M number o r exceed i t .I f t h e t r a n s i t i o n i s performed w i t h n = 0.4-0.3 o r l e s s , it becomes d i f f i c u l t Yt o c o n t r o l t h e i n c r e a s e i n v e r t i c a l v e l o c i t y , and t h e a i r c r a f t may reachVv > 35-40 m/sec and subsequently exceed t h e p e r m i s s i b l e M number. Therefore, It h e t r a n s i t i o n t o t h e descent should be performed with n = 0.6-0.55, which Y( a s w i l l be s e e n below) corresponds t o attainment o f a v e r t i c a l speed of15-17 m/sec i n t h e f i r s t 5-6 s e c . The second s t a g e o f t h e descent c o n s i s t s of maintaining a v e r t i c a l speedof 35-40 m/sec with l a n d i n g g e a r up o r 65-70 m/sec with l a n d i n g g e a r down,w i t h t h e M number i n c r e a s i n g t o t h e m a x i m u m p e r m i s s i b l e v a l u e a t t h e sametime. The a i r c r a f t should continue d e s c e n t a t t h i s M number down t o 6500- ­ /1526000 m. The p r a c t i c a l l y p e r m i s s i b l e M number i s r e t a i n e d f o r 50-60 s e c , t h e nd e c r e a s e s as t h e maximum i n d i c a t e d speed i s reached. S u b s e q u e n t l y , asdescent i s continued a t c o n s t a n t i n d i c a t e d speed, t h e M number drops (byapproximately 0.08-0.1 by 5000 m), and t h e v e r t i c a l speed d e c r e a s e s from35-40 t o 20-25 m/sec. Flying t e s t s have shown t h a t it i s n o t n e c e s s a r y t o attempt t o b r i n g t h ea i r c r a f t up t o t h e p e r m i s s i b l e M number, b u t r a t h e r descent can be formed a tan M number 0.02-0.04 less t h a n t h e p e r m i s s i b l e , s i n c e i f t h e p e r m i s s i b l e146
  • 157. M number i s exceeded, subsequent d e c e l e r a t i o n o f t h e a i r c r a f t w i l l s h a r p l y d e c r e a s e t h e v e r t i c a l speed. I t cannot be excluded t h a t d u r i n g t h e p r o c e s s of a descent t h e v e l o c i t y of t h e a i r c r a f t w i l l exceed t h e p e r m i s s i b l e v a l u e ( e i t h e r p e r m i s s i b l e M number o r i n d i c a t e d s p e e d ) . I n t h e s e c a s e s , i t i s n e c e s s a r y f i r s t of a l l t o h a l t f u r t h e r i n c r e a s e i n M number, by s l i g h t l y d e c r e a s i n g t h e v e r t i c a l speed (by 5-7 m/sec), t h e n once more d e c r e a s e t h e v e r t i c a l speed by 5-7 m/sec, and when t h e M number reaches i t s p e r m i s s i b l e v a l u e , t o r e - e s t a b l i s h t h e c o n s t a n t v e r t i c a l speed o f 35-40 m/sec ( o r 65-70 m/sec with landing g e a r down). The t h i r d s t a g e i n t h e descent i s a smooth t r a n s i t i o n back t o h o r i z o n t a l f l i g h t . This must be performed when t h e safe a l t i t u d e i s reached w i t h an~ overload n = 1 . 1 - 1 . 2 , corresponding t o a l o s s of 350-400 m a l t i t u d e . The Y t r a n s i t i o n from t h e d e s c e n t ( c r e a t i o n o f n n o t o v e r 1 . 2 ) i s achieved by Y observing t h e change i n a l t i t u d e , overload and v e r t i c a l speed, not allowing t h e maneuver t o b e performed i n l e s s t h a n 300-400 m. As we can s e e from Figure 101, t h e f l y i n g a l t i t u d e of t h e a i r c r a f t with landing g e a r up d e c r e a s e s by an average o f 1000 m each 30-32 sec, and t h e t o t a l time of descent i s 2 min 30 sec-2 min 40 s e c . With t h e l a n d i n g g e a r down, descent from 10,000 t o 5000 m occurs i n approximately 2 min. The i n d i c a t e d speed g r a d u a l l y i n c r e a s e s from t h e c r u i s i n g speed (480-500 km/hr) t o t h e maximum p e r m i s s i b l e speed (700 km/hr) r e t a i n i n g t h i s l a t t e r speed f o r 20-25 s e c from 6500 down t o 5000 m ( l a n d i n g g e a r u p ) . The M number i s i n c r e a s e d from t h e c r u i s i n g v a l u e of 0.78-0.82 t o 0.85 ( f o r t h i s c o n c r e t e c a s e ) which i t r e t a i n s f o r 50-52 s e c , t h e n d e c r e a s e s . The v e r t i c a l speed i n c r e a s e s over 17-20 s e c t o a v a l u e of 35-40 m/sec ( l a n d i n g g e a r u p ) , t h e n r e t a i n s t h i s r a t e down t o 7000-7200 m , a f t e r which (due t o t h e a t t a i n m e n t of an i n d i c a t e d speed of 700 km/hr, which must be maintained by d e c e l e r a t i n g t h e a i r c r a f t with t h e e l e v a t o r ) it i s decreased. With t h e landing g e a r , t h e v e r t i c a l speed reaches 65-70 m/sec and r e t a i n s t h i s l e v e l f o r 50-60 s e c . The overload i s decreased d u r i n g 5-6 sec of t h e i n i t i a l t r a n s i t i o n from ­ / 153 i t s i n i t i a l v a l u e (n = 1) t o 0.6-0.4, then i n c r e a s e s t o i t s i n i t i a l v a l u e and Y f u r t h e r (depending on t h e p i l o t s o p e r a t i o n o f t h e s t i c k ) , remaining between 1.1 and 0 . 9 . The p i t c h a n g l e 6 v a r i e s from ( c r u i s i n g f l i g h t ) t o -(7-8O) w i t h 2 landing g e a r up o r -(20-2Zo) with landing g e a r down. The angle of i n c l i n a t i o n o f t h e t r a j e c t o r y i n a s t a b l e descent i s 0 = 19 + $I - a. For example, l e t u s determine a n g l e 0 i f t h e descent i s performed a t M = 0.86 w i t h V = 38 m/sec, where H = 8000 m , t h e weight o f t h e Y a i r c r a f t i s 34 t , t h e wing s e t t i n g angle $I = l o ; w e know from c a l c u l a t i o n t h a t f o r t h e s e c o n d i t i o n s c = 0.171, a = l o , q = 1885 kg/m2. Then Y 147
  • 158. V = a = 308-0.86 = 265 m/sec = 955 km/hr, and a n g l e 0 = 29 = 8 " , s i n c e M I n o r d e r t o achieve a d e s c e n t with l a n d i n g g e a r down w i t h a v e r t i c a l speed of 70 m/sec and a forward speed o f 955 km/hr, a n g l e 0 = 15-16". - /154 Figure 101. Recording of Parameters During Emergency Descent of Turbojet A i r c r a f t : y - W i t h landing g e a r u p from H = 10,000 m y M i n i t = 0.78; ----- , W i t h landing gear down and preliminary d e c e l e r a t i o n from H = 11,200 m , M i n i t = 0.8 The method of p i l o t i n g an a i r c r a f t w i t h landing g e a r up d u r i n g anemergency descent c o n s i s t s of t h e following. Before beginning t h e d e s c e n t ,engines a r e s e t a t t h e i d l e and, by moving t h e s t i c k r a p i d l y forward, t h ep i l o t p u t s t h e a i r c r a f t i n a d e s c e n t . During t h i s maneuver, t h e p i l o t mustcheck t h e i n d i c a t i o n s of t h e v a r i o m e t e r , overload i n d i c a t o r and M numberindicator.148
  • 159. A t t h e moment when V = 15-17 m/sec i s a t t a i n e d , p r e s s u r e on t h e s t i c k must be reduced, p u l l i n g Y t g e n t l y back s o as t o r e t a r d t h e i n c r e a s e i n v e r t i c a l speed s l i g h t l y . When V = 25-30 m/sec i s achieved, t h e s t i c k must b e Y p u l l e d back smoothly t o r e t a r d t h e i n c r e a s e i n v e r t i c a l v e l o c i t y s t i l l more, g r a d u a l l y going over t o a s t a b l e descent a t a constant speed of 35-40 m/sec. During t h e p r o c e s s o f i n c r e a s i n g V from 30 t o 35-40 m/sec, t h e M number Y i n d i c a t o r must bewatched, t o avoid exceeding t h e maximum p e r m i s s i b l e v a l u e . Subsequently, a c o n s t a n t v e r t i c a l speed of 35-40 m/sec is maintained u s i n g t h e variometer, and t h e M number i s not allowed t o exceed t h e maximum p e r m i s s i b l e u n t i l t h e maximum p e r m i s s i b l e i n d i c a t e d speed i s reached ( a t approximately 6500 m). When t h e maximum p e r m i s s i b l e i n d i c a t e d speed i s achieved, t h e descent i s continued a t t h i s speed u n t i l a safe a l t i t u d e i s reached. The load can b e r e l i e v e d u s i n g t h e e l e v a t o r trimmer i n t h e process o f s t a b l e descent when an i n d i c a t e d speed of 580-620 km/hr i s achieved, so t h a t a p r e s s u r e o f 5-10 kg i s maintained on t h e c o n t r o l s t i c k . I f t h e f o r c e i s not r e l i e v e d by t h e t r i m m e r , i t w i l l reach 50-60 kg. A s t h e i n d i c a t e d speed i n c r e a s e s from 480-490 (beginning of descent) t o 680-700 km/hr, t h e e l e v a t o r trimmer i s moved away by 2.5-3", and t h e d e f l e c t i o n of t h e trimmer reaches 4-4.5" by t h e time an i n d i c a t e d speed of 700 km/hr i s reached. A s t h e assigned a l t i t u d e i s reached, t h e a i r c r a f t i s brought out of t h e descent i n such a way t h a t i t l o s e s no more than 300-350 m a l t i t u d e i n t h e maneuver. T h i s corresponds t o an overload of n = 1.16-1.2. A t a v e r t i c a l speed of 5-6 m/sec, t h e engines can be t r a n s f e r y e d t o t h e r e q u i r e d regime. P i l o t i n g t h e a i r c r a f t during an emergency descent with landing gear down d i f f e r s only s l i g h t l y from t h e above. A f t e r t h e engines a r e s h i f t e d t o t h e i d l e , t h e landing g e a r c o n t r o l l e v e r i s moved t o t h e "downT1p o s i t i o n , and t h e a i r c r a f t i s d e c e l e r a t e d u n t i l t h e landing g e a r a r e completely down ( a t high impact p r e s s b r e s , t h i s may r e q u i r e 20-22 s e c ) , a f t e r which t h e a i r c r a f t i s put i n t o t h e descent by smoothly but f o r c e f u l l y moving t h e s t i c k forward. Due t o t h e i n c r e a s e i n drag r e s u l t i n g from lowering t h e landing g e a r , t h e overload involved i n t h e t r a n s i t i o n may be s l i g h t l y l e s s t h a n i n t h e preceding c a s e ( t h e value may reach 0.3-0.4), s i n c e t h e a c c e l e r a t i o n of t h e a i r c r a f t t o t h e /155 maximum p e r m i s s i b l e M number occurs somewhat more slowly. When a v e r t i c a l speed of 22-24 m/sec i s reached, t h e p r e s s u r e on t h e s t i c k must be decreased, and a t V = 35-40 m/sec t h e r a t e of i n c r e a s e i n Y v e r t i c a l speed must be decreased, and a v e r t i c a l speed must be gradually brought up t o 65-70 m/sec. 149 I
  • 160. Chapter IX. The Landing §1. Diagrams o f L a n d i n g Approach /155 The d e s c e n t of an a i r c r a f t i n t h e r e g i o n of t h e a i r f i e l d t o t h e a l t i t u d eo f c i r c l i n g f l i g h t i s g e n e r a l l y performed u s i n g t h e o u t e r marker beacon(OMB) o r t h e e n t r a n c e c o r r i d o r beacon u s i n g t h e d i r e c t i o n f i n d e r - r a n g e f i n d e rsystem, t h e on-board and ground based r a d a r s . During t h e p r o c e s s of t h e d e s c e n t , t h e a i r c r a f t i s guided t o t h e a i r f i e l ds o t h a t t h e f l y i n g t i m e i n t h e r e g i o n o f t h e a i r p o r t i s 5-6 min. This allowst h e f u e l e x p e n d i t u r e t o be decreased ( t h e a i r c r a f t f l i e s f o r a s h o r t p e r i o d o ftime with l a n d i n g g e a r down), and decreases t h e f l y i n g t i m e and c o s t of a i rtravel. Therefore, t h e approach i s e i t h e r d i r e c t o r u s e s t h e s h o r t e s t p a t h , i nwhich t h e a i r c r a f t i s brought i n i n t h e r e g i o n of t h e t h i r d t u r n (Figure 102).I f t h e approach i s d i r e c t , a t 25-30 km from t h e a i r f i e l d t h e a i r c r a f t descends /156t o 400-600 m and d e c r e a s e s i t s speed t o t h e landing g e a r down speed. Whent h i s a l t i t u d e i s reached, t h e landing g e a r a r e lowered a t 12-15 km from t h eOMB ( t h i s range i s checked u s i n g t h e range f i n d e r o r by commands from t h ee a r t h ) , and t h e f l a p s a r e lowered by 15-20". The f l a p s a r e lowered completelybefore entering the glide. During a descending approach, t h e speed o f t h e a i r c r a f t i s decreasedi n t h e r e g i o n of t h e t h i r d t u r n d u r i n g t h e p r o c e s s o f descent t o t h e c i r c l i n ga l t i t u d e , and t h e landing g e a r a r e lowered. The f l a p s are dropped by 15-20"between t h e t h i r d and f o u r t h t u r n s . The f o u r t h t u r n i s performed with t h i sf l y i n g c o n f i g u r a t i o n , u s u a l l y a t 12-16 km from t h e runway, t h e f l a p s a r ed e f l e c t e d f u l l y and t h e a i r c r a f t follows t h e course t o t h e runway a t c o n s t a n ta l t i t u d e u n t i l it enters the glide path. With forward movement speeds i n t h e d e s c e n t of 350-500 km/hr and landingspeeds of 200-250 km/hr, a j e t a i r c r a f t w i l l cover c o n s i d e r a b l e d i s t a n c ed u r i n g t h e p r o c e s s o f descent and speed r e d u c t i o n . T h e r e f o r e , t h e e x t e n t o ft h e t u r n s and p a r t i c u l a r l y of t h e s t r a i g h t l i n e . s e c t o r s between t u r n s w i l l becorrespondingly i n c r e a s e d . A s a r e s u l t , a f t e r t h e f o u r t h t u r n t h e a i r c r a f tw i l l be a t a c o n s i d e r a b l e d i s t a n c e from t h e runway (12-16 km). The i n c l i n a t i o n of t h e g l i d e p a t h i s g e n e r a l l y 2" 40 min-4, as ar e s u l t of which t h e t r a j e c t o r y of t h e a i r c r a f t ( a f t e r i t e n t e r s t h e g l i d ep a t h ) i s smooth. The g l i d e p a t h i s e n t e r e d a t 7.5-8.5 km from t h e runway. The OMB i s g e n e r a l l y l o c a t e d 4 km from t h e runway, t h e boundary markerbeacon (BMB) a t 1000 m from t h e runway. The a l t i t u d e over t h e OMB should be200 m a over t h e BMB - - 60 m . For t h e s e f l y i n g a l t i t u d e s , t h e v e r t i c a lv e l o c i t y component o f t h e a i r c r a f t should b e 3-3.5 m/sec.150
  • 161. Figure 102. Diagram o f Approach t o Landing ( a ) and G1 i d e ( b )52. F l i g h t A f t e r E n t r y i n t o G l i d e Path. Selection o f G l i d i n g Speed According t o t h e norms of ICAO, t h e g l i d i n g speed d u r i n g t h e d e s c e n t ont h e g l i d e p a t h should be 30% g r e a t e r t h a n t h e s t a l l speed f o r t h e l a n d i n gc o n f i g u r a t i o n of t h e a i r c r a f t , i . e . , V = 1 . 3 Vs (where V is the s t a l l gl 0speed with f l a p s i n t h e g l i d i n g p o s i t i o n ) . A s w can s e e from Figure 16, f o r a maximum f l a p angle of 38", flow es e p a r a t i o n on t h e wing begins a t c = 1 . 8 5 . For a mean landing weight o f 35 t Yand a wing a r e a of 110 m2, t h i s corresponds t o a s t a l l speed = 1 4 . 4 ~ 3 5 , 0 0 0 / 1 1 0 * 1 . 8 5= 190 km/hr. Vs 0Then t h e g l i d i n g speed i s Before t h e beginning o f l e v e l i n g o f f , g l i d i n g i s performed a t c o n s t a n tspeed, i n t h i s c a s e 250 km/hr. With t h e s t a n d a r d a n g l e o f i n c l i n a t i o n of t h e - /157 151
  • 162. 2 O 40 min, t h e v e r t i c a l r a t e o f descent V = V s i n 0 = 69.5.0.0466 = Y gl= 3.24 m/sec ( h e r e s i n 2" 40 min = 0.0466, V = 250 km/hr = 69.5 m/sec) gl . Establishment of a c o n s t a n t g l i d i n g speed a f t e r complete lowering oft h e f l a p s f a c i l i t a t e s p i l o t i n g , s i n c e i t does not r e q u i r e a change i n t h eo p e r a t i n g regime o f t h e engines o r a d e c r e a s e i n t h e speed from t h e momentof e n t r y i n t o t h e g l i d e p a t h u n t i l t h e a i r c r a f t p a s s e s o v e r t h e OMB, BMB and500-m mark, s o t h a t t h e p i l o t i s less d i s t r a c t e d from t h e i n s t r u m e n t s . I f t h e a i r c r a f t e n t e r s t h e g l i d e p a t h a t 400 m a l t i t u d e and 8 km rangefrom t h e runway (Figure 102), f l i g h t t o t h e OMB i n calm a i r ( t h e a i r c r a f tc r o s s e s t h e beacon a t 200 m a l t i t u d e ) r e q u i r e s t = 2 0 0 : 3.24 = 61 s e c . The d i f f e r e n c e i n a l t i t u d e s of f l i g h t over t h e OMB and BMB i s 140 m,and t h e time of d e s c e n t f o r t h i s d i f f e r e n c e t = 140: 3.24 = 43 s e c . Thef l y i n g speed of 250 km/hr corresponds t o an angle of a t t a c k ci = 5" (Figure 1 6 ) . Let u s now determine, assuming I$ = l o , t h e p o s i t i o n of t h ea i r c r a f t concerning t h e landing g l i d e p a t h , i . e . , t h e p i t c h a n g l e :i = -2" 40 min + 5 - l o = 1 20 min.? Thus, t h e a i r c r a f t a x i s h a s a p o s i t i v e angle w i t h n e g a t i v e descentangle 0. I f , due t o high mechanization of t h e wing ( t h r e e s l i t f l a p s andsecondary c o n t r o l s u r f a c e s ) t h e g l i d i n g speed i s decreased (240-220 km/hr),t h e p i t c h angle i n c r e a s e s . Therefore, t h e f l y i n g time from t h e moment t h ea i r c r a f t e n t e r s t h e g l i d e p a t h u n t i l it f l i e s over t h e OMB and BMB a t lowerspeeds i s i n c r e a s e d , and t h e p i l o t s r e s e r v e time i n c r e a s e s . As a r e s u l t ,t h e f o u r t h t u r n can be formed c l o s e r t o t h e end o f t h e runway. As t h e g l i d i n g speed i s decreased a t t h e same t r a j e c t o r y a n g l e , t h ev e r t i c a l speed i s decreased, and with t h e i n c r e a s i n g angle of a t t a c k t h ep i t c h angle i n c r e a s e s , worsening t h e view from t h e p i l o t s c a b i n . Let u s analyze t h e engine o p e r a t i o n regime r e q u i r e d f o r g l i d i n g f l i g h tof t h e a i r c r a f t . With t h e landing g e a r down, f l a p s down and a i r b r a k e extended, t h e aero­dynamic q u a l i t y o f t h e a i r c r a f t K = 5-6 and t h e g l i d i n g angle 0 = 9-10"( t a n 0 = 1 / K = 1 / 5 . 5 = 0.183, 0 10") , b u t i n t h i s c a s e t h e engine t h r u s tshould be n e a r zero. A c t u a l l y , t h e a i r c r a f t descends along t h e g l i d e p a t h with engineso p e r a t i n g a t angle 0 = 2" 40 min. This a n g l e corresponds t o q u a l i t y152
  • 163. For c = 1.06 ( a n g l e of a t t a c k So, Figure 1 6 ) , we produce c = 0.19 Y X(without a i r b r a k e ) . From t h i s v a l u e o f c we must s u b t r a c t t h e v a l u e of Xc o e f f i c i e n t cR o f r e q u i r e d engine t h r u s t , i n o r d e r t o m a i n t a i n K = 21.5 wherec = 1.06: Y /158from whichThis v a l u e of t h r u s t c o e f f i c i e n t corresponds t o a t h r u s t consumption P = c qS = 0.141*300*110 = 4650 kg, i . e . , 2325. kg t h r u s t f o r each engine R(with a two-engine a i r c r a f t ) . This t h r u s t i s s e v e r a l times g r e a t e r t h a n t h e i d l i n g t h r u s t (300-500 k g ) . I f t h e a i r b r a k e i s extended, t h e t h r u s t must be i n c r e a s e d ( t o m a i n t a i n t h e g l i d i n g angle unchanged, s i n c e c i s i n c r e a s e d t o X0.226) : c --*- 1 % -0.226=@~0493-0,226.= 10,1771; R-21.5 P=O ,177 -300-110=5840 kg As we can see, t h e t h r u s t i s i n c r e a s e d by almost 25%. I f a f t e r t h e a i r b r a k e i s extended t h e engine o p e r a t i n g regime i s l e f tunchanged, t h e angle o f i n c l i n a t i o n o f t h e d e s c e n t t r a j e c t o r y w i l l bei n c r e a s e d t o 4" 30 min and t h e a i r c r a f t may come down b e f o r e t h e beginning oft h e runway. In o r d e r t o determine t h e new angle of d e s c e n t , we must f i r s tf i n d t h e q u a l i t y of t h e a i r c r a f t from t h e e q u a t i o n c = (1.06/K) - 0 . 2 2 6 = R= -0.141 :and t h e n f i n d t h e d e s c e n t angle 153
  • 164. .. The e f f e c t i v e n e s s o f t h e a i r b r a k e i s q u i t e h i g h , s i n c e as c is increased Xt h e l i f t of t h e wing remains p r a c t i c a l l y t h e same. T h e r e f o r e , as t h e landingg e a r a r e lowered t h e a i r c r a f t h a s no tendency t o wing s t a l l , b u t only shows achange i n t h e i n c l i n a t i o n o f t h e t r a j e c t o r y . 53. Stages i n t h e Landing The f l i g h t of t h e a i r c r a f t (descent) from 15 m (according t o t h e ICAOnorms) c o n s i s t o f t h e f o l l o w i n g main s t a g e s : I) g l i d i n g from 15 m a l t i t u d e a t .V = 1 . 3 Vs u n t i l l e v e l i n g o f f i s begun; 2 ) l e v e l i n g o f f u n t i l t h e moment of gl 0l a n d i n g and 3) t h e l a n d i n g run. F i g u r e 103 shows a diagram of t h e d e f i n i t i o n of r e q u i r e d runway l e n g t hand a p r o f i l e o f a i r c r a f t f l i g h t from 15 m downward. The t o t a l l e n g t h o f t h e h o r i z o n t a l p r o j e c t i o n o f t h e t r a j e c t o r y of t h ea i r b o r n e s e c t o r and t h e landing run i s c a l l e d t h e l a n d i n g d i s t a n c e . The I 59 1r e q u i r e d runway l e n g t h i s determined f o r s t a n d a r d and d e s i g n m e t e o r o l o g i c a lc o n d i t i o n s with t h e maximum landing weight of an a i r c r a f t and d r y runway. Gliding - - s t r a i g h t l i n e f l i g h t of the a i r c r a f t on a descending t r a j e c t o r y at constant velocity. Gliding i s usually 1 performed a t 250­ 220 km/hr i n d i c a t e d , anding d i s t a n c e with an angle o f a t t a c k requ i red runway l e n g t h = c1 = 5-5.5" and landing d i s t x 1.43 c = 0.95-1.1. Y Figure 103. P r o f i l e of Descent o f A i r c r a f t Prelanding g l i d i n g from H = 15 m i s not gliding i n its p u r e form, s i n c e t h e engines c r e a t eapproximately 1800-2000 kg t h r u s t each. This t h r u s t i s r e q u i r e d t o r e t a i n t h ea i r c r a f t speed and r e t a i n good motor r e a d i n e s s i n c a s e i t becomes necessary t oc i r c l e once more o r f o r a d d i t i o n a l t h r u s t t o c o r r e c t t h e landing p a t t e r n . Ift h e a i r b r a k e i s extended, t h e engine o p e r a t i n g regime must b e i n c r e a s e d by5-6%, i n c r e a s i n g t h e s a f e t y i n case a second c i r c l e i s r e q u i r e d .154
  • 165. When g l i d i n g from 15 m t o t h e h e i g h t where t h e l e v e l i n g i s begun, t h ea i r c r a f t t r a v e l s 150-200 m. The v e r t i c a l speed i n t h e s e c t o r i s 3-5 m/sec. With t h e a i r b r a k e extended, t h e q u a l i t y i s decreased t o 4.5-5, and t h eangle o f i n c l i n a t i o n o f t h e t r a j e c t o r y can b e i n c r e a s e d when n e c e s s a r y t o9-11. I n t h i s c a s e , t h e l e n g t h of t h e g l i d i n g s e c t o r from 15 m downd e c r e a s e s t o 100-150 m. The v e r t i c a l speed can b e i n c r e a s e d t o 8-9 m/sec. Extending t h e f u s e l a g e a i r b r a k e c r e a t e s p i t c h i n g moment and f a c i l i t a t e sb a l a n c i n g t h e a i r c r a f t , s i n c e t h e f l a p s t e n d t o c r e a t e a p i t c h i n g moment i nt h e o p p o s i t e d i r e c t i o n . The a i r c r a f t must b e balanced s o t h a t s l i g h t p u l l i n gloads are f e l t on t h e c o n t r o l s t i c k a t a l l times. Leveling o f f . During l e v e l i n g o f f , which begins a t an a l t i t u d e o f8-10 m, t h e movement o f t h e a i r c r a f t i s curved and t h e speed d e c r e a s e s . Byp u l l i n g t h e s t i c k back, t h e p i l o t i n c r e a s e s t h e l i f t , which becomes g r e a t e rt h a n t h e weight component and t h e r e f o r e t h e t r a j e c t o r y i s curved. I n /160p r a c t i c e , d u r i n g l e v e l i n g o f f t h e a i r c r a f t does n o t f l y h o r i z o n t a l l y , b u tr a t h e r a t a s l i g h t a n g l e t o t h e ground (0.5-0.8). I n performing t h i s oper­a t i o n , t h e p i l o t d e c r e a s e s t h e angle of i n c l i n a t i o n of t h e t r a j e c t o r y and t h ev e r t i c a l r a t e of d e s c e n t t o t h e p o i n t t h a t a l T s o f t l f touchdown i s provided.T h i s d e c r e a s e i n speed r e s u l t s from two f a c t o r s : f i r s t o f a l l , t h e angle ofa t t a c k i s i n c r e a s e d , i n c r e a s i n g d r a g Q ( f o r s t a b l e l a n d i n g a n g l e s of a t t a c k9-10", t h e drag i n c r e a s e s by 25-30%) and, secondly, b e f o r e t h e beginning ofl e v e l i n g o f f t h e p i l o t t h r o t t l e s back t h e engines and t h e r e b y d e c r e a s e s t h e i rt h r u s t . Leveling o f f i s completed a t an a l t i t u d e of 1-0.5 m , s o t h a t t h etouchdown occurs on t h e main wheels a t l a n d i n g speed with s l i g h t p a r a c h u t i n g .I n o r d e r t o r e t a i n l i f t d u r i n g t h e process of l e v e l i n g o f f , t h e angle ofa t t a c k must b e i n c r e a s e d t o t h e landing a n g l e of a t t a c k . During p a r a c h u t i n g ,t h e l i f t i s less t h a n t h e weight of t h e a i r c r a f t by 25-30%. When an a i r c r a f t l a n d s w i t h a i r b r a k e r e t r a c t e d , t h e l e n g t h of t h el e v e l i n g s e c t o r i s i n c r e a s e d , while i f t h e a i r b r a k e i s extended, due t o t h eb e t t e r braking t h e l e n g t h of t h e landing s e c t o r i s decreased by 50-100 m. During t h e l e v e l i n g s e c t o r , t h e speed of t h e a i r c r a f t i s decreased from The l e n g t h o f t h e l e v e l i n g o p e r a t i o n depends on t h e d i f f e r e n c e g l to "wbetween t h e s e speeds. With a d i f f e r e n c e of 30 km/hr, i t amounts t o 350-400 m .The g r e a t e r t h e landing angle of a t t a c k (8-lo), t h e longer t h e b r a k i n g of t h ea i r c r a f t and t h e g r e a t e r t h e l e n g t h o f t h e l e v e l i n g s e c t o r . As a r e s u l t , t h elanding d i s t a n c e i n c r e a s e s , i n s p i t e of t h e f a c t t h a t t h e l e n g t h of t h e run i sdecreased s l i g h t l y by landing a t h i g h angle of a t t a c k . As f l y i n g t e s t s haveshown, i t i s more s u i t a b l e t o "brake" on t h e ground ( d u r i n g t h e run) t h a n i nt h e a i r , when t h e aerodynamic q u a l i t y is r a t h e r h i g h (6-7). This l e a d s us t ot h e following conclusion: i n o r d e r t o avoid l e n g t h e n i n g t h e h o l d i n g s e c t o ru n n e c e s s a r i l y , l a n d i n g should b e performed with V = V - 20 km/hr. 1dg gl The run. The speed a t which t h e a i r c r a f t t o u c h e s t h e ground i s c a l l e dt h e landing speed. I t can b e determined from t h e f o l l o w i n g formula: 155
  • 166. B iwhere c i s t h e l i f t i n g c o e f f i c i e n t a t t h e moment t h e a i r c r a f t touches t h e Y 1dgground. The run begins from t h e moment t h e a i r c r a f t wheels touch t h e l a n d i n gs t r i p . The movement o f t h e a i r c r a f t d u r i n g t h i s s e c t o r i s s t r a i g h t and slow.A t f i r s t t h e run i s accomplished on t h e main wheels, t h e n by moving t h e s t i c kforward t h e p i l o t lowers t h e nose wheels. Most of t h e r u n occurs on t h r e ep o i n t s with a low a n g l e of a t t a c k . On t h e p o l a r curve, t h i s corresponds t ot h e s t a n d i n g angle o f a t t a c k 1-3" (Figure 6 5 ) . Immediately a f t e r grounding, when t h e a i r c r a f t i s r o l l i n g on two p o i n t s , /161t h e s p o i l e r s are d e f l e c t e d and wheel b r a k i n g b e g i n s . Whereas a t t h e moment oflanding c o e f f i c i e n t c = 1 . 4 - 1 . 7 , a f t e r t h e s p o i l e r s a r e extended, due t o t h e Yflow s e p a r a t i o n on t h e wing, it i s decreased t o 0.08-0.12. The l i f td e c r e a s e s s h a r p l y and complete loading o f t h e l a n d i n g g e a r wheels o c c u r s . I t should b e noted t h a t a t t h e moment t h e s p o i l e r s are extended an e g a t i v e p i t c h moment i s a c t i n g on t h e a i r c r a f t and t h e p i l o t must push t h es t i c k forward s l i g h t l y t o h o l d t h e a i r c r a f t a t t h e l a n d i n g a n g l e of a t t a c k . Extending t h e s p o i l e r s d e c r e a s e s t h e speed o f t h e a i r c r a f t by 40-50 km/hr,which causes t h e a i r c r a f t t o t e n d t o drop i t s nose r a p i d l y , t o which t h e p i l o tmust r e a c t by p u l l i n g t h e s t i c k back t o allow t h e nose wheel t o drop smoothly. Figure 104 shows an a i r c r a f t d u r i n g t h e l a n d i n g r u n w i t h s p o i l e r sextended and b r a k i n g p a r a c h u t e o u t . During t h e p r o c e s s of t h e r u n , t h ea i r c r a f t i s d e c e l e r a t e d by t h e drag o f t h e a i r c r a f t and t h e f r i c t i o n o f t h ewheels on t h e ground. The s l i g h t engine t h r u s t d e c r e a s e s t h i s d e c e l e r a t i n gforce. The diagram of f o r c e s a c t i n g on t h e a i r c r a f t d u r i n g t h e landing run i st h e same as during t h e t a k e o f f run (Figure 8-6). The only d i f f e r e n c e i s t h a td u r i n g t h e landing run t h e t h r u s t P i s c o n s i d e r a b l y less than t h e sum o fd e c e l e r a t i n g f o r c e s F and Q. f During t h e l a n d i n g r u n , t h e summary b r a k i n g f o r c e i s d e f i n e d as t h ed i f f e r e n c e between d e c e l e r a t i n g f o r c e s and t h e t h r u s t of t h e engines:Rbr = Q + Ff - P . A s a r e s u l t of t h e e f f e c t s o f t h e b r a k i n g f o r c e , a n e g a t i v ea c c e l e r a t i o n ( i . e . , d e c e l e r a t i o n ) appears156
  • 167. I t f o l l o w s from t h e formula t h a t t h e g r e a t e r t h e sum Q + F the greater /162 fw i l l be jx. The f r i c t i o n f o r c e F depends on t h e c o e f f i c i e n t o f f r i c t i o n o f fwheels w i t h t h e s u r f a c e o f t h e e a r t h f and t h e f o r c e o f normal p r e s s u r e o ft h e a i r c r a f t on t h e e a r t h N . I t h a s been determined by t e s t i n g t h a t f o r a i r -c r a f t with d i s k brakes and s p o i l e r s running on d r y c o n c r e t e f = 0.2-0.3 . . ( c o n s i d e r i n g braking) Force N depends on t h e l a n d i n g weight o f t h e a i r c r a f t and t h e l i f t :N = G - Y. The f o r c e of f r i c t i o n can b e expressed by t h e following formula:then A t t h e beginning o f t h e landing r u n , when t h e l i f t i s only s l i g h t l y lessthan t h e weight, t h e f o r c e of f r i c t i o n w i l l be low (low difference G - Y ) .For example, a t 200-220 km/hr, t h e f o r c e of f r i c t i o n i s 4000-5000 kg ( f o r ana i r c r a f t w i t h a landing weight of 35-40 t ) . A t t h e end of t h e r u n , when t h el i f t i s s l i g h t , t h e f o r c e of f r i c t i o n i n c r e a s e s . Figure 104. A i r c r a f t During Run w i t h S p o i l e r s Extended and Braking Parachute O u t ( a ) and Diagram of O p e n i n g of S p o i l e r ( b ) : 1 , Inner s p o i l e r s ; 2 , Outer s p o i l e r s ; 3 , S p o i l e r ; 4 , Front f l a p ; 5 , Door; 6 , Flap The f o r c e o f a i r c r a f t d r a g a t t h e beginning of t h e landing r u n (when t h espeed i s n e a r t h e l a n d i n g speed, and angle of a t t a c k a = 9-10"> i s r a t h e rg r e a t (Q = 5000-6000 kg f o r t h e same w e i g h t s ) . T h i s i s f a c i l i t a t e d by t h elowered f l a p s and t h e a i r b r a k e . 157
  • 168. I 1 The l a n d i n g d i s t a n c e (Figure 103) i s t h e summary l e n g t h of t h e s e c t o r s of g l i d i n g , l e v e l i n g and l a n d i n g ~ r u n . For a i r c r a f t w i t h two-engines i n t h e t a i l p o r t i o n o f t h e f u s e l a g e , t h e l a n d i n g d i s t a n c e i s 1000-1200 m, and t h e r e q u i r e d runway l e n g t h (according t o ICAO) i s 1400-1700 m. S4. L e n g t h of Post-landing Run and Methods of Shortening It The k i n e t i c energy of t h e a i r c r a f t a t t h e moment of touchdown i sd i s s i p a t e d and absorbed by t h e work o f t h e b r a k i n g f o r c e s : t h e aerodynamicdrag, .the f r i c t i o n of t h e wheels on t h e s u r f a c e o f t h e runway, t h e d r a g o fb r a k i n g p a r a c h u t e s , t h r u s t r e v e r s a l , e t c . The dependences o f t h e s e b r a k i n gf o r c e s on t h e speed o f t h e run a r e shown on F i g u r e 105. The u n i t o f b r a k i n gf o r c e (drag f o r c e ) used i s t h e aerodynamic d r a g of t h e a i r c r a f t a t touchdown. /163 -For example, f o r t h e TU-124, a t t h e moment o f touchdown w i t h f l a p s a t 30" anda i r b r a k e extended a t 225 km/hr, cx = 0.18, t h e aerodynamic drag Q = 4600 kg,t h e p a r a c h u t e d r a g i s approximately 5500 kg and t h e b r a k i n g f o r c e o f t h ewheels i s about 2500 kg. A s t h e speed o f t h e landing r u n d e c r e a s e s , t h e d r a gf o r c e of t h e p a r a c h u t e and t h e aerodynamic d r a g of t h e a i r c r a f t drop s h a r p l y ,while t h e f o r c e o f f r i c t i o n o f t h e wheels i n c r e a s e s . Thrust r e v e r s a l o f t h eengines i s p r a c t i c a l l y independent o f t h e r a t e o f movement o f t h e a i r c r a f t . j .- m t:p= 45 The l e n g t h o f t h e l a n d i n g run o f an a i r c r a f t can b e determined u s i n g t h e f ormu 1a Y m I 3 I al m 0 36 72 ro8 r08 144 f80 YKMJ hr Figure 105. Nature of Change i n Braking Forces During Post-landing Run where j i s t h e mean a c c e l e r a t i o n o f xmlr of Aircraft (calculated) : braking (deceleration) o f t h e a i r c r a f t 1 , Braking f o r c e ; during t h e landing r u n , m/sec2. 2 , Aerodynamic drag o a i r c r a f t ; 3 , Drag o f As we can s e e from t h e formula, with braking parachute; f i x e d l a n d i n g speed t h e l e n g t h of t h e run 4 , Thrust reversa can b e decreased by i n c r e a s i n g t h e mean braking acceleration. During t h e f i r s t h a l f o f t h e l a n d i n g run [Figure 105) t h e d e c e l e r a t i o n of ~Ia i r c r a f t movement i s achieved under t h e i n f l u e n c e of a l l t h e s e d e c e l e r a t i n gf o r c e s , a f t e r which t h e main r o l e i s played by t h e b r a k i n g f o r c e of t h e wheelsand t h r u s t r e v e r s a l ( i f t h e r e i s a t h r u s t r e v e r s e r on t h e a i r c r a f t ) . A t t h e p r e s e n t t i m e , braking wheels are equipped w i t h s p e c i a l automaticb r a k i n g d e v i c e s , t h e p r i n c i p l e of o p e r a t i o n of which i s based on t h e usage o ft h e f o r c e o f i n e r t i a of a flywheel r o t a t i n g i n p a r a l l e l w i t h t h e wheel.158
  • 169. If t h e wheel r o t a t e s without s l i p p i n g , t h e flywheel i n t h e automatic d e v i c er o t a t e s i n synchronism with t h e l a n d i n g wheel. I f t h e wheel begins t o s l i d e ,t h e flywheel i n t r o d u c e s an a c c e l e r a t i o n and, working through a s p e c i a l d e v i c e ,i n t e r r u p t s t h e supply o f p r e s s u r e t o t h e b r a k e , as a r e s u l t of which t h eb r a k i n g f o r c e on t h e wheel i s decreased. A f t e r t h e r o t a t i n g speed of t h ewheel i s i n c r e a s e d once more and synchronism i s e s t a b l i s h e d between r o t a t i o no f wheel and flywheel, t h e p r e s s u r e t o t h e brakes i s j n c r e a s e d t o t h e r e q u i r e dl e v e l and t h e wheel i s once more braked. I n o p e r a t i o n , t h i s c y c l e i s u s u a l l yr e p e a t e d q u i t e r a p i d l y and a c t u a l l y t h e p r e s s u r e i n t h e brakes never d e c r e a s e scompletely. Thus, t h i s d e v i c e p r o v i d e s optimal b r a k i n g , pumping a t t h eboundary of s l i d i n g 1 . When t h i s d e v i c e i s t u r n e d on, t h e p i l o t immediatelyprovides f u l l p r e s s u r e i n t h e b r a k e s ( d e p r e s s e s b r a k e p e d a l s completely). Smoothly d e p r e s s i n g t h e b r a k e s , a s i s recommended f o r nonautomaticb r a k i n g , i n t h i s c a s e o n l y i n c r e a s e s t h e l e n g t h o f t h e l a n d i n g run, s i n c e t h emaximum b r a k i n g regime will n o t be used. The usage of automatic brakes has allowed t h e l e n g t h o f t h e l a n d i n g run /164t o be decreased by an a d d i t i o n a l 20-25%.. The s e r v i c e l i f e o f t h e pneumaticsystem h a s a l s o been i n c r e a s e d . The mean a c c e l e r a t i o n of automatic b r a k i n g i s1 . 7 - 1 . 8 m/sec2 ( d i s k b r a k e s ) . In a i r c r a f t with s p o i l e r s opened a t t h e momentof touchdown, t h e e f f e c t i v e n e s s of t h e brakes i s even g r e a t e r and = 2.25-2.5 m/sec2. For example, i n an a i r c r a f t with s p o i l e r sJxmlr ( j m = 2.25 m/sec2) with a l a n d i n g speed o f 216 km/hr (60 m/sec), Llr = 800 m.For t h e TU-104 a i r c r a f t (no s p o i l e r s ) with V = 240 km/hr (66.7 m/sec) w i t h 142an average b r a k i n g a c c e l e r a t i o n of 1 . 3 m/sec2 (drum brake) t h e l a n d i n g runl e n g t h i s 1700 m. For t h e TU-104 w i t h d i s k brakes (with an average a c c e l e r ­a t i o n o f 1.55 m/sec2) t h e l a n d i n g run l e n g t h i s 1430 m . Even g r e a t e r b r a k i n g a c c e l e r a t i o n (drag) can b e produced by r e l e a s i n g ab r a k i n g p a r a c h u t e . For example, i f t h e p a r a c h u t e i s open a t 225-215 km/hr,t h e drag i s i n c r e a s e d by 4600-4900 kg (TU-124 a i r c r a f t ) . Figure 106a shows a diagram of t h e usage o f a braking p a r a c h u t e . A f t e rtouchdown, a b u t t o n i s p r e s s e d dropping t h e p a r a c h u t e from i t s c o n t a i n e rthrough h a t c h 1. A f t e r t h i s , t h e p i l o t chute p u l l s t h e braking chute o u t ,c r e a t i n g r e s i s t a n c e t o t h e movement of t h e a i r c r a f t . The p a r a c h u t e i sconnected t o t h e a i r c r a f t by c a b l e 3 through c a t c h 2 . A t t h e end of t h e r u n ,t h e braking p a r a c h u t e s a r e disconnected. Braking p a r a c h u t e s 4 a r es t r i p t y p e , and t h e s t r e n g t h o f t h e l i n e s and canopy i s s u f f i c i e n t f o r run /165 -speeds of 260-230 km/hr. In a s t r i p type parachute, the a i r p a r t i a l l y passesthrough t h e canopy and t h e r e f o r e f o r t h i s t y p e o f chute Acx = 0.25-0.55 ( f o ran o r d i n a r y p a r a c h u t e A c = 1 . 2 - 1 . 3 ) . For example, one f o r e i g n b r a k i n g Xp a r a c h u t e with a canopy diameter of 9 . 7 6 m and A c = 0.55 c r e a t e s a b r a k i n g X A. V. C h e s t n o v , Letnaya Ekspzuatatsiya S h o Z e t a [ F l y i n g Operation of Air­c r a f t ] , Voyenizdat. P r e s s , 1962. 159 J
  • 170. f o r c e of 17.25 t a t 296 km/hr ( m i l i t a r y t r a n s p o r t a i r c r a f t ) . The l e n g t h of t h e l a n d i n g r u n on an i c e covered runway can be reduced by30-40% by u s i n g a b r a k i n g p a r a c h u t e . Under t h e s e c o n d i t i o n s , i t s e f f e c t i v e ­n e s s i s p a r t i c u l a r l y n o t i c e a b l e . However, t h e less t h e speed, t h e less t h ee f f e c t i v e n e s s of t h e p a r a c h u t e . For example, t h e b r a k i n g p a r a c h u t e s on aTU-104 d e c r e a s e t h e run l e n g t h by 25-30% (wet o r i c e covered s t r i p ) . Thus,under s t a n d a r d c o n d i t i o n s f o r a l a n d i n g weight o f 58 t , t h e r u n l e n g t h i s1730 m, w h i l e t h e usage o f t h e p a r a c h u t e reduces t h i s f i g u r e t o 1250-1350 m.The b r a k i n g f o r c e i s 10-14 t . Figure 06. Usage of t h e Braking Parachute ( a ) and Diagram of I n s t a l l a t i o n and Operation of Thrust Reverse s ( b ) o n Two External A i r c r a f t Engines: 1 , V i e w from r e a r , reversed flow i n c l i n e d by 20" from v e r t i c a ; 2 , Apertures f o r gas o u t l e t d i r e c t e d a t a n g l e o p p o s i t e t o f l i g h t ; 3 , A t moment of touchdown, r e v e r s e doors c l o s e d , during braking t h e y d i r e c t g a s i n d i r e c t i o n o p p o s i t e movement. During t a x i i n g , doors s e t i n i n t e r m e d i a t e p o s i t i o n . One d e f e c t of t h i s method of reducing t h e r u n l e n g t h i s t h e f a c t t h a twith a s i d e wind s t r o n g e r t h a n 6-8 m/sec a t an a n g l e of o v e r 45" t o t h e runway,t h e p a r a c h u t e w i l l be d e f l e c t e d from t h e a x i s of t h e a i r c r a f t and w i l l tend t ot u r n t h e a i r c r a f t i n t o t h e wind. AS t h e s i d e wind i n c r e a s e s i n speed, t h ep r o b a b i l i t y o f r o t a t i o n a l s o i n c r e a s e s . However, even i n t h i s c a s e i t i srecommended t h a t t h e b r a k i n g chute b e used d u r i n g t h e f i r s t h a l f o f t h elanding r u n , b e i n g extended immediately a f t e r touchdown ( i n p r a c t i c e with ad e l a y o f 5-7 s e c ) . Another d e f e c t i s t h e f a c t t h a t t h e d i s c a r d e d p a r a c h u t emust b e r a p i d l y removed from t h e runway, t r a n s p o r t e d , checked and packed. Thes e r v i c e l i f e of a b r a k i n g p a r a c h u t e (with an average a c c e l e r a t i o n o f1.55 m/sec2) i s 40-50 l a n d i n g s . C a l c u l a t i o n o f t h e d r a g produced by t h ep a r a c h u t e i s performed u s i n g t h e formula160
  • 171. I-l-11 1 1 .11 IIIIII.-1111111IIIII I 1 1 . 11 11111 1 I I 11111111111111=~111~111111111.1111111111ll I I I I I 11111 111111111 I II II where Acx i s t h e drag of t h e parachute r e l a t e d t o t h e wing area o f t h e aircraft; S i s t h e wing area; q i s t h e impact p r e s s u r e . , For example, f o r t h e b r a k i n g parachute o f a TU-124 with Scan = 40 m2, = 0.54 (S = 105.35 m2) : - C x par 0.54s 0.54.40 Acx pa -9.205. S 105.35 E j e c t i o n of t h e braking parachute a t lower speed i s l e s s e f f e c t i v e . A t t h e end of t h e landing run, due t o t h e d e c r e a s e i n speed and t h e angle of a t t a c k , which w i l l b e equal t o t h e parked angle, f o r c e Q i s p r a c t i c a l l y equal t o zero. I t i s considered t h a t i n t h e process of t h e e n t i r e landing run, an average braking f o r c e a c t s on t h e a i r c r a f t , c r e a t i n g a average n e g a t i v e acceleration j xav = . . 1 95- br . G The g r e a t e s t v a l u e o f n e g a t i v e a c c e l e r a t i o n i s achieved a f t e r t h e braking /166 parachute i s extended and amounts t o 4.4-4.2 m/sec2. I n c r e a s i n g t h e landing speed by 5% (from 210 t o 220 km/hr) i n c r e a s e s t h e l e n g t h o f t h e landing run by approximately 1 0 % . Therefore, a d e c r e a s e i n landing speed i s t h e most e f f e c t i v e means of decreasing t h e run l e n g t h . A n increase i n j by t h e usage o f s p o i l e r s and a braking parachute o r t h r u s t xav r e v e r s a l o f t h e engines can s i g n i f i c a n t l y s h o r t e n t h e landing run. When t h e engine t h r u s t i s r e v e r s e d , t h e r e a c t i o n j e t i s d i r e c t e d forward and e x i t s upward and downward a t an angle t o t h e h o r i z o n t a l . For example, i n t h e two outboard engines of t h e English "Comet" t u r b o j e t a i r c r a f t , t h e r e a c ­ t i o n j e t e x i t s upward and downward a t 45" t o t h e h o r i z o n t a l . The r e v e r s e r ( t h e d e v i c e which d e f l e c t s theflow) i s r o t a t e d a t 20" t o t h e v e r t i c a l , i n o r d e r t o d i r e c t t h e j e t away from t h e f u s e l a g e and landing gear (Figure 106 b ) . 161
  • 172. With s u f f i c i e n t l y r a p i d movement of t h e a i r c r a f t , t h e j e t w i l l bed e f l e c t e d rearward and w i l l not e n t e r t h e a i r i n t a k e s , while a t very lowspeeds o r a t r e s t of t h e a i r c r a f t t h e stream w i l l move f a r forward. The o p e r a t i n g time o f t h e r e v e r s e r i n a landing i s g e n e r a l l y n o t over15 s e c . The doors of t h e r e v e r s i n g device a r e operated pneumatically. Ther e v e r s e r i s put i n o p e r a t i o n bymoving a s p e c i a l l e v e r forward. The t h r o t t l e sc o n t r o l l i n g t h e outboard engines must f i r s t be p u t i n t h e i d l e p o s i t i o n andl i f t e d . The e f f e c t i v e n e s s of t h r u s t r e v e r s a l i s decreased with decreasinga i r c r a f t speed. However, when necessary t h r u s t r e v e r s a l can be used u n t i l t h e a i r c r a f tcomes t o a complete s t o p . Thrust r e v e r s a l should be a p p l i e d t h e moment t h e a i r c r a f t touches t h erunway. The maximum r e v e r s e t h r u s t t h e o r e t i c a l l y i s 70% of t h e forwardt h r u s t , b u t i n p r a c t i c e only about 50% i s r e a l i z e d . The usage of t h r u s t r e v e r s a l makes it p o s s i b l e t o decrease t h e landingrun l e n g t h by 20-25%. Also, i n t h e "Comet-4B" a i r c r a f t t h e s i z e o f t h e f l a p si s i n c r e a s e d and t h e i r angle of d e f l e c t i o n i s i n c r e a s e d t o 8 0 ° , g r e a t l yreducing t h e landing speed. I n a i r c r a f t with engines l o c a t e d i n t h e wing and n e a r t h e f u s e l a g e , t h eusage of t h r u s t r e v e r s a l i s d i f f i c u l t due t o t h e thermal e f f e c t s of t h ereversed j e t s on t h e f u s e l a g e . I t i s e a s i e s t t o u s e t h r u s t r e v e r s e r s onengines mounted on p i l o n s , as on t h e Boeing 707, DC-8, e t c . I f t h e r e a r ef o u r engines mounted on t h e t a i l of t h e f u s e l a g e , t h e r e v e r s e r s a r e i n s t a l l e donly i n t h e outboard engines. A s was noted, i n a d d i t i o n t o braking p a r a c h u t e s , motor switch off duringt h e landing run, and t h r u s t r e v e r s a l , s p o i l e r s and a i r b r a k e s a r e a l s o used.The s p o i l e r s a r e p l a t e s which can be extended o r d e f l e c t e d , mounted on t h eupper s u r f a c e of t h e wings. One, two o r t h r e e s p o i l e r s can be used on each / 167wing. The s p o i l e r s a r e extended a f t e r t h e a i r c r a f t wheels touch t h e runway. Bys e p a r a t i n g t h e flow from t h e upper wing s u r f a c e , t h e s p o i l e r s decrease t h el i f t i n g f o r c e s h a r p l y and c r e a t e considerable a d d i t i o n a l drag. The graph on Figure 107 shows t h a t with t h e s p o i l e r s closed t h e aero­dynamic q u a l i t y of t h e a i r c r a f t decreases from 6 t o 4.4 upon t r a n s i t i o n fromt h e landing p o s i t i o n ( a = l o " ) t o t h e landing run p o s i t i o n (a = 1 " ) ; openingof t h e s p o i l e r s during t h e run decreases t h e aerodynamic q u a l i t y by a na d d i t i o n a l f a c t o r of 4 (from 6 t o 1 . 5 ) . Extending t h e s p o i l e r s has approximately t h e same i n f l u e n c e on t h edependence c = f ( a ) . Y162
  • 173. S5. Length o f Landing Run A s a Function o f Various Operational Factors The l e n g t h o f t h e landing run i s e s s e n t i a l l y i n f l u e n c e d by t h e a i r c r a f t weight, c o n d i t i o n of t h e runway, d i r e c t i o n and speed o f wind, a i r temperature, e t c . The l e n g t h o f t h e l a n d i n g r u n a l s o depends on t h e actions of t h e p i l o t i n control of the aircraft . The weight of t h e a i r c r a f t i n f l u e n c e s t h e l e n g t h of t h e landing run p r i m a r i l y through t h e l a n d i n g speed. A s t h e weight of t h e a i r c r a f t i s i n c r e a s e d , t h e square o f t h e Figure 107. C o e f f i c i e n t c.. As l a n d i n g speed i s a l s o i n c r e a s e d and Y consequently t h e l e n g t h o f t h e landing a Function of A n g l e o f Attack run i s i n c r e a s e d t o t h e same e x t e n t . and Polar Curve o f A i r c r a f t For example, w i t h landing weight o f During Landing ( f l a p s down, 30,000 kg, t h e l e n g t h o f t h e landing A i rbrake and Spoi 1 e r s extended) r u n under s t a n d a r d c o n d i t i o n s is 930 m , whereas with a landing weight of 32,000 kg, i . e . , i n c r e a s e d by 1.065 times, t h e run l e n g t h i si n c r e a s e d by t h e same number o f times and w i l l be 930-1.065 = 990 m . Thus, i f t h e a i r c r a f t weight i s i n c r e a s e d by 6.5%, t h e run l e n g t h w i l l bei n c r e a s e d by t h e same f a c t o r . The temperature of t h e surrounding a i r i n f l u e n c e s t h e run l e n g t hp r i m a r i l y through t h e d e n s i t y . As t h e t e m p e r a t u r e i s i n c r e a s e d with unchangedp r e s s u r e , t h e d e n s i t y o f t h e a i r i s decreased.2 I f t h e temperature i si n c r e a s e d by a c e r t a i n f a c t o r , t h e v a l u e of v Idg i s i n c r e a s e d by t h e same /168f a c t o r . Thus, i f t h e t e m p e r a t u r e i s i n c r e a s e d by 5% o v e r t h e s t a n d a r dtemperature, V2 w i l l b e i n c r e a s e d by approximately t h e same p e r c e n t . 1dg A decrease i n d e n s i t y leads t o a decrease i n t h e drag Q during t h e run.Also, d u r i n g t h e r u n t h e engines c r e a t e a s l i g h t t h r u s t and a s t h e temperaturei s i n c r e a s e d , t h i s t h r u s t i s decreased, which h e l p s t o reduce t h e run l e n g t h .I f w e i g n o r e t h e i n f l u e n c e o f temperature on d r a g and t h r u s t , w e can approx­i m a t e l y c o n s i d e r t h a t an i n c r e a s e i n t e m p e r a t u r e o f 5% ( f o r example from 15 t o3OoC (from 288 t o 303OK) w i l l r e s u l t i n an i n c r e a s e i n run l e n g t h o fapproximately 5%. I t should be noted t h a t under c o n d i t i o n s o t h e r t h a n t h es t a n d a r d c o n d i t i o n s , t h e l a n d i n g speed i n d i c a t e d by t h e instrument ( t h e broad 163
  • 174. arrow) w i l l b e t h e same as a t s t a n d a r d c o n d i t i o n s , s i n c e w i t h a change i n a i rd e n s i t y t h e v e l o c i t y i n d i c a t o r d e c r e a s e s t h e i n d i c a t e d speed due t o methodice r r o r . The f i n e n e e d l e o f t h e i n d i c a t o r shows t h e t r u e speed i n t h i s c a s e . The i n f l u e n c e o f head winds and t a i l winds on t h e l e n g t h of t h e landingr u n i s t h e same a s t h i s i n f l u e n c e on t h e l e n g t h of t h e t a k e o f f r u n . The b r a k i n g e f f e c t i s always g r e a t e s t with t h e maximal speeds ofu t i l i z a t i o n of s p o i l e r s and p a r a c h u t e . Therefore, a d e l a y i n u s i n g t h es p o i l e r s of 1.5-2 s e c i n c r e a s e s t h e run l e n g t h by 100-150 m, w h i l e e j e c t i o n oft h e p a r a c h u t e a t 180-140 km/hr decreases i t s b r a k i n g e f f e c t by 35-50%. Thewheel b r a k e s should be a p p l i e d immediately a f t e r t h e s p o i l e r s are extended,i . e . , a t 250-220 km/hr.56. S p e c i f i c Features of Landing R u n s on Dry, Ice o r Snow Covered Runways A t t h e p r e s e n t t i m e we s t i l l do not have s u f f i c i e n t d a t a on methods ofdetermining t h e e f f e c t o f b r a k i n g on wet o r snow covered runways. I n s p i t e of t h e v a r i e t y of means of b r a k i n g , t h e p r i n c i p a l means remainst h e d i s k wheel b r a k e s . I t has been e s t a b l i s h e d t h a t when l a n d i n g on a d r yc o n c r e t e runway, about 70% of t h e energy o f movement of t h e a i r c r a f t i sabsorbed by t h e b r a k e s , and 30% by aerodynamic d r a g of t h e a i r c r a f t (usage off l a p s and a i r b r a k e s ) . When landing on a wet runway, o n l y about 50% of t h ek i n e t i c energy i s absorbed by t h e b r a k e s , o r i f t h e t i r e s a r e worn -- evenl e s s . The wheel b r a k e s have an important r o l e t o p l a y d u r i n g a landing run i ff l i g h t i s t e r m i n a t e d a t speeds less t h a n t h e s e p a r a t i o n speed by 15-20%, i nwhich t h e s p o i l e r s and landing p a r a c h u t e are less e f f e c t i v e . The p r e s s u r e i nt h e t i r e s has a g r e a t i n f l u e n c e on t h e e f f e c t i v e n e s s of b r a k i n g : t h e l e s s t h ep r e s s u r e , t h e g r e a t e r t h e c o n t a c t a r e a and t h e more r e l i z b l y t h e brakesoperate . A t t h e p r e s e n t time, t h e runway l e n g t h r e q u i r e d f o r a i r c r a f t o p e r a t i o n i sdetermined e i t h e r on t h e b a s i s of t h e c o n d i t i o n of t h e p r o v i s i o n of s a f e t y ofi n t e r r u p t e d o r extended t a k e o f f ( s e e Figure 7 1 ) , o r from t h e c o n d i t i o n s of t h e /169c o n d i t i o n s of t h e landing c h a r a c t e r i s t i c s of t h e a i r c r a f t ( s e e Figure 1 0 3 ) .These c h a r a c t e r i s t i c s a r e g e n e r a l l y c a l c u l a t e d f o r a d r y runway s u r f a c e .However, a t most a i r p o r t s due t o c l i m a t i c c o n d i t i o n s o v e r one t h i r d of t h ey e a r o r perhaps even. more t h e runway s u r f a c e s are m o i s t , snow covered o rf r o z e n . S t a t i s t i c s show t h a t on t h e world s c a l e , one l a n d i n g of twelve i sperformed on a wet runway’.’[Technical Information Department, S tAa tier T rcai n snpt ofrit c ResearchONTIs tGOSNIIf GArI _____I_ .__ Zarubezhnyy Aviatransport , (Foreign --- S e i -- ) No. 7, In itute o C i v i l A v i a t i o n ] , 1965.164
  • 175. The experience o f o p e r a t i o n of domestic t u r b o j e t and turboprop a i r c r a f t , as w e l l as d a t a from f o r e i g n p r a c t i c e i n d i c a t e t h a t t h e p r e s e n c e of s l u s h (wet snow, water) on runway s u r f a c e s h a s t h e following n e g a t i v e i n f l u e n c e on t h e design o f a i r c r a f t and landing o p e r a t i o n s : 1) a d d i t i o n a l d r a g appears as t h e s l u s h s t r i k e s t h e a i r c r a f t , p a r t i c u l a r l y i n t h e c a s e o f a i r c r a f t with heavy l a n d i n g g e a r ; 2 ) t h e danger arises t h a t l i q u i d may e n t e r t h e engine a i r i n t a k e ; 3) c o n t r o l l a b i l i t y of t h e a i r c r a f t i s reduced; and 4) t h e 1andiv.g run l e n g t h i s s i g n i f i c a n t l y i n c r e a s e d . Pavements f o r runways i n c l u d e c o n c r e t e , a s p h a l t , etc. On a moist o r wet runway, t h e wheel r o l l d r a g i n c r e a s e s , b u t t h e coupling f o r c e between wheel and runway d u r i n g b r a k i n g d e c r e a s e s ( i n comparison t o d r y pavement). This r e s u l t s i n an i n c r e a s e i n t h e l a n d i n g run l e n g t h of t h e a i r c r a f t . This i n c r e a s e i s so g r e a t t h a t i n many c a s e s t h e length of t h e runway may be i n s u f f i c i e n t t o complete t h e l a n d i n g r u n . A moist r u n w a y ’ i s understood t o b e t h e c o n d i t i o n i n which t h e pavement i s moistened w i t h water ( a f t e r r a i n ) , while a w e t runway means t h a t t h e r e i s a l a y e r o f water on t h e runway 2 - 3 mm t h i c k . T e s t s performed i n t h e U A S showed t h a t w i t h a c e r t a i n t h i c k n e s s o f water on t h e runway and with c e r t a i n parameters of t h e t i r e s , t h e c r i t i c a l speed can be reached a t which t h e t i r e s a r e completely s e p a r a t e d from t h e s u r f a c e of t h e road by hydrodynamic f o r c e s c r e a t e d by t h e l i q u i d between t h e t i r e and t h e s u r f a c e o f t h e runway (Figure 108 a ) . This speed i s c a l l e d t h e s k i d d i n g speed o r speed o f hydro­ planing. The e f f e c t o f aquaplaning s i g n i f i c a n t l y i n c r e a s e s t h e landing run l e n g t h on a w e t runway. I n v e s t i g a t i o n s have shown t h a t aquaplaning a r i s e s a t speeds averaging o v e r 160 km/hr. When t h i s o c c u r s , t h e c o n t a c t between wheels and pavement i s l o s t and a f l i m o f water appears between them. This r e s u l t s i n a l o s s of e f f e c t i v e n e s s of b r a k e s and makes i t d i f f i c u l t t o m a i n t a i n t h e d i r e c t i o n of t h e landing r u n . The phenomenon of aquaplaning i s explained by t h e f a c t t h a t a hydrodynamic f o r c e a c t i n g on t h e s u r f a c e of t h e pavement a r i s e s as t h e a i r c r a f t moves over t h e runway. When i t s v e r t i c a l component / 170 becomes equal t o o r g r e a t e r t h a n t h e weight of t h e a i r c r a f t , c o n t a c t o f t h e wheels with t h e runway i s l o s t . The graph on Figure 108 b was produced t h e o r e t i c a l l y and confirmed e x p e r i m e n t a l l y . Using t h i s graph (with known p r e s s u r e i n t h e t i r e s ) , we can e s t a b l i s h t h e l i m i t i n g speed, above which usage of t h e wheel b r a k e s during a landing on w e t s u r f a c e i s u s e l e s s , o r even dangerous i n c a s e of a s t r o n g s i d e wind, so t h a t o n l y aerodynamic brakes should b e used. A s soon as t h e speed drops below t h e aquaplaning speed, t h e wheel brakes can b e u s e d . A t t h e moment t h e b r a k e s a r e a p p l i e d , a f r i c t i o n coupling f o r c e appears between a i r c r a f t wheels and runway. I n some c a s e s b r a k i n g may r e s u l t i n wheel lockup (100% s k i d ) i . e . , a s i t u a t i o n i n which t h e movement o f t h e a i r c r a f t with n o n r o t a t i n g wheels ( s k i d ) causes t h e f o r c e of f r i c t i o n t o d e c r e a s e , i n c r e a s i n g t h e l e n g t h of t h e landing run. The i n t e r a c t i o n of t h e b r a k i n g wheel w i t h t h e runway s u r f a c e i s g e n e r a l l y e v a l u a t e d by t h e coupling 165I
  • 176. c o e f f i c i e n t o r c o e f f i c i e n t of f r i c t i o n , equal t o t h e r a t i o o f t h e t a n g e n t i a lb r a k i n g f o r c e t o t h e normal l o a d i n g on t h e wheel. .q D i r e c t i o n of movement 320 [I Wheelf f e c t i v e ine brakes I n f -0 a, a, C r i t i c a l speed f o r a i r c r a f t i n question / Whee 1 brakes effective 6M G i ven a m 0 1 I 1 2 I 3 1 4 Mdl 5 6 7 2 3 pressure i n t i r e s , k d c m D 5 - - Figure 108. Formation of Hydrodynamic L i f t i n g Force A s Wheels Roll Along W t Runway ( a ) and Aquaplaning S p e e d e A s a Function of P r e s s u r e and T i r e s ( b ) : 1-2, Hydro­ dynamic l i f t and d r a g O a c l e a n , d r y s u r f a c e , t h e coupling c o e f f i c i e n t o f t h e t i r e s i s q u i t e nhigh and, i f t h e r u b b e r does n o t melt o r burn due t o t h e h i g h temperature a tt h e p o i n t o f c o n t a c t with t h e runway s u r f a c e , t h i s c o e f f i c i e n t may v a r ybetween 0 . 7 and 0.8 depending on t h e t r e a d p r o f i l e (dry c o n c r e t e ) . As t h espeed of t h e a i r c r a f t i s i n c r e a s e d , t h e c o e f f i c i e n t d e c r e a s e s by 2-3 t i m e s . T h e r e f o r e , t h e mean v a l u e of coupling c o e f f i c i e n t f o r a d r y c o n c r e t erunway i s 0.15-0.25; f o r a moist runway t h i s f i g u r e i s 0.1-0.21 and f o r a w e t /171runway, about 0 . 2 l 1 . For an a s p h a l t runway (according t o t h e d a t a of t h eS t a t e Planning I n s t i t u t e and t h e S c i e n t i f i c Research I n s t i t u t e f o r C i v i lAviation) 2 , t h e coupling c o e f f i c i e n t f o r a l l of t h e pavement c o n d i t i o n sanalyzed above is somewhat h i g h e r : from 0.33 t o 0.23; f o r snow covered cementand a s p h a l t pavements i t i s 0.3-0.25. Therefore t h e c a l c u l a t e d l a n d i n g runl e n g t h o f an a i r c r a f t on t h e s e pavements i s 15-20% l e s s . When landing on an i c e covered runway, t h e e f f e c t i v e n e s s o f t h e b r a k e s i ss h a r p l y decreased, by an average of 25-30% i n comparison w i t h a l a n d i n g on ad r y , c o n c r e t e runway. Due t o t h i s , i t i s g e n e r a l l y recommended t h a t a b r a k i n gp a r a c h u t e be used, t h a t one o r two engines be s h u t down, e t c . I t i s knownt h a t r a p i d dropping o f t h e f r o n t wheel o n t o t h e runway a f t e r touchdown c r e a t e st h e b e s t c o n d i t i o n s f o r b r a k i n g . However, as a r u l e , t h i s method i s mosts u i t a b l e f o r a d r y runway pavement, s i n c e on w e t pavement, f r o z e n o r ~~ ~ ~ ~- ~.. ~ .. .. . . .~ ~ - .- .. ~. ._ _ - .--__._ - .. . . . - , . Chestnov, A. V . , Letnaya EkspZuatatsiya S m o Z e t a [Flying Operation of t h eA i r c r a f t ] , Voyenizdat. P r e s s , 1962. GPI and NIIGA.166
  • 177. snow covered pavement, t h e b r a k i n g e f f e c t of t h e wheels i s reduced. Undert h e s e c o n d i t i o n s , we must keep i n mind t h e f a c t t h a t running with t h e f r o n twheel up c r e a t e s a d d i t i o n a l aerodynamic d r a g , which i s t h e main b r a k i n ge f f e c t d u r i n g t h i s p o r t i o n of t h e run. I t i s p a r t i c u l a r l y d i f f i c u l t t operform a landing ( o r t a k e o f f ) on a runway covered with w e t snow. Experienceh a s shown t h a t a l a y e r of wet snow 25 mm t h i c k i n c r e a s e s t h e t a k e o f f runl e n g t h by 60%, and t h a t a l a y e r 75" t h i c k makes a t a k e o f f impossible. The maximum p e r m i s s i b l e depth of a l a y e r of l i q u i d o r water h a s beene x p e r i m e n t a l l y e s t a b l i s h e d a s 12.7 mm. This depth w i l l r e q u i r e an i n c r e a s e i nt a k e o f f r u n l e n g t h of 20-30%.57. Landing w i t h S i d e Wind The s i d e wind means t h e wind v e l o c i t y component d i r e c t e d p e r p e n d i c u l a r t ot h e runway. A t t h e p r e s e n t t i m e , l a n d i n g s w i t h s i d e winds a r e made by t h e method ofcourse l e a d , i . e . , d r i f t o f t h e a i r c r a f t i s compensated f o r by c r e a t i n g ac e r t a i n l e a d angle E i n t h e course of t h e a i r c r a f t a f t e r e x i t from t h e f o u r t ht u r n (Figure 109). I f t h e c o u r s e of t h e a i r c r a f t i s changed by angle E ,determined from t h e r e l a t i o n s h i p t a n E = W/Vg, t h e ground speed V w i l l be gd i r e c t e d along t h e runway. Thus, i f V = 250 km/hr, while W = 10 m/sec, t h e gl e a d angle E = 8 " . However, d u r i n g l e v e l i n g o f f and holding t h e speed o f t h ea i r c r a f t w i l l d e c r e a s e and t h e i n i t i a l l e a d angle w i l l become t o o low; t h ea i r c r a f t w i l l begin t o d r i f t o f f of t h e runway. T h e r e f o r e , a t t h e moment oftouchdown, t h e l e a d angle must be i n c r e a s e d by approximately 1-1.5". The crew should have good v i s i b i l i t y from t h e c o c k p i t a t l e a d angles of /172 -10-15", which a r e r e q u i r e d with a s i d e wind above 15 m/sec. When d r i f t i s compensated f o r by a v a r i a t i o n i n landing c o u r s e , t h el o n g i t u d i n a l a x i s of t h e a i r c r a f t does n o t correspond t o t h e d i r e c t i o n ofmovement, and f l i g h t i s performed without s l i p p i n g o r bank. A t t h e moment oftouchdown, t h e c o n t r o l wheel should be t u r n e d i n t h e d i r e c t i o n o f t h e d r i f t ,r o t a t i n g t h e a i r c r a f t along t h e runway by l e a d a n g l e E . I f when t h i s maneuveri s performed t h e l o n g i t u d i n a l a x i s s t i l l makes a c e r t a i n angle with t h ed i r e c t i o n of t h e runway, s i d e f o r c e Z w i l l a c t a g a i n s t t h e wheels, t e n d i n g t or o t a t e t h e a i r c r a f t along t h e runway, s i n c e it i s a p p l i e d behind t h e c e n t e r o fg r a v i t y of t h e a i r c r a f t ; however, t h i s e f f e c t i s n o t dangerous f o r t h e landingorgans. A s w e can s e e from Figure 110, t h e nose wheel p r e s e n t s no moment,s i n c e i t i s o r i e n t e d f r e e l y along t h e d i r e c t i o n of movement while t h e s i d ef r i c t i o n f o r c e on t h e main wheels c r e a t e s s t a b i l i z i n g moment, t e n d i n g t or o t a t e t h e a i r c r a f t t o l i n e up with t h e runway. With a s i d e wind, g l i d i n gshould be performed a t h i g h e r speeds (10 km/hr h i g h e r ) , and t h e landing speedshould be 5-10 km/hr h i g h e r t h a n t h e normal recommended speed. The p i l o t mustc o n t r o l h i s a i r c r a f t on t h e approach t o t h e l a n d i n g s t r i p c a r e f u l l y , beings u r e n o t t o l e v e l o f f high o r touchdown h a r d . The f r o n t l e g must be lowered 167
  • 178. immediately a f t e r l a n d i n g i n o r d e r t o avoid zooming and t o m a i n t a i n t h ed i r e c t i o n from t h e l a n d i n g run u s i n g t h e c o n t r o l wheel. The c o n t r o l s t i c kshould b e pushed forward t o t h e s t o p i n o r d e r t o b r i n g t h e nose wheel down t ot h e pavement. When l a n d i n g w i t h a s i d e wind, t h e l e n g t h o f t h e landing run i s i n c r e a s e d - /173by 10-15%. The maximum p e r m i s s i b l e v a l u e o f s i d e wind component (90" t orunway a x i s ) i s 12-15 m/sec. I n case o f a l a r g e r o t a t i o n a l moment, t h e down­wind engine may b e switched o f f , t h e b r a k i n g p a r a c h u t e can b e r e l e a s e d , t h r u s tr e v e r s a l and b r a k i n g can b e used..58. T h e "Minimum" Weather f o r Landings and Takeoffs The t a k e o f f - l a n d i n g c h a r a c t e r i s t i c s of an a i r c r a f t determine t h el i m i t i n g m e t e o r o l o g i c a l c o n d i t i o n s ("minimum weather") f o r which o p e r a t i o n oft h e a i r c r a f t ( t a k e o f f and landing) can be p e r m i t t e d . The c o n d i t i o n s i n c l u d e : a) minimum c e i l i n g ; b) minimum v i s i b i l i t y a trunway l e v e l ; c) minimum l a t e r a l component o f wind speed Wz. The minimum c e i l i n g determines t h e f l y i n g a l t i t u d e t o which t h e a i r c r a f tshould come down o u t o f t h e clouds and c l e a r v i s i b i l i t y of r e f e r e n c e p o i n t s ont h e ground o r runway l i g h t s should be e s t a b l i s h e d . A t t h i s a l t i t u d e , t h e crewcan guide t h e a i r c r a f t down on t h e landing l i n e v i s u a l l y . For t u r b o j e ta i r c r a f t landing a t a i r f i e l d s equipped w i t h IL S, w i t h a g l i d e p a t h angle o f2" 40 min, t h e minimum cloud cover c e i l i n g i s 60-100 m. The minimum v i s i b i l i t y i s considered t h e range a t which t h e crew o f ana i r c r a f t begins t o s e e r e f e r e n c e p o i n t s on t h e ground and t h e beginning of t h erunway during t h e daytime, o r landing l i g h t s and t h e i l l u m i n a t e d runways u r f a c e a t n i g h t . This range should be s u f f i c i e n t t o make it p o s s i b l e t oc o r r e c t i n a c c u r a c i e s i n a i r c r a f t course and s e p a r a t i o n from runway a x i s . Theaccuracy of guidance o f t h e a i r c r a f t r e l a t i v e t o t h e c e n t e r l i n e o f t h erunway depends on t h e accuracy of o u t p u t of c o u r s e d a t a by on-board and groundb a s e apparatus and t h e p r e c i s i o n of p i l o t i n g according t o t h e i n d i c a t o r onboard t h e a i r c r a f t . Experiments performed by GOSNII G A 1 have e s t a b l i s h e d t h a tf o r passenger j e t a i r c r a f t t h e mean v a l u e of t o t a l d e v i a t i o n from t h e runwaya x i s i s 560 m. Coming down out of t h e clouds with t h i s amount of e r r o r , t h ep i l o t must c o r r e c t t h e e r r o r with two s e q u e n t i a l t u r n s (Figure 1 1 1 ) . Duringt h i s t i m e , t h e a i r c r a f t continues t o descend on t h e g l i d e p a t h , g e n e r a l l ybetween 2" 40 min and 4" ( t h e h i g h e r v a l u e f o r a i r f i e l d s w i t h d i f f i c u l tapproaches). The time r e q u i r e d t o c o r r e c t l a t e r a l d e f l e c t i o n i s i n f l u e n c e dc o n s i d e r a b l y by t h e i n e r t i a of t h e a i r c r a f t , i t s d e l a y (4-5 s e c ) t o movements . S M. Yeger Proyektirovaniye Passazhirskikh Rgaktivnykh Smnozetov [Designof J e t Passenger A i r c r a f t ] Mashinostroyeniye P r e s s , 1964.168
  • 179. of t h e c o n t r o l organs and t h e c h a r a c t e r i s t i c s o f l a t e r a l and t r a n s v e r s e s t a b i l i t y . Furthermore, an a d d i t i o n a l 2-3 sec is r e q u i r e d f o r crew r e a c t i o n from t h e t i m e when t h e runway can f i r s t be s e e n . T h e r e f o r e , it i s r e q u i r e d /174 t h a t upon approach t o t h e BMB o r a f t e r f l y i n g over t h e BMB t h e crew o f t h e a i r c r a f t must b e a b l e t o see t h e beginning of t h e runway from t h e p o i n t o f beginning of l e v e l i n g o f f down t o t h e touchdown (which i n p r a c t i c e i s 250-300 m from t h e beginning o f t h e runway). Minimum v i s i b i l i t y i s t h e n 800-1200 m y o r 1500 m f o r n i g h t l a n d i n g s . Thus, t h e t r a n s i t i o n t o v i s u a l f l i g h t ( e x i t from t h e cloud cover a t60-100 m f o r a g l i d e p a t h a n g l e o f 2 40 min) occurs a t 1250-1500 m from t h ebeginning o f t h e runway and d u r i n g t h e subsequent 6-7 s e c o f f l i g h t (240­250 km/hr v e l o c i t y ) t h e crew must have a c l e a r view of t h e runway, t h e p o i n to f beginning of l e v e l i n g off and t h e p o i n t of touchdown. During t h i s t i m e ,t h e p i l o t can perform c o u r s e maneuvers i f t h e a i r c r a f t i s coming i n a t ana n g l e , completing h i s maneuvers by t h e t i m e he reaches an a l t i t u d e o f 40-50 m( a t 600-800 m from t h e runway). Below an a l t i t u d e of 50 m y it i s forbiddenf o r a j e t a i r c r a f t t o p u l l up f o r a second c i r c l e . This a l t i t u d e correspondsapproximately t o f l i g h t over t h e BMB, and t h e crew should t a k e a l l s t e p s t oa s s u r e a normal landing from t h i s p o i n t . Figure 109. Elimination Figure 110. Diagram o f of Landing D r i f t by Landing R u n After Touch­ Course Lead Method down w i t h Lead A n g l e E ( f l i g h t w i t h leading course) 169
  • 180. Figure 1 1 1 . Determination o f "Minimum Weather" With l a t e r a l d e v i a t i o n s of 60 m and a g l i d i n g speed o f 250-240 km/hr,t h e r e q u i r e d ground l e n g t h t o b r i n g t h e a i r c r a f t over t o t h e landing l i n e i s800-900 m. If t h e a i r c r a f t comes o u t o f t h e clouds a t 100 m a l t i t u d e and1800-1900 m range from t h e runway and t h e p i l o t , upon s e e i n g t h e runway,d e c i d e s t o t u r n t h e a i r c r a f t , h e can complete h i s maneuver a t 600-700 m fromt h e runway and b r i n g t h e a i r c r a f t onto t h e l a n d i n g course. With g r e a t e rd e v i a t i o n s (70-100 m) t h e r e q u i r e d ground l e n g t h i s 1000-1200 m and t h e p i l o tw i l l not be a b l e t o b r i n g t h e a i r c r a f t onto t h e course l i n e and perform h i slanding i n t h e s p a c e a v a i l a b l e . T h e r e f o r e , t h e r a d a r c o n t r o l l e r guiding t h ea i r c r a f t i n t o a landing, upon determining t h i s abnormal d e v i a t i o n of t h ea i r c r a f t from i t s c o u r s e , should f o r b i d t h e l a n d i n g ( b e f o r e t h e a i r c r a f t g e t sdown t o 50 m a l t i t u d e ) and r e q u i r e t h e a i r c r a f t t o go i n t o a second c i r c l e . The "minimum weather" i s e s t a b l i s h e d n o t o n l y from c o n s i d e r a t i o n s ofs a f e t y of l a n d i n g o f t h e a i r c r a f t under poor weather c o n d i t i o n s , b u t a l s o fromc o n s i d e r a t i o n s of t a k e o f f s a f e t y . As was s t a t e d above, t h e h e i g h t a t whicht h e a i r c r a f t f l i e s over t h e BMB i n c a s e of extended t a k e o f f with one non­o p e r a t i n g motor i s 20-25 m . I f t h e h e i g h t o f o b s t a c l e s i n t h i s f l i g h t s e c t o ri s not o v e r 11-14 m , t h e r e i s no l i m i t on t h e c e i l i n g . H o r i z o n t a l v i s i b i l i t yshould b e a t l e a s t 600-800 m. This q u a n t i t y i s determined as f o l l o w s . During a climb a f t e r t a k e o f f , t h e p i t c h a n g l e 9 = 6-8" (depending on t h eangle of t h e climbing t r a j e c t o r y 0). The a n g l e of view downward from t h ecrews cabin f o r modern a i r c r a f t i s 15-20". A f t e r t a k e o f f a t 60-70 m a l t i t u d e (when t h e l a n d i n g g e a r and f l a p s a r er a i s e d ) t h e crew should see t h e runway o r o r i e n t a t i o n p o i n t s on t h e s u r f a c esuch as approach l i g h t s ( i n o r d e r t o maintain t h e t a k e o f f course) a t l e a s t400-500 m i n f r o n t o f t h e a i r c r a f t . The a d d i t i o n a l v i s i b i l i t y r e s e r v e due t o170
  • 181. t h e slower r e a c t i o n o f t h e p i l o t i s g e n e r a l l y 2-3 sec, corresponding t o ana d d i t i o n a l 200-300 m. Thus, t h e minimum v i s i b i l i t y d u r i n g a t a k e o f f should b e600-800 m.S9. Moving into a Second Circle An a i r c r a f t may move i n t o a second c i r c l e d u r i n g any s t a g e of t h e landingapproach, i n c l u d i n g t h e l e v e l i n g o f f . High power r e s e r v e makes it p o s s i b l e t omove o f f i n t o a second c i r c l e even w i t h one motor o u t o f o p e r a t i o n (TU-104,TU-124, TU-134). The decreased pickup of t u r b o j e t engines does i n f l u e n c e t h e behavior o ft h e a i r c r a f t a t t h e moment t h e t r a n s i t i o n i s made t o t h e second c i r c l e . Theproblem i s t h a t t h e t i m e r e q u i r e d f o r t h e engine t o s h i f t from t h e i d l i n gregime (300-600 kg t h r u s t ) t o t h e nominal t h r u s t regime o r h i g h e r i s 15­1 8 sec, while i n p r a c t i c e a f t e r 6-7 s e c , i . e . , a f t e r t h e t h r o t t l e i s p l a c e d i nt h e "maximum t h r u s t " p o s i t i o n , t h e engine t h r u s t reaches a v a l u e s u f f i c i e n t t oprovide n o t o n l y h o r i z o n t a l f l i g h t , b u t some climb. On t h e b a s i s o f t h i s , au n i f i e d method of p i l o t i n g i n c a s e it becomes n e c e s s a r y t o make a secondc i r c l e h a s been developed (by Candidate of Technical Sciences M. V . Rozenblat). A f t e r deciding t o e n t e r a second c i r c l e , t h e p i l o t s e t s t h e t h r o t t l e t ot h e maximum p o s i t i o n . I f t h e a i r b r a k e has been extended, i t s switch i ss h i f t e d t o t h e " r e t r a c t " p o s i t i o n . The a i r c r a f t i s brought out o f t h edescent and t h e speed i s r e t a i n e d unchanged u n t i l t h e a i r c r a f t begins t o /176climb. S i x t o e i g h t sec a f t e r t h e t h r o t t l e s a r e pushed i n t o t h e maximump o s i t i o n , t h e engines w i l l develop t h r u s t equal t o 75-80% of t h e maximum(Figure 1 1 2 , p o i n t 2 ) , which w i l l overcome t h e d r a g of t h e a i r c r a f t with someexcess power a v a i l a b l e . When t h e a v a i l a b l e power exceeds t h e r e q u i r e d power,t h e a i r c r a f t w i l l begin t o climb. When necessary ( f o r example with i n c r e a s e d v e r t i c a l d e s c e n t r a t e ) i no r d e r t o d e c r e a s e t h e r a t e o f d e s c e n t , immediately a f t e r t h e engines a r es h i f t e d t o t h e maximum regime t h e f l i g h t speed can be smoothly reduced by10-15 km/hr, b u t never below t h e e s t a b l i s h e d g l i d i n g speed. A f t e r t h e a i r c r a f t i s s h i f t e d i n t o a climb and t h e engines reach t h em a x i m u m regime, t h e landing g e a r a r e brought up, causing t h e f l y i n g speed t oi n c r e a s e s h a r p l y . When a s a f e speed i s achieved and an a l t i t u d e o f 80-100 mi s reached, t h e f l a p s are r a i s e d , and t h e engines a r e s h i f t e d t o t h e nominalo r c r u i s i n g regime. The landing g e a r should n o t be r a i s e d u n t i l t h e enginesr e a c h a regime p r o v i d i n g s u f f i c i e n t t h r u s t f o r f l i g h t , s i n c e t h e drag o f t h ea i r c r a f t is i n c r e a s e d when t h e l a n d i n g g e a r s t o r a g e bay doors a r e openedcausing t h e r a t e of d e s c e n t t o i n c r e a s e . The graph o f F i g u r e 1 1 2 shows t h a tt h e a i r c r a f t continues t o descend u n t i l t h e engines r e a c h t h e r e q u i r e d regime;when t h e v e r t i c a l v e l o c i t y component V = 3.5-4 m/sec, t h e a d d i t i o n a l descent Yw i l l b e 15-20 m . With V = 5-7 m/sec, t h e a d d i t i o n a l d e s c e n t w i l l be 30-40 m Yi f t h e speed i s r e t a i n e d t h e same, o r 20-25 m i f t h e f l i g h t speed i s decreased 171
  • 182. by 10-15 km/hr. T h e r e f o r e , t h e lowest s a f e a l t i t u d e f o r t h e d e c i s i o n t o makea second c i r c l e with l a n d i n g g e a r down, f l a p s i n t h e landing p o s i t i o n andairbrake on i s u s u a l l y 50 m. With t h e a d d i t i o n a l d e s c e n t o f up t o 30 m, analtitude r e s e r v e i s t h u s guaranteed. If t h e speed of the aircraft is decreased by lo-. 15 km/hr i n t h e range of g l i d i n g speeds 240-260 km/hr, t h e a d d i t i o n a l climb r e s u l t i n g from k i n e t i c energy i s 18-25 m. F i g u r e 112. Change i n A l t i t u d e and F l i g h t S p e e d of TU-124 A i r c r a f t upon T r a n s i t i o n t o Second C i r c l e from A l t i t u d e of 75 m (average weight 33 t , 6f = 30" and A a b = 4 0 " ) : 1 , Moment of t h r o t t l e s h i f t and beginning of r e t r a c t i o n of a i r b r a k e ; 2 , Moment of achieve­ ment of 75-80% maximum t h r u s t b y e n g i n e s ; 3 , Moment of t r a n s i t i o n of e n g i n e s t o takeoff regime and b e g i n n i n g of r a i s i n g of landing g e a r ; 4 , B e g i n n i n g of r a i s i n g of f l a p s172
  • 183. Chapter x. Cornering - /17791. Diagram o f Forces Operating D u r i n g Cornering O f a l l of t h e curved t r a j e c t o r y maneuvers i n t h e h o r i z o n t a l and v e r t i c a lp l a n e s , t h e t r a n s p o r t a i r c r a f t i s p e r m i t t e d t o perform o n l y t h e c o r n e r i n gmaneuver -- f l i g h t i n a curved t r a j e c t o r y i n t h e h o r i z o n t a l p l a n e w i t h a360-degree t u r n . A p o r t i o n o f a c o r n e r i n g maneuver i s c a l l e d a t u r n . As t a b l e c o r n e r i n g maneuver without s l i p p i n g i s considered p r o p e r . I n o r d e r t o perform c o r n e r i n g it i s n e c e s s a r y t h a t an unbalanced f o r c e a c t on t h e a i r c r a f t , curving t h e t r a j e c t ­ o r y , and d i r e c t e d perpendic­ u l a r t o the trajectory (Figure 113). This f o r c e i s a component o f t h e l i f t i n g f o r c e Y s i n y (where y i s t h e bank a n g l e ) , produced when t h e a i r c r a f t i s banked. T h i s force is called centripetal; i t r e s u l t s i n t h e appearance o f a f o r c e equal and o p p o s i t e t o the centrifugal force: G V:! -m-,? V pcF-L7- r Figure 113. Forces Acting on A i r c r a f t D u r i n g Cornering: a , Proper c o r n e r i n g ; b , Cornering w i t h outward s l i p (nose where m i s t h e mass of t h e of a i r c r a f t d e f l e c t e d toward i n t e r i o r aircraft; of turn) V i s t h e speed i n t h e turn ; r i s t h e r a d i u s of t h e turn. As t h e banking angle i s i n c r e a s e d i n a proper t u r n , t h e l i f t i n g f o r c e /178must be i n c r e a s e d so t h a t i t s v e r t i c a l component Y cos y c o n t i n u e s t o b a l a n c et h e weight o f t h e a i r c r a f t . The f o r c e s a c t i n g on t h e a i r c r a f t d u r i n g a h o r i z o n t a l t u r n should s a t i s f yt h e following e q u a l i t i e s 173
  • 184. If Y i s expressed through t h e overload n = Y/G, t h e nThis formula shows t h e r e l a t i o n s h i p between overloading, which must be used t operform t h e h o r i z o n t a l t u r n and t h e banking a n g l e y (Figure 1 1 4 ) . As we can y-see from t h e graph, i n o r d e r t o perform a h o r i z o n t a l t u r n a t y = 6 0 " , we mustcreate n = 2. Y I n passenger a i r c r a f t , t h e bank angle i s u s u a l l y s e t a t 2 0 - 3 0 ° , which a f f o r d s t h e necessary maneuverab i 1i t y . 40 I During an approach t o landing under i n s t r u ­ w 1 I ment f l i g h t r u l e s , t h e bank cannot exceed 15. I .I f 2 3 4 5 -67 With most modern a i r c r a f t , h o r i z o n t a l t u r n s a r e performed u s i n g t h e a i l e r o n s a l o n e , almost Figure 114. Over- without u s i n g t h e r u d d e r , with t h e a i r c r a f t load A s a F u n c t i o n " i t s e l f " s e l e c t i n g an a n g u l a r t u r n i n g r a t e s o of Banking Angle t h a t t h e r e w i l l be no s l i p p a g e . This has become p o s s i b l e due t o t h e high degree o f d i r e c t i o n a l s t a b i l i t y , which g r e a t l y f a c i l i t a t e s maintenanceof s o - c a l l e d "coordination," i . e . , a combination o f o p e r a t i o n s o f t h e a i l e r o n sand rudder f o r which t h e v e l o c i t y v e c t o r remains i n t h e p l a n e of symmetry oft h e a i r c r a f t and no s l i p p i n g occurs1.52. Cornering Parameters Cornering parameters i n c l u d e t h e r a d i u s o f t h e h o r i z o n t a l t u r n , time oft h e t u r n , angular v e l o c i t y of t h e t u r n , e t c . The following formulas are known f o r t h e r a d i u s and time o f a h o r i z o n t a lturn :m a r S t a b i 1 i t y of t h e A i r c r a f t ," Letchikuo Prakticheskoy Aerod?k"ke [ P r a c t i c a l Aerodynamics f o r t h e P i l o t ] ,Voyenizdat. P r e s s , 1961.174
  • 185. I I1 I I I l l 11.11 11111where V i s t h e speed d u r i n g t h e c o r n e r i n g maneuver; cor g is the acceleration of gravity; /179 n i s t h e overload; y is t h e bank a n g l e o f t h e a i r c r a f t . W can see from t h e formula t h a t t h e r a d i u s of t h e t u r n depends s t r o n g l y eon t h e f l i g h t speed, i n c r e a s i n g r a p i d l y with i n c r e a s i n g speed. The r a d i u s oft h e h o r i z o n t a l t u r n can be d e c r e a s e d by i n c r e a s i n g t h e overloading, i . e . , byi n c r e a s i n g t h e bank a n g l e of t h e a i r c r a f t . During c o r n e r i n g , t h e a i r c r a f t has an angular v e l o c i t y o f Let us c a l c u l a t e t h e r a d i u s of t u r n s performed d u r i n g t h e landingapproach around a l a r g e , r e c t a n g u l a r course ( y = 1 S 0 , t a n 15" = 0.268). If t h e bank a n g l e s and t h e t u r n s a r e g r e a t e r t h a n 15", t h e maneuver­a b i l i t y of t h e a i r c r a f t i n c r e a s e s and t h e landing approach time d e c r e a s e s ( t h er e s e r v e of p i l o t s time i n c r e a s e s ) . F o r a l l a i r c r a f t , t h e f i r s t t u r n i n t h e approach t o landing beginsaccording t o t h e diagram a t 2800 m a l t i t u d e and 450 km/hr i n d i c a t e d speed.Let u s d e f i n e t h e r a d i u s o f t h e f i r s t t u r n f o r a mean a l t i t u d e o f 2000 m ,keeping i n mind t h a t t h e i n d i c a t e d speed of 450 km/hr corresponds t o a meana i r speed of 486 km/hr (135 m/sec): Where y = 20" ( t a n 20" = 0.363), w e produce r = 5100 m. Let us determine t h e r a d i u s o f t h e t h i r d t u r n when f l y i n g a t V 1nd = .= 350 km/hr and y = 15":Note: Tg = Tan 175
  • 186. r= m 9480 - ~ 3 6 0 0 9 -81-0,268 A t a n g l e y = 20" and t h e same speed, t h e r a d i u s o f t h e t u r n w i l l b e2660 m. On t h e f o u r t h t u r n a t Vind = 320 km/hr and y = 15" ( l a n d i n g g e a r down,f l a p s down 1 5 " ) , r = 3000 m, and a t 20" bank, r = 2200 m . Let us determine t h e time f o r a t u r n w i t h a bank a n g l e o f 15". A ni n c r e a s e i n t h e r a d i u s of a t u r n a l s o r e s u l t s i n an i n c r e a s e i n time r e q u i r e dt o perform t h e t u r n . The formula p r e s e n t e d f o r t i s used t o c a l c u l a t e cort h e time f o r a complete c o r n e r i n g maneuver, i . e . , a 360-degree t u r n .Usually, t h e a i r c r a f t performs t u r n s o f 180, 90 o r fewer d e g r e e s . The time r e q u i r e d f o r a 180-degree t u r n ( f i r s t and second t u r n s performedtogether) is f=0;64. -.3 1 0.5=161.5 sec=2 min 41.5 sec. 0.265 The t i m e f o r t h e t h i r d t u r n i s /180 97.2 t-0.64. -- .0.25=58 S ~ G . 0-268 The time f o r t h e f o u r t h t u r n i s t=0.64.L-OO25=53 89 0 S ~ C . 0.265 The a n g u l a r v e l o c i t y o f r o t a t i o n d u r i n g t h e performance of t h e f o u r t hturn i s w- V --=0.03rad/sec=1.7 89 deg/sec; r 3000176
  • 187. CHAPTER X I STABILITY AND C O N T R O L A B I L I T Y OF A I R C R A F T §1. General Concepts on A i r c r a f t Equilibrium I n studying t h e s t a b i l i t y and c o n t r o l l a b i l i t y o f an a i r c r a f t , it i s r e p r e s e n t e d as a body moving under t h e i n f l u e n c e o f e x t e r n a l f o r c e s and r o t a t i n g under t h e i n f l u e n c e of t h e moments o f t h e s e f o r c e s . I n any f l i g h t , e q u i l i b r i u m o f f o r c e s and moments a c t i n g on t h e a i r c r a f t must be observed. Equilibrium of t h e a i r c r a f t i n f l i g h t i s what w e c a l l t h e s t a t e i n which t h e f o r c e s and moments a c t i n g on t h e a i r c r a f t cause no r o t a t i o n , i . e . , t h e given s t a t e i s n o t d i s r u p t e d . I n a l l f l i g h t modes, t h e a i r c r a f t should be balanced both i n t h e l o n g i t u d i n a l and l a t e r a l d i r e c t i o n s . Balancing means achievement o f equi­ l i b r i b r i u m of moments u s i n g t h e c o n t r o l s u r f a c e s i n any f l i g h t mode. Equilibrium of f o r c e s and moments a c t i n g on t h e a i r c r a f t i s analyzed r e l a t i v e t o t h e t h r e e c o o r d i n a t e axes passing through i t s c e n t e r of g r a v i t y . The coordinate axes used (Figure 115) are t h e l o n g i t u d i n a l a x i s of t h e a i r c r a f t ox, t h e t r a n s v e r s e axis oz and t h e v e r t i c a l a x i s oy. Figure 115 a l s o shows t h e following moments: M i s t h e yaw o r t r a c k angle, r o t a t i n g t h e a i r c r a f t about a x i s oy, and i s Tonsidered p o s i t i v e i f t h e a i r c r a f t r o t a t e s i t s bow t o t h e l e f t ; M i s t h e bank moment o r t h e t r a n s v e r s e X moment, r o t a t i n g a i r c r a f t around t h e ox a x i s , and i s considered p o s i t i v e i f t h e a i r c r a f t r o t a t e s toward t h e r i g h t wing; M i s t h e p i t c h moment o r t h e Z l o n g i t u d i n a l moment, r o t a t i n g t h e a i r c r a f t about t h e oz a x i s , and i s c a l l e d p o s i t i v e i f t h e a i r c r a f t tends t o l i f t i t s bow. Equilibrium o f t h e a i r c r a f t about t h e s e axes i s divided i n t o longitud­ i n a l e q u i l i b r i u m (about t h e a x i s oz) , t r a n s v e r s e e q u i l i b r i u m (about t h e a x i s ox) and t r a c k e q u i l i b r i u m (about t h e a x i s oy). Three c h a r a c t e r i s t i c forms o f body e q u i l i b r i u m are known: s t a b l e , u n s t a b l e and n e u t r a l e q u i l i b r i u m . A example i l l u s t r a t i n g t h e s e forms of n e q u i l i b r i u m might b e t h e behavior o f a b a l l on s u r f a c e s of v a r i o u s forms. The behavior of a b a l l on a concave curved s u r f a c e c h a r a c t e r i z e s s t a b l e equilibrium, on a convex s u r f a c e -- u n s t a b l e e q u i l i b r i u m and on a f l a t s u r f a c e -- n e u t r a l e q u i l i b r i u m . 177I
  • 188. -r - r rP > O i f r Figure 115. S y s t e m of A i r c r a f t Axes and Symbols Used f o r Moments of Angular V e l o c i t i e s , D e f l e c t i o n o f Control Surfaces and Forces on Command Levers Although a i r c r a f t e q u i l i b r i u m i s a more complex phenomenon t h a n t h ee q u i l i b r i u m of a b a l l , i n f l i g h t an a i r c r a f t may b e i n t h e s t a b l e , u n s t a b l eo r n e u t r a l s t a t e s . I n correspondence with t h e s e forms o f e q u i l i b r i u m , t h ea i r c r a f t i s c a l l e d s t a b l e , u n s t a b l e o r n e u t r a l . An u n s t a b l e o r n e u t r a la i r c r a f t cannot s a t i s f y t h e requirements o f normal c o n t r o l i n f l i g h t .52. S t a t i c and Dynamic S t a b i l i t y The s t a b i l i t y o f an a i r c r a f t i s i t s a b i l i t y t o r e t a i n i t s f l i g h t regimeo r r e t u r n t o i t s i n i t i a l balanced regime i n c a s e of an a r b i t r a r y d e v i a t i o nr e s u l t i n g from e x t e r n a l p e r t u r b a t i o n s , without t h e a i d of t h e p i l o t . A t t h e p r e s e n t t i m e , books on aerodynamics f r e q u e n t l y d i v i d e s t a b i l i t ya r b i t r a r i l y i n t o s t a t i c and dynamic s t a b i l i t y , although i n a c t u a l i t y an a i r ­c r a f t simply h a s s t a b i l i t y , meaning t h e a b i l i t y of t h e a i r c r a f t t o r e t u r n t omovement a t t h e i n i t i a l kinematic parameters ( v e l o c i t y , angle o f a t t a c k , e t c . )a f t e r a p e r t u r b a t i o n i s removed o r , as t h e y s a y , t h e a b i l i t y o f t h e a i r c r a f tt o r e t a i n t h e i n i t i a l f l i g h t regime. T h e r e f o r e , t h e s t a b i l i t y o f an a i r c r a f t c o n s i s t s o f s t a t i c s t a b i l i t y andgood damping p r o p e r t i e s , which determine and c h a r a c t e r i z e t h e q u a l i t y of t h et r a n s i e n t p r o c e s s when t h e e q u i l i b r i u m of t h e a i r c c r a f t i s d i s r u p t e d . This i sf r e q u e n t l y c a l l e d dynamic s t a b i l i t y .178
  • 189. .-. .. . . .. . . , ,, ..., Let us analyze t h e s e p r o p e r t i e s o f an a i r c r a f t i n d i v i d u a l l y i n somewhatmore d e t a i l . I n f l i g h t , an a i r c r a f t i s s u b j e c t t o t h e effects of t u r b u l e n c e of t h eatmosphere, a s w e l l as s h o r t d u r a t i o n p e r t u r b a t i o n s c r e a t e d by random devi­a t i o n s o f t h e c o n t r o l s u r f a c e s by t h e p i l o t , e t c . The p e r t u r b i n g momentsd i s r u p t t h e e q u i l i b r i u m of f o r c e s , causing t h e t r a j e c t o r y of t h e a i r c r a f t t ocurve and t h e v e l o c i t y of t h e a i r c r a f t t o change. The summary movement of t h ea i r c r a f t produced by adding t h e i n i t i a l unperturbed and supplementary motions,i s c a l l e d t h e p e r t u r b e d movement. S t a t i c s t a b i l i t y means t h e p r o p e r t y o f an a i r c r a f t causing it t o creates t a b i l i z i n g moments when e q u i l i b r i u m i s d i s r u p t e d . For example, i f a n e g a t i v ep i t c h i n g moment arises and acts on t h e a i r c r a f t when t h e angle of a t t a c k i si n c r e a s e d , t h i s w i l l b e a s t a b i l i z i n g moment. Also, on t h e r i g h t wingcauses a moment t o a r i s e t e n d i n g t o t u r n t h e a i r c r a f t t o t h e r i g h t , it w i l la l s o b e a s t a b i l i z i n g moment. Thus, i f when e q u i l i b r i u m i s d i s r u p t e d , moments a r i s e tending t o r e s t o r et h e i n i t i a l e q u i l i b r i u m p o s i t i o n of t h e a i r c r a f t , t h e a i r c r a f t i s c a l l e ds t a t i c a l l y s t a b l e . The presence of s t a t i c s t a b i l i t y makes it p o s s i b l e f o r t h ep i l o t t o c o n t r o l t h e a i r c r a f t normally, and t o t a k e proper c o n t r o l a c t i o n s i nemergency s i t u a t i o n s . Dynamic s t a b i l i t y means t h e tendency o f an a i r c r a f t , a f t e r a p e r t u r b i n gf o r c e i s removed, t o r e s t o r e t h e i n i t i a l f l i g h t regime ( v e l o c i t y , a l t i t u d e ,overloading, f l i g h t d i r e c t i o n ) without i n t e r f e r e n c e from t h e p i l o t . Dynamics t a b i l i t y of t h e a i r c r a f t i s c h a r a c t e r i z e d by: t h e period of damping o fo s c i l l a t i o n s T, t h e t i m e of damping of o s c i l l a t i o n s Td (during which time t h ei n i t i a l amplitude of o s c i l l a t i o n s i s decreased by a f a c t o r o f 2 0 ) , t h ed e c r e a s e i n o s c i l l a t i n g amplitude A i n one p e r i o d md = A1/A3 (Figure 116) andt h e r e l a t i v e o s c i l l a t i o n damping c o e f f i c i e n t 6. C o e f f i c i e n t 5 determines t h eq u a l i t y of t h e t r a n s i e n t process o r , i n o t h e r words, t h e i n t e n s i t y o f dampingo f o s c i l l a t i o n s from a p e r t u r b i n g movement. I n a dynamically s t a b l e a i r c r a f t , p e r t u r b e d movement must b e damped. Themovement may b e e i t h e r a p e r i o d i c ( n o n o s c i l l a t i n g ) , i n which a p e r t u r b e d - /183movement i s r a p i d l y damped, o r p e r i o d i c ( o s c i l l a t i n g ) , i n which damping occurswith a c e r t a i n amplitude and r e q u i r e s somewhat more time (Figure 117). A n e u t r a l a i r c r a f t shows no tendency toward damping o r i n c r e a s e i np e r t u r b a t i o n s (Figure 117 b ) , while a dynamically u n s t a b l e a i r c r a f t shows atendency toward i n c r e a s e d amplitude of p e r t u r b a t i o n s with t i m e (Figure 117 c ) . Weak damping and o s c i l l a t i n g p e r i o d s which are t o o long are c h a r a c t e r ­i s t i c s of poor a i r c r a f t s t a b i l i t y . A s t h e p e r i o d i s i n c r e a s e d , t h e perturbedmovement o f t h e a i r c r a f t i s " s t r e t c h e d out," i . e . , extends over a longerp e r i o d of t i m e . 179
  • 190. As w e can see from Figure 118, t h e behavior of a d namically u n s t a b l e a i r c r a f t d i s c h a r a c t e r i e by an a p e r i o d i c i n c r e a s e i n t h e p i t c h angle, t h a t of a dynamically s t a b l e a i r c r a f t by damping o s c i l l a t i o n s . If n e i t h e r s t a b i l i z i n g ilor d e s t a b i l ­ i z i n g moments a r i s e when t h e a i r c r a f t /184 - d e v i a t e s from t h e e q u i l i b r i u m s t a t e , t h e aircraft is called s t a t i c a l l y neutral Figure 116. Determin­ (Figure 118 c ) . stion of Characteristics o f Short Period Damping S t a t i c s t a b i l i t y alone i s i n s u f f i c i e n t Perturbed Movement t o i n s u r e t h a t t h e a i r c r a f t w i l l have ( A I , A 2 a r e amplitudes) dynamic s t a b i l i t y . This r e q u i r e s a d d i t i o n a l damping and i n e r t i a l p r o p e r t i e s , as w e l l asa p r o p e r r e l a t i o n s h i p of c h a r a c t e r i s t i c s of s t a t i c s t a b i l i t y r e l a t i v e t o t h evarious axes. a) b) The damping moments formed when the aircraft is r o t a t e d have a tremendous r o l e t o p l a y i n suppression of o s c i l l a t i o n s and p r o v i s i o n o f good c o n t r o 11a b i li t y f o r example, 1ong it ud i na1 damping ( p i t c h damping) i s c r e a t e d p r i m a r i l y by the horizontal t a i l s u r f aces, while yaw damping ( t r a c k Figure 117. C h a r a c t e r i s t i c s o f Perturbed Move­ damping) i s produced m e n t o f S t a b l e ( a ) , Neutral ( b ) and Unstable ( c ) by t h e v e r t i c a l t a i l A i r c r a f t (arrow shows i n i t i a l equilibrium surfaces of the pos i t ion) a i r c r a f t . When r o t a t i o n about t h e ox a x i s occurs, t h ewings c r e a t e a t r a n s v e r s e damping moment. With weak damping, a i r c r a f t o s c i l l a t i o n s w i l l b e a t t e n u a t e d slowly,p a r t i c u l a r l y a t a l t i t u d e s of 10,000-11,000 m , and a g r e a t d e a l o f t i m e w i l l b er e q u i r e d f o r r e s t o r a t i o n of e q u i l i b r i u m . With t o o s t r o n g damping, t h e r e t u r nt o t h e e q u i l i b r i u m s t a t e i s a l s o delayed. The i n e r t i a l p r o p e r t i e s of an a i r c r a f t a r e c h a r a c t e r i z e d by i t s a b i l i t yt o r e t a i n t h e s t a t e of e q u i l i b r i u m o r i t s previous angular r o t a t i o n a l180
  • 191. v e l o c i t y . The g r e a t e r t h e moment o f i n e r t i a , t h e more slowly t h e a i r c r a f tr e a c t s t o d e f l e c t i o n s o f t h e s t i c k and p e d a l s . J e t a i r c r a f t have high momentsof i n e r t i a r e l a t i v e t o t h e y and z axes, s i n c e t h e y have a r e l a t i v e l y longf u s e l a g e , i n which t h e main mass o f t h e load i s c o n c e n t r a t e d about t h e c e n t e ro f g r a v i t y . The moment of i n e r t i a r e l a t i v e t o t h e x a x i s i s less, s i n c e t h ewing span i s less t h a n t h e l e n g t h o f t h e f u s e l a g e . a) w i n i gust wind gust wind g u s t Figure I 18. Behavior of Dynamical l y Unstable ( a ) , S t a b l e ( b ) and Neutral ( c ) A i r c r a f t During Perturbed Mot ion §3. C o n t r o l l a b i l i t y of an A i r c r a f t The c o n t r o l l a b i l i t y o f an a i r c r a f t i s an important p i l o t i n g c h a r a c t e r ­i s t i c , and means i t s c a p a b i l i t y t o respond t o t h e p i l o t s movements o f t h erudder and a i l e r o n s with corresponding movements i n space o r , as t h e y s a y , t h e ­ / 185a b i l i t y o f t h e a i r c r a f t t o "follow t h e c o n t r o l s u r f a c e s . " I n c o n t r o l l i n g t h ea i r c r a f t , t h e p i l o t moves t h e s t i c k and p e d a l s and e v a l u a t e s t h e behavior oft h e a i r c r a f t by t h e f o r c e s on t h e c o n t r o l s u r f a c e s . By moving t h e v a r i o u ss u r f a c e s , t h e p i l o t overcomes t h e i n e r t i a l , damping and r e s t o r i n g momentsa c t i n g on t h e a i r c r a f t . I f t h e f o r c e s a r e extremely h i g h , t h e p i l o t w i l l become f a t i g u e d d u r i n gmaneuvering. Such a i r c r a f t a r e d e s c r i b e d as being heavy t o c o n t r o l .Unnecessarily l i g h t c o n t r o l should a l s o b e avoided, s i n c e it makes p r e c i s ec o n t r o l of movements o f c o n t r o l s u r f a c e s d i f f i c u l t and may cause t h e a i r c r a f tt o shake. The c o n t r o l s u r f a c e s should make it p o s s i b l e t o balance t h e a i r c r a f t i na l l f l i g h t regimes used. This i s e v a l u a t e d u s i n g b a l a n c i n g c u r v e s , whichc h a r a c t e r i z e t h e change i n b a l a n c e angles of c o n t r o l s u r f a c e d e f l e c t i o n (andcorrespondingly t h e p o s i t i o n o f t h e c o n t r o l l e v e r s , a s w e l l a s t h e f o r c e s onthem) a t v a r i o u s s t a b l e f l i g h t regimes as a f u n c t i o n of a change i n one of t h eparameters determining t h e regime ( f o r example, f l i g h t speed, M number, angleof a t t a c k o r s l i p a n g l e , e t c . ) . The p i l o t a l s o judges t h e c o n t r o l l a b i l i t y of an a i r c r a f t from t h e r e a c ­t i o n of t h e a i r c r a f t t o d e f l e c t i o n s of "the c o n t r o l l e v e r s during maneuvering. C o n t r o l l a b i l i t y i s d i v i d e d i n t o t h r e e forms: l o n g i t u d i n a l , directional andt r a n s v e r s e . The a b i l i t y of t h e a i r c r a f t t o r o t a t e about t h e ox a x i s under t h ei n f l u e n c e o f t h e a i l e r o n s i s c a l l e d t r a n s v e r s e c o n t r o l l a b i l i t y , about t h e oya x i s under t h e i n f l u e n c e of t h e r u d d e r i s c a l l e d d i r e c t i o n a l c o n t r o l l a b i l i t y 181
  • 192. and about t h e oz a x i s under t h e i n f l u e n c e o f t h e e l e v a t o r i s c a l l e d l o n g i t u d ­ .i n a l c o n t r o 1l a b i l i t y C h a r a c t e r i s t i c s of l o n g i t u d i n a l c o n t r o l l a b i l i t y i n c l u d e t h e amount o fe l e v a t o r and s t i c k t r a v e l r e q u i r e d t o change t h e a i r c r a f t v e l o c i t y by a f i x e damount, as well a s t h e f o r c e , a p p l i e d t o t h e s t i c k by t h e p i l o t . One of t h emost important c h a r a c t e r i s t i c s i s t h e f o r c e g r a d i e n t w i t h r e s p e c t t o over­l o a d i n g APel/An showing t h e f o r c e which must b e a p p l i e d t o t h e s t i c k t o Ychange overloading by one u n i t . The following parameters are used as c h a r a c t e r i s t i c s o f t r a n s v e r s e . c o n t r o 1l,abi 1i t y 1) The f o r c e which must b e a p p l i e d t o t h e s t i c k t o g i v e t h e a i r c r a f t ana n g u l a r r o t a t i o n v e l o c i t y about t h e ox a x i s of 1 r a d / s e c : AP Pa - - A , " boxwhere APa i s t h e f o r c e a p p l i e d t o t h e a i l e r o n c o n t r o l l e v e r ; Amx i s t h e change i n a n g u l a r v e l o c i t y o f 1 r a d / s e c ; 2 ) The f o r c e which must b e a p p l i e d t o t h e c o n t r o l l e v e r t o /186balance t h e a i r c r a f t i n s t r a i g h t l i n e f l i g h t w i t h a s l i p of one degree o r abank o f one degree:where A @ i s t h e change i n s l i p angle o f one degree; Ay i s t h e change i n bank angle of one degree; 3 ) The change i n a n g u l a r v e l o c i t y o f a bank when t h e d e f l e c t i o n of t h ea i l e r o n s i s changed by one degree:where Amx i s t h e ehange i n a n g u l a r v e l o c i t y o f t h e bank; A6 i s t h e change a i l e r o n a n g l e of one degree. a182
  • 193. The c h a r a c t e r i s t i c s o f d i r e c t i o n a l c o n t r o l l a b i l i t y are t h e following parameters : 1) The f o r c e which must b e a p p l i e d t ? t h e pedals t o impart an angular v e l o c i t y of 1 r a d / s e c t o t h e a i r c r a f t : where APn i s t h e f o r c e a p p l i e d t o t h e p e d a l s ; Au i s t h e change i n angular v e l o c i t y of 1 r a d / s e c ; Y 2) t h e f o r c e which must be a p p l i e d t o t h e pedals t o d e f l e c t t h e rudder when t h e a i r c r a f t i s balanced i n s t r a i g h t l i n e f l i g h t with a s l i p of one degree o r a bank of one degree; 3 ) t h e change i n angular v e l o c i t y when t h e rudder i s d e f l e c t e d by one degree, i . e . , t h e bank r e a c t i o n of t h e a i r c r a f t t o d e f l e c t i o n of t h e rudder: where A6n i s t h e change i n t h e rudder angle of one degree. We can s e e from t h e d e f i n i t i o n s of a i r c r a f t s t a b i l i t y and c o n t r o l l a b i l i , t y t h a t t h e y c h a r a c t e r i z e opposite p r o p e r t i e s o f t h e a i r c r a f t : s t a b i l i t y must b e p r e s e n t t o maintain t h e f l i g h t regime unchanged, while c o n t r o l l a b i l i t y must be p r e s e n t t o allow it t o b e changed. However, t h e r e i s a c e r t a i n i n t e r r e l a t i o n ­ s h i p between s t a b i l i t y and c o n t r o l l a b i l i t y . O a s t a b l e a i r c r a f t , t h e n a t u r e of t h e movements of t h e c o n t r o l l e v e r s n and r e q u i r e d d e f l e c t i o n s during p i l o t i n g are s i m p l i f i e d , and i t i s e a s i e r t o determine t h e f l i g h t regime. I t h a s been t h e o r e t i c a l l y proven and confirmed by p r a c t i c e t h a t t h e h i g h e r t h e s t a b i l i t y of t h e a i r c r a f t , t h e less t h e delay and g r e a t e r t h e accuracy with which i t follows a d e f l e c t i o n o f t h e c o n t r o l s u r f a c e s . Therefore, s t a b i l i t y and c o n t r o l l a b i l i t y provide f o r complete /187 u t i l i z a t i o n o f t h e maneuvering c a p a c i t y o f t h e a i r c r a f t , a s s u r i n g t h e r e q u i r e d accuracy and s i m p l i c i t y o f p i l o t i n g and are an important c o n d i t i o n f o r f l i g h t safety, 183 I . . . ..- . _ .. . __ .. __ .._. __ . .
  • 194. S4. Centering of t h e A i r c r a f t and Mean Aerodynamic Chord The p o s i t i o n of t h e c e n t e r o f g r a v i t y of an a i r c r a f t r e l a t i v e t o t h ewings i s c a l l e d t h e c e n t e r i n g o f t h e a i r c T a f t and i s determined by t h ed i s t a n c e ( i n p e r c e n t ) from t h e o r i g i n of t h e mean aerodynamic cord(Figure 119) : - x -5.100%; -T=: g +.loo %, - MAC MACwhere b i s t h e mean aerodynamic cord o f t h e wing; mac x i s t h e h o r i z o n t a l d i s t a n c e from t h e l e a d p o i n t of t h e mac t o t h e tc e n t e r of g r a v i t y ; y t i s t h e v e r t i c a l d i s t a n c e from t h e mac t o t h e c . g . Figure 119. Diagram f o r Determining MAC of Trapezoidal S w e p t Wing ( r . 1 . f . = r e f e r e n c e 1 i n e of a i r c r a f t ; A , p o s i t i o n of c e n t e r of g r a v i t y corresponding t o t i p p i n g of a i r c r a f t o n t o t a i l ) Since y i s small i n magnitude, xt i s of primary s i g n i f i c a n c e i n an ta n a l y s i s o f s t a b i l i t y and c o n t r o l l a b i l i t y . The c e n t e r of g r a v i t y may b e e i t h e r above o r below t h e r e f e r e n c e l i n e oft h e a i r c r a f t , depending on t h e a c t u a l weight of t h e a i r c r a f t ( f u e l load) andplacement of motors. I n f l i g h t , t h e c . g . of t h e a i r c r a f t should b e i n s t r i c t l y definedp o s i t i o n s i n r e f e r e n c e t o t h e mac, guaranteeing continued s t a b i l i t y andc o n t r o l l a b i l i t y as t h e f u e l i s consumed. The f u e l r e p r e s e n t s 25-45% o f t h e184
  • 195. weight o f t h e a i r c r a f t . I n o r d e r t o achieve t h e l e a s t displacement o f t h e c . g . i n f l i g h t , t h e f u e l i s consumed i n a predetermined o r d e r , c o n t r o l l e d by an automatic d e v i c e (Figure 120). As w e can s e e from t h e graph, i n o r d e r t o remain w i t h i n t h e r e q u i r e d range of c e n t e r i n g s t (x= 21-30% MAC), t h e loaded a i r c r a f t without f u e l must have x t = 23.3-28.5% MAC (corresponding t o s e c t o r AB on t h e f i g u r e ) . Then, with any f u e l load c e n t e r i n g , o f t h e a i r c r a f t w i l l n o t go beyond t h e s e l i m i t s . For example, i f a c e n t e r i n g of 26% mac was produced f o r t h e loaded a i r c r a f t without f u e l ( l a n d i n g g e a r down) , when 8.5 t of f u e l is taken on t x = 26.7%, o r with 10.5 t -- 24.3% MAC. A f t e r t h e l a n d i n g g e a r a r e r e t r a c t e d , t h e c e n t e r i n g moves a f t one p e r c e n t and w i l l amount t o 26.7 and 25.2% r e s p e c t i v e l y . With a f u e l remainder of 6.65 t , t h e c e n t e r i n g w i l l b e f u r t h e s t t o t h e r e a r , and with a remainder o f 3.15 t -- f u r t h e s t t o t h e f r o n t . With c e n t e r i n g Yt = 42-50% MAC, f o r a i r c r a f t with motors on t h e wings and 48-53% i f t h e motor i s l o c a t e d i n t h e r e a r p o r t i o n o f t h e fuselage, the c e n t e r o f g r a v i t y i s l o c a t e d i n t h e p l a n e of t h e main landing gear s t r u t s ; with c e n t e r i n g f u r t h e r t o t h e r e a r , t h e a i r c r a f t may t i p onto its t a i l (Figure 119). Figure 120. Change i n Centering of A i r c r a f t i n F l i g h t As a Function o f Quantity of F u e l i n Tanks ( y t = 0.8 g/cm3) S5. Aerodynamic Center o f Wing and A i r c r a f t . Neutral Centering W know t h a t t h e r e i s a p o i n t on t h e cord of t h e wing about which t h e e moment o f aerodynamic f o r c e s does n o t change when t h e angle o f a t t a c k i s changed. For example (Figure 121) with an angle of a t t a c k a l , l i f t i n g f o r c e Y c r e a t e s a l o n g i t u d i n a l moment M Z r e l a t i v e t o a c e r t a i n p o i n t F 1 (Figure 1 2 1 a ) . A s t h e a n g l e of a t t a c k i s changed t o a 2 , t h e l i f t i n g f o r c e /189 -- i n c r e a s e s , b u t i t s arm l e n g t h r e l a t i v e t o p o i n t F i s decreased a s a r e s u l t of displacement of t h e c e n t e r o f p r e s s u r e ( F i g u r e 1 2 1 b ) . The new moment may b e 185I
  • 196. H I I Ig r e a t e r t h a n o r less t h a n t h e preceding moment. This depends on t h e way i nwhich t h e r e l a t i o n s h i p between t h e v a l u e s o f f o r c e and a r m l e n g t h change. I ti s p o s s i b l e t o s e l e c t a p o i n t F such t h a t t h e v a l u e o f t h e arm l e n g t h changesi n i n v e r s e p r o p o r t i o n t o t h e aerodynamic f o r c e . Then, t h e moment r e l a t i v e t ot h i s p o i n t w i l l n o t change as t h e a n g l e o f a t t a c k i s changed. This p o i n t i sc a l l e d t h e aerodynamic c e n t e r o f t h e wing. Thus, i f a3 > c1 > c1 and 2 1L1 > Z 2 > Z , t h e n YIZl = Y2Z2 = Y Z i s t h e c o n s t a n t moment of aerodynamic ~ 3 3f o r c e r e l a t i v e t o t h e aerodynamic c e n t e r o f t h e wing with v a r i o u s a n g l e s ofa t t a c k . With wing shapes used, t h e aerodynamic c e n t e r i s l o c a t e d 23 t o 25% o ft h e d i s t a n c e along i t s cord. Figure 121. Explanation of Aerodynamic Center o f Wing ( a , b, c) and of A i r c r a f t ( d ) W can draw an important conclusion from t h e d e f i n i t i o n of t h e aero­ edynamic c e n t e r : t h e increments o f aerodynamic f o r c e s a r i s i n g when t h e angleo f a t t a c k i s changed a r e a p p l i e d t o t h e aerodynamic c e n t e r . A c t u a l l y , f o r c eY = Y + AY, a p p l i e d a t cp2, can b e d i v i d e d i n t o f o r c e Y1 a p p l i e d t o cpl and 2 1f o r c e Y, a p p l i e d a t t h e aerodynamic c e n t e r (Figure 1 2 1 b ) . Since t h e moment o f f o r c e AY r e l a t i v e t o p o i n t F i s equal t o z e r o , t h el o n g i t u d i n a l moment of t h e wing a t angle o f a t t a c k c1 w i l l be t h e same as a t 2angle o f a t t a c k a 1 The h o r i z o n t a l t a i l s u r f a c e s , l i k e t h e wing, have t h e i r own aerodynamic /=center.186 .~ . . .... . . .
  • 197. When t h e angle o f a t t a c k i s changed, a d d i t i o n a l l i f t i n g f o r c e a r i s e s on t h e wing, and ends on t h e h o r i z o n t a l t a i l s u r f a c e s , a p p l i e d t o t h e aero­ dynamic c e n t e r s of t h e wing and h o r i z o n t a l t a i l s u r f a c e s (Figure 1 2 1 d ) . The r e s u l t a n t of p a r a l l e l f o r c e s AYw and AYht i s a p p l i e d a t d i s t a n c e s i n v e r s e l y p r o p o r t i o n a l t o t h e v a l u e s o f t h e s e f o r c e s . The p o i n t o f a p p l i c a t i o n o f t h i s r e s u l t a n t i s c a l l e d t h e aerodynamic c e n t e r of t h e a i r c r a f t . W must n o t e h e r e e t h a t f o r a i r c r a f t o f known t y p e s , b o t h t h e h o r i z o n t a l t a i l s u r f a c e l i f t i n g f o r c e and i t s increment AYht are d i r e c t e d downward, no matter what t h e angle o f a t t a c k of t h e wing. As w e can s e e from t h e f i g u r e , t h e moment of supplementary f o r c e s r e l a t i v e t o t h e a i r c r a f t aerodynamic c e n t e r i s zero; consequently, t h e l o n g i t u d i n a l moment o f t h e aircraft relative t o this 40 c e n t e r does n o t change when t h e angle o f a t t a c k i s changed. 1 F.t max r e a r 1 IStabi 1 i t y Reserve T h e r e f o r e , t h e p o s i t i o n of t h e a i r c r a f t aerodynamic c e n t e r does n o t change when t h e angle 30 42 43 44 I , ,4 8 M 95 I ,7 4 46 of a t t a c k i s changed. The aerodynamic c e n t e r of Figure 122. Neutral Centering o f Air­ the a i r c r a f t is shifted t o the c r a f t w i t h Respect t o Overloads As a r e a r under t h e i n f l u e n c e o f Function of M Number (example): aerodynamic f o r c e increments a , Maximal indicated speed 1 imita­ arising i n the stabilizer, t i o n ; b , Minimum permissible f u s e l a g e and engine c e l l s . For indicated s p e e d l i m i t a t i o n example, i f f o r t h e wing without t h e h o r i z o n t a l t a i l s u r f a c e ) X = 2 0 - 2 2 % mac, f o r F the aircraft xF = 46-50% mac. If t h e loads on t h e a i r c r a f t a r e so d i s t r i b u t e d t h a t t h e c e n t e r of g r a v i t y o f t h e a i r c r a f t corresponds with i t s aerodynamic c e n t e r , t h e a i r c r a f t becomes n e u t r a l i n t h e l o n g i t u d i n a l r e s p e c t . I n t h i s c a s e , t h e c e n t e r i n g i s c a l l e d n e u t r a l . Since i n t h i s c a s e t h e l o n g i t u d i n a l moment of t h e a i r c r a f t w i l l n o t change as a f u n c t i o n of angle of a t t a c k , we must conclude t h a t n e u t r a l c e n t e r i n g i s t h e aerodynamic c e n t e r of t h e e n t i r e a i r c r a f t 1 . N e u t r a l a i r c r a f t c e n t e r i n g s are c a l c u l a t e d f o r v a r i o u s a l t i t u d e s and f l i g h t speeds (Figure 122). r-l-.V. Ostoslavskry, Aerodinamika SamoZeta [Aerodynamics o f t h e A i r c r a f t ] , Oborongiz. P r e s s , 1957. 187 I
  • 198. As w e can s e e from t h e f i g u r e , a t Mach numbers M 0.6, n e u t r a l c e n t e r i n g moves somewhat (by 1.1-1.7% mac) forward ( r e l a t i v e t o i t s i n i t i a l v a l u e s o f 45-43% mac), w h i l e a t a l t i t u d e s over 6,000 m i t s h i f t s n o t i c e a b l y t o t h e r e a r as a r e s u l t of t h e effect of t h e compressibility o f t h e a i r . For H = 11,000 m, t h e change i n n e u t r a l c e n t e r i n g from 42 t o 49% macn o t e d i s explained by a displacement o f t h e c e n t e r o f p r e s s u r e o f t h e wing t ot h e rear a t M numbers g r e a t e r t h a n t h e c r i t i c a l M number of t h e wing p r o f i l e(approximately M > 0.7-0.72). A f t e r determining t h e f a r t h e s t forward p o s i t i o n o f t h e n e u t r a l c e n t e r i n g ,t h e l i m i t i n g rearward c e n t e r i n g f o r o p e r a t i o n i s defined 10-12% less t h a nn e u t r a l c e n t e r i n g . The d i s t a n c e between t h e n e u t r a l and l i m i t i n g r e a rc e n t e r i n g i s c a l l e d t h e r e s e r v e of s t a b i l i t y f o r c e n t e r i n g . 96. Longitudinal Equilibrium Figure 123. Diagram o f Forces and Moments Act i n g on A i r c r a f t About Transverse Axis The p i l o t m a i n t a i n s l o n g i t u d i n a l e q u i l i b r i u m o r b a l a n c i n g by u s i n g t h ee l e v a t o r and s e l e c t i n g t h e n e c e s s a r y motor t h r u s t . Any s t a b l e f l i g h t regimei s c h a r a c t e r i z e d by angle of a t t a c k a , f l i g h t speed V , a l t i t u d e H and t h ea n g l e of t r a j e c t o r y i n c l i n a t i o n 0. I n o r d e r t o achieve l o n g i t u d i n a l e q u i ­l i b r i u m o f t h e a i r c r a f t , t h e f o r c e s a c t i n g i n t h e d i r e c t i o n s o f t h e ox andoy axes and t h e moments o f t h e s e f o r c e s a c t i n g r e l a t i v e t o t h e oz a x i s must bei n e q u i l i b r i u m (Figure 123). I n h o r i z o n t a l f l i g h t , t h r e e c o n d i t i o n s o f e q u i l i b r i u m must b e observed. /192 The f i r s t c o n d i t i o n i s : t h e l i f t i n g f o r c e of t h e a i r c r a f t Y must b e equalt o i t s weight. W know t h a t t h e l i f t i n g f o r c e of an a i r c r a f t i s c r e a t e d by t h e wing, eh o r i z o n t a l t a i l s u r f a c e and p a r t i a l l y by t h e engine n a c e l l e s . The l i f t i n g188
  • 199. f o r c e c r e a t e d by t h i s f u s e l a g e i s r e l a t i v e l y s l i g h t , and i s considered t o b ep a r t o f t h e l i f t i n g f o r c e of t h e wing. As w e can see from t h e f i g u r e , t h e s ef o r c e s create moments about t h e t r a n s v e r s e a x i s which d e c r e a s e o r i n c r e a s e t h eangle o f a t t a c k . The l i f t i n g f o r c e of t h e wing i n c r u i s i n g f l i g h t c r e a t e sn e g a t i v e p i t c h moment MZw = YwZ. The l i f t i n g f o r c e o f t h e h o r i z o n t a l t a i l s u r f a c e i s d i r e c t e d downward,and i n a l l f l i g h t regimes used i n p r a c t i c e c r e a t e s t h e p i t c h moment In o r d e r f o r f o r c e Yht t o b e n e g a t i v e , t h e angle of a t t a c k of t h eh o r i z o n t a l t a i l s u r f a c e aht must a l s o be n e g a t i v e . A s we can see from F i g u r e 124, a < a by t h e angle o f downwash of t h e ht wstream E ( t h e downwash o f t h e s t r e a m r e s u l t s from t h e a c t i o n o f t h e a i r c r a f t htwing on t h e a i r stream). Also, a i s i n f l u e n c e d by t h e angle of t h e hts t a b i l i z e r C$ ( g e n e r a l l y zero t o - 4 ) . Thus, a = a + C$ - ht w chord stabi 1 izer -4 / wing I direction o f chord w i n g chord , / s t a b i 1 i zed chord Figure 124. Determination of A n g l e of Attack of Horizontal Tai 1 S u r f a c e ( r 2 e q u a l s r e f e r e n c e l i n e of a i r c r a f t ; V equals f l i g h t speed; VI equals v e l o c i t y of d i v e r t e d stream) For o r d i n a r y a i r c r a f t with t h e s t a b i l i z e r on t h e f u s e l a g e a t a f l i g h tspeed o f M = 0.75-0.85 and c = 0.3-0.4, E = 2-3. For example, w i t h aw = 3 " , YE = 2.68 and C$ = -2, a n g l e a = 3 - 2 - 2.68 = - 1.68. The g r e a t e r t h eangle of a t t a c k ( g r e a t e r t h e l k h i n g c a p a c i t y o f t h e wing), t h e g r e a t e r t h edownwash angle of t h e a i r stream. I n o r d e r t o determine t h e summary l o n g i t u d i n a l moment a c t i n g on t h e - /193a i r c r a f t , w must add t h e l o n g i t u d i n a l moment r e s u l t i n g from engine t h r u s t e 189
  • 200. (M ) t o t h e moments of t h e wings and h o r i z o n t a l t a i l s u r f a c e . z en The axis of an engine l o c a t e d i n t h e r e a r p o r t i o n o f t h e f u s e l a g e is placed above t h e c e n t e r of g r a v i t y of t h e a i r c r a f t ; t h e r e f o r e , t h e t h r u s t o f t h e motors creates a d i v i n g moment M = P 2 Zen en en Thus, t h e summary l o n g i t u d i n a l moment a c t i n g on t h e a i r c r a f t i s d e t e r ­ mined by t h e sum of t h e l o n g i t u d i n a l moments o f t h e wing, h o r i z o n t a l t a i l s u r f a c e and motor t h r u s t . E q u a l i t y of t h e l o n g i t u d i n a l moment t o zero i s t h e second c o n d i t i o n of e q u i 1ibrium. The t h i r d c o n d i t i o n f o r l o n g i t u d i n a l e q u i l i b r i u m of an a i r c r a f t i s e q u i l i b r i u m o f t h e f o r c e s a c t i n g i n t h e d i r e c t i o n of t h e ox a x i s . I n o r d e r f o r t h i s c o n d i t i o n t o be f u l f i l l e d , t h e t h r u s t o f t h e engines must b e equal t o t h e drag of t h e a i r c r a f t : Pen = Q. I f t h i s c o n d i t i o n i s n o t f u l f i l l e d , t h e movement of t h e a i r c r a f t w i l l be a c c e l e r a t e d o r d e c e l e r a t e d and, consequently, t h e l i f t i n g f o r c e w i l l b e changed and t h e f l i g h t t r a j e c t o r y w i l l curve. These t h r e e c o n d i t i o n s f o r l o n g i t u d i n a l b a l a n c i n g o f t h e a i r c r a f t aref u l f i l l e d by varying t h e p o s i t i o n of t h e e l e v a t o r by t h e r e q u i r e d angle and bya d j u s t i n g engine t h r u s t , depending on v e l o c i t y , a l t i t u d e , f l y i n g weight,c e n t e r i n g , e t c . W n o t e t h a t when e q u i l i b r i u m c o n d i t i o n s a r e f u l f i l l e d , t h e er e s u l t a n t of t h e aerodynamic f o r c e s and t h e t h r u s t of t h e engines can beconsidered t o be a p p l i e d t o t h e c e n t e r o f g r a v i t y of t h e a i r c r a f t , and a l lf o r c e s a r e balanced, i . e . , Pen = Q and Y = G . Therefore, t h e s e f o r c e s w i l ln o t be shown on f i g u r e s i n t h e following, o n l y t h e a d d i t i o n a l f o r c e s andmoments and t h e i r increments a r i s i n g under t h e i n f l u e n c e o f p e r t u r b a t i o n sbeing shown.57. S t a t i c Longitudinal Overload S t a b i l i t y A d i s r u p t i o n i n l o n g i t u d i n a l s t a b i l i t y o f an a i r c r a f t i s accompanied by achange i n t h e angle o f a t t a c k a t f l i g h t speed, t h e angle of a t t a c k changing a tf i r s t more r a p i d l y t h a n v e l o c i t y . Subsequently, on t h e o t h e r hand, t h e speedchanges more r a p i d l y . For example, by p u l l i n g t h e s t i c k toward himselfq u i c k l y , t h e p i l o t can i n c r e a s e t h e angle o f a t t a c k by a f a c t o r of two o rt h r e e times o r more. However, i n o r d e r f o r t h e a i r c r a f t t o change i t s f l i g h tspeed by 1 . 5 times, he must use n o t a f r a c t i o n o f a second, b u t dozens ofseconds o r even s e v e r a l minutes. This s h a r p d i f f e r e n c e i n t h e n a t u r e of t h echange i n angle of a t t a c k and v e l o c i t y when l o n g i t u d i n a l e q u i l i b r i u m i sd i s r u p t e d has made it necessary t o d i s t i n g u i s h between l o n g i t u d i n a l angle ofa t t a c k s t a b i l i t y (overload s t a b i l i t y ) and v e l o c i t y s t a b i l i t y . The s t a b i l i t y of t h e a i r c r a f t i n t h e f i r s t moment a f t e r e q u i l i b r i u m i sd i s r u p t e d i s c h a r a c t e r i z e d by i t s angle of a t t a c k s t a b i l i t y o r overload190
  • 201. s t a b i l i t y . This name i s given t o t h i s form of s t a b i l i t y s i n c e when t h e angleo f a t t a c k i s i n c r e a s e d o r decreased ( a t c o n s t a n t v e l o c i t y ) t h e l i f t i n g f o r c ei s changed, s o t h a t t h e overload i s a l s o changed. The v a l u e of t h e overload shows t h e e x t e n t t o which t h e e x t e r n a l load i sg r e a t e r t h a n t h e weight of t h e a i r c r a f t . The overload i s always r e l a t e d t ot h e d i r e c t i o n i n which i t i s b e i n g analyzed. I n f l i g h t , t h e e x t e r n a l loadsa c t i n g on t h e ox and oz axes a r e s l i g h t . Thus, t h e d r a g o f t h e a i r c r a f t ,which i s 10-12 times less t h a n t h e weight o f t h e a i r c r a f t , acts along t h e oxa x i s ; t h e loads a r i s i n g only d u r i n g s l i p p i n g o r as a r e s u l t o f s i d e wind g u s t sact along t h e oz a x i s . - - V __c ---f &kcen te r wing chord ­ f i g u r e 125. Forces Acting on A i r c r a f t Entering a V e r t i c a l Wind Gust Therefore, t h e main overload i s t h a t a c t i n g i n t h e d i r e c t i o n o f t h e oyaxis. I n t h i s c a s e , t h e e x t e r n a l load i s t h e l i f t of t h e a i r c r a f t Y andI f c o n s t a n t c i s maintained a t t h e given a i r c r a f t speed, t h e l i f t i n g f o r c e Yw i l l a l s o b e c o n s t a n t . The overload w i l l a l s o be unchanged, equal t o z e r o . A a i r c r a f t i s c a l l e d overload s t a b l e i f it tends t o r e t a i n t h e overload nof t h e i n i t i a l f l i g h t regime independently, without i n t e r f e r e n c e by t h e p i l o t . I f an a i r c r a f t i s overload s t a b l e , when t h e angle of a t t a c k i s changedt h e moments change so t h a t t h e r o t a t i o n of t h e a i r c r a f t which t h e y causer e s u l t s i n disappearance of t h e a d d i t i o n a l overload. Let us assume t h a t ana i r c r a f t i n s t r a i g h t and l e v e l f l i g h t with an overload n = 1 and v e l o c i t y V Ye n t e r s an ascending c u r r e n t with v e l o c i t y W (Figure 125). This causes t h ed i r e c t i o n of t h e r e s u l t i n g v e l o c i t y t o b e changed, causing an i n c r e a s e i n t h eangle of a t t a c k and an i n c r e a s e i n l i f t i n g f o r c e AY (always a t t h e aerodynamic 191
  • 202. c e n t e r ) o r an i n c r e a s e i n overload An = AY/G. I f f o r c e AY causes a d i v i n g Yr o t a t i o n o f t h e a i r c r a f t , t h e a i r c r a f t i s s t a b l e . A s w e can s e e from t h e - /195f i g u r e , t h i s w i l l r e s u l t i f t h e c e n t e r of g r a v i t y o f t h e a i r c r a f t i s l o c a t e di n f r o n t of t h e aerodynamic c e n t e r . Consequently, t h e appearance of a d i v i n gmoment when t h e a n g l e of a t t a c k i s i n c r e a s e d i s a c h a r a c t e r i s t i c o f overloads t a b i l i t y of t h e a i r c r a f t . If t h e e x t e r n a l a c t i o n l e d t o a d e c r e a s e i n t h e a n g l e of a t t a c k , ap i t c h i n g moment would a r i s e which would t e n d t o i n c r e a s e t h e a n g l e o f a t t a c k ,i . e . , r e s t o r e t h e i n i t i a l overload regime. With a c e r t a i n p o s i t i o n of t h e c e n t e r of g r a v i t y ( a t t h e aerodynamicc e n t e r ) , t h e a i r c r a f t w i l l n o t r e a c t t o d i s r u p t i o n of e q u i l i b r i u m and w i l lshow no tendency e i t h e r t o r e t u r n t o i n i t i a l o v e r l o a d o r t o f u r t h e r movementaway from t h e i n i t i a l v a l u e . This p o s i t i o n o f t h e c e n t e r o f g r a v i t y , as wasd i s c u s s e d above, i s c a l l e d n e u t r a l c e n t e r i n g . Movement of t h e c e n t e r ofg r a v i t y t o t h e r e a r , behind n e u t r a l c e n t e r i n g , r e s u l t s i n t h e appearance ofoverload i n s t a b i l i t y of t h e a i r c r a f t , s i n c e f o r c e AY w i l l cause an i n c r e a s e i nt h e p i t c h moment a r i s i n g when e q u i l i b r i u m i s d i s r u p t e d . Thus, overload s t a b i l i t y of t h e a i r c r a f t w i l l b e c h a r a c t e r i z e d by t h ep o s i t i o n of t h e c e n t e r o f g r a v i t y of t h e a i r c r a f t r e l a t i v e t o t h e n e u t r a lc e n t e r i n g o r t h e aerodynamic c e n t e r . T h e r e f o r e , i n a d d i t i o n t o l e a d i n gc e n t e r i n g , which d e f i n e s t h e c a p a b i l i t y of b a l a n c i n g o f t h e a i r c r a f t i nf l i g h t and during landing w i t h maximum displacement of t h e e l e v a t o r , we a i s 0determine p e r m i s s i b l e rear c e n t e r i n g from t h e c o n d i t i o n of p r o v i s i o n of normaloverload s t a b i l i t y f o r t h e a i r c r a f t . W can see from our a n a l y s i s t h a t a change i n overload s t a b i l i t y i n ef l i g h t may r e s u l t from a change i n t h e p o s i t i o n of t h e c e n t e r of g r a v i t y , aswell as a change i n n e u t r a l c e n t e r i n g - - t h e aerodynamic c e n t e r of t h ea i r c r a f t . The n e u t r a l c e n t e r i n g o f t h e a i r c r a f t may change i n f l i g h t as t h ev e l o c i t y o r engine o p e r a t i n g mode i s changed, a s w e l l as when c o n t r o l i sr e l e a s e d . I f overload s t a b i l i t y i n c r e a s e s with unchanged c e n t e r of g r a v i t y ,t h i s i n d i c a t e s an i n c r e a s e i n t h e d i s t a n c e between t h e c e n t e r of g r a v i t y andn e u t r a l c e n t e r i n g . On t h e o t h e r hand, i f overload s t a b i l i t y d e c r e a s e s , t h ed i s t a n c e between t h e c e n t e r of g r a v i t y and n e u t r a l c e n t e r i n g must b edecreased. A s a r u l e , n e u t r a l c e n t e r i n g s a r e determined f o r a i r c r a f t with f i x e de l e v a t o r ; i f t h e c o n t r o l i s r e l e a s e d , c e n t e r i n g i s moved forward by approx­imately 1-2% mac. The o p e r a t i n g mode o f t h e engine i n f l u e n c e s t h e l o n g i t u d i n a l s t a b i l i t y oft h e a i r c r a f t t o o v e r l o a d s . I n j e t a i r c r a f t , t h e downwash of t h e a i r stream i nt h e a r e a of t h e s t a b i l i z e r changes n o t only under t h e i n f l u e n c e of t h e wing,b u t a l s o due t o t h e e f f e c t of t h e exhaust gases of t h e j e t engine on t h esurrounding medium. The stream l e a v i n g t h e engine a t high v e l o c i t y a t t r a c t s ac e r t a i n amount o f t h e surrounding a i r along with i t . This surrounding a i rchanges t h e d i r e c t i o n o f t h e s t r e a m a s it approaches i t . Usually, t h e192
  • 203. h o r i z o n t a l t a i l s u r f a c e i s l o c a t e d above t h e stream (Figure 126), and t h er e s u l t a n t of t h e a i r flow toward t h e stream d e c r e a s e s t h e a n g l e of a t t a c k oft h e h o r i z o n t a l t a i l s u r f a c e (makes t h e stream downwash more n e g a t i v e ) . /196 During a climb, t h e o p e r a t i n g regime of t h e engines i s nominal and t h estream l e a v i n g t h e motor i s a t i t s h i g h e s t power l e v e l . The downwash of t h i sstream i s t h e n maximal and d e c r e a s e s t h e angle o f a t t a c k o f t h e h o r i z o n t a lt a i l s u r f a c e s i g n i f i c a n t l y (makes t h e a n g l e of a t t a c k a considerably htnegative). When t h e angle o f a t t a c k o f t h e wing i s i n c r e a s e d ( a i r c r a f t e n t e r s av e r t i c a l wind g u s t ) t h e a n g l e of a t t a c k o f t h e h o r i z o n t a l t a i l s u r f a c e becomesmore n e g a t i v e due t o t h e i n c r e a s e d downwash o f t h e stream r e s u l t i n g from t h echange i n l i f t o f t h e wing and a l s o from t h e stream o f gases. The r e s u l t a n tof t h e i n c r e a s e i n l i f t i n g f o r c e of t h e h o r i z o n t a l t a i l s u r f a c e AYht, a p p l i e da t i t s aerodynamic c e n t e r and d i r e c t e d downward, w i l l d e c r e a s e t h e r e s t o r i n gmoment of t h e h o r i z o n t a l t a i l s u r f a c e and make t h e a i r c r a f t less e f f e c t i v e i nr e t u r n i n g t o i t s i n i t i a l f l i g h t regime. This i n d i c a t e s t h e d e c r e a s e i nl o n g i t u d i n a l s t a b i l i t y r e s e r v e , i . e . , t h e aerodynamic c e n t e r of t h e a i r c r a f ti s moved forward along t h e cord a s a r e s u l t o f t h e engines o p e r a t i n g a thigh t h r u s t . F i g u r e 126. P u m p i n g E f f e c t o f J e t Engine Exhaust Gas Stream on Surrounding Air Stream When g l i d i n g a t low engine s e t t i n g , t h e i n f l u e n c e of t h e stream from t h eengines can be ignored. I n t h i s c a s e , t h e downwash of t h e stream on t h es t a b i l i z e r w i l l b e determined by t h e i n f l u e n c e of t h e wing alone. The angleof a t t a c k of t h e h o r i z o n t a l t a i l s u r f a c e i n c r e a s e s (becomes l e s s n e g a t i v e ) andi t s e f f e c t i v e n e s s i s i n c r e a s e d . Longitudinal o v e r l o a d s t a b i l i t y of t h ea i r c r a f t is increased. This increase i n a i r c r a f t s t a b i l i t y i s equivalent t o adisplacement o f t h e n e u t r a l c e n t e r i n g of t h e a i r c r a f t (aerodynamic c e n t e r )backward along t h e mac. This i s why a i r c r a f t s t a b i l i t y i s s l i g h t l y lower i n aclimb t h a n i n a g l i d e . Overload s t a b i l i t y of t h e a i r c r a f t can b e e s t i m a t e d by t h e overload f o r c eg r a d i e n t APel/Any. 193
  • 204. 58. Diagrams of Moments /197 The degree of l o n g i t u d i n a l s t a b i l i t y o f an a i r c r a f t i s determined bywind t u n n e l t e s t i n g . Models are t e s t e d w i t h v a r i o u s d e f l e c t i o n s of t h ee l e v a t o r , and t h e l o n g i t u d i n a l moment M i s measured u s i n g s p e c i a l scales. By Zdetermining moment M a t s e v e r a l s e q u e n t i a l a n g l e s o f a t t a c k , w e can c o n s t r u c t Zgraphs c a l l e d moment diagrams mZ = f(a) f o r v a r i o u s M numbers (Figure 127). m*ipi 4’ tch M=qS Figure 127. C o e f f i c i e n t o f Longitudinal Moment mZ A s a Function of A n g l e o f Attack ( 6 e l = 0) The l o n g i t u d i n a l moment c o e f f i c i e n t ( a dimensionless q u a n t i t y such as cxand c ) can b e determined u s i n g t h e following formula: YThe p i t c h moments may b e e i t h e r p o s i t i v e o r n e g a t i v e . A c t u a l l y , i n f l i g h t t h e e l e v a t o r always h a s some b a l a n c i n g d e f l e c t i o n .The angle of a t t a c k a t which mZ = O ( M = 0 ) i s c a l l e d balanced, s i n c e a t t h i s Zangle a t h e a i r c r a f t i s i n t h e s t a t e of e q u i l i b r i u m . As we can s e e , as t h eangle of a t t a c k i s i n c r e a s e d t o c1 ) the a i r c r a f t acts stably, since sup(cy supt h e d i v i n g moment which a r i s e s causes it t o r e t u r n t o i t s i n i t i a l p o s i t i o n . A random d e c r e a s e i n t h e angle o f a t t a c k by -Aa causes a p o s i t i v e p i t c hmoment((+m ) which r e t u r n s t h e a i r c r a f t t o i t s i n i t i a l e q u i l i b r i u m p o s i t i o n ,c o r r e s p o n h g t o location of t h e center of gravity i n f r o n t o f t h e aero­dynamic c e n t e r . S e c t o r AB of curve mZ = f(a) corresponds t o i n s e n s i b l e e q u i l i b r i u m of t h ea i r c r a f t , s i n c e an i n c r e a s e i n t h e angle of a t t a c k causes no change i n t h el o n g i t u d i n a l moment. S e c t o r BC of t h e moment diagram corresponds t o (over- ­ /198load) u n s t a b l e behavior of t h e a i r c r a f t : when t h e angle o f a t t a c k changes, ana d d i t i o n a l p o s i t i v e p i t c h moment a r i s e s , t e n d i n g t o i n c r e a s e it s t i l l f u r t h e r .194
  • 205. 59. S t a t i c Longitudinal Velocity S t a b i l i t y A v e l o c i t y s t a b l e a i r c r a f t i s one which r e s t o r e s i t s assigned v e l o c i t ywithout i n t e r f e r e n c e of t h e p i l o t a f t e r p e r t u r b a t i o n . For s i m p l i c i t y o fd i s c u s s i o n , w e can c o n s i d e r t h a t t h e angle of a t t a c k does n o t change when t h ev e l o c i t y i s changed. L e t u s assume t h a t an a i r c r a f t f l y i n g h o r i z o n t a l l y a tc o n s t a n t v e l o c i t y V begins t o descend f o r some r e a s o n (Figure 128 a ) . Due t ot h e d e s c e n t , it i n c r e a s e s i t s v e l o c i t y by AV. Figure 128. Behavior of A i r c r a f t After Random Descent ( a ) and F1 i g h t T r a j e c t o r y o f Velocity Unstable A i r c r a f t ( b ) I f angle of a t t a c k cy. or c remains unchanged, due t o t h e i n c r e a s e i n Yv e l o c i t y , t h e l i f t i n g f o r c e a l s o i n c r e a s e s by AY. Due t o t h i s , t h e t o t a ll i f t i n g f o r c e becomes g r e a t e r t h a n t h e weight components and t h e a i r c r a f tt r a j e c t o r y begins t o curve upward, t h e v e l o c i t y begins t o d e c r e a s e , and AYa l s o begins t o d e c r e a s e . A f t e r a c h i e v i n g i t s i n i t i a l a l t i t u d e ( p o i n t c) t h ea i r c r a f t w i l l have i t s i n i t i a l v e l o c i t y V , b u t i t s t r a j e c t o r y w i l l be curveds l i g h t l y upward. T h e r e f o r e , t h e a i r c r a f t w i l l c o n t i n u e t o climb. Due t o t h ei n c r e a s e i n a l t i t u d e , t h e v e l o c i t y w i l l begin t o d e c r e a s e , i . e . , AV w i l lbecome n e g a t i v e . This makes AY n e g a t i v e , and t h e t r a j e c t o r y begins t o curvedownward, e t c . T h u s , t h e a i r c r a f t w i l l o s c i l l a t e . I f t h e a i r c r a f t i s v e l o c i t y s t a b l e , t h e s e o s c i l l a t i o n s w i l l be damped andt h e a i r c r a f t w i l l come out o f o s c i l l a t i o n s a t i t s i n i t i a l a l t i t u d e andv e l o c i t y . O s c i l l a t i o n damping occurs due t o t h e f a c t t h a t t h e f o r c e s involvedi n t h e o s c i l l a t i n g p r o c e s s a r e always d i r e c t e d s o a s t o even t h e t r a j e c t o r y .As w e can see from t h e figure, when t h e t r a j e c t o r y i s d e f l e c t e d downward andAV i s p o s i t i v e , p o s i t i v e increments AY a r e a l s o produced; when t h e t r a j e c t o r yd e f l e c t s upward and AV i s n e g a t i v e , n e g a t i v e AY r e s u l t s . N a t u r a l l y , i np r a c t i c e t h e p i l o t w i l l n o t w a i t u n t i l t h e o s c i l l a t i o n s damp o u t of t h e i r ownaccord. H e t a k e s c o n t r o l of t h e a i r c r a f t and immediately e l i m i n a t e s them. 195
  • 206. However, i t sometimes occurs t h a t , i n s p i t e o f an i n c r e a s e i n v e l o c i t y ,t h e l i f t i n g f o r c e i s not i n c r e a s e d , b u t r a t h e r decreased, s i n c e t h e l i f t i n gf o r c e depends n o t only on v e l o c i t y , but a l s o on c Y . Due t o t h e i n f l u e n c e ofc o m p r e s s i b i l i t y i n f l i g h t a t l a r g e M numbers o r due t o e l a s t i c deformations,c may i n c r e a s e s o s h a r p l y with i n c r e a s e d v e l o c i t y t h a t t h e l i f t i n g f o r c e Ydecreases r a t h e r than i n c r e a s e s . I n t h i s c a s e , t h e f l i g h t t r a j e c t o r y w i l lcurve e v e r more s h a r p l y downward ( i f t h e p i l o t does not t a k e c o n t r o l o f t h ea i r c r a f t q u i c k l y u s i n g t h e e l e v a t o r ) , t h e speed w i l l i n c r e a s e and t h e a i r c r a f tw i l l go i n t o a d i v e (Figure 128 b ) . No r e t u r n t o t h e i n i t i a l p o s i t i o n occurs. Figure 129. Dependence o f Force on Elevator Control on M Number (nominal mode, h o r i z o n t a l f l i g h t , H = 1 0 , 0 0 0 m y tremor d e f l e c t e d by T = 2 . 3 " ) I t i s e a s i e s t f o r t h e p i l o t t o judge v e l o c i t y s t a b i l i t y from t h e n a t u r eof t h e change i n f o r c e s on t h e c o n t r o l s t i c k when t h e a i r c r a f t v e l o c i t y o rM numher changes. A s we know, balancing o f an a i r c r a f t a t v a r i o u s speeds ofh o r i z o n t a l f l i g h t r e q u i r e s varying f o r c e on t h e s t i c k . Figure 129 shows t h e f o r c e s r e q u i r e d t o balance t h e a i r c r a f t a t variousM nbmbers (see 510 of t h i s c h a p t e r ) . Thus, where ?- = 28% mac and M = 0.62, tt h e f o r c e on t h e s t i c k i s equal t o zero, s i n c e t h e a i r c r a f t i s balanced by t h e trimmer and, consequently, t h e s t i c k can be r e l e a s e d i n t h i s p o s i t i o n . This i s t h e balanced regime. A s t h e a i r c r a f t a c c e l e r a t e s t o l a r g e M numbers, p r e s s u r e f o r c e s w i l l a r i s e on t h e s t i c k ( i f t h e trimmer i s l e f t i n i t s i n i t i a l p o s i t i o n ) , i n d i c a t i n g t h a t t h e a i r c r a f t i s v e l o c i t y s t a b l e . Actually, suppose t h e M number i n c r e a s e s t o 0 . 7 4 . W can s e e from t h e graph t h a t i n eo r d e r t o hold t h i s new speed (M = 0.74), t h e p i l o t must apply a p r e s s u r e o f - /200P = +10 kg t o t h e s t i c k , i . e . , c r e a t e a d i v i n g moment with t h e e l e v a t o r i n o r d e r t o balance t h e p o s i t i v e p i t c h which has a r i s e n . W can conclude from t h e above t h a t if a t M = 0.62 with t h e s t i c k er e l e a s e d , a random i n c r e a s e i n M number t o 0 . 7 4 o c c u r s , a p o s i t i v e p i t c hmoment should a c t on t h e a i r c r a f t , i n c r e a s i n g t h e angle of a t t a c k , and t h ea i r c r a f t w i l l r e t u r n without i n t e r f e r e n c e from t h e p i l o t t o i t s i n i t i a lv e l o c i t y (M = 0 . 6 2 ) . Consequently, t h i s a i r c r a f t i s v e l o c i t y s t a b l e . Asimilar p i c t u r e w i l l occur i f t h e v e l o c i t y i s decreased.196
  • 207. A t Mach numbers M > 0.8, t h e c o m p r e s s i b i l i t y o f a i r begins t o have as i g n i f i c a n t i n f l u e n c e , and t h e p r e s s u r e f o r c e r e s u l t a n t ( c e n t e r o f p r e s s u r e )i s d i s p l a c e d rearward; an a d d i t i o n a l n e g a t i v e p i t c h moment begins t o act ont h e a i r c r a f t . Therefore, whereas a t M = 0.74, a f o r c e o f 10 kg must b ea p p l i e d t o t h e s t i c k , a t M = 0.82 t h e f o r c e w i l l only b e 8 kg, i . e . , t h ep r e s s u r e f o r c e on t h e s t i c k i s decreased, and some v e l o c i t y i n s t a b i l i t yappears. However, s i n c e t h e a i r c r a f t wing i s swept, t h e phenomenon o f p u l l i n gi n t o a d i v e (during a c c e l e r a t i o n ) , a p r o p e r t y of v e l o c i t y i n s t a b i l i t y , is notobserved . A decrease i n pushing f o r c e i s observed i n a narrow range o f M numbers,then beginning a t M = 0.88-0.9, t h e f o r c e r e q u i r e d i n c r e a s e s once more,i n d i c a t i n g t h e appearance o f a c o n s i d e r a b l e p o s i t i v e p i t c h moment, i n c r e a s i n gwith i n c r e a s i n g M number.910. Longitudinal Controllability Longitudinal overload s t a b i l i t y determines t h e c h a r a c t e r i s t i c s ofl o n g i t u d i n a l c o n t r o l l a b i l i t y of an a i r c r a f t , r e l a t e d t o r o t a t i o n of t h e a i r ­c r a f t about t h e o z a x i s and c r e a t i o n of overloads. I f t h e performance of a maneuver r e q u i r e s t h a t t h e overload be changed,t h e p i l o t should do t h i s by d e f l e c t i n g t h e e l e v a t o r , d i s r u p t i n g t h e equi­librium and overcoming t h e moments attempting t o r e t u r n t h e a i r c r a f t t o i t si n i t i a l overload. The primary moments p r e v e n t i n g r o t a t i o n o f t h e a i r c r a f t about t h e o z a x i sa r e : t h e a i r c r a f t overload s t a b i l i t y moment, t h e damping moment and t h emoment of i n e r t i a . The g r e a t e r t h e s e moments p r e v e n t i n g r o t a t i o n of t h e a i r c r a f t , t h eg r e a t e r t h e angle t o which t h e e l e v a t o r must be d e f l e c t e d and t h e g r e a t e r t h ef o r c e r e q u i r e d a t t h e c o n t r o l s t i c k i n o r d e r t o change t h e overload. Sincet h e p i l o t f e e l s t h e value of f o r c e a p p l i e d t o t h e s t i c k and t h e overloadr e s u l t i n g from i t , l o n g i t u d i n a l c o n t r o l l a b i l i t y of t h e a i r c r a f t can b e s t bee v a l u a t e d by t h e g r a d i e n t of overload f o r c e APel/Any and t h z e l e v a t o r t r a v e lused A6el/An . Y The overload f o r c e g r a d i e n t i s numerically equal t o t h e r a t i o of /201a d d i t i o n a l f o r c e AP on t h e s t i c k t o t h e i n c r e a s e i n overload An produced as el Ya result of t h i s force. Let u s assume t h a t t h e a i r c r a f t i s performing h o r i z o n t a l f l i g h t andn = 1 (Figure 130). Then, i n o r d e r t o produce n = 2 , t h e p i l o t must p u l l Y Yt h e s t i c k toward himself with a f o r c e of 40-70 kg ( f o r small M numbers, 40 kgand f o r M = 0.7-0.8, 50-70 k g ) . Since overload s t a b i l i t y c h a r a c t e r i z e s t h ea b i l i t y of t h e a i r c r a f t t o r e t a i n t h e i n i t i a l overload regime, obviously t h ehigher t h e s t a b i l i t y t h e g r e a t e r t h e force required at t h e control s t i c k t o 197
  • 208. change t h e overload. W can a l s o see on e Figure 130 t h a t i f t h e c e n t e r i n g moves f u r t h e r forward, t h e f o r c e r e q u i r e d t o change n i n c r e a s e s . Y This i s explained by an i n c r e a s e i n t h e d i s t a n c e between t h e c e n t e r o f g r a v i t y of t h e a i r c r a f t and i t s aerodynamic c e n t e r . Thus, t h e f u r t h e r forward t h e centering of the a i r c r a f t , t h e h e a v i e r it i s t o c o n t r o l . The l i m i t i n forward c e n t e r i n g is s e l e c t e d from t h e c o n d i t i o n of a i r c r a f t b a l a n c i n g d u r i n g t a k e o f f and l a n d i n g . Figure 120. Overload Force Gradient AP /An and Elevator Travel I n o r d e r t o exclude (during el Y t a k e o f f ) s t r e a m s e p a r a t i o n from A6el/An As a Function of M Number the horizontal t a i l surface, the Y e l e v a t o r can be d e f l e c t e d 20-25" ( H = 10,000 m) upward. During landing, t h e p i l o t should i n c r e a s e c t o YC B p u l l i n g t h e s t i c k toward h i m s e l f , h e i n c r e a s e s t h e angle of a t t a c k , y Y 1dgc r e a t i n g p o s i t i v e p i t c h moments. When t h e angle o f a t t a c k i s i n c r e a s e d , ani n c r e a s e i n l i f t Ay o c c u r s , a p p l i e d t o t h e aerodynamic c e n t e r and c r e a t i n g an e g a t i v e p i t c h moment opposing t h e p i l o t . The g r e a t e r t h e d i s t a n c e betweent h e aerodynamic c e n t e r and t h e c e n t e r of g r a v i t y , t h e g r e a t e r t h i s h i n d e r i n gmoment w i l l be. Since t h e movement of t h e e l e v a t o r i s c o n s i d e r a b l e a t lowv e l o c i t i e s , i t may b e found t h a t t h e l i m i t n g d e f l e c t i o n of t h e e l e v a t o r i si n s u f f i c i e n t t o t i l t t h e a i r c r a f t t o i t s landing a n g l e . Therefore, t h emaximum rearward p o s i t i o n of t h e c e n t e r of g r a v i t y i s f i x e d s o t h a t t h ep e r m i s s i b l e d e f l e c t i o n of t h e e l e v a t o r i s s u f f i c i e n t t o allow t h e p i l o t t oland. The usage of an a.djustable s t a b i l i z e r makes i t p o s s i b l e t o f l y i na i r c r a f t with more forward c e n t e r i n g , s i n c e i n t h i s case t h e e f f e c t i v e n e s s ofthe elevator is increased. Usually, some r e s e r v e i n e l e v a t o r d e f l e c t i o n ( 3 - 4 " , b u t no l e s s t h a n 10%o f t h e complete d e f l e c t i o n o f t h e e l e v a t o r ) i s i n s t a l l e d . Let us now analyze t h e d e f l e c t i o n o f t h e e l e v a t o r A6el/Any necessary t oc r e a t e an a d d i t i o n a l u n i t of overload. A s we can s e e from Figure 130, as t h ev e l o c i t y i n c r e a s e s , t h e e f f e c t i v e n e s s of t h e e l e v a t o r s a l s o i n c r e a s e s s h a r p l y .198
  • 209. c For example, whereas a t M = 0.5, t h e e l e v a t o r must be d e f l e c t e d by 8" i n o r d e r t o cause a double overload, a t M = 0.78 t h e required deflection is only 4". The b a l a n c i n g curves, showing t h e h r dependence o f e 1e v a to r de f 1 t i on ec on M number, are a l s o used t o char­ a c t e r i z e longitud­ inal controllability Figure 131. Balancing Curves of Elevator (Figure 131). Deflection (produced a s a r e s u l t of f l y i n g t e s t s ) : a , I n s t r a i g h t f l i g h t a t nominal e n g i n e According t o o p e r a t i n g mode; b , Coming i n f o r a landing these curves, f o r example with r e a r c e n t e r i n g s (X = t = 28% mac), maintenance of l o n g i t u d i n a l e q u i l i b r i u m a t M = 0.62 r e q u i r e s t h a t t h e e l e v a t o r b e d e f l e c t e d from i t s n e u t r a l p o s i t i o n by 1 . 2 " downward; a t M = 0.74, 1.5" downward; a t M = 0.82, t h e b a l a n c i n g downward d e f l e c t i o n o f t h e ­ /203 e l e v a t o r i s decreased s l i g h t l y , becoming once again +l. . 2 Thus, as t h e a i r c r a f t a c c e l e r a t e s from M = 0.62 t o M = 0.74, l o n g i t u d ­ i n a l b a l a n c i n g r e q u i r e s t h a t t h e e l e v a t o r d e f l e c t i o n b e moved downward by 0 . 3 " , while f u r t h e r a c c e l e r a t i o n t o M = 0.82 r e q u i r e s t h a t it b e decreased by t h e same amount. Beginning a t M = 0.88-0.9, t h e p o s i t i v e p i t c h moment i n c r e a s e s s h a r p l y , and t h e e l e v a t o r must b e d e f l e c t e d c o n s i d e r a b l y downward. 511. Construction of Balancing Curve f o r Deflection of Elevator Using t h e moment diagrams f o r v a r i o u s d e f l e c t i o n s of t h e e l e v a t o r , we can determine-for t h e s e d e f l e c t i o n s c o e f f i c i e n t s c with mZ = O(cy , c ,... ,c 1 Y 1 y2 Yn and c o n s t r u c t t h e b a l a n c i n g diagram f o r d e f l e c t i o n of e l e v a t o r as a f u n c t i o n of c (Figure 132). The l e f t branch o f t h e graph ( l e f t of c ) can be Y y5 produced by wind t u n n e l t e s t i n g o f a model, while t h e r i g h t branch can only be produced i n t e s t f l i g h t s t e s t i n g t h e s t a b i l i t y and c o n t r o l l a b i l i t y o f t h e a i r c r a f t a t high angles of a t t a c k ; i n t h e s e t e s t s , t h e d e f l e c t i o n o f t h e e l e v a t o r a s a f u n c t i o n o f c i s determined f o r each M number. For t h i s , t h e Y 199
  • 210. a i r c r a f t i s p l a c e d i n t h e regime c > c and h e l d i n t h i s regime u n t i l t h e Y Y SUPbeginning o f "pickup," allowing US t o determine t h e degree of s t a b i l i t y of t h ea i r c r a f t and s u f f i c i e n c y of t h e e l e v a t o r s t o b r i n g t h e a i r c r a f t out of t h i sregime. The a i r c r a f t i s a l s o braked i n o r d e r t o determine t h e minimumv e l o c i t y and n a t u r e of i t s behavior a t t h i s v e l o c i t y . The b a l a n c i n g curves on Figure 133 g i v e us an i d e a o f t h e n a t u r e o f t h e dependence o f e l e v a t o r d e f l e c t i o n del f o r a i r c r a f t e q u i l i b r a ­ t i o n with r e s p e c t t o l o n g i t u d i n a l moments a t s t a b l e f l i g h t regimes on coefficient c . Y A s we see, t h e s e curves a r e s i m i l a r i n form t o t h e moment diagram, f o r which p r o p o r t i o n ­ a l i t y of the deflection of elevator t o t h e c o e f f i c i e n t of l o n g i t u d i n a l moment m is also characteristic. Z In o r d e r t o r e c o r d t h e d e f l e c ­ t i o n s of t h e e l e v a t o r d u r i n g f l i g h t tests, the a i r c r a f t is accelerated t o Figure 132. Construction o f M = 0.65-0.85, and t h e n /204 Elevator D e f l e c t i o n Balancing a t c o n s t a n t M number, t h e e l e v a t o r i s D i ag ram "fed" toward t h e p i l o t i n o r d e r t o cause t h e a i r c r a f t t o climb. This "feeding" of t h e e l e v a t o r i s performedwith c with c o n s t a n t i n c r e a s e i n o v e r l o a d n t o 2-3. Y SUP Y Let us analyze t h e movement of t h e a i r c r a f t upon t r a n s i t i o n t o l a r g eangles of a t t a c k ( c > c ) , when t h e p i l o t i s c o n t r o l l i n g t h e a i r c r a f t . Y Y SUP Let us assume t h a t as a r e s u l t of t h e i n f l u e n c e of a powerful ascendinga i r c u r r e n t ( o r as a r e s u l t of c r e a t i o n of an overload i n a t e s t f l i g h t ) t h eaircraft arrives a t c > c (Figure 133). I t was noted i n c h a p t e r I1 t h a t Y1 YU Pif c i s exceeded, l o n g i t u d i n a l s t a b i l i t y o f t h e a i r c r a f t may b e d i s - Y SUPr u p t e d , s i n c e as a r e s u l t of r e d i s t r i b u t i o n o f p r e s s u r e on t h e wing, s o - c a l l e d"capture" - - i n v o l u n t a r y p r o g r e s s i v e i n c r e a s e i n t h e angle o f a t t a c k - - occurs. The angle o f a t t a c k n e a r which "capture" occurs i s c a l l e d t h e "capture"angle of a t t a c k ( t h e c o e f f i c i e n t c and overload above which "capture" begins Ya r e named s i m i l a r l y ) . I f a t t h e moment of c a p t u r e t h e p i l o t moves t h e e l e v a t o r downward by , by t h e time t h e angle of a t t a c k c1 ( c ) i s achieved f o r which 6*el 1 1 Yl200 I
  • 211. . 8 max gel mac considering deformation t h e balancing /,////////, I , I , . . , / I/ / / L .,I.I11111 / / / / / / / I / / / . I L deflection, further /205 1 i n c r e a s e i n t h e angle min of a t t a c k does n o t - -t4=@75 7 h occur and t h e a i r c r a f t _ _ _ M=a,S 2 :,/k g 1 i s balanced a t angle of -4 : I a t t a c k ct and w i l l 1 ________---- --- r e t a i n t h i s angle2. The behavior of an a i r c r a f t i n t h i s curved f l i g h t with n > 1 w i l l Y b e c h a r a c t e r i z e d by a tendency t o i n c r e a s e t h e p i t c h angle without i n c r e a s i n g t h e angle of attack. In order t o return Figure 133. Required Elevator Deflection As the aircraft t o its a Function of c i n i t i a l f l i g h t regime, Y t h e p i l o t s t i l l has t h e e l e v a t o r r e s e r v e A6s e p a r a t i n g t h e balancing e l e v a t o r d e f i e c t i o n from t h e maximal d e f l e c t i o n ,corresponding t o complete d e f l e c t i o n downward ( t o t h e s t o p ) . Tne f u r t h e r t h ep i l o t moves t h e e1evato.r downward from t h i s balancing p o s i t i o n , t h e g r e a t e rt h e angular v e l o c i t y with which t h e a i r c r a f t w i l l begin t o decrease t h e angleof a t t a c k , i . e . , t h e more r a p i d l y t h e overload w i l l b e decreased t o u n i t y . A p o s i t i o n should not a r i s e i n which t h e r e q u i r e d downward e l e v a t o rd e f l e c t i o n t o r e s t o r e balancing is g r e a t e r than t h a t a v a i l a b l e , i n c l u d i n gc o n s i d e r a t i o n of deformation of f o r c e t r a n s m i t t i n g hardware. Otherwise, itw i l l be impossible t o balance t h e a i r c r a f t , and t h e p i l o t w i l l not be a b l e t or e t u r n i t t o t h e i n i t i a l f l i g h t regime. Figure 133 shows t h a t with more forward c e n t e r i n g ( 2 5 % mac) t h e e l e v a t o rr e s e r v e i s g r e a t e r , and t h e c o n t r o l l a b i l i t y i s b e t t e r . This r e s u l t s from t h ef a c t t h a t with forward c e n t e r i n g i n t h e i n i t i a l balancing regime t h e e l e v a t o rc o n t r o l s t i c k must b e h e l d c l o s e r t o t h e p i l o t than with rearward c e n t e r i n gand, consequently, t h e e l e v a t o r r e s e r v e t o maximum d e f l e c t i o n i s i n c r e a s e d . I t has been noted i n t h e p r o c e s s of f l i g h t t e s t s t h a t a f t e r an a i r c r a f ti s put i n a high overload p o s i t i o n , s o a r i n g r e q u i r e s t h a t a p o s i t i v e p i t c hmoment be c r e a t e d by applying a f o r c e of 80-100 kg t o t h e s t i c k . This f o r c e ,which e q u a l i z e s t h e aerodynamic load a c t i n g on t h e d e f l e c t e d e l e v a t o r , deformst h e f o r c e t r a n s m i t t i n g elements, s h o r t e n i n g them. A s a r e s u l t , f u l l forwardd e f l e c t i o n of t h e s t i c k d i d not r e s u l t i n f u l l d e f l e c t i o n o f t h e e l e v a t o r .With maximum d e f l e c t i o n s o f t h e e l e v a t o r (29-31O) t h e a c t u a l angle of p o s i t i o n M. V . Rozenblat, PiZoter o Peregrazke [To t h e P i l o t Concerning Overloading],k r o f l o t Redizdat P r e s s , 1964. 201
  • 212. was only 24-25", due t o deformation (Figure 134). The only method of c r e a t i n g a r e s e r v e o f e l e v a t o r movement f o r a i r c r a f t c o n t r o l i n t h i s case i s unloading of t h e c o n t r o l c a b l e by u s i n g t h e e l e v a t o r trimmer. When t h e trimmer o f t h e e l e v a t o r i s d e f l e c t e d , t h e h i n g e momentsd e c r e a s e , and t h e d e f l e c t i o n of t h e e l e v a t o r i s i n c r e a s e d as a r e s u l t ofunloading o f t h e c o n t r o l c a b l e s . During t h e p r o c e s s of f l i g h t t e s t s o f an a i r c r a f t a t h i g h a n g l e s ofa t t a c k , t h e f o l l o w i n g p e c u l i a r i t y was discovered. W know t h a t when a back- eswept wing moves a t high a n g l e s o f a t t a c k , flow s e p a r a t i o n b e g i n s where t h ea i l e r o n s a r e l o c a t e d . This l e a d s t o a change i n t h e a i l e r o n hinge moment sucht h a t b o t h a i l e r o n s t e n d t o move upward by approximately 2-4". This phenomenon /206h a s come t o be c a l l e d " f l o a t i n g " o f t h e a i l e r o n s . I n i t s e f f e c t , it i se q u i v a l e n t t o an a d d i t i o n a l d e f l e c t i o n of t h e e l e v a t o r upward, s i n c e it causesan a d d i t i o n a l l o s s i n l i f t a t t h e t e r m i n a l p o r t i o n of t h e wing where the l i f tp r o p e r t i e s a r e worsened by t h e s e p a r a t i o n . "Floating" o f a i l e r o n s worsensl o n g i t u d i n a l i n s t a b i l i t y o f t h e a i r c r a f t with swept wings a t high a n g l e s o fa t t a c k and makes c a p t u r e of t h e a i r c r a f t even s h a r p e r . The design-aerodynamic measures analyzed i n 53 of Chapter I11 improve t h e overloads t a b i l i t y c h a r a c t e r i s t i c s of a swept wing a i r c r a f t a t h i g h a n g l e s of a t t a c k . mechanical d e v i c e s o r by d e c r e a s i n g t h e s i z e of t h e a i l e r o n s . The c a b l e deformation A p i l o t flying apassenger a i r c r a f t with a swept wing should avoid a r e a s with s t r o n gt u r b u l e n c e , i n which t h e c h a r a c t e r i s t i c s of l o n g i t u d i n a l overload s t a b i l i t yappear s o unfavorably.202
  • 213. 112. Vertical G u s t s . P e r m i s s i b l e M Number i n Cruising F l i g h t During f l i g h t through atmospheric t u r b u l e n c e , i n t e n s i v e and f r e q u e n t v e r t i c a l g u s t s o f a i r r e s u l t i n l a r g e l o n g i t u d i n a l and l a t e r a l o s c i l l a t i o n s of t h e a i r c r a f t . The a c c e l e r a t i o n s a r i s i n g i n t h i s case l e a d t o t h e appearance o f i n e r t i a l f o r c e s c h a r a c t e r i z e d by overloads on t h e a i r c r a f t . A v e r t i c a l /207 ­ g u s t i s a v e r t i c a l a i r movement r e s u l t i n g i n an i n c r e a s e i n overload i n n o t over 2 sec. The h o r i z o n t a l components of wind g u s t s have no e s s e n t i a l s i g n i f i c a n c e f o r t h e movement o f t h e a i r c r a f t . For example, h o r i z o n t a l wind g u s t s up t o 6-15 m/sec cause