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### Theme 2

1. 1. SECTION 1. AERODYNAMICS OF LIFTING SURFACES THEME 2. WING AND AIRFOIL Wing is the main aircraft lifting surface which creates lifting force. Together withother structural members wing has to provide all aircraft qualifying standards. Inparticular they include: producing minimal aerodynamic drag, specified characteristicsof longitudinal and directional stability and controllability. All these requirements areprovided with right choice of wing geometrical parameters. The wing of modern aircraft, as usual, has a plane of symmetry coincided to basicaircraft plane. Basic wing characteristics are parameters of the airfoils from which the wing isformed, wing planform, aerodynamic twist and cross-cut V. 2.1. Wing geometrical characteristics As it was mentioned above, wing geometrical characteristics are determined byairfoil geometrical parameters. Airfoil is the wing cross section by plane perpendicular to its span and parallel tothe basic aircraft plane. Airfoil shape is determined by upper and low outlines. Let usconsider the main airfoil geometrical parameters (Fig. 2.1). Segment AB of straight line connecting two most outlying points of airfoil is anairfoil chord b . Segments, perpendicular to chord and located between top and lowoutlines determine the airfoil thickness. Fig. 2.1. Airfoil geometrical parameters. 13
2. 2. Maximum airfoil thickness c is determined by segment with maximum length.Airfoil thickness ratio c is ratio of maximum airfoil thickness c to chord b : c c c= or in percents c = ⋅ 100% . b b Chordwise distance from leading point A to point corresponding to maximumairfoil thickness is marked as x c and determined from chord proportion - xc x xc = or in percents x c = c ⋅ 100% . b b For airfoil concavity (camber) the center line of airfoil is drawn. Center line of airfoil – is the line passing through the centers of circles inscribedinto the airfoil. Value of concavity or airfoil camber f will be determined by maximumdistance between center line of airfoil and its chord. Ratio of maximum airfoil camber to fairfoil chord f = is named as center-line camber. Usually this value is determined in b fpercents f = ⋅ 100% . b Position of maximum airfoil camber is determined by relative coordinate: xf xf xf = or in percents x f = ⋅ 100% . b b Some types of airfoils have center line which has back camber near trailing edge(Fig. 2.2). Such airfoils are named as S - shaped. Fig. 2.2. Center line of S - shaped airfoil. 14
3. 3. Thickness ratio c of modern aircraft airfoils usually lies in limits of 2% up to14% . By c value airfoils by convention are divided into three groups: c ≤ 0 .08( c ≤ 8% ) - thin; 0 .08 ≤ c ≤ 0 .12 ( 8% ≤ c ≤ 12% ) - medium; c ≥ 0 .12 ( c ≥ 12% ) - thickairfoils. Thicker airfoils are used on subsonic aircraft, thinner - on supersonic. Forsubsonic aircraft x c lies in limits 25K30% , for supersonic - 40K50% . Center-linecamber f usually is no more than 2% . Lets consider the main parameters characterized wing planform (Fig. 2.3). Wingplanform is determined by wing projection onto wing base plane. Wing base plan is the plane comprising the center chord and perpendicular to base, aircraft plane. Base plane of separate wing is perpendicular to wing symmetry plane. (Plane is parallel to plane x0 z ). Angle ψ of cross-cut V is determined by angle between wing base plane and quarter-chord line projection onto plane perpendicular to center chord. (Plane is parallel to plane y0 z ). Angle ψ is usually not more than ± 10 o for contemporary aircraft. At larger angles ψ wing planform is Fig. 2.3. determined for «straightened wing», that means ψ = 0 . Wing planform are of great variety. The most widespread are tapered one (wingwith straight edges). Aerodynamics uses such concepts as «wing with ventral section», «wingcomprised of outer panels» (Fig. 2.4). 15
4. 4. The wing with ventral section is the wing which leading and trailing edges areprolonged inside fuselage. The wing formed by outer panels is the wing formed by aircraft air-flow partsand separated from fuselage by side cross-sections. In case of wing location on fuselagethe concept of root chord is used. Naturally, characteristics of such wings are different therefore it is necessary toexplain which wing type is under calculation. a) b) Fig. 2.4. Wing: а - «wing with ventral part»; b - «wing formed by outer panels» Geometrical characteristics of tapered wings. (Fig. 2.5). l - wing span; b0 - center (root) chord; bw .t . - wing tip chord; χ - sweep; χ l .e . = χ 0 - leading edge sweep; χ t .e . = χ 1 - trailing edge sweep; χ m - sweep at m part-chord line. Fig. 2.5. 16
5. 5. Wing span l (both for wing formed by outer panels and wing with ventral part)is the distance between two planes parallel to aircraft base plane (wing symmetry plane)and touching to wing tips. Center wing chord b0 is the chord ling in base aircraft plane. In case of separatewing center chord lies in its plane of symmetry. Wing area S is the area of wing projection onto its base plane. Among non-dimensional parameters aspect ratio λ and taper η are the mostimportant. l2 Wing aspect ratio λ is determined as a ratio of span square to wing area λ = . S b0 Wing taper η is the ratio of the center chord b0 to the tip chord bk : η = . bk 1Sometimes the concept of backward taper η = is used. η While determining aspect ratio and taper it is necessary to choose carefully valuesof wing span l and center chord b0 dependently on what type of wing is under viewing:«wing with ventral part» or «wing formed by outer panels». Usually area of wing with ventral part is used as characteristic area at aircraftaerodynamics calculations (Fig. 2.4). 1 Area of tapered wing is determined as: S = ( b + bk ) ⋅ l . 2 0 For example. Wing of subsonic aircraft has the following relative parametersλ ≈ 6K12 ; 1 ≤ η ≤ 3 . For supersonic aircraft - λ ≈ 2K4 ; 10 ≤ η ≤ ∞ . Optimal aspectratio for contemporary subsonic passenger-carrier airplane is equal to λ ≈ 6K8 . There exists connection between sweep angles which is determined as 4m ⎛ η − 1 ⎞ tg χ m = tg χ 0 − ⎜ ⎟ , 0 ≤ m ≤ 1. (2.1) λ ⎝η + 1 ⎠ 17
6. 6. Besides tapered wings contemporary aircraft use wings with the followingplanform (Fig. 2.6): with curvilinear edges (a); edge with fracture (b); wing withextension (c). a) b) c) Рис. 2.6. In some cases area of extensions is included in wing area. If total area ofextensions is no more than 20% from wing area then extensions are not taken intoaccount for λ and η determination. While calculating the longitudinal static stability and position of aerodynamiccenter by angle of attack the concept of mean aerodynamic chord is used. Mean aerodynamic chord (MAC) b A is the conventional chord of equivalentwing which has the same aerodynamic characteristics M z , Y , X in its planform as theinitial wing. Ratio of distance between aerodynamic center and center of mass at angleof attack changing to MAC b A is the universal characteristic of longitudinal staticstability. Let us determine b A and coordinate of MAC leading edge x A relatively towing nose by using moment M z equality for given and rectangular wing (Fig. 2.7). Letus assume that coefficients of moment and normal force of cross-sections alongspanwise are constant. A coordinate of aerodynamic center calculated relatively toMAC nose and related to MAC length is stable and it is expedient to use it to comparean aerodynamic center position of wings having different planform. 18
7. 7. MAC length and coordinate of MAC nose are determined in the following way: l 2 1 bA = S ∫ b 2 ( z )dz ; (2.2) − l2 l 2 1 Fig. 2.7. Mean aerodynamic chord of wing xA = S ∫ b( z ) x( z )dz . (2.3) having a complex planform − l2 While wing arrangement aerodynamic and geometric twist is used for theimprovement of aircraft aerodynamic characteristics. Geometrically flat wing - all cross-sections chords are parallel to base aircraftplane. At geometrical twist local wing chords are turned relatively to each other andform local twist angle ϕ ( z ) . Twist angle ϕ w is measured from center chord. At that0( b0 ) ≤ ϕ ( z ) ≤ ϕ w( bw .t . ) . We distinguish linear and linear conical twist. At linear twist law: ϕ ( z ) = ϕ w z , where z = 2 z . (2.4) l The linear conical twist is characterized by the fact that leading and trailingedges remain straight: ηz ϕ( z ) = ϕw . (2.5) 1 + (η − 1) z Negative twist (that means leading edge of tip cross-section is lower then trailingedge) ϕ w < 0 is usually used for real aircraft structures. Aerodynamic twist means spanwise installation of different airfoils with differentconcavity. Fig. 2.8. shows the changing of airfoil thickness ratio c , concavity f ,concavity coordinate x f , and airfoil setting angle ϕ spanwise of wing outer panel ofTU-154B airplane. 19
8. 8. A wing has the following geometrical parameters: bb = 7 .45 m ; bw .t . = 2 .183 m ; l w = 37 .55 m ; S = 180 m 2 ; λ = 7 .83 ; η = 3 .41 . Geometrical parameters may be approximately placed by grade of importance as: λ , χ , η keeping in mind their influence onto aerodynamic characteristics. Taper η mainly affects aerodynamic load distribution along wing and therefore the center of pressure and aerodynamic center positions and moment characteristics Wing with λ ≤ 2K3 are considered stub wing; wing with λ → ∞ corresponds to an airfoil. If we have sweep at a quater-chord line χ 1 ≤ 20 o K25 o then wings are called 4 non-tapered. The division of wings into tapered and non-tapered is connected with peculiarity of their air-flow about them and appearance of new effects affected onto aerodynamic characteristics. Fig. 2.8. Wing of aircraft TU-154B Twist also affects aerodynamic loaddistribution along wing. The best air-flow of wing at large angles of attack, decreasingof induced drag at fixed lifting force and necessary conditions for balancing may beprovided by twist. 20