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Subsonic Airplane Design


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Subsonic Airplane Design

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Subsonic Airplane Design

  1. 1. Subsonic Airplane Design Christopher Weyant Joseph Rebolledo COSMOS at UC Davis Cluster 3 August 3, 2006
  2. 2. Presentation Outline <ul><li>Main factors that allow flight </li></ul><ul><li>Ratios to interpret these factors </li></ul><ul><li>Important design considerations </li></ul><ul><li>Case study- Helios </li></ul>
  3. 3. I. Factors that Allow Airplane Flight <ul><li>Lift </li></ul><ul><li>Weight </li></ul><ul><li>Thrust </li></ul><ul><li>Drag </li></ul><ul><li>Center of mass </li></ul><ul><li>Center of pressure </li></ul>
  4. 4. Forces in Airplane Flight
  5. 5. How Lift is Created <ul><li>Observe streamlines </li></ul><ul><ul><li>Must be downwards pressure force to hold them to wing </li></ul></ul>
  6. 6. How Lift is Created <ul><li>Imagine boxes stacked above and below wing </li></ul><ul><li>Top of box must have higher pressure than bottom </li></ul><ul><li>Lower pressure on top of wing than bottom </li></ul><ul><li>Pressure gradient causes lift </li></ul>high pressure low pressure= next high pressure low pressure pressure force pressure force
  7. 7. Lift <ul><li>Three main ways to increase lift: </li></ul><ul><ul><li>Increase angle of attack </li></ul></ul><ul><ul><li>Camber </li></ul></ul><ul><ul><li>Vortex-Induced Lift </li></ul></ul>
  8. 8. Lift <ul><li>Change angle of attack </li></ul><ul><li>2. Camber </li></ul><ul><li>3. Vortex induced lift </li></ul><ul><li>- Watch for separation </li></ul>
  9. 9. Weight <ul><li>Weight measures the downward gravitational pull on the aircraft </li></ul><ul><li>Several components contribute to the weight of an aircraft: </li></ul><ul><ul><li>Physical plane </li></ul></ul><ul><ul><li>Fuel </li></ul></ul><ul><ul><li>Payload </li></ul></ul>
  10. 10. Weight Considerations <ul><li>Lift must exceed weight to take off </li></ul><ul><li>In obtaining lift, drag must be less than thrust to accelerate and take off </li></ul>
  11. 11. How Thrust is Created <ul><li>Propulsive device exerts force on air </li></ul><ul><li>Equal and opposite force exerted back on plane </li></ul><ul><li>Makes plane go forward and overcome drag </li></ul>
  12. 12. Thrust <ul><li>Pressure and sheer stress distribution on surface area cause thrust </li></ul><ul><li>Thrust equation </li></ul><ul><li>T=ṁ(V ∞ - V j ) </li></ul><ul><ul><li>T; thrust [newtons; kgm/s 2 ] </li></ul></ul><ul><ul><li>ṁ; mass flow through device [kg/s] </li></ul></ul><ul><ul><li>V ∞ ; velocity of air leaving plane [m/s] </li></ul></ul><ul><ul><li>V j ; velocity of air ahead of plane [m/s] </li></ul></ul>
  13. 13. Thrust <ul><li>Total power generated by propulsive device </li></ul><ul><li>= TV ∞ +1/2ṁ(V j -V ∞ ) 2 </li></ul><ul><li>(power available) + (wasted/ KE) </li></ul>
  14. 14. Thrust vs. Efficiency <ul><li>Useful power ( η p ) </li></ul><ul><li>= 2/(1+V j /V ∞ ) </li></ul><ul><li>100% efficiency has V j = V ∞ </li></ul><ul><li>However, then no thrust </li></ul><ul><li>Tradeoff </li></ul>
  15. 15. How Drag is Created <ul><li>Friction drag </li></ul><ul><ul><li>Drag due to friction over surface </li></ul></ul><ul><li>Pressure drag </li></ul><ul><ul><li>Inequality of surface pressure that causes drag </li></ul></ul><ul><li>Induced drag </li></ul><ul><ul><li>Pressure drag associated with wing tip vortices </li></ul></ul>
  16. 16. Center of Pressure <ul><li>Sum pressure forces into a single force </li></ul><ul><li>Point through which lift and drag act </li></ul><ul><li>Also, the point at which there is no moment </li></ul><ul><li>To find, plot distributed load and find centroid </li></ul>
  17. 17. Center of Mass <ul><li>Average location of weight </li></ul><ul><li>Balance object on that point </li></ul><ul><li>Point from which gravity can be drawn </li></ul><ul><li>To find, cg = ( ∫ [x * w(x)]dx) / ( ∫ [w(x)]dx) </li></ul><ul><ul><li>  Sum of weights of slices times distances to nose divided by the sum of the weights; weighted average </li></ul></ul><ul><ul><li>x= distance from nose tip of aircraft back to slice [m] </li></ul></ul><ul><ul><li>dx= small slices perpendicular to x [m] </li></ul></ul><ul><ul><li>w(x)= weight of slice contained in dx; newton [kgm/s 2 ] </li></ul></ul><ul><ul><li>Assume weight is distributed symmetrically around center line </li></ul></ul>
  18. 18. Centers of Mass and Pressure <ul><li>Center of pressure is behind center of mass </li></ul><ul><li>Leads to increased stability by correcting for angle of attack </li></ul><ul><li>Horizontal stabilizer provides downwards force </li></ul><ul><li>Wing provides upwards lift </li></ul><ul><li>When angle of attack increases, wing lift increase and horizontal stabilizer rotates nose back down </li></ul><ul><li>They must be on same line, so as to not create torque along the yaw or roll axes </li></ul>
  19. 19. II. Useful Non-dimensional Ratios <ul><ul><li>Mach number </li></ul></ul><ul><ul><li>Reynolds number </li></ul></ul><ul><ul><li>Aspect ratio </li></ul></ul><ul><ul><li>Coefficient of lift </li></ul></ul><ul><ul><li>Coefficient of drag </li></ul></ul>
  20. 20. Mach Number <ul><li>Compressibility effects </li></ul><ul><li>Ma= speed airplane/ speed sound= V/a </li></ul><ul><ul><li>Ma<1; subsonic </li></ul></ul><ul><ul><li>Ma≈1; transonic </li></ul></ul><ul><ul><li>Ma>1; supersonic </li></ul></ul><ul><ul><li>Ma>>1; hypersonic </li></ul></ul><ul><li>Ma 2 =-( Δρ / ρ )/( Δ V/V) </li></ul><ul><li> = change in density/change in velocity </li></ul>
  21. 21. Reynolds number <ul><li>Viscosity effects </li></ul><ul><li>Re= ρ ∞ v ∞ c/ μ ∞ </li></ul><ul><ul><li>pressure vs. viscosity </li></ul></ul><ul><ul><li>ρ ∞ = free stream air density [kg/m 3 ] </li></ul></ul><ul><ul><li>V ∞ = free stream air velocity [m/s] </li></ul></ul><ul><ul><li>c= chord length [m] </li></ul></ul><ul><ul><li>μ ∞ = ambient coefficient of viscosity; [Kg/ms] </li></ul></ul><ul><li>Less than 2300 is laminar </li></ul><ul><li>Over 2300 is turbulent </li></ul>
  22. 22. Aspect Ratio <ul><li>Three dimensional effects </li></ul><ul><li>Tells how skinny wing is </li></ul><ul><li>AR= b 2 /S </li></ul><ul><ul><li>b= wingspan [m] </li></ul></ul><ul><ul><li>S= planform area of wing [m 2 ] </li></ul></ul>
  23. 23. Coefficient of Lift <ul><li>C L = L/( ½ ρ V 2 S) </li></ul><ul><ul><li>C L =coefficient of lift [dimensionless] </li></ul></ul><ul><ul><li>L= lift; newton [kgm/s 2 ] </li></ul></ul><ul><ul><li>ρ = air density [kg/m 3 ] </li></ul></ul><ul><ul><li>V= velocity; [m/s] </li></ul></ul><ul><ul><li>S= planform wing area [m 2 ] </li></ul></ul>
  24. 24. Coefficient of Drag <ul><li>C D = D/( ½ ρ V 2 S) </li></ul><ul><ul><li>C D =coefficient of drag [dimensionless] </li></ul></ul><ul><ul><li>D= drag; newton [kgm/s 2 ] </li></ul></ul><ul><ul><li>ρ = air density [kg/m 3 ] </li></ul></ul><ul><ul><li>V= velocity [m/s] </li></ul></ul><ul><ul><li>S= planform wing area [m 2 ] </li></ul></ul>
  25. 25. III. Design of Subsonic Airplanes <ul><li>Stalling velocity </li></ul><ul><li>Wing design </li></ul><ul><li>Induced drag </li></ul><ul><li>Angle of attack </li></ul><ul><li>Ceiling altitude </li></ul><ul><li>Evaluating airfoils </li></ul>
  26. 26. Stalling Velocity <ul><li>V stall = √(2/ ρ ∞ )(W/S)(1/C L max ) </li></ul><ul><ul><li>V stall = stalling velocity [m/s] </li></ul></ul><ul><ul><li>ρ ∞ = free stream air density [ kg/m 3 ] </li></ul></ul><ul><ul><li>W= weight; newtons [ kgm/s 2 ] </li></ul></ul><ul><ul><li>S= planform surface area of wing [m 2 ] </li></ul></ul><ul><ul><li>C L max = maximum lift coefficient [dimensionless] </li></ul></ul>
  27. 27. Implications <ul><li>Gets larger at higher altitudes, due to decreasing air density </li></ul><ul><li>Increases with weight </li></ul><ul><li>Decreases with planform wing area </li></ul><ul><li>Decreases with higher C L max </li></ul>
  28. 28. Different Types of Wings <ul><li>High aspect- ratio straight wing </li></ul><ul><li>Low aspect- ratio straight wing </li></ul><ul><li>Swept wing </li></ul><ul><li>Delta wing </li></ul><ul><ul><li>Simple delta </li></ul></ul><ul><ul><li>Cropped delta </li></ul></ul><ul><ul><li>Notched delta </li></ul></ul><ul><ul><li>Double delta </li></ul></ul>
  29. 29. Prandtl’s Lifting Line Theory <ul><li>a=a o /(1+(a o /  e 1 AR) </li></ul><ul><li>a= lift slope for finite wing [per radian] </li></ul><ul><li>a 0 = lift slope for infinite wing [per radian] </li></ul><ul><li>e 1 = ratio of tip chord to root chord [dimensionless] </li></ul><ul><li>AR= b 2 /S [dimensionless] </li></ul>
  30. 30. Implications <ul><li>Lift slope decreases with aspect ratio </li></ul><ul><li>Straight wing to maximize e 1 </li></ul><ul><li>Experimentally, C L max decreases with aspect ratio </li></ul>
  31. 31. Prandtl- Glauert Rule <ul><li>a o,comp = a 0 / √1 - M ∞ 2 </li></ul><ul><li>a o = incompressible lift slope [per radian] </li></ul><ul><li>M ∞ = free stream mach number [dimensionless] </li></ul>
  32. 32. Combined <ul><li>a comp = a o / √1-M ∞ +a o /(  e 1 AR) </li></ul><ul><li>a o = incompressible lift slope [per radian] </li></ul><ul><li>a comp = compressible lift slope [per radian] </li></ul><ul><li>M ∞ = free stream mach number [dimensionless] </li></ul><ul><li>e 1 = ratio of tip chord to root chord [dimensionless] </li></ul><ul><li>AR= b 2 /S [dimensionless] </li></ul><ul><li>Works well for .3<Ma<.7 </li></ul>
  33. 33. Implications <ul><li>Same as before, but modified to account for compressible flows </li></ul><ul><li>Lift slope decreases with aspect ratio </li></ul><ul><li>Straight wing to maximize e 1 </li></ul><ul><li>Experimentally, C L max decreases with aspect ratio </li></ul>
  34. 34. Equation for Induced Drag <ul><li>C Di = (C L 2 )/(  (AR)e) </li></ul><ul><li>Where: </li></ul><ul><ul><li>C L ; coefficient of lift [dimensionless] </li></ul></ul><ul><ul><li>AR; aspect ratio [dimensionless] </li></ul></ul><ul><ul><li>e; spanwise efficiency factor, how C Di for wing relates to ideal wing with the same aspect ratio [dimensionless] </li></ul></ul>
  35. 35. Implications <ul><li>Biggest source of drag for low speed aircraft </li></ul><ul><li>Wings with the largest possible aspect ratio </li></ul><ul><li>For low speed aircraft, aspect ratios as high as 15 or more are used </li></ul>
  36. 36. Angle of Attack <ul><li>Angle that wing is inclined to flow </li></ul><ul><li>Want only small angle of attack needed to achieve adequate lift at low speed </li></ul><ul><li>Can be built into wing through camber </li></ul>
  37. 37. Ceiling Altitude <ul><ul><li>( R/C) max = maximum rate of climb [m/sec] </li></ul></ul><ul><ul><li>η pr = propeller efficiency; power available/ shaft power [dimensionless] </li></ul></ul><ul><ul><li>P= power [W] </li></ul></ul><ul><ul><li>W= weight newtons [ kgm/s 2 ] </li></ul></ul><ul><ul><li>ρ ∞ = free stream air density [kg/m 3 ] </li></ul></ul><ul><ul><li>K= Coefficient of Cl 2 in drag polar [dimensionless] </li></ul></ul><ul><ul><li>C D.O= Zero lift drag coefficient [dimensionless] </li></ul></ul><ul><ul><li>S= planform surface area of wing [m 2 ] </li></ul></ul><ul><ul><li>L/D max = maximum lift to drag ratio [dimensionless] </li></ul></ul>(R/C) max =( η pr P/W)–[(2/ ρ ∞ )√K/3C D.0 (W/S)] 1/2 *(1.55/(L/D max ))
  38. 38. Implications <ul><li>η pr P/W want big </li></ul><ul><ul><li>Bigger engine, more efficient propeller, less weight </li></ul></ul><ul><li>K wants smaller </li></ul><ul><ul><li>Higher aspect ratio </li></ul></ul><ul><li>W/S want small </li></ul><ul><li>- Less weight </li></ul><ul><li>- Larger surface area of wing </li></ul><ul><li>L/D max want big </li></ul><ul><ul><li>Less drag </li></ul></ul><ul><ul><li>More lift </li></ul></ul>
  39. 39. Limits on Reducing Drag <ul><li>Aspect ratio and surface area have to be within a range </li></ul><ul><li>Makes aircraft heavier which requires more lift </li></ul><ul><li>Increases skin friction drag which requires more power </li></ul><ul><li>If aspect ratio is too high, loose stability </li></ul>
  40. 40. Evaluating Airfoils
  41. 41. Explanation <ul><li>For these graphs, Re= 200,500 </li></ul><ul><li>First graph shows C D and C L of airfoil </li></ul><ul><ul><li>Want high C L for given C D </li></ul></ul><ul><li>Second shows  and  C L </li></ul><ul><ul><li>Want high C L for given  </li></ul></ul><ul><li>Third shows  and CM </li></ul><ul><ul><li>Want low CM for given  </li></ul></ul>
  42. 42. Coffin Corner <ul><li>Problem faced by high altitude low speed flight </li></ul><ul><li>If slow down at high altitude, stall </li></ul><ul><li>If speed up, break sound barrier and generate too much drag and stall </li></ul>
  43. 43. IV. Case Study- Helios <ul><li>Part of HALE </li></ul><ul><li>$103 million from NASA </li></ul><ul><li>$36 million from industry </li></ul>
  44. 44. Goals for Helios <ul><li>Reach 100,000 ft. </li></ul><ul><li>Have non-stop flight for 24 hours, and to have at least 14 hours above 50,000 ft. </li></ul>
  45. 45. Significance of Helios <ul><li>Study atmospheric science </li></ul><ul><li>Observe the Earth </li></ul><ul><li>Serve as telecommunication system </li></ul>
  46. 46. Helios Aircraft Statistics <ul><li>Wing span of 247 ft </li></ul><ul><li>Length of 12 ft </li></ul><ul><li>Wing chord of 8 ft </li></ul><ul><li>Wing area is 1,976 sq ft </li></ul><ul><li>Aspect ratio of 31 to 1 </li></ul><ul><li>Gross weight is 1,600 lb </li></ul><ul><li>Payload of 726 lbs </li></ul><ul><li>Airspeed of 19 to 27 mph </li></ul><ul><li>Up to 170 mph at altitude </li></ul><ul><li>72 trailing edge elevators </li></ul>
  47. 47. Helios Propulsion Statistics <ul><li>14 brushless DC electric motors, 1.5 kW each </li></ul><ul><li>62,000 solar cells </li></ul><ul><li>Endurance of several days to several months </li></ul>
  48. 48. Helios Accomplishes a Goal (2001) <ul><li>Unofficial altitude record of 96,863 ft </li></ul><ul><li>Stayed over 96,000 ft for over 40 min </li></ul><ul><li>Did not meet flight endurance goal </li></ul><ul><li>Scientists worked on for 2003 flight </li></ul>
  49. 49. Helios Malfunctions <ul><li>3,000 ft. up in restricted Navy airspace </li></ul><ul><li>Control difficulties </li></ul><ul><li>Severe oscillations occurred </li></ul><ul><li>Structural damage lead to crash </li></ul><ul><li>No environmental effect, but plane lost </li></ul><ul><li>75 percent by weight recovered </li></ul>
  50. 50. Summary <ul><li>Main factors that allow flight </li></ul><ul><li>Ratios to interpret these factors </li></ul><ul><li>Important design considerations </li></ul><ul><li>Case study- Helios </li></ul>
  51. 51. Acknowledgements <ul><li>Professor Hafez </li></ul><ul><li>Professor Horsley </li></ul><ul><li>Michael Paskowitz </li></ul><ul><li>Margarita Montes </li></ul><ul><li>Tim McGuire </li></ul><ul><li>Taylor Roche </li></ul><ul><li>Beth Kuspa </li></ul>
  52. 52. Bibliography <ul><li> </li></ul><ul><li>Aircraft Performance and Design by John D. Anderson, Jr. </li></ul><ul><li> </li></ul><ul><li> </li></ul>