Aerodynamics 101 How do those things really fly?

1. Aerodynamics 101How do those things really fly? Dr. Paul Kutler Saturday, March 31, 2007 Monterey Airport

2. Airbus 380 An aerodynamics challenge

3. FA-18 Condensation Pattern Aerodynamics involves multiple flow regimes

4. Legacy Aircraft Aerodynamics is a maturing science

5. Outline • Terms and Definitions • Forces Acting on Airplane • Lift • Drag • Concluding remarks

6. Terms and Nomenclature • Airfoil • Angle of attack • Angle of incidence • Aspect Ratio • Boundary Layer • Camber • Chord • Mean camber line • Pressure coefficient • Leading edge • Relative wind • Reynolds Number • Thickness • Trailing edge • Wing planform • Wingspan

7. Force Diagram

8. Airfoil Definitions

9. Definition of Lift, Drag & Moment L = 1/2  V2 CL S D = 1/2  V2 CD S M = 1/2  V2 CM S c

10. A Misconception • A fluid element that splits at the leading edge and travels over and under the airfoil will meet at the trailing edge. • The distance traveled over the top is greater than over the bottom. • It must therefore travel faster over the top to meet at the trailing edge. • According to Bernoulli’s equation, the pressure is lower on the top than on the bottom. • Hence, lift is produced.

11. How Lift is Produced • Continuity equation • Bernoulli’s equation • Pressure differential • Lift is produced

12. The Truth • A fluid element moving over the top surface leaves the trailing edge long before the fluid element moving over the bottom surface reaches the trailing edge. • The two elements do not meet at the trailing edge. • This result has been validated both experimentally and computationally.

13. Airfoil Lift Curve (cl vs. )

14. Lift Curve - Cambered & Symmetric Airfoils

15. Slow Flight and Steep Turns L = 1/2  V2 CL SOutcome versus Action • Slow Flight • Lift equals weight • Velocity is decreased • CL must increase •  must be increased on the lift curve • Velocity can be reduced until CLmax is reached • Beyond that, a stall results

16. Slow Flight and Steep TurnsL = 1/2  V2 CL SOutcome versus Action(Concluded) • Steep Turns (“Bank, yank and crank”) • Lift vector is rotated inward (“bank”) by the bank angle reducing the vertical component of lift • Lift equals weight divided by cosine  • Either V (“crank”), CL or both must be increased to replenish lift • To increase CL, increase  (“yank”) on the lift curve • To increase V, give it some gas • More effective since lift is proportional to the velocity squared

17. Stalling Airfoil

18. Effect of Bank Angle on Stall Speed • L = 1/2  V2 CL S •  equals the bank angle • At stall CL equals CLmax • L = W / cos  • Thus • Vstall = [2 W / ( CL max S cos )] 1/2 • Airplane thus stalls at a higher speed • Load factor increases in a bank • Thus as load factor increases, Vstall increases • This is what’s taught in the “Pilot’s Handbook”

19. Effect of CG Location on Stall Speed

20. Surface Oil Flow - Grumman Yankee = 40,110 , &240

21. Airfoil Pressure Distribution NACA 0012, M ∞ = 0.345,  = 3.930

22. Supercritical Airfoil & Pressure Distribution

23. Drag of an Airfoil D = Df+ Dp + Dw D = total drag on airfoil Df = skin friction drag Dp = pressure drag due to flow separation Dw = wave drag (for transonic and supersonic flows)

24. Skin Friction Drag • The flow at the surface of the airfoil adheres to the surface (“no-slip condition”) • A “boundary layer” is created-a thin viscous region near the airfoil surface • Friction of the air at the surface creates a shear stress • The velocity profile in the boundary layer goes from zero at the wall to 99% of the free-stream value •  =  (dV/dy)wall •  is the dynamic viscosity of air [3.73 (10) -7 sl/f/s]

25. The Boundary Layer • Two types of viscous flows • Laminar • Streamlines are smooth and regular • Fluid element moves smoothly along streamline • Produces less drag • Turbulent • Streamlines break up • Fluid element moves in a random, irregular and tortuous fashion • Produces more drag • w laminar < w turbulent • Reynolds Number • Rex =  V∞ x /  • Ratio of inertia to viscous forces

26. Boundary Layer Thickness(Flat Plate) • Laminar Flow •  = 5 x / Rex1/2 • Turbulent Flow •  = 0.16 x / Rex1/7 • Turbulent Flow-Tripped B.L. •  = 0.37 x / Rex1/5 • Example: Chord = 5 f, V∞ = 150 MPH, Sea Level • Rex = 6,962,025 •  = 0.114 inches Laminar B.L. •  = 1.011 inches Turbulent B.L. •  = 7.049 inches Tripped Turbulent B.L.

27. Infinite vs. Finite Wings AR = b2 / S

28. Finite Wings

29. The Origin of Downwash

30. The Origin of Induced Drag Di = L sin i

31. Elliptical Lift Distribution CD,I = CL2/ (e AR)

32. Change in Lift Curve Slopefor Finite Wings

33. Ground Effect • Occurs during landing and takeoff • Gives a feeling of “floating” or “riding on a cushion of air” between wing and ground • In fact, there is no cushion of air • Its effect is to increase the lift of the wing and reduce the induced drag • The ground diminishes the strength of the wing tip vortices and reduces the amount of downwash • The effective angle of attack is increased and lift increases

34. Ground Effect(Concluded) • Mathematically Speaking • L = 1/2  ∞V∞2S CL • An increased angle of attack, increases CL • Hence L is increased • D = 1/2 ∞ V∞2 S [CD,0 +  CL2/( e AR)] • CD,0is the zero lift drag (parasite) •  CL2/( e AR) is the induced drag • e is the span efficiency factor •  = (16 h / b)2 / [1 + (16 h / b)2 ] • b is the wingspan • h is the height of the wing above the ground

35. Wing Dihedral () • Wings are bent upward through an angle , called the dihedral angle • Dihedral provides lateral stability, i.e., an airplane in a bank will return to its equilibrium position • This is a result of the lift on the higher wing being less than the lift on the lower wing providing a restoring rolling moment

36. Drag of a Finite Wing D = Df+ Dp + Dw + Di D = total drag on wing Df = skin friction drag Dp = pressure drag due to flow separation Dw = wave drag (for transonic and supersonic flows) Di = Induced drag (drag due to lift)

37. Drag of a Wing(Continued) • Induced drag - drag due to lift • Parasite drag - drag due to non-lifting surfaces • Profile drag • Skin friction • Pressure drag (“Form drag”) • Interference drag (e.g., wing-fuselage, wing-pylon)

38. FlapsA Mechanism for High Lift

39. Effect of Flaps on Lift Curve

40. High Lift Devices • No flap • Plain flap • Split flap • L. E. slat • Single slotted flap • Double-slotted flap • Double-slotted flap with slat • Double-slotted flap with slat and boundary layer suction • Not shown - Fowler flap

41. Shape ComparisonModern vs. Conventional Airfoils

42. Maximum Lift Coefficient ComparisonModern vs. Conventional Airfoils

43. What’s Next on the Agenda • Boeing 787 Dreamliner Boeing 787

44. What’s Next on the Agenda • Boeing Blended Wing-Body Configuration Boeing 797

45. Concluding Remarks • What was not discussed • Transonic flow • Drag-divergence Mach number • Supersonic flow • Wave drag • Swept wings • Compressibility effects • Boundary layer theory • The history of aerodynamics

46. Airbus 380 Interior Good aerodynamics results in improved creature comforts

47. Questions and Answers

48. Backup Slides

49. Winglets • Reduced induced drag • Equivalent to extending wingspan 1/2 of winglet height • Less wing bending moment and less wing weight than extending wing • Hinders spanwise flow and pressure drop at the wing tip • Looks modern/esthetically pleasing Boeing 737 Winglet

50. Vortex Generators