Aircraft Design: A Systems Engineering Approach, M. Sadraey, Wiley, 2012 Chapter 5 Wing Design Figures 1
Identify and prioritize wing design requirements (Performance, stability, producibility, operational requirements, cost, flight safety) Select number of wings Select wing vertical location Select/Design high lift device Select/Determine sweep and dihedral angles (, ) Select or design wing airfoil section Determine other wing parameters (AR, i w, t ) Calculate Lift, Drag, and Pitching moment Requirements Satisfied? Yes No Optimization Calculate b, MAC, C r, C t Figure 5.1. Wing design procedure 2
1. Monoplane 2. Biplane 3. triwing Figure 5.2. Three options in number of wings (front view) a. High wing b. Mid wing c. Low wing b. Parasol wing Figure 5.3. Options in vertical wing positions 3
1. Cargo aircraft Lockheed Martin C-130J Hercules (high wing) (Courtesy of Antony Osborne) 4
2. Passenger aircraft Boeing 767 (low wing) (Courtesy of Anne Deus) 5
3. Homebuilt aircraft Pietenpol Air Camper-2 (parasol wing) (Courtesy of Jenny Coffey) 6
4. Military aircraft Hawker Sea Hawk FGA6 (mid wing) (Courtesy of Antony Osborne) Figure 5.4. Four aircraft with different wing vertical positions 7
x-location of Maximum thickness Thickness Maximum thickness Maximum camber Mean camber line Leading edge radius Leading edge Chord line Trailing edge x-location of Maximum camber Chord Figure 5.5. Airfoil geometric parameters a. Small angle of attack b. Large angle of attack Figure 5.6. Flow around an airfoil 8
a. Small angle of attack b. Large angle of attack Figure 5.7. Pressure distribution around an airfoil Trailing edge 1 0.8 Flight angle of attacks 0.6 0.4 Pressure center 0.2 Aerodynamic center +0.1 0 C m Leading edge -0.1 Pitching moment coefficient 0-0.2-4 o 0 o 4 o 8 o 12 o 16 o 20 o Angle of attack ( ) Figure 5.8. The pressure center movement as a function of angle of attack 9
a. The force on pressure center b. Addition of two equal forces c. Force on aerodynamic center Figure 5.9. The movement of resultant force to aerodynamic center V M o L F ac D Figure 5.10. The aerodynamic lift, drag, pitching moment 10
C l C lmax C l i C l o 0 C s (deg) Figure 5.11. The variations of lift coefficient versus angle of attack C l C l gentle abrupt Figure 5.12. Stall characteristics 11
C m_c/4 + (deg) Figure 5.13. The variations of pitching moment coefficient versus angle of attack C m_ac + C l Figure 5.14. The variations of pitching moment coefficient versus lift coefficient 12
C d C d min C (C lmin d /C l ) min 0 C l Figure 5.15. The typical variations of drag coefficient versus lift coefficient C d C dmin 0 C li C ld C l Figure 5.16. The variations of C l versus C d for a laminar airfoil 13
C C l d (C l /C d ) max 0 l Figure 5.17. The typical variations of lift-to-drag ratio versus angle of attack 14
Thick and highly cambered Symmetric Cambered airfoil with deflected high lift device Thin and lightly cambered Supersonic double wedge Figure 5.18. Five sample airfoil sections 15
0.1 y/c -0.1 0 0.2 0.4 0.6 0.8 1.0 a. NACA 1408 airfoil section b. NACA 23012 airfoil section 0.2 0.1 y/c -0.1 0 0.2 0.4 0.6 0.8 1.0 y/c -0.2 0 0.2 0.4 0.6 0.8 1.0 c. NACA 63 3-218 airfoil section Figure 5.19. A four-digit, a five-digit and a 6-series airfoil sections [3] c d NACA four digit airfoils NACA five digit airfoils 0.005 0.0045 0.004 NACA 6-series airfoils c l 16
Figure 5.20. C l -, C m -, and C d -C l graphs of NACA 63 2-615 airfoil section [3] 17
C t max C lmax fu = c l C dminfu = 0.0045 C m = -0.03 C l and C d for (C l /C d ) max o = -1.5 s = 12 (t/c) max = 9% Figure 5.21. The locations of all points of interest of NACA 63-209 airfoil section (flap-up) [3] C li = 0.2 18
Figure 5.22. Maximum lift coefficient versus ideal lift coefficient for several NACA airfoil sections (Data from [3]) 19
Wing zerolift and wave drag coefficient 0.03 0.02 t/c=12% t/c=9% t/c=6% 0.01 t/c=4% 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Mach number Figure 5.23. Variation of wing zero-lift and wave drag coefficient versus Mach number for various airfoil thickness ratio. i w Wing chord line at root Figure 5.24. Wing setting (incidence) angle Fuselage center line 20
c l c l i set Figure 5.25. Wing setting angle corresponds with ideal lift coefficient a. AR = 26.7 b. AR = 15 c. AR = 6.67 d. AR = 3.75 e. AR = 1 Figure 5.26. Several rectangular wings with the same planform area but different aspect ratio 21
C L 2d airfoil (infinite AR) 3d wing (low AR) increasing AR Figure 5.27. The effect of AR on C L versus angle of attack graph a. Rectangle ( =1) b. Trapezoid 0 < < 1 (straight tapered) c. Triangle (delta) = 0 Figure 5.28. Wings with various taper ratio 22
C L =0 Elliptical lift distribution =1 =0.8 root semispan Figure 5.29. The typical effect of taper ratio on the lift distribution ac LE C r MAC C t b Figure 5.30. Mean Aerodynamic Chord and Aerodynamic Center in a straight wing 23
C L Front view y/s -b/2 +b/2 Figure 5.31. Elliptical lift distribution over the wing C L C Lmax C L C Lmax 0 0 root tip root tip a. Non-elliptical (tip stalls before the root) b. Elliptical (root stalls before the tip) Figure 5.32. Lift distribution over a half wing 24
C. C L Total lift generated by a half wing C. C L Total lift generated by a half wing Bending moment arm 0 0 root tip root Bending moment arm tip a. Non-elliptical (load is farther from root) b. Elliptical (load is closer to root) Figure 5.33. Load distribution over a half wing Lift Fuselage Low wing Figure 5.34. The fuselage contribution to the lift distribution of a low wing configuration 25
Lift Wing Flap Flap Figure 5.35. The flap contribution to the lift distribution 26
x Fuselage center line a y y b LE c y C/2 y y d C/4 e y TE Figure 5.36. Five wings with different sweep angles 27
M M cos ( ) Fuselage center line Stagnation streamline (lateral curvature exaggerated) Wing C C/cos ( ) Figure 5.37. The effective of the sweep angle of the normal Mach number 28
C L AR= 7 AR= AR= 7 AR= AR=7 AR=10 AR=10 AR=7 0 o 10 o 20 o 30 o 40 o Sweepback angle (deg) Figure 5.38. Effect of wing sweepback on ac position for several combinations of AR and 29
C L Swept wing Basic unswept wing root tip y/s Figure 5.39. Typical effect of sweep angle on lift distribution M > 1 Fuselage center line y Wing Oblique shock wave Figure 5.40. The sweep angle and Mach angle in supersonic flight 30
Fuselage center line highly swept inboard low sweep angle outboard Figure 5.41. Top view of a wing with two sweep angels C r /2 b/2 C r MAC C t b eff Figure 5.42. Effective wing span in a swept wing 31
A C r /2 B C C t /2 C/2 chord line b/2 Figure 5.43. The wing of Example 5.3( and angles are exaggerated) C r /2 C r /4 A B C C/4 K J I C/2 = 30 L H D b/2=6.325 m TE F L G C t /2 E b eff /2 Figure 5.44. The top view of the right wing of Example 5.4 32
1. Grumman F-14D (Courtesy of Antony Osborne) 33
2. Pilatus PC-21 (Courtesy of Antony Osborne) 34
3. Fokker 70 (Courtesy of Anne Deus) Figure 5.45. Sweep angles for three aircraft 35
r root tip t a. geometric twist root tip b. Aerodynamic twist Figure 5.46. Wing twist C L Without twist With twist root b/2 y/s 36
Figure 5.47. The typical effect of a (negative) twist angle on the lift distribution xy plane z z a. Dihedral b. Anhedral Figure 5.48. Dihedral, anhedral (aircraft front view) xy plane L right Restoring moment L left xy plane z gust xy plane airstream z a. before gust b. after gust Figure 5.49. The effect of dihedral angle on a disturbance in roll (aircraft front view) 37
1. Airbus A330-dihedral (Courtesy of A J Best) 38
2. British Aerospace Sea Harrier-anhedral (Courtesy of Jenny Coffey) Figure 5.50. Two aircraft with different dihedral angles 39
Pressure distribution of the wing when HLD deflected C P Pressure distribution of original wing f x/c Figure 5.51. Example of pressure distribution with the application of a high lift device C l C lmax C m C d C dmin S C li C l without flap deflection with flap deflection Figure 5.52. Typical effects of high lift device on wing airfoil section features 40
9. Kruger flap a. Trailing edge high lift device b. Leading edge high lift device Figure 5.53. Various types of high lift devices 41
Fuselage Center Line C C f b f /2 b/2 a. Top-view of the right wing Leading edge Chord line Trailing edge C f fmax C b. The side-view of the inboard wing (flap deflected) Figure 5.54. High lift device parameters Fuselage Center Line Flap Aileron Wing tip C b/2 Figure 5.55. Typical location of the aileron on the wing 42
Wing tip Fuselage Center Line 1 2 3 4 5 6 7 C t b/2 Figure 5.56. Dividing a wing into several sections C L 1 2 3 4 5 6 5 6 7 y/s Figure 5.57. Angles corresponding to each segment in lifting-line theory 43
Lift coefficient 0.35 Lift Distribution 0.3 0.25 0.2 0.15 0.1 0.05 0 0 1 2 3 4 5 6 7 8 semi-span Location (m) Figure 5.58. The lift distribution of the wing in example 5.5 44
Fuselage Center Line a. Fence over the wing b. Fence over the wing of General Dynamics F-16XL Figure 5.59. Example of a stall fence 45
1. Panavia Tornado GR4 with its long span flap (Courtesy of Antony Osborne) 46
2. Mikoyan-Gurevich MiG-29 with a low AR, and high sweep angle (Courtesy of Antony Osborne) 47
3. Piper Super Cub with strut-braced wing (Courtesy of Jenny Coffey) 48
4. Sailplane Schleicher ASK-18 with high AR (Courtesy of Akira Uekawa) Figure 5.60. Four aircraft with various wing characteristics 49
Ideal lift coefficient Wing setting angle Figure 5.61. Airfoil section NACA 66 2-415 Ideal lift coefficient 50
Lift coefficient 0.7 Lift distribution 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 y/s Figure 5.62. The lift distribution of the wing (AR = 7, = 0.3, t =0, i w =2 deg) 51
Lift coefficient 0.45 Lift distribution 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 y/s Figure 5.63. The lift distribution of the wing (AR = 7, = 0.8, t =-1.5, i w =1.86 deg) 52
C r = 1.78 m MAC = 1.608 m C t = 1.42 m C f = 0.32 m b f /2 = 3.375 m b/2 = 5.63 m a. Top view of the right half wing i w = 1.86 deg Horizontal Fuselage Center Line ( fus =0) b. Side view of the aircraft in cruising flight i w = 1.86 deg w = 8.88 deg Fuselage Center Line ( fus =7 deg) fus =7.02 deg Horizontal c. Side view of the aircraft in take-off Figure 5.64. Wing parameters of Example 5.6 53
C l C d Flap down f = 60 deg Flap up Flap up C m C m Re =6,000,000-24 -16-8 0 8 16 24 (deg) -1.2-0.8-0.4 0 0.4 0.8 1.2 1.6 16 24 C l Figure 5.65. Airfoil section NACA 2415 54