Estimation of Lift Coefficient Prof. Rajkumar S. Pant Aerospace - PowerPoint PPT Presentation

Estimation of Lift Coefficient Prof. Rajkumar S. Pant Aerospace Engineering Department IIT Bombay AE-332M / 714 Aircraft Design Capsule-4

2-D and 3-D Lift Coefficient Source: Brandt et al., Intro. To Aeronautics: A Design Perspective, 2 nd ed, AIAA Education Series, 2004, pp 96 AE-332M / 714 Aircraft Design Capsule-4

Estimation of span efficiency factor e AR = Wing Aspect Ratio  t max = sweep of maximum thickness line = sweep at 30% of chord for low speed aircraft = sweep at 50% of chord for high speed aircraft Source: Brandt et al., Intro. To Aeronautics: A Design Perspective, 2 nd ed, AIAA Education Series, 2004, pp 107 AE-332M / 714 Aircraft Design Capsule-4

Concept of Absolute AoA  It is difficult to keep track of α L=0 in design  It is affected by aerofoil camber and twist distribution  Hence, we define Absolute AoA ( α a )  α a = α – α L=0  When Lift = 0, α a = 0  Max. AoA α max limited to ~15 deg  Take-off or Landing Considerations  Thus α a max = ( α max – α L=0 ) = (15 – α L=0 ) AE-332M / 714 Aircraft Design Capsule-4

ESTIMATION OF C L,MAX AE-332M / 714 Aircraft Design Capsule-4

Drivers of Max. Lift Coefficient  Wing geometry  Increase in Λ reduces C Lmax  Increase in AR increases C Lmax  Airfoil shape  Increase in t/c and L. E. radius increase C Lmax  Reynolds Number  Surface Texture  Interference from Fuselage, Pylons, Nacelles  T. E. Flap and/or L.E. Slat Geometry & Span  Larger chord and Span increase C Lmax  Swept Flaps have lower C Lmax AE-332M / 714 Aircraft Design Capsule-4

Flaps as High Lift Devices  Landing Setting  30 ≤ δ flap ≤ 60  C L,Land = C Lmax  Lower Landing Distance  Takeoff Setting  15 ≤ δ flap ≤ 30  C L,TO = 0.80 C Lmax  Better climb performance AE-332M / 714 Aircraft Design Capsule-4

Types of Flaps C Lmax = A C Lmax = 1.5A C Lmax = 1.6A C Lmax = 1.65A C Lmax = 1.9A Source: Brandt et al., Intro. To Aeronautics: A Design Perspective, 2 nd ed, AIAA Education Series, 2004, pg. 102 AE-332M / 714 Aircraft Design Capsule-4

Types of Flaps- 1/4 AE-332M / 714 Aircraft Design Capsule-4

Types of Flaps-2/4 AE-332M / 714 Aircraft Design Capsule-4

Types of Flaps-3/4 AE-332M / 714 Aircraft Design Capsule-4

Types of flaps- 4/4 AE-332M / 714 Aircraft Design Capsule-4

Typical Values of Max. Lift Coefficient  Unflapped wings  Swept wing ( Λ 0.25c = 60 o ) 0.75  Swept wing ( Λ 0.25c = 45 o ) 1.00  Unswept wing 1.50  Flapped Wings  Plain Flap 1.75  Slotted Flap 2.25  Fowler Flap 2.50  Double Slotted Flaps 2.75  Double Slotted Flaps and Slats 3.00  Triple Slotted Flaps and Slats 3.50  Blown Flaps ≈ 5.00 AE-332M / 714 Aircraft Design Capsule-4

Effect of Sweep on C L,max Source: Daniel P Raymer, Aircraft Design, A Conceptual Approach, AIAA Publications AE-332M / 714 Aircraft Design Capsule-4

Estimation of Wing C L,max General Cases Wings with low Λ 0.25c , AR > 5, λ ≈ 0.5, large flaps Wing C Lmax ≈ 0.9 Airfoil C Lmax Wings with partial span flaps         S S   flapped unflapped   C 0.9 C C L L L   max max S max S  flapped unflapped  ref ref AE-332M / 714 Aircraft Design Capsule-4

Flapped & Unflapped Area Source: Daniel P Raymer, Aircraft Design, A Conceptual Approach, AIAA Publications AE-332M / 714 Aircraft Design Capsule-4

Effect of LeX and Strakes For low AoAs, in which strakes are not effective AE-332M / 714 Aircraft Design Capsule-4

Effect of Horizontal Tail & Canard AE-332M / 714 Aircraft Design Capsule-4

Effect of Horizontal Tail & Canard     o C       21 c 10 3 z    L avg       h 1         0 725 . 7 AR l b h AE-332M / 714 Aircraft Design Capsule-4

Effect of High Lift Devices  Most Flaps increase α L=0 but don’t change C L α  Equivalent to increase in α a  For full span flaps,  α a3-D   α a2-D   α a2-D = increment in absolute AoA for airfoil   α a3-D = increment in absolute AoA for 3-D wing  For Partial Span Flaps,  α a =  α a2D (S f /S) Cos Λ h.l.  S f /S = Ratio of Flapped Area to Wing Ref. Area  Λ h.l. = Sweep of Flap Hinge Line  C Lmax, flapped = C Lmax, no flaps + C L α .  α a  Note:  α a-2D = 10 0 @ Takeoff, 15 0 @ Landing AE-332M / 714 Aircraft Design Capsule-4

Definition: Flapped Area Hinge Sweep Line AE-332M / 714 Aircraft Design Capsule-4

Example LIFT COEFFICIENT ESTIMATION AE-332M / 714 Aircraft Design Capsule-4

Lift Coefficient Estimation of F-16 AE-332M / 714 Aircraft Design Capsule-4

F-16 Aircraft Geometry AE-332M / 714 Aircraft Design Capsule-4

Useful Data for F-16  NACA 64 A -204 airfoil, c l α = 0.1 per degree  Sweep of Max. Thickness line = Λ tmax = 24 o  Max. Absolute AoA = 14 deg  Distance from the quarter chord of the main wing’s mean chord to the same point on horizontal tail, l h = 4.48 m  Wing taper ratio, λ = 1.07 m/5.03 m = 0.21  Height of center line of HT from Wing = 0.3048 m AE-332M / 714 Aircraft Design Capsule-4

Estimation of Wing Efficiency Factor  NACA 64 A -204 airfoil, c l α = 0.1 per degree  Λ tmax = 24 o  Calculate Wing and Tail aspect ratios 2 2 b 5.49 2 2 b 9.144       t AR 3 AR 3 t S 10.03 S 27.87 t  Estimation of span efficiency factor e 2 2   e          2 2 2 o 2 AR 4 AR ( 1 tan ) 2 3 4 9 1 ( tan 24 ) t max = .703 = e t AE-332M / 714 Aircraft Design Capsule-4

Estimation of Lift Curve Slope c l  C  = 0.0536 / o = C L  L t  57 3 . c l   1  e AR  S S  strake C C L ( with strake ) L ( without strake )   S  27.87 1.86 = (0.0536 / o ) = 0.0572 / o 27.87 AE-332M / 714 Aircraft Design Capsule-4

Estimation of Lift Curve Slope contd.     o C       21 c z 10 3    L  avg      h 1         0 725 . AR l 7 b h    o o      21 0.0572/ 3.048 m 10 3 (0.21) 0.3048 m      1 =     0.725 3 4.48 m 7 9.14 m = 0.48     S C C C L 1    t + ( whole aircraft ) ( with strake ) L L       t S = 0.0572 / o + 0.0536 / o (1-.48) (10.03/27.87) = .067 / o = 0.067 / o AE-332M / 714 Aircraft Design Capsule-4

Comparison of Lift Coefficient Slopes for various aircraft AE-332M / 714 Aircraft Design Capsule-4

Estimation of Max Lift Coeff. S       f cos = 4.9 o a a h l . .  S 2 D C Lmax = 0.067/ o (14 o +4.9 o ) = 1.27 for takeoff S       f cos = 7.36 o a a h l . .  S 2 D C Lmax = 0. 067 / o (14 o +7.36 o ) = 1.43 for landing AE-332M / 714 Aircraft Design Capsule-4

Military Aircraft DRAG ESTIMATION AE-332M / 714 Aircraft Design Capsule-4