Question

Aerodynamics:

3. Design an untwisted elliptical wing to fly at 200 km/hr in sea-level air with the fol- lowing specifications: lift- 45,000 N planform area-30 m2 wing span s 12m The absolute angle of attack au cannot exceed 12° to avoid stall. For the wing of min- imum induced drag, specify its aspect ratio, wing span, maximum chord, the design and the power required to compensate induced drag. If the wing span is limited to within 10 m, can a wing be designed to meet all other specifications? Explain.

Answer 1

Given that Untwisted Elliptical wing to fly at = 200 kn/hr lift = 45,000N planform area = 30m^2 wing Span lessthanorequalto 12m angle = 12 degrees = 200 times (1000/3600) = 55.5 m/s coefficient lift (C_L) C_L = L/1/2 rho v^2 s C_L = 4500/1/2 times 1.225 times (55.5)^2 times 30 C_L = 4500/56599.59 C_L = 0.795 Induced drag = 1/2 rho times v^2 SC_Di \r\n C_Di = C_1^2/pi times rho times AR wing span Efficiency (0.95 - 0.99) Aspect Ratio (AR) = b^2/3 = (1.2)^2/3 = 4.8 C_Di = (0.795)^2/pi times 0.99 times 4.8 = 0.632025/14.92884 C_Di = 0.042335 Now, D_i = 1/2 times 1.225 times (55.5)^2 times 30 times 0.042 D_i = 2395.2 Power required (p) p = D_i times v = 1/2 times rho v^2 times rho times C_Di times v p = 2395.2 times 55.5 \r\n p = 132.92 mu w Standard mean chod = s/b = 30/12 = 2.5m