When an aeroplane is flying at an airspeed which is 1.3 times its basic stalling speed, the coefficient of lift as a percentage of the maximum lift coefficient (CLmax) would be approximately:

• A. 75%
• B. 40%
• C. 90%
• D. 59%

Answer: (D)

When an aeroplane is in level flight, lift must balance weight. The stall speed is defined at the maximum lift coefficient, CLmax, so at stall V = Vs and CL = CLmax. The lift equation L = 0.5 ρ V^2 S CL shows that for a given weight (L = W) the required lift coefficient scales inversely with the square of the speed: CL ∝ W / (0.5 ρ V^2 S). Using the stall condition, you get the relationship CL/CLmax = (Vs / V)^2.

If the speed is 1.3 times the stalling speed, then CL/CLmax = 1 / (1.3)^2 ≈ 1 / 1.69 ≈ 0.59, or about 59%. So the coefficient of lift is roughly 59% of CLmax at 1.3 Vs.