Question

Which of the following is the correct integrated range equation of cruise method 2?

(a) R=\(\frac{1}{C}\Big(\frac{2W_i}{S_{\rho}}\Big)^{\frac{1}{2}}\frac{C_L}{C_D}2\Big(1-\omega^{\frac{-1}{2}}\Big)\)

(b) R=\(\Big(\frac{2W_i}{S_{\rho}}\Big)^{\frac{1}{2}}\frac{C_{L}^{0.5}}{C_D}2\Big(1-\omega^{\frac{-1}{2}}\Big)\)

(c) R=\(\frac{1}{C}\Big(\frac{2W_i}{S_{\rho}}\Big)^{\frac{1}{2}}\frac{C_{L}^{0.5}}{C_D}2\Big(1-\omega^{\frac{-1}{2}}\Big)\)

(d) R=\(\frac{1}{C}\Big(\frac{2W_i}{S_{\rho}}\Big)^{\frac{1}{2}}\frac{C_{L}^{0.5}}{C_D}2\Big(1-\omega\Big)\)

I had been asked this question during an internship interview.

Asked question is from Cruise Method 2 topic in chapter Cruising Performance of Aircraft Performance

Answer 1

The correct answer is (c) R=\(\frac{1}{C}\Big(\frac{2W_i}{S_{\rho}}\Big)^{\frac{1}{2}}\frac{C_{L}^{0.5}}{C_D}2\Big(1-\omega^{\frac{-1}{2}}\Big)\)

Explanation: The correct equation of cruise method 2 is R=\(\frac{1}{C}\Big(\frac{2W_i}{S_{\rho}}\Big)^{\frac{1}{2}}\frac{C_{L}^{0.5}}{C_D}2\Big(1-\omega^{\frac{-1}{2}}\Big)\) where R is range of the cruise, C is specific fuel consumption, S is span, ρ is density, CL is coefficient of lift, Cl/Cd is ratio of coefficient of lift to drag, Wi is initial weight and ω is fuel ratio.