Question

Which of the following is the correct integrated range equation of cruise method 3?

(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=\(\frac{V}{C}\int_{W_i}^{W_f}\frac{dW}{D}\)

(c) R=\(\Big[\frac{V_{mdi}}{C}E_{max}\Big]2u_i\Big\{tan^{-1}\Big[\frac{1}{u_{i}^2}\Big]-tan^{-1}\Big[\frac{1}{\omega u_{i}^2}\Big]\Big\}\)

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

I have been asked this question in semester exam.

My doubt is from Cruise Method 3 topic in division Cruising Performance of Aircraft Performance

Answer 1

Correct choice is (c) R=\(\Big[\frac{V_{mdi}}{C}E_{max}\Big]2u_i\Big\{tan^{-1}\Big[\frac{1}{u_{i}^2}\Big]-tan^{-1}\Big[\frac{1}{\omega u_{i}^2}\Big]\Big\}\)

To elaborate: The correct equation of cruise method 3 is R=\(\frac{V}{C}\int_{W_i}^{W_f}\frac{dW}{D}\) where R is range, V is velocity, C is specific fuel consumption, D drag and Wf, Wiare final and initial weights.