Question

Which of the following indicates the range formula in cruise method 3?

(a) R=\(\frac{1}{C}\Big(\frac{2}{\rho SC_L}\Big)^{\frac{1}{2}}\int_{W_i}^{W_f}\frac{dW}{W^{\frac{1}{2}}}\)

(b) R=\(\Big(\frac{2}{\rho SC_L}\Big)^{\frac{1}{2}}\frac{L}{D}\int_{W_i}^{W_f}\frac{dW}{W^{\frac{1}{2}}}\)

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

This question was addressed to me in an interview for job.

The origin of the question is Cruise Method 3 in portion Cruising Performance of Aircraft Performance

Answer 1

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

The explanation is: The correct equation of cruise method 3 is R=\(\Big[\frac{V_{mdi}}{C}E_{max}\Big]2u_i\Big\{tan^{-1}\Big[\frac{1}{u_{i}^2}\Big]-tan^{-1}\Big[\frac{1}{\omega u_{i}^2}\Big]\Big\}\) where R is range of the cruise, C is specific fuel consumption, Emax is endurance, Vmdi is relative airspeed and ω is fuel ratio.