Question

A prop-driven aircraft is cruising with 90% propeller efficiency. If, range of aircraft is 7*10^6 ft, C=1.38*10^-7 s^-1 and L/D = 14 then what will be the fuel weight fraction for the cruise?

(a) 0.9216

(b) 0.9261

(c) 0.9289

(d) 0.9365

The question was asked by my college professor while I was bunking the class.

My doubt stems from Conceptual Sketch Sizing topic in portion Conceptual Sketch Sizing of Aircraft Design

Answer 1

Correct choice is (b) 0.9261

The best explanation: Given, a prop-driven aircraft,

Range R = 7*10^6 ft, C = 1.38*10^-7 s^-1, L/D =14

Here, propeller efficiency is 90% hence, η = 0.9

Now cruise weight fraction is given by range formula. For, prop-driven aircraft it is given by,

Wcruise / W0 = \(e^{\left(-\frac{R*C}{\eta*\frac{L}{D}}\right)}\) = \(e^{-(\frac{7 * 10^ 6* 1.38 * 10^ {-7}}{0.9*14})}\) = 0.9261.