Question

A jet aircraft is cruising at 12000ft. What will be the cruise leg (mission phase ‘n’) weight fraction?

(a) Wn/Wn-1 = \(e^{\left(-\frac{R*C}{V*\frac{L}{D}}\right)}\)

(b) Wn/Wn+1 = \(e^{\left(-\frac{R*C}{V*\frac{L}{D}}\right)}\)

(c) Wn/Wn-2 = \(e^{\left(-\frac{R*C}{V*\frac{L}{D}}\right)}\)

(d) Wn/Wn-1 = \(e^{\left(-\frac{R*C}{V*\frac{L}{D}}\right)}\)

This question was addressed to me in an international level competition.

Enquiry is from Conceptual Sketch Sizing in section Conceptual Sketch Sizing of Aircraft Design

Answer 1

The correct answer is (a) Wn/Wn-1 = \(e^{\left(-\frac{R*C}{V*\frac{L}{D}}\right)}\)

Easiest explanation: Aircraft is cruising at 12000ft and the cruise mission leg is nth mission phase of whole mission profile. Here, we will use Breguet range formula to find Weight fraction. Breguet range formula,

R = (V/C) * (L/D) * ln (Wn-1/ Wn)

Now by re-arranging, cruise mission leg weight fraction is,

Wn/Wn-1 = \(e^{\left(-\frac{R*C}{V*\frac{L}{D}}\right)}\)