Question

If supersonic aircraft has fuel fraction of 0.937 as climb and accelerating segment fuel fraction then, find the cruise mach number. Consider aircraft is accelerating from 0.1M.

(a) 2.0

(b) 30.5

(c) 5

(d) 1.4

The question was posed to me in an online interview.

I want to ask this question from Rubber-Engine Sizing topic in section Initial Sizing of Aircraft Design

Answer 1

Right option is (a) 2.0

Explanation: Given, fuel fraction =0.937

For supersonic aircraft accelerating from 0.1M, fuel fraction is given by,

Fuel fraction = 0.991 – 0.007M -0.01M^2.

0.937 = 0.991 – 0.007M -0.01M^2.

0.01M^2 + 0.007M -0.054 = 0.

Now, dividing by 0.01 then,

M^2 + 0.7M -5.4 = 0.

Hence, by solving above equation,

M = 2.0 or M = -2.7. Since Mach number cannot be negative, answer is 2.0.