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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.

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. Correct Answer 2.0

Given, fuel fraction =0.937 For supersonic aircraft accelerating from 0.1M, fuel fraction is given by, Fuel fraction = 0.991 – 0.007M -0.01M2. 0.937 = 0.991 – 0.007M -0.01M2. 0.01M2 + 0.007M -0.054 = 0. Now, dividing by 0.01 then, M2 + 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.

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