Discussion
An aircraft has an empty weight fraction of \( 0.52 \), a fuel fraction of \( 0.26 \) and a payload of \( 20 \) t. Its take-off weight is
Answer: B
Correct answer: 91 t
The three fractions must sum to the whole, so
\[ W_0 = W_{payload} + \frac{W_e}{W_0}W_0 + \frac{W_f}{W_0}W_0 \]\[ W_0 = \frac{20}{1 - 0.52 - 0.26} = \frac{20}{0.22} \approx 91 \text{ t} \]Twenty tonnes of payload therefore demands a ninety-tonne aeroplane, because each tonne of payload drags with it structure and the fuel to carry both. That amplification is the central fact of aircraft sizing.
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