Discussion
Using the Breguet equation with \( V = 250 \) m/s, \( c = 1.7 \times 10^{-4} \) per second, \( L/D = 18 \) and a weight ratio of \( 1.4 \), the range is nearest to
Answer: D
The Breguet range equation for a jet is \[ R \;=\; \frac{V}{c}\,\frac{L}{D}\,\ln\!\frac{W_1}{W_2}. \] Taking the logarithm first, \( \ln 1.4 = 0.336 \). Then \[ \frac{V}{c} \;=\; \frac{250}{1.7 \times 10^{-4}} \;=\; 1.47 \times 10^{6}\ \text{m}, \] and multiplying by the remaining two factors, \[ R \;=\; \left(1.47 \times 10^{6}\right)\left(18\right)\left(0.336\right) \;=\; 8.9 \times 10^{6}\ \text{m} \;=\; 8900\ \text{km}. \] Note the units: \( V/c \) has the dimensions of a length, so the whole expression comes out in metres and must be divided by a thousand. A specific fuel consumption of \( 1.7 \times 10^{-4} \) per second is about 0.6 lb per lbf per hour, which is typical of a cruising turbofan. The logarithm means that doubling the fuel fraction does far less than double the range.
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