Engine Performance and Matching Questions and Answers

Answer: C

The ratio for maximum propulsion efficiency is 1.0.

Propulsive efficiency, with flight speed \(V\) and exhaust velocity \(V_{e}\), is

\[ \eta_{p} = \frac{2V}{V + V_{e}} = \frac{2}{1 + V_{e}/V} \]

It rises toward 1 as \(V/V_{e}\) approaches 1, when no kinetic energy is left in the wake. At that point the thrust \(\dot{m}(V_{e} - V)\) is zero, which is why practical engines run below it, but the ratio for maximum efficiency is 1.0.

A ratio of 0 gives zero efficiency, 0.5 gives 2/3, and a ratio of 2 would mean the jet is slower than the aircraft, which produces drag rather than thrust.

Answer: C

The highest propulsive efficiency below Mach 0.5 belongs to the Turboprop engine.

Propulsive efficiency is roughly \(\eta_{p} = \frac{2}{1 + V_{e}/V_{0}}\): it is highest when the engine accelerates a large mass of air by a small amount, so the jet speed \(V_{e}\) is close to the flight speed \(V_{0}\). A propeller does exactly that, which is why turboprops dominate at low flight speeds.

A turbofan moves less air with a faster jet, and a turbojet even less air with a much faster jet, so both waste more kinetic energy in the exhaust at low speed. A ramjet produces no static thrust and works only at high speed, so it is the worst choice here.