To go deeper into the subject of propulsive effectiveness, we can consider the propulsive efficiency. Marine engineers call it the Froude efficiency after William Froude (1810-1879) who first used it. It is defined as the ratio of useful power output to the rate of energy input. For flight, propulsive efficiency is expressed as:
Its principal use for flight is to indicate that the various propulsion systems operate best in different speed ranges. This is shown qualitatively by figure 65.* The propeller is the most efficient propulsive method at low speeds, while the jet engine achieves best efficiency only at relatively high flight speeds. The very high exhaust velocities of the rocket make its propulsive efficiency high only at very high flight speeds. Figure 66, from an NACA figure of the 1950s, shows similar information in a slightly different way.
* Since thrust is the mass flow rate change in fluid velocity, propulsive efficiency is
where m is mass flow rate, Vj
, is exhaust jet velocity, and
Vo , is flight