What does propulsive efficiency mean?
Answer:
It is a quantitative metric of the losses incurred by an energy conversion mechanism designed to convert other forms of energy in to kinetic and/or gravitational potential energy.
The less losses there are in proportion to the energy converted, the higher the efficiency is.
Losses include (but are not limited to) heating, electromagnetic emissions, acoustical emissions.
As I recall it is the ratio of the work done divided by the energy available. If the exhaust were to end up with no motion, you would have 100 percent propulsive efficiency, but you would not have much thrust.
Its been a long time since I did this calculation but here's the idea. You have an engine that is putting out exhaust at 1000 mph relative to the vehicle. This produces a particular thrust depending on the size of the engine. If the plane is standing still on the runway, the propulsive efficiency is zero, since no work is done on the plane and all the energy goes into the exhaust.
The closer the plane is to 1000 mph the higher the propulsive efficiency, because more of the energy is going into doing work (force x distance) and less is spent in motion of the exhaust.
However, high jet speeds give you high thrust, thus you have a trade off between propulsive efficiency and thrust. That is why propeller planes are more fuel efficient than jet engines, the speed of the exhaust is lower and more of the thrust goes into pushing the plane.
The various ducted fan type jet engines represent ways to try to get better propulsive efficiency and thus save fuel.
Now trying to put it into a formula
VJ is the jet speed going out the nozzle
AS is the aircraft speed
DV is the difference : VJ - AS
this is the speed of the exhause
its energy is proportional to DV squared
that energy goes to stirring up the atmosphere rather than pushing the vehicle
the energy available is proportional to VJ squared
the loss as a percent is their ratio (DV/VJ) squared
the efficiency is one minus (DV/VJ) squared
the loss is the kinetic energy of the exaust
(been a long time but thats as i recall)
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