Jet Propulsion/Propulsive efficiency

The propulsive efficiency is defined as:

$\eta _{p}={\frac {PropulsiveWorkDeliveredToVehicle}{MechanicalWorkGeneratedByEngine}}$

The mechanical work generated by the engine is crudely split between the work difference between the input and exit mass flows from the engine as well as to the work imparted to the vehicle. For a jet engine in the air frame of reference the input mass flow has zero kinetic energy. Thus for a jet engine with a constant relative exit velocity (a close approximation of a turbojet) the propulsive efficiency increases with aircraft velocity.

Mathematically the propulsive efficiency :

$\eta _{p}={\frac {2u_{0}}{u_{e}+u_{0}}}$

where

$u_{0}=$ velocity of the vehicle

$u_{e}=$ velocity of the exhaust

Thus reducing the exhaust velocity will give a higher propulsive efficiency. The thrust of the engine is given by

$F={\dot {m}}(u_{e}-u_{0})$

where ${\dot {m}}$ is the mass flow through the engine. Thus to for a given thrust the exhaust velocity can be decreased if the mass flow is increased. This is usually done by adding a fan or a propeller to the turbojet, resulting in a turbofan or turboprop engine. The reduction in exhaust velocity also reduces the exhaust noise, but has the disadvantage that the thrust reduces more markedly with speed than for a turbojet.