The power of a gas generator is converted into thrust by accelerating a gas flow. Efficiency increases if more gas is accelerated to a lower velocity:

• Thrust of a jet engine is given by $$ F = \dot m * (v_e - v_0)$$ with $ \dot m$ = gas stream in kg/s, $v_e$ = exit velocity of the gas stream in m/s, and $v_0$ = aircraft air speed.
• The propulsion efficiency of a jet engine (with complete expansion) is defined as $$ \eta_p = \frac {2}{1 + v_e/v_0} $$

So for a given thrust, if $V_e$ is reduced and $\dot m$ proportionally increased, the propulsion efficiency increases.

Notes:

1. Complete expansion of the exhaust stream takes place if it does not reach the local speed of sound. If it does, it means there is a choked exhaust and part of the thrust is produced by higher pressure behind the exhaust. This can be accounted for by computing an effective $v_{e_{off}}$ that would produce the same thrust.
2. Propulsive efficiency is 1 = 100% if $v_e$ = $v_0$, but unfortunately there is no thrust anymore.

The gas generator is the core of the jet engine: the combination of compressor - combustor - turbine. The difference is in extraction of power by the turbine. If the turbine is larger, it can extract more power from the gas stream to drive the compressor + fan. If there is no bypass fan, less power is extracted from the gas flow by the turbine, and the exhaust speed is higher.

The power of a gas generator is converted into thrust by accelerating a gas flow. Efficiency increases if more gas is accelerated to a lower velocity:

• Thrust of a jet engine is given by $$ F = \dot m * (v_e - v_0)$$ with $ \dot m$ = gas stream in kg/s, $v_e$ = exit velocity of the gas stream in m/s, and $v_0$ = aircraft air speed.
• The propulsion efficiency of a jet engine (with complete expansion) is defined as $$ \eta_p = \frac {2}{1 + v_e/v_0} $$

So for a given thrust, if $V_e$ is reduced and $\dot m$ proportionally increased, the propulsion efficiency increases.

Notes:

1. Complete expansion of the exhaust stream takes place if it does not reach the local speed of sound. If it does, it means there is a choked exhaust and part of the thrust is produced by higher pressure behind the exhaust. This can be accounted for by computing an effective $v_{e_{off}}$ that would produce the same thrust.
2. Propulsive efficiency is 1 = 100% if $v_e$ = $v_0$, but unfortunately there is no thrust anymore.