How nozzle thrust and specific impulse are calculated
A rocket nozzle turns hot, high-pressure gas into fast exhaust. Chamber pressure and throat area set the mass flow through the characteristic velocity c*; how far the gas expands before it leaves the nozzle sets the exhaust velocity. EngBench treats the flow as one-dimensional and isentropic, the standard first-pass model.
- Characteristic velocity:
c* = √(R·Tc) / Γ - Mass flow:
ṁ = Pc·At / c* - Thrust:
F = ṁ·Ve + (Pe − Pa)·Ae - Specific impulse:
Isp = F / (ṁ·g₀)
Worked example: kerosene booster engine
A LOX/RP-1 engine at 70 bar with a 250 mm throat, expanding to 0.7 bar, flows 196 kg/s with a c* of 1,754 m/s. The expansion ratio is 11.4 and the exit Mach number 3.43. At sea level it makes 543 kN with an ideal Isp of 283 s.
Good to know
- Thrust peaks when the exit pressure equals ambient. A sea-level engine is slightly over-expanded at launch and under-expanded higher up.
- If exit pressure drops below about 40% of ambient, the flow separates from the wall. That causes side loads and unsteady thrust, so upper-stage nozzles can't fire at sea level.
- Real engines deliver about 92–98% of ideal performance, losing some to combustion efficiency, divergence and the boundary layer.
- Pro adds sea-level and vacuum performance, a divergence correction for conical and bell nozzles, and thrust across the climb.