Momentum plus (p_e − p_0) A_e
Across a control volume around the engine, net thrust is the outgoing minus incoming stream momentum, plus the unbalanced pressure force at a non-ideally expanded exit: F = ṁ_a ((1+f) u_e − u_0) + (p_e − p_0) A_e, with f = ṁ_f / ṁ_a. A static, perfectly expanded engine with 50 kg/s of air, 600 m/s of exit speed, and f = 0.02 therefore makes 30,600 N, and TSFC is ṁ_f / F. TSFC is reported in kg/(N·s) and in the aviation unit (lbm/h)/lbf.
This identity does not invent an exit speed from chamber conditions — for a nozzle thrust coefficient from chamber pressure and area ratio, see the C-D nozzle page. For an ideal cycle efficiency, see the Brayton cycle calculator. For Isp and a rocket mass flow, see specific impulse.
Sources
- Hill and Peterson, Mechanics and Thermodynamics of Propulsion.
- Mattingly, Elements of Propulsion; Cumpsty, Jet Propulsion.
- TSFC as fuel-mass-flow per unit thrust.
Frequently asked questions
What if I do not know the fuel/air ratio?
Enter a fuel mass flow instead, or leave both blank to compute a cold-jet (f = 0) thrust.
When is the pressure term zero?
When the nozzle is perfectly expanded (p_e = p_0) or when you omit the pressure and area inputs.
Is a negative TSFC meaningful?
Only if the computed “thrust” were negative (a net drag). Check that the exit speed is larger than the flight speed for a jet that is actually producing thrust.