15.2 Engine performance — thrust, power, SFC, efficiencies and ratings (with worked examples)

Scope

B1 only, level 2 (not examined for category A): gross thrust, net thrust, choked-nozzle thrust, thrust distribution, resultant thrust, thrust horsepower, equivalent shaft horsepower, specific fuel consumption; engine efficiencies; bypass ratio and EPR; pressure, temperature and velocity of the gas flow; ratings, static thrust, effects of speed, altitude and hot climate, flat rating, limitations. Expect calculation questions.

Thrust definitions

Term	Formula (SI)	Meaning
Momentum (gross) thrust	ṁ × V_j	Thrust from the jet alone
Ram (intake momentum) drag	ṁ × V_a	Momentum of the air taken in at flight speed
Net thrust	ṁ (V_j − V_a) + A_j (P_j − P_a)	Gross thrust minus ram drag (plus pressure thrust)
Pressure thrust	A_j × (P_j − P_a)	Extra thrust when the nozzle is choked and exit pressure P_j exceeds ambient P_a

where ṁ = mass flow (kg/s), V_j = jet velocity, V_a = aircraft (inlet) velocity, A_j = nozzle exit area, P_j = static pressure at the nozzle exit.

Static thrust: with the aircraft stationary V_a = 0, so net thrust = gross thrust.

Choked nozzle: in a convergent nozzle the gas cannot exceed Mach 1 at the throat. Once the nozzle pressure ratio exceeds the critical value (about 1.85–1.9 for exhaust gas), the nozzle is choked: velocity stays at sonic and the remaining pressure energy appears as pressure thrust over the nozzle area.

Worked example 1 — net thrust with a choked nozzle: ṁ = 80 kg/s, V_a = 150 m/s, V_j = 550 m/s, A_j = 0.3 m², P_j − P_a = 20 kPa. Momentum thrust: 80 × (550 − 150) = 32,000 N. Pressure thrust: 0.3 × 20,000 = 6,000 N. Net thrust = 38,000 N (38 kN). Gross thrust = 80 × 550 + 6,000 = 50,000 N; ram drag = 80 × 150 = 12,000 N; 50,000 − 12,000 = 38,000 N (check).

FAA imperial form: F = Ms (V2 − V1) ÷ g (lb, ft/s, g = 32.2 ft/s²).

Thrust distribution and resultant thrust

Thrust is the resultant of forward and rearward gas loads acting on all engine components. Typically the compressor, diffuser and combustion chamber experience large forward forces (pressure rises / gas accelerated against them), while the turbine and exhaust nozzle experience rearward forces. The net (resultant) of all of these is the engine's thrust, transmitted to the aircraft through the engine mounts / thrust bearing (the location ball bearing on each spool).