Library / Aerospace / AER-07
Aerospace
Net thrust of a jet engine
Thrust from the momentum change of the air and fuel through an engine.
- Ref
- AER-07
- Rev
- v1
- Field
- Aerospace
- Result
- F [kN]
F in newtons. ṁ_a the intake air mass flow, ṁ_e = ṁ_a(1 + f) the exit mass flow including fuel, Ve exit velocity, V0 flight speed, pe and p0 exit and ambient pressure, Ae exit area. The calculator takes a pressure-matched nozzle, so the last term is zero.
A jet engine pushes the aircraft by throwing air backwards faster than it arrived. Thrust is the extra momentum given to each second’s worth of air and fuel.
Calculator
- Specific thrust F/ṁa362 N·s/kg
- Thrust power F·V04.525 MW
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Thrust falls with flight speed because the intake momentum is subtracted: a static engine gives the most thrust.
- Fuel flow adds a small bonus to the exit mass; ignoring it typically underestimates thrust by 1–3%.
- Efficiency is best when exhaust speed is close to flight speed, which is why turbofans move a lot of air slowly.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kN) | Local step | Change in result |
|---|---|---|---|---|---|---|
| ṁa Intake air flow | 5 to 500 kg/s | 1.81 | 181 | 179.2 | +10% | +10 % |
| Ve Exit velocity | 350 to 1,000 m/s | 5.35 | 38.5 | 33.15 | +10% | +16.9 % |
| V0 Flight speed | 0 to 300 m/s | 15.6 | 30.6 | 15 | +10% | −6.91 % |
| f Fuel-air ratio | 0.01 to 0.04 | 17.8 | 18.7 | 0.9 | +undefined% | — |
Sweep of Exit velocity
| Exit velocity (m/s) | Net thrust (kN) |
|---|---|
| 350 | 5.35 |
| 431.3 | 9.494 |
| 512.5 | 13.64 |
| 593.8 | 17.78 |
| 675 | 21.93 |
| 756.3 | 26.07 |
| 837.5 | 30.21 |
| 918.8 | 34.36 |
| 1,000 | 38.5 |
Sweep one variable
Variables and how each one contributes
Net thrust
What the equation gives you. Everything else feeds it.
Intake air flow
Air swallowed by the engine each second. Directly proportional.
Fuel-air ratio
Fuel mass per unit of air mass, typically 0.01–0.04. Adds fuel mass to the exhaust, a small positive effect.
Exit velocity
Speed of the exhaust relative to the engine. The most direct lever: thrust rises almost one-for-one with exit velocity.
Flight speed
Speed of the air entering the engine relative to it. Reduces thrust: the faster the aircraft flies, the less extra speed the engine can add.
Worked example with the values above
- Exit mass flow: ṁe = 50 × (1 + 0.02) = 51 kg/s.
- Momentum terms: 51 × 600 − 50 × 250 = 18,100 N.
- Net thrust 18.1 kN (pressure term zero).
Assumptions and limits
- Steady one-dimensional flow, one uniform exit.
- Pressure-matched nozzle (pe = p0).
- Speeds relative to the engine; ignores intake drag and installation losses.
Common mistakes
- Forgetting the intake momentum.
- Using exit velocity relative to the ground.
- Using this for a propeller engine without conversion.
Statistics and uncertainty
Thrust is a difference of two similar large quantities, so errors are magnified. With the exit term about 2.4 times the intake term, a 2% error in Ve becomes roughly a 3.4% error in thrust.
Where it is used
- Engine selection and thrust-lapse estimates.
- Missile and aircraft performance.
- Comparing turbojet and turbofan layouts.
Maths you need
- Momentum: mass × velocity
- Newton’s second law: force is the rate of change of momentum