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Burn Time from Propellant Load

Also known as burn time · how long will the engine fire · propellant duration · engine run time · burn duration from flow rate

tb=mpm˙t_b = \frac{m_p}{\dot m}

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

See also
Propellant Mass Flow Rate from Thrust and Isp — Where the flow rate in the denominator comes from, given thrust and Isp.Tsiolkovsky Rocket Equation — The propellant load here is exactly the m₀ − m_f that equation turns into delta-v.Rocket Thrust from Mass Flow — Thrust and burn time trade directly against each other at a fixed propellant load.

Learning zone

Propellant divided by flow rate. It is the simplest arithmetic on this page and it constrains more of a stage's design than anything else on it, because burn time is what the nozzle cooling, the tank structure, the guidance timeline and the trajectory shaping are all built around.

The number that goes in the numerator should be the USABLE propellant, not the tanked propellant, and the difference is not negligible. Every stage leaves residuals behind: liquid trapped in feed lines and pump volutes, ullage gas that was never liquid, a flight performance reserve held back against dispersions in engine output, and on a cryogenic stage the boil-off between loading and lift-off. One to three percent of the load is typical, and a burn time computed on the tanked figure is optimistic by exactly that much — which matters, because the last few seconds of an ascent burn are the ones that decide the orbit.

The constant-flow assumption behind the division holds well for a liquid engine at a fixed throttle setting and not at all for a solid motor. A solid burns from an exposed surface, and the shape of that surface changes continuously as the grain is consumed, so thrust follows a curve set by the geometry: a star-shaped core gives roughly constant thrust, a simple cylindrical bore gives thrust that rises steadily as the burning area grows. Solid motor design is largely the art of choosing a grain cross-section that produces the thrust-versus-time curve the mission wants, and no simple division describes it.

Typical durations are worth having in mind, because they explain the hardware. Launch vehicle first stages burn 120 to 180 seconds; upper stages run 300 to 500; a solid booster is often under 130. Those times are short enough that regenerative cooling — running the fuel through the chamber wall before burning it — can keep a chamber intact at 3500 K, and long enough that the same chamber would melt in seconds if the cooling failed. Burn time is the reason a rocket engine can be built out of metal at all.

Burn Time from Propellant Load
tb=mpm˙t_b = \frac{m_p}{\dot m}
mpṁtb
Where
  • tbt_b= Burn time (s)
  • mpm_p= Propellant mass (kg)
  • m˙\dot m= Propellant mass flow rate (kg/s)
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