Scaling Liquid Rocket Engines Up/Down in Size

(Last Updated 2 December 2012)

Notes:

This was developed to help me deal with scaling down real-life rocket engines into Kerbal Space Program scale, where Kerbals are half the size of humans, and thus everything is scaled down appropriately; e.g. a three-man command module in real life is 4m in diameter, but with Kerbals, it is 2m in diameter.

Rocket engine scaling is not linear – e.g. you can’t make an engine 50% smaller in dimensional parameters and then get 50% of the thrust. I used Glenn Research Center’s RocketThrust Simulator v1.5b, which you can use online (HERE) to carry out my experiments. I kept the same parameters for each run, scaling up and down the Throat Area for each run to see what effect that would have on engine thrust.

This should not be considered definitive; but more of a “rule of thumb” to give you an idea of what happens if you “rubber band” an existing engine to be a bit larger or smaller in dimensions.

I also used the evaluation copy of Rocket Propulsion Analysis, Standard Edition to develop the rubber banding rules for engine sizes related to chamber pressure.

(Raw Data gathered from RocketThrust Simulator v1.5b in Excel Format to help develop this scaling rule-of-thumbXLS in ZIP)

Rough Rules of Thumb:

Thrust Scaling
      Quadruple Thrust: Scale up size by a factor of 2 (200%)
      Double Thrust: Scale up size by a factor of 1.415 (141.5%).
      Half Thrust: Scale down size by a factor of 0.71 (71%)
      Quarter-Thrust: Scale down size by a factor of 0.5 (50%)

Dimensional Scaling:
      Quadruple Size: Scale up thrust by a factor of 16 (1,600%)
      Double Size: Scale up thrust by a factor of 4 (400%)
      Half Size: Scale down thrust by a factor of 0.25 (25%)
      Quarter Size: Scale down thrust by a factor of 0.0625 (6.25%)

Dimensional Rubber Banding

TScaled = S2

Where:

TScaled: Factor of difference in thrust that the scaled up or down engine gets over the baseline engine.

S: Factor that the engine is scaled against the baseline engine.

Example One:

We take an engine and scale it in all dimensions to be 0.5 times the size of the baseline (half-scale). The equation would be:

0.52 = 0.25

Thus our scaled-down engine would have 25% the thrust of the baseline engine.

Example Two:

We take an engine and scale it in all dimensions to be 1.5 times the size of the baseline. The equation would be:

1.52 = 2.25

Thus our scaled-up engine would have 225% the thrust of the baseline engine.

Chamber Pressure Rubber Banding

In Vacuum (0~ PSI)

In a virtual vacuum chamber pressure and thrust march in lockstep, e.g. if you want to increase thrust by 25%, you increase chamber pressure by 25%, and vice versa – if you want to reduce thrust by 50%, you’d cut chamber pressure by 50%. Also, chamber pressure has no effect on ISP.

The reason why upper stage engines such as RL10 have moderate chamber pressures of 300 psia, instead of going for 100~ psia or lower is for two reasons:

  1. So that they can function (relatively) deep into the atmosphere, which makes them more useful than a straight up engine which can only function in absolute vacuum.

  2. A higher chamber pressure means a smaller overall engine, meaning you can fit them into dimensionally constrained upper stage shroud diameters, or cluster them for said applications; which overcomes the increased cost of the higher chamber pressure specification.

For a crude rule of thumb scaler that works with Throat Diameter, Nozzle Diameter, and Nozzle Lengths; use this:

PScaled = S-0.4968

Where:

PScaled: Factor of difference in chamber pressure that the scaled up or down engine gets over the baseline engine.

S: Factor that the engine is scaled against the baseline engine.

Example One:

We take an engine and increase it’s chamber pressure to be 2.5 times that of the baseline engine while keeping thrust constant. The equation would be:

2.5-0.4968 = 0.634

Thus some of our higher pressure engine’s dimensions would be 63.43% the size the baseline engine’s dimensions.

This means that if you had a hypothetical rocket engine with a chamber pressure of 100 psia and a nozzle diameter of 100 inches; if you increased the chamber pressure by 2.5x; the 250-psia engine would have a nozzle diameter of 63.43 inches.

At Sea level (14.7~ PSI)

Too complicated to rubber band with a simple equation. Get an actual program that analyzes rocket propulsion elements and use that to rubber band.

Expansion Ratio Dimensional Rubber Banding

Nozzle Length Scaler

RatioScaled = 0.992 * S0.536

Thus if we change our Expansion Ratio to be 50% that of the baseline, our Nozzle length scales down to be:

0.992 * 0.50.536 = 68.4% the size of the baseline

Nozzle Exit Diameter Scaler

RatioScaled = S0.483

Thus if we change our Expansion Ratio to be 200% that of the baseline, our Nozzle Exit Diameter scales up to be:

20.483. = 139% the size of the baseline