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The SpaceX Raptor uses a 78:22 O2:CH4 ratio. It also has combustion chamber pressures higher than any other rocket engine ever built.

My questions are:

  • What's the math / chemistry that determines what ratio optimizes Isp?
  • How much does combustion chamber pressure matter in determining what the optimal O2:CH4 is?
  • Can we raise Isp by running more CH4 rich in combustion chambers of higher pressure?
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  • $\begingroup$ Partial duplicate addressing the first question: Merlin engine stoichiometry $\endgroup$ – Russell Borogove Dec 31 '20 at 18:52
  • $\begingroup$ Here's an explanation of the Isp equation. On the one hand, the chemical makeup terms $R_{gas}$ and $k$ are independent of the pressure and temperature terms, but on the other hand, the chemical makeup of the exhaust will change with different characteristics in the combustion chamber. I suspect that hotter & higher pressure chambers favor leaner mixes up to complete combustion (because the heat can dissociate the exhaust products), but engines are limited by cooling constraints. $\endgroup$ – Russell Borogove Dec 31 '20 at 23:53
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This doesn't have a simple answer.

From a pure chemistry standpoint you can observe that one CH4 molecule will completely react with two O2 molecules. CH4 has a molecular weight of 16, O2 has a molecular weight of 32. Thus you need 4x as much O2 by weight.

However, there are two other factors involved:

  1. You can actually end up with more thrust with a bit of unburned fuel in the exhaust--what counts is velocity, not energy, and the lower molecular weight can help. I think it's only relevant for hydrolox but I'm not sure.

  2. Very hot oxygen is an extremely powerful oxidizer. You do not want it touching your engine anywhere or you're liable to end up with I have seen beautifully described as engine-rich exhaust. This is a matter of the physics of the engine as opposed to one of chemistry. You must add enough extra fuel to ensure the safety of the engine even if this lowers the performance of the rocket.

Note that if you care about your engine this means you always must ensure that the oxygen shuts down before the fuel does. (If you're simply going to discard the stage at that point it doesn't matter, but if you plan to relight, or plan to recover the engine it does.)

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