What is the ratio of Liquid Hydrogen to LOX

[Spaced Out]

Just curious because playing KSP made me curious about the ratio.

[Gaarst]

The stoichiometric ratio is 8:1 (LOX to LH mass), but having excess hydrogen in the exhaust increases the specific impulse of the engine, so in practice it will be lower. It differs for different engines, but it's usually between 5:1 and 7:1.

• 5:1 for the HM7B, CE-20 and LE-5
• 5.5:1 for the J-2 and YF-77
• 5.5 to 5.9:1 for the RL-10
• 5.9:1 for the LE-7
• 6:1 for the RS-25, RS-68, RD-0120 and YF-75D
• 6.7:1 for the Vulcain 2

Note that liquid hydrogen tanks are usually much larger than liquid oxygen tanks because the latter is much denser.

Edited August 17, 2017 by Gaarst

[magnemoe]

4 hours ago, Gaarst said:

The stoichiometric ratio is 8:1 (LOX to LH mass), but having excess hydrogen in the exhaust increases the specific impulse of the engine, so in practice it will be lower. It differs for different engines, but it's usually between 5:1 and 7:1.

Yes, note that the hydrogen in an nuclear thermal engine is not much hotter than an h2+o2 engine, however as you only use H2 who moves faster than oxygen or water at same temperature the isp is far higher. 

[sevenperforce]

The other reason to have excess hydrogen in the exhaust is to incorporate unburned propellant, thus providing a heat sink to control the reaction temperature. Even a regeneratively cooled combustion chamber will melt to slag in any extended burn if its reactants are pure-stoichiometric. With other propellant combinations, you can run ox-rich for the same effect if running fuel-rich would result in coking. Of course then you're dealing with hot oxygen, which is kind of like using cocaine to wean someone off of caffeine, but oh well.

It should also be noted that changing your mixture ratio during flight can be very beneficial. You can start oxygen-rich for extra thrust and then transition to fuel-rich for better specific impulse as your need for thrust decreases.

[DerekL1963]

15 minutes ago, sevenperforce said:

Of course then you're dealing with hot oxygen, which is kind of like using cocaine to wean someone off of caffeine, but oh well.

Quoted because I simply must point out how absurd and true this is.

[tomf]

You can work out the stoichiometric ratio for LH/LOX pretty easily

The reaction is 2H₂+O₂->2H₂O so for every molecule of oxygen you need 2 of hydrogen. A molecule of Oxygen weighs 32 and a molecule of hydrogen weighs 2 (from their atomic weighs) so the mass ratio is 8-1

[Iskierka]

It's actually not true that adding more LH2 improves specific impulse. Because of how energetic the LH2-LOx reaction is, the reaction fails due to being too hot when stoichiometric, limiting out at around 3600-3800K, but with pretty much the exact same impulse as a 5.5:1 fuel-rich engine. Because of the reaction stopping, there's actually a very wide range of fuel mixes with basically identical impulse, the advantage to fuel-rich being that the excess hydrogen keeps it cooler for the same impulse - the 5.5:1 engine might be under 2600K, making it much easier to cool and otherwise manage. The impulse gets a flat range because yes, a lighter exhaust is faster for the same temperature, but you lose temperature at a balanced rate as you add hydrogen, so it doesn't provide any extra performance.

For fun (or disappointment knowing we can't do it), note that if the reaction didn't fail at high temperature, LH2-LOx would be capable of towards 570 seconds stoichiometric. It'd also be on the order of 6700K chamber temperature, so good luck holding the engine together, but if you can solve the cooling it would be outstanding. More energy adds more than throwing in light material - it just balances out with hydrolox due to the temperature-limited reaction, making the energy unavailable.

The alternative choice, which in the above list from Gaarth you can see that modern engines start to prefer, is that if you mix in more oxidizer and accept the increased heat, you significantly improve overall propellant density, allowing smaller tankage. Hydrogen isn't dense at all, so using relatively large amounts increases the overall size of the tank for the fuel mass to get your dV. Using less, and more dense oxygen instead, small tanks that are easier to manage, and potentially lighter. As such you see the Vulcain 2, the most modern first-stage engine, where it makes the most difference, pushing all the way to 6.7:1. Note that the flat range of equal Isp for all mixtures only applies when fuel-rich, however; it's another property of hydrogen being light that it can cool the mixture and keep high Isp. Heavy oxygen doesn't work, so the goal is to push towards stoichio, and ideally leave it there for maximum propellant density.

As for nuclear thermal rockets, they're not just somewhat cooler, they're significantly cooler - even 1500K would be very hot. They still get high Isp due to how light hydrogen is, and that they can get that temperature with no need for a fuel reaction at all - therefore they can push the equivalent ratio to infinity fuel:oxidizer, without losing energy.