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Methalox rocket engines (Liquid Methane and Liquid Oxygen) have theoretical specific impulse in the high 300's.

Hydrolox rocket engines (Liquid Hydrogen and Liquid Oxygen) have theoretical specific impulse in the mid 400's.

Is there a chemical propellant combination with performance better than Methalox but worse than Hydrolox?

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Is there a chemical propellant combination with performance better than Methalox but worse than Hydrolox?

There are, but there are no good combinations in that range.

Wikipedia's table lists a few things between methane/LOX at 3615m/s (369s) and hydrogen/LOX at 4462m/s (455s).

Of some note are pentaborane (B5H9) with LOX at 3758 m/s (383s) and diborane (B2H6) with LOX at 4016 m/s (409s); both are somewhat toxic, and can ignite in the presence of air.

Most fuels that work with LOX work a little better with liquid fluorine, so the common hydrocarbons that underperform methane with LOX will fall between methane/LOX and hydrogen/LOX using LF2 as an oxidizer, but doing so is dangerously impractical.

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    $\begingroup$ Dangerously impractical understates how dangerous and bad an idea liquid Fluroine. It makes the common hypergolics look safe. $\endgroup$ – geoffc Feb 18 '18 at 0:01
  • $\begingroup$ Yes... A good hypergolic pair of substances is hypergolic with each other and little else. Fluorine compounds tend to be hypergolic with far too many substances, including some commonly found in storage, plumbing, safety equipment or staff of the facilities. $\endgroup$ – SF. Feb 1 at 10:01
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If money is no problem, you can go for deuterium. It has about 90% of the specific impulse of hydrogen, while being twice as dense. It also appears to be ten times more expensive than hydrogen at the moment of writing.

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  • $\begingroup$ That's really neat! $\endgroup$ – ORcoder Sep 28 '18 at 19:07
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    $\begingroup$ Only 10x the price? That’s cheaper than I would have guessed. $\endgroup$ – Russell Borogove Sep 28 '18 at 19:55

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