Chemical propulsion

Draft

Every vehicle that has reached orbit has done so on chemical propulsion. The choice of propellant combination is the earliest and least reversible decision in a vehicle programme, because it fixes tank volume, engine cycle, ground infrastructure and operability all at once.

Where the energy comes from

Chemical propulsion converts the enthalpy of a combustion reaction into directed kinetic energy. The ideal exhaust velocity from an energy balance is

Ideal exhaust velocity

v_e = \sqrt{\frac{2\gamma}{\gamma-1}\cdot\frac{R_u T_c}{M}\left[1 - \left(\frac{p_e}{p_c}\right)^{(\gamma-1)/\gamma}\right]}

The term that matters is $T_c/M$ : chamber temperature over the mean molecular mass of the exhaust. Performance goes as the square root of that ratio.

This explains an otherwise puzzling fact. Hydrogen and oxygen do not release the most energy per kilogram of any practical combination, but hydrolox has the highest specific impulse by a wide margin, because its exhaust is mostly water and unburned hydrogen with a very low molecular mass. Engines are deliberately run fuel-rich, at a mixture ratio near 6:1 rather than the stoichiometric 8:1, accepting a lower flame temperature in exchange for lighter exhaust. The molecular mass term wins.

The combinations

Combination	Vacuum $I_{sp}$	Bulk density	Mixture ratio	Character
LOX / LH₂	430 to 465 s	0.36 g/cm³	~6:1	Highest $I_{sp}$ , worst density, deep cryogen
LOX / CH₄	355 to 380 s	0.83 g/cm³	~3.6:1	Mild cryogen, clean burning, reusable
LOX / RP-1	330 to 350 s	1.03 g/cm³	~2.6:1	Dense, well understood, cokes
N₂O₄ / MMH	315 to 340 s	1.19 g/cm³	~1.65:1	Storable, hypergolic, highly toxic
Solid (APCP)	265 to 295 s	1.80 g/cm³	premixed	Simplest, densest, cannot be shut down
Hydrazine monopropellant	220 to 235 s	1.00 g/cm³	none	Single fluid, catalytic decomposition
Cold gas	60 to 80 s	varies	none	Trivially simple, negligible performance

Representative flight engines: RL10B-2 at 465.5 s is the highest specific impulse of any production engine ever flown; RS-25 delivers 452 s in vacuum; Merlin 1D vacuum 348 s; Space Shuttle SRB 268 s.

Density impulse decides first stages

Specific impulse is the wrong figure of merit for a booster. A first stage is volume-limited as much as mass-limited, because tank structure scales with volume and a bulkier propellant means a larger, heavier and higher-drag vehicle. The relevant quantity is density impulse, specific impulse multiplied by bulk density:

Combination	$I_{sp}$	Density	Density impulse
LOX / LH₂	450 s	0.36	162
LOX / CH₄	370 s	0.83	307
LOX / RP-1	340 s	1.03	350
N₂O₄ / MMH	330 s	1.19	393
Solid	270 s	1.80	486

The ordering reverses completely. Hydrogen has the best specific impulse and by far the worst density impulse; solids have the worst specific impulse and the best density impulse.

That inversion explains the observed pattern of vehicle design. Strap-on boosters are solid, because for the first thirty seconds nothing matters except delivering enormous thrust from a small package. First stages are kerolox or methalox. Upper stages, where the vehicle is already fast and high and volume is cheap, are hydrolox. A hydrogen first stage is possible, as the Delta IV demonstrated, but it needs an enormous tank and had poor liftoff thrust-to-weight, which is why it was usually flown with solid augmentation.

Storability and handling

Performance is only half the selection criterion. The other half is what the propellant does when you are not using it.

Deep cryogens: Liquid hydrogen boils at 20 K and liquid oxygen at 90 K. Both boil off continuously, so tanks must be topped until moments before launch and cannot be held loaded. Hydrogen also embrittles metals and leaks through seals that hold every other fluid.
Mild cryogens: Liquid methane boils at 112 K, close enough to liquid oxygen that both can share a common bulkhead and similar insulation. Boil-off is far more manageable, which matters for in-space storage.
Storable propellants: Hypergolics remain liquid at room temperature indefinitely. This is why they dominate satellite propulsion and why every missile derived vehicle uses them.
Solids: Cast once and stored for years, ready to fire on command. The trade is absolute: once ignited, a solid motor cannot be throttled, shut down or restarted.

Hypergolic propellants ignite on contact with no ignition system at all, which removes an entire failure mode from a restartable in-space engine. The price is that MMH and UDMH are carcinogenic and N₂O₄ is acutely toxic and corrosive. Ground handling requires self-contained atmospheric protective ensembles, and the operational overhead is one reason new designs avoid them where a cryogen will do.

Why methane won

Nearly every clean-sheet launch vehicle designed since about 2012 burns methane: Raptor, BE-4, Vulcain successor studies, Prometheus, ZQ-2. Four reasons, none of which is specific impulse alone.

It does not coke. RP-1 deposits carbon when heated in regenerative cooling channels, which fouls the passages and limits how many times an engine can be flown without teardown. Methane burns clean, so an engine can be reused far more times between inspections. For a reusable booster this is decisive; see Reusable launch systems.

The density is workable. At 0.83 g/cm³ bulk it is well clear of hydrogen’s 0.36, so tanks stay a reasonable size while specific impulse improves 30 s over kerosene.

It is a mild cryogen. Methane and oxygen have similar enough boiling points to share insulation and a common bulkhead, simplifying the vehicle and making long-duration in-space storage plausible. That matters for propellant depots.

It can be manufactured on Mars. The Sabatier reaction combines Martian atmospheric CO₂ with hydrogen to produce methane and water, and electrolysing the water yields the oxygen. A methalox vehicle can in principle refuel for the return trip; a kerolox one cannot. See Mars.

Solid motors

A solid motor is a case packed with a cast grain of oxidiser, fuel and binder, typically ammonium perchlorate with aluminium powder in a hydroxyl-terminated polybutadiene matrix.

Thrust is set by burning surface area, and the grain cross-section is designed to produce the desired thrust profile: a star-shaped bore gives high initial thrust that tapers, a circular bore gives thrust that rises as the bore widens. The Shuttle SRBs used a tapered star to reduce thrust through max dynamic pressure.

The advantages are density, simplicity, storability and very high thrust-to-weight. The disadvantage is singular and severe: there is no off switch. Once the grain ignites it burns to completion. A solid motor cannot be shut down, cannot be throttled meaningfully, and cannot be tested before flight without consuming the article. Every crewed vehicle that has used solids has had to design an abort system around this fact.

References

Sutton, G. P. and Biblarz, O. Rocket Propulsion Elements, 9th ed., Wiley, 2017, chapters 5, 7 and 12.
Huzel, D. K. and Huang, D. H. Modern Engineering for Design of Liquid-Propellant Rocket Engines, AIAA, 1992.
Clark, J. D. Ignition! An Informal History of Liquid Rocket Propellants, Rutgers University Press, 1972. The definitive account of propellant selection, including the ones that did not work.
Gordon, S. and McBride, B. J. “Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications”, NASA RP-1311, 1994. The CEA code, still the standard tool for theoretical performance.