Liquid Propellant Primer

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When somebody online asks the question “what’s the best liquid rocket propellant mix”, you are bound to hear a preposterous amount of b*llshit flying as everybody tries to champion their favorite mix, refusing to heed the opposition’s remarks.

“It’s Hydrolox without a doubt”, says a boring square who really never got over STS, “look at that absolute unit of a specific impulse.”.

“Nothing holds a candle to Methalox”, says a pimply-faced kid who does unspeakable things at night with a picture of a certain African-American billionaire, “it’s the hottest sh*t going around today, and it’s also really damn cheap.”.

“Bollocks”, says a man who was already old when Gagarin went up, “what you really need is density impulse, and Kerolox’ll give you that.”.

“You’re all wrong”, says yet another figure in a thick Russian accent, trailing ice crystals and the smell of cheap vodka, “look no further than Hypergolics, good specific and density impulses, and they’re really easy to work with.”.

At this point the situation starts degenerating pretty badly, and it won’t take long before you have Hugo Boss-wearing vegetarians proposing Ethanol in liquid Oxygen just because the Germans did, or somebody asking you to dilute liquid Fluorine in your Oxygen, just try it, and some utter lunatic asking you to run a dynamic-mixture Kero-Hydro-Lox tripropellant rocket like the people in old country did when vodka was cheap and communism plenty and, by the time some smart-ass mentions the yanks actually fired a rocket burning Lithium in Fluorine and then added Hydrogen until satisfied, back when the cocaine rained like snow in the offices of Rocketdyne, I am about to get an actual unironic aneurysm.

The reality is that the question itself is terribly flawed - there is no all-around best liquid rocket propellant mix; rather, you have several mixes with different strengths and weaknesses, and an important part of designing your very own rocket is to choose the mix that works better for your use case.

Measures of merit for rocket propellants

Broadly speaking, one can pinpoint four main measures of merit in the choice of a liquid rocket propellant mix:

1. Specific Impulse
2. Density Impulse
3. Handling Concerns
4. Cost

The first one, specific impulse, simply refers to how much a kilogram of mix can kick you downrange - an extremely important parameter for a very simple reason: the rocket equation shows how the final velocity change of your rocket depends linearly on your specific impulse and logarithmically on your mass ratio, so doubling your specific impulse doubles the total velocity change you can make while doubling your mass ratio not so much.

The second one, density impulse, is merely specific impulse times the specific gravity of the propellant mixture, and is an extremely underrated measure of merit as far as rocket propellants in popular knowledge are concerned: propellant tanks, unfortunately, are not massless nor of negligible drag and, being stuck with a low density-impulse propellant, you risk ending up in a situation where you just can’t achieve the mass ratio you need for your mission because the tanks cut so much into your payload margin it ends up being negative. On the other hand, a high density-impulse propellant can stick a lot of gas into the same tank, allowing you to get some embarrassing mass ratios in a nice slender rocket and partly offsetting a lower specific impulse it may have.

The third one, handling concerns, is a fuzzy category that groups together all those little issues that may crop in the design and operation of an actual rocket vehicle: does your propellant need an external ignition system, or is it a nice, easy hypergol? Is your propellant mix storable, or are you using cryogenic rocket propellants? Can your fuel or oxidizer be used to cool the engine bell, or will you have to find another solution? Are your fuel and oxidizer generally inoffensive chemicals, or will you need special precautions when handling them? All these questions, and many more, sketch you a general concept of how the rocket will be operated and the complexity of such an endeavor.

The last measure of merit is, of course, cost - how much bang for your buck you get. Large rockets and small rockets procured in large numbers and/or flown many times can rapidly burn outrageous amounts of chemicals and thus even a very small cost saving in mixture choice can end up saving quite a bit of money in the long run. While most rocket propellants are too cheap to matter, some of the exotic high-performance mixes can get unaffordable.

As a final note, it is important to remember that the measures of merit given above are not given in order of importance; instead, their relative importance depends heavily on the use case of the rocket in question: a tactical rocket system will heavily prioritize measures 2 and 3 above anything else, while a launch vehicle will prioritize measures 1 and 2, with 3 and 4 being given secondary importance and, even within the launch vehicle example, you will have a lower stage prioritizing 2 above all while the upper stage stresses 1 more and so on and so forth.

Additionally, your mixture choice may be conditioned by external factors such as availability, political/logistical/health, and safety choices - as an example, while the US Army and US Air Force operated many storable hypergolic rocket propulsion systems in their history, the US Navy was always wary of them due to fear of fires aboard ships.

Fuels and Oxidizers and Exhaust oh my

The reaction happening within a bipropellant rocket engine is naught but a simple redox one - the oxidizer, well, duh, oxidizing the fuel, a lot of chemical bonds being broken and their energy heating up the resulting compound(s) until they become rather hot gases and get blasted outta the rocket’s tailpipe. A good grasp of the chemistry being involved here goes most of the way of getting a bearing on the already-mentioned measures of merit.

First of all, let’s talk about what we want from a rocket propellant mix to get a high specific impulse.

An absolute conservation-of-energy-dictated upper bound on the exhaust velocity (and therefore specific impulse) of a chemical rocket propellant combination can be given by this simple equation:

$V_{eMAX}={\sqrt {2E_{s}}}$

• where $V_{eMAX}$ is the exhaust velocity.
• where $E_{s}$ is the specific energy of the propellant mixture.

However, this is far from the whole game. To make good use of the propellant’s specific energy, the exhaust’s average molar mass must be as low as possible. This is because, assuming perfect expansion, the equation for a rocket’s exhaust velocity is:

$V_{e}={\sqrt {{\frac {2k}{k-1}}\cdot {\frac {R}{M}}\cdot E_{s}\cdot C_{p}}}$

• Where $k$ is the heat capacity ratio.
• Where $R$ is the ideal gas constant.
• Where $M$ is the exhaust’s average molar mass.
• Where $C_{p}$ is the exhaust’s specific heat.