The ideal rocket equation defines the performance of chemical rockets – it looks like this:

total change in velocity = exhaust velocity * log (liftoff mass/final mass)

So the performance of all rockets, the Falcon 9 included, is mostly defined by just two parameters, the exhaust velocity and the ratio of initial to final mass. The latter is defined by the mass of the tank, engines and whatever add-ons are attached for things like reuseability, while the former is the sole responsibility of the engines. In rocketry, the exhaust velocity is usually divided by the acceleration due to gravity (for weird historical reasons [1]) to get a number called specific impulse. This is a measure of the efficiency of the rocket – how effectively it converts fuel into momentum, and a higher value allows more payload, into higher orbits, with fewer stages, and greater ability to attach things like landing legs.

SpaceX currently use nine liquid oxygen/kerosene Merlin 1D engines for the first stage, and one Merlin 1D Vacuum for the second stage. In the future, they expect to migrate to a liquid oxygen/liquid methane engine called the Raptor. This is because, as Elon Musk said:

“Right now, I’d say, engines are our weakest point at SpaceX” [2]

But what exactly is the performance of these engines, and what makes this their weakest point? Well, the Merlin 1D has (at sea level) a specific impulse of 282s, and a thrust of 756kN. This is all very well, but those numbers don’t mean much without context. To understand what they mean, we’ve put together a graph of most of the serious rockets engines ever to see flight, to see where SpaceX falls. Since this could be of general interest, we’ve also uploaded the full data set [3] for others to play with. We’ve concentrated on first stage engines here, but upper stages are equally interesting, and hopefully we can perform the same analysis on them in a later post.

This graph tells us several things, and we can go through them one by one. Firstly, we can see that kerosene/liquid oxygen (often called kerolox for short) is a very common fuel type, with plenty of precedent to draw from, both modern and historical. Liquid methane/liquid oxygen (methalox), on the other hand, is essentially unprecedented as far as actual rocket engines go (although it has been proposed a number of times in the past [4]), and so we can only use physics, or as public statements by SpaceX, to learn about the engine’s performance.

As far as thrust goes, the Merlins are low but perfectly reasonable. Thrust doesn’t appear in the rocket equation, but it’s important, because if you don’t have enough of it, your rocket will just sit on the launchpad until you’ve burnt enough fuel to lighten the rocket sufficiently. Looking at the graph, it’s important to remember the data are for individual engines, while Merlins are launched in clusters of nine, giving them a collective thrust at about the level of a Saturn V F-1 engine (remember also that the Saturn V itself used a cluster of five F-1s).

The graph also shows us how much of difference fuel choice makes. Even the most efficient kerolox engines have an efficency below that of the least efficient liquid hydrogen/liquid oxygen (hydrolox) engines, and in turn, solid rocket motors have an efficiency even lower than that. Hypergolic fuels*, which can be stored at room temperature, and will burn spontaneously once mixed, have about the same efficiency as kerolox. This is a good reflection of what physics predicts, which is that the lighter your combustion products are, the higher your exhaust velocity [5]. Hydrolox produces only water (molecular mass 18), while methalox and kerolox also produce different amounts of carbon dioxide (molecular mass 44), which explains the difference very neatly.

That said, the Merlin engines have quite high efficiency for what they are – it can be seen they are ahead of the pack as far as kerolox engines go. This becomes more significant when you consider that the few engines with higher specific impulse that it all use a staged combustion cycle, while the Merlin uses a gas generator cycle (this isn’t evident from the graph but can be seen in the raw data). What this means is as follows: to pump fuel from the tank to the combustion chamber, all rockets use (at least one) pre-burner, which burns a little of the fuel to power the pump. In a gas generator cycle, the exhaust from this burner is simply vented, while in a staged combustion cycle, it is sent back into the combustion chamber. This more complicated design is what allows the Atlas V and others to get such high efficiency from kerolox, while SpaceX prefer the simpler design and the small performance penalty. Once you take into account that it is a kerolox, gas generator engine, the Merlin turns out to have about the best efficiency of any engine in its class. This doesn’t refute Musk’s statement about it being their weakest point, but it suggests that it’s because of design decisions made long before the Falcon 1 even took flight, rather than any lack of engineering skill on the engines side of SpaceX. In future, this should be reversed by the Raptor engine.

*The ones in this graph, specifically, are Dinitrogen tetroxide (N2O4)/Unsymmetrical dimethylhydrazine (UDMH), Nitric acid/UDMH, Nitric acid/Kerosene and N2O4/Aerozine-50

[1] https://www.youtube.com/watch?v=nnisTeYLLgs

[2] http://shitelonsays.com/transcript/elon-musk-at-mits-aeroastro-centennial-part-2-of-6-2014-10-24

[3] https://thephysicsofspacex.wordpress.com/physics-of-spacex-first-stage-engines/ Sourced mostly from astronautix.com, with occasional help from Wikipedia. Not a complete survey, not guaranteed to be accurate and not to be cited as a primary source (but as a secondary source is great).

Update: reddit user Kona314 has cleaned up the raw data and put it in a google sheets form, which can be found here.

[4] http://www.astronautix.com/props/loxlch4.htm

[5] More specifically, exhaust velocity scales as the inverse square root of the molecular mass: https://en.wikipedia.org/wiki/Rocket_engine_nozzle#One-dimensional_analysis_of_gas_flow_in_rocket_engine_nozzles