This post follows our comparison of first stage engines, which can be found here. As a reminder, in 2014 Elon Musk said [1]:

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

To expand this quote a little:

“Right now, I’d say, engines are our weakest point at SpaceX, but they will become as strong as the structures and avionics in the next generation… our weakest point is engines with respect to specific impulse, but not with respect to thrust-to-weight. We actually have the highest thrust-to-weight of any engine, I think maybe ever, but our specific impulse, the efficiency of the engine is about 10% worse than a staged-combustion engine using the same propellant.”

Since engine design is so fundamental to the performance of the rockets SpaceX launch, it’s worth explaining what Musk said in a little more detail, in this case regarding upper stage engines. As background, SpaceX have their name on three families of upper stage engine – the (now obsolete) Kestrel, used in the Falcon 1, the Merlin 1D Vac (in use for the Falcon 9), and the still-in-development Raptor. The first two are fueled by kerosene and liquid oxygen (a combination known as kerolox), while the latter will use methane and liquid oxygen (methalox) [2].

So what defines a ‘good’ upper stage engine? The purpose of such an engine is to get a payload which is already above the atmosphere into its desired orbit. The Tsiolkovsky ideal rocket equation describes this process accurately:

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

(where log refers to the natural logarithm, specifically). A good engine in terms of raw performance therefore has a high exhaust velocity (usually referred to as specific impulse, which is just exhaust velocity divided by the acceleration due to gravity), and a low mass. In the real world, an engine also needs enough thrust to reach orbit before gravity pulls the rocket back below the atmosphere, but not so much thrust that the stack is damaged by the acceleration in the later part of the burn (many engines, including the Merlin series, have the ability to throttle, which can help mitigate this). Plotted after the next paragraph are the specific impulse, mass and thrust of SpaceX’s two flight-tested engine families, against most of the other rocket engines to have seen orbital flight.

Since the Raptor has not yet flown, and thus its specifications could still change, it is not included in the chart. In fact, no methane/liquid oxygen engine has ever made it to the launchpad for us to compare the Raptor to. In lieu of this, we have estimated theoretical upper limits for methalox and similar fuels, by simply assuming perfect conversion of all the stored chemical energy into kinetic energy. Our calculation can be found here: it finds that hydrogen/liquid oxygen (hydrolox) has a maximum of 532.5s, methalox has 458.7s and kerolox has 452.7s. It should be noted that these are not necessarily achievable limits, and that real rocket engines will have lower efficiencies. These limits are plotted as vertical bars alongside the aforementioned data [3].

Starting with the upper limits, we can see that practical hydrolox and kerolox engines operate at about 100 seconds below their upper limits – by extension, we should expect methalox engines like the Raptor to behave similarly. The methalox upper limit is very slightly higher than that of kerolox, but this discrepancy is small even compared to the variation among different engines with the same fuel type. The conclusion we would be that methane will behave a lot more like kerosene than hydrogen (but is hardly a drop-in replacement). Note also that the Raptor will use the more efficient staged combustion cycle (versus the Merlin’s gas generator cycle).

The first graph (mass vs specific impulse) shows us an intriguing fact about the Kestrel – it is in fact the lightest kerolox engine ever to make orbit, by more than a factor of two: 52 vs 121kg for the next lightest engine, the RD-0109. The RD-0109 is also notable for being the engine that first put a human (Yuri Gagarin) into space. Having a low mass is a significant benefit on the last stage – every kilogram shaved off the engine is an additional kilogram of payload, regardless of destination. It should also be noted, though, that the Kestrel was pressure-fed, which introduces additional complexity (hence: weight) to the tank, which the RD-0109 and others would not have to deal with.

It can also be seen that for all the enormous complexity of the space shuttles main engines [5], their specific impulse is quite similar to other liquid hydrogen engines. However, it should be noted that unlike other hydrolox engines, they were reused, and had to work within the atmosphere as well as outside it.

The thrust vs specific impulse graph shows an unusually high thrust for the Merlin family, even when compared to much larger launch systems (note that the Shuttle uses three main engines, and Saturn V used five on the second stage and one on the third stage). This is probably due to the Merlin’s heritage, being originally designed as a first stage engine on the Falcon 1, and later being adapted for upper stage use on the Falcon 9. On the first stage, high thrust is important to reduce gravity losses; these are less significant on the second stage and so most dedicated second stage engines have lower thrust as a consequence. Ion engines (electric propulsion) have vastly lower thrusts than the chemical engines discussed here, but are still capable of performing some of the same tasks as these engines.

This can also be seen in the Kestrel’s very low thrust – it was a dedicated upper-stage engine, with a small payload, and thus did not need to push the payload with a great deal of force.

In the quote at the start, Musk mentioned the high thrust-to-weight ratio as one of the Merlin’s strongest points. Our analysis confirms that the engines do indeed have the highest thrust-to-weight of all the upper stages we surveyed; and this was true even before some of the upgrades SpaceX has made to the thrust over the lifetime of the Merlin. Thrust-to-weight ratio is arguably the most important performance parameter after specific impulse (as it corrects for the size and scale of the engine), and the value seen is a testament to the skill of SpaceX’s engineers.

In addition to all of this, the Merlin 1D has never failed in 21 flights (CRS-7 was a tank overpressure event, unrelated to the performance of the engine), and costs comparatively little – around $1 million each [6]. All in all, remarkable for SpaceX’s “weakest point”.

Correction: A previous version of this article contained an error in the specific impulse upper limit calculations which mistakenly led to methalox having a lower Isp limit than kerolox – this has now been corrected. Credit to reddit user /u/somewhat_brave for noticing the mistake.

References:

[1] At MIT’s Aero/Astro Centennial – see link for full transcript.

[2] Tom Mueller, SpaceX’s Vice President of Propulsion, has confirmed this will be the case (see linked tweet).

[3] Raw data here as a pdf, and here in a csv format. Data sourced from astronautix.com, and occasionally Wikipedia, spaceflightnow or SpaceX’s offical website. Data are individual rocket engines (as opposed to clusters) which have seen flight. We excluded manuvering thrusters, ullage motors, and ion thrusters from the analysis.

[4] From the r/SpaceX community FAQ, under ‘Why use methane and not RP-1?‘. See this, and the previous question, for a fuller discussion of methalox combustion.

[5] Look at the diagram on the last page of the linked presentation as a quick demonstration of just how complicated those engines are.

[6] According to a former SpaceX employee, anyway.