Musk explains why SpaceX prefers clusters of small engines

An important source of loss in smaller engines is viscosity. Proportionally, more of the working fluid is in contact with the internal surfaces, more of it is inside the boundary layer, which is the only place where viscosity matters.

For a large engine, your boundary layer goes up as the area (square), and the contained goes up as the volume (cube). (The growth of the boundary layer goes up as something like the square root.) It's one of the few places in rocket science where the square-cube law helps provide a useful result, despite the insistence of many a misguided layperson. Even here, it may be something like a 2.5-cube law.

It's true that pressure vessels in principle don't care about scale when it concerns mass per unit volume (at a constant pressure). But a combustion chamber's thrust is (to zeroth order) proportional to cross sectional area, not volume.

The combustion chamber only needs to be a certain length (L star) to achieve efficient combustion. Any longer and you're just adding mass with no benefit. But there are practical limits to shape of the combustion chamber. You can't have it too squat or it loses structural efficiency. Thus, above a certain size, you're better off from a mass efficiency standpoint with having a bunch of smaller combustion chambers than one big huge one.

And this is true even more for the nozzle. You can use a much shorter, and thus lighter, nozzle if you have a smaller engine. For the same expansion ratio, therefore, clustering a bunch of smaller engines is more mass efficient than a single big engine.

(But if you go REALlY small, you have minimum gauge issues and you lose thermal and combustion efficiency.)

I read most of that, and did not weep, 20 years ago when I was getting my degree in aero/astro engineering. Neither of your links support what you're trying to say.

The walls get linearly thicker, and your intuition about why the walls need to get thicker is incorrect.

The Soviets won the first round of the space race (until the mid-60s) because of multiple factors, but mainly because of the laser-focus at the highest levels to push the technology as far as it could go. It helped a lot that they had an engineering genius heading the program (Sergey Korolev), and the top politician during that time (Nikita Khrushchev) was a forward-thinking progressive (relatively speaking - please keep it in context) who was a big fan of space.

Korolev (pronounce: Karalyov) died in the mid-60s, just before the Moon program had started to gear up for the big time. Khrushchev was ousted also during the mid-60s by retrograde bureaucrats.

With both the political and the technical leadership in turmoil, the program fell on very hard times. The didn't get enough funds, could not get proper testing done, and pushed a lot of QA to the live launches. Predictably, the results were "spectacular" - but in a bad way.

A little before that time America finally got its resolve together ("We choose to go to the Moon in this decade and do the other things, not because they are easy, but because they are hard...") and started pouring massive amounts of financial and engineering efforts into its space program. Again predictably, the results were spectacular - but in a good way.

If your leadership is indifferent and you don't have the stuff you need, you lose. If you work hard and put all your energies into it, you win. And that applied to both sides, each in its turn. Who knew?

Good book on this topic (and related):

https://www.amazon.com/Korolev-Masterminded-Soviet-Drive-Ame...

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I wish Korolev was around these days so he could see Elon Musk's multi-engine design. I think he would like it. In a (somewhat vague) sense, I see the Falcon Heavy as late vindication for the tremendous efforts, against all odds, of the engineers who busted their asses trying to shoot the N1 into the Moon. The idea was sound, it was just not yet the right time for it.

> You can't have it too squat or it loses structural efficiency.

I'm not sure what you mean. Over "squatness," if we mean l-star to cross-sectional area, the 'structural efficiency' remains constant, in that we've contained (square) more fluid for (thickness x perimeter = square) more wall material, and done so for (square) more thrust.

> You can use a much shorter, and thus lighter, nozzle if you have a smaller engine.

A nozzle, again, can be modeled as a pressure vessel. (Neglecting shear stress in the first analysis.) So, if we concede that pressure vessel mass ratios are invariant under scale, then so are exhaust nozzles. What we are really worried about is the amount of fluid that is in the boundary layer for heat transfer and shear reasons, and this gets slightly worse with engine size. The area-Mach relations govern the size of the exit bell, so the exit surface for a larger engine grows linearly with the throat area, and we're back to the pressure vessel scaling laws.

> You can use a much shorter, and thus lighter, nozzle if you have a smaller engine.

The point being that, if your nozzles are 9 times smaller, they're only 9 times lighter.

It's difficult to talk to everyday SpaceX enthusiasts, who seem to have most of their information second-hand. When, for example, to I bring up frozen flow vs. equilibrium flow in this discussion? When do I point out the combustion instability limitations of larger engines? When do I point out the exorbitant research costs associated with taming those instabilities? When will any of that ever dissuade a layperson from their enthusiasm for the square-cube law?