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What damages a rocket depends on the rocket.

For the SSMEs, it was just plain use which damaged them. The SSMEs were engineering marvels, but the ludicrous nature of the Shuttle demanded extreme performance, which meant that they ran on razor thin margins. By the time they finished a ~8 minute burn, they had taken enough of a beating to need a lot of refurbishment. SpaceX's Merlins, on the other hand, are much lower performance and built more for robustness.

Think of it like an F1 race car, which needs a lot of work after every race and a new engine several times a season, versus a daily driver which can probably go 50,000 miles without ever opening the hood. (Not that this is recommended.)

But what specific thing does the SSME's had to do that Merlins doesn't?

In your race car example, you can differentiate it from a daily driver that the F1 car has to endure tremendous accelerations, cornering and down forces acting on it and an engine that reaches insane rpm's that puts tremendous amount of stress on all the critical engine components..

Can you differentiate between these rocket engines in that way?

Sorry I'm typing from mobile so my posts may be even less informative than usual.

The main thing that the SSME has to do that's different from the Merlins is quite simply generate more thrust and a higher specific impulse. The SSME is a much higher performing engine. It achieves this performance through fuel choice and design, namely by using liquid oxygen/liquid hydrogen vs using RP-1(which is basically kerosene) and by being a staged combustion rather than gas gen cycle engine. While it has much higher performance than Merlin, that performance comes at significantly greater overall complexity, particularly in the turbomachinery and pre-burner components.

The SSME also has to run from sea level all the way into space, whereas the Merlin is able to have one design optimized for sea level and a second design optimized for space.

The difference in efficiency is striking. The SSME's specific impulse (the closest equivalent to MPG in a car) is 452 in vacuum and 366 at sea level. Merlin's is 311/282 for the sea level version, and 348 for the vacuum version.

Of course, this is not a criticism of Merlin, just a comparison. By being less efficient, they're able to optimize for other stuff like cheapness and robustness.

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