This ignores the fact that due to basic physics a second stage needs 1/10th the thrust of the first stage. If you have more power than that on the second stage you likely have an engine that is heavier than strictly required. Using seven engines instead of nine optimizes for cost at the expense of second stage performance. Assuming you use the same engine design on both stages.
Couple of issues
With the Falcon Heavy, you've still got the same single Merlin-1D boosting the second stage.
But on the Falcon Heavy, the second stage has to boost almost 3x the weight
That implies that the Merlin-1D is grossly overpowered as a second stage
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And given that a Merlin-1D is only 470kg, a larger Cangqiong engine wouldn't actually be that much heavier. Call it 100kg.
Then put that into the context of a Falcon Full Thrust second stage which weighs 111 tonnes plus payload of at least 5 tonnes. That's 116+ tonnes
The Falcon Heavy has an even heavier payload
An extra 100kg weight on the second stage accounts for less than 0.1% of the overall weight of 116+ tonnes
So I think it's obvious that it's better to optimise the rocket engines for the 1st stage
I reckon you can almost certainly get a much larger efficiency improvement with a 7 engine design on a Pallas rocket rather than 9 engines on a Falcon.
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Yes, this all assumes you use the same engines for the 1st stage and the 2nd stage.
But in the future when rocket launches are far more prevalent, you might as well design a second stage rocket engine which is optimised for vacuum operation AND to be lower cost because it doesn't have to be reused.
Again, that argues for the current crop of engines to be optimised for the 1st stage rather than 2nd stage
SpaceX also went with nine engines on the first stage because this way you need less throttle down requirements on the basic engine design if you want to land back on the first stage. SpaceX at one point also had a five engine expendable first stage design, the Falcon 5, but they decided against it and in favor of first stage reuse with the nine engines.
I think we can take it that throttle down requirements for a 7 engine reusable rocket have been thought out.
After all, it is one of the most fundamental design characteristics if you want to recover the rocket, and we know this is a critical requirement for all the rocket startups in China.
And note that the Blue Origin New Glenn is going with 7 engines on each 1st stage rocket. So why are they also going with 7 engines instead of 9?
Also, wiki has a SpaceX press release stating the Falcon 5 first stage as being reusable, not expendable.
