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You also have to carry the weight of the corresponding track to at least a couple thousand feet to jettison it safely I bet. It's also at the point where the rocket is at it3 heaviest so the assistance it could give would be really limited.

I think you'd have much better luck turning the rocket into some kind of a sabot round and spending a week compressing a bunch of air into huge tanks and launching it that way. That's how subs launch ICBMs.

The reason that's not done is that rockets aren't reliable enough yet and nobody wants to bet their billion dollar cargo on the engines starting the first time, every time. If you lose every 100th ICBM it's a bummer, but it doesn't make MAD not happen.

https://www.youtube.com/watch?v=1aPvGGvnAGQ

For non-human spaceflight, a 1% loss is an option. Insurance ussually assumes a 5ish percent chance that the payload wont survive and another 5ish that it wont be delivered into the ideal orbit.

never mind the actual sums involved, 1% on top of 10% is a 10% increase in coverage. Is coverage inclusive of the time lost in labor as well?

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