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I know next to nothing about Rocketry and Space Flight. I assume that the majority of the force generated by a rocket's engine is simply the result of throwing gasses out of the bottom very fast, and relying on Newton III.

But when the rocket is near enough to the ground for the exhaust to be meaningful interacting with the surface (e.g. during take off, or during SpaceX's booster landings) does the engine thrust increase to any significant degree? (perhaps due some of the gaseous particles hitting the ground and then bouncing back upwards?)

If yes, can you give any indication of HOW much? Is it enough that launch/landing mechanics need to take it into account?, or is it no more significant than, say, air densities/pressures varying due to temperature or breezes.

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There is very little, if any, ground effect at the launch of a large rocket. Having those hot gases bounce off the ground and back onto the rocket might well spell the start of a very bad day for the rocket. The exhaust from a launching rocket is directed away from the rocket by a flame trench to militate against these potentially very bad effects.

There might be some ground effect thrust enhancement (or possibly dis-enhancement) during the controlled landing of a rocket under thrust, e.g., on the Moon or on a barge. These effects will generally be extremely transient in nature, and hence can be pretty much ignored.

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