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Is there some formula I can apply to the weight of a gun, along with the force of thrust it creates, and calculate if it will be able to lift itself off the ground or not? Without actually handling the gun, of course.

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    $\begingroup$ The same way you do with a rocket, actually. You just through the fuel overboard in discrete lumps instead of continuously. (Of course, any engineer in the room will tell you that batch processes often suffer in overall throughput compared to continuous ones...) $\endgroup$ – dmckee Mar 21 '16 at 3:38
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    $\begingroup$ What kind of "gun" are we talking about? Weapons? How about projectile velocity times mass as a first order estimate (discounting for the momentum of the escaping gas). $\endgroup$ – CuriousOne Mar 21 '16 at 3:39
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Given the pieces mentioned in your question: the weight of the gun and force it creates, the answer is a trivial yes. If the force is greater than the weight, it could lift.

The problem is in calculating that force. A rocket is designed to produce force continuously for a period, and given the fuel and some other parameters makes it possible to calculate the average thrust over that period. The gun produces force only for a short period of time. As an example, it might generate a force in excess of its weight for only a couple hundredths of a second because the forces diminish as the gas in the firing chamber expands.

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  • $\begingroup$ You can ask the question about a fully automatic firearm which is a kind of batch-mode rocket. Bit the results are generally disappointing. $\endgroup$ – dmckee Mar 21 '16 at 4:59
  • $\begingroup$ @dmckee That's an excellent idea. Yes, then calculating an average force (over one cycle of firing) becomes useful. $\endgroup$ – BowlOfRed Mar 21 '16 at 7:02

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