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Different grain geometries in solid-fuel rockets produce various thrust curves:



thrust curves of various grain geometries

I can imagine it's not too difficult to obtain a thrust curve of a specific grain geometry with a measurement while the engine burns. But are thrust curves also obtained in any way through calculation, without physical testing? And if yes, with what methods or formulae?

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    $\begingroup$ Should be simple geometry. Thrust is proportional to the amount of surface area that's exposed. $\endgroup$ – Hobbes Feb 15 '16 at 12:40
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    $\begingroup$ I believe it would be easier to perform it "backwards". You start with the grain at the end of the burn, and then add infinitesimal/numerical step/layer varying its shape for needed thrust profile change, repeating by adding a new layer conforming to the required 'step' thrust on top of the prior one, until you arrive at the launch moment (or run out of free space). Simply create the new layer so that at the start of its burn it has the needed change of thrust, at the end - shape of the next layer's start of burn. (create the graph first, then progress backwards through the $t$ axis). $\endgroup$ – SF. Feb 15 '16 at 13:48
  • $\begingroup$ Is the geometry number 2 only theoretical or is it used in praxis? How to fix the central cylinder during the full burn? $\endgroup$ – Uwe May 18 '17 at 19:39
  • $\begingroup$ @Uwe: a) make it slightly conical so it burns near the nozzle faster than at the fixed tip, b) small non-combustible support structures aren't disallowed. $\endgroup$ – SF. May 19 '17 at 11:00
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You might find some answers here: http://www.thrustcurve.org/. It's a reference for hobby rocket motors, but they can get pretty large and the larger ones have a lot of variation in grain geometry (star, moonburners, c-slot, etc).

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