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Calculate Center of Thrust

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If I have a rocket with some known number of engines $n$, each producing thrust with arbitrary direction $T_n$ and center of thrust $r_n$, the total thrust amount and direction $T_{total}$ is equal to the sum of all thrust vectors:

$$ T_{total}=\sum_i^nT_n $$

How is the center of thrust calculated from these parameters?

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1 comment thread

Not sure you can based on only that data? (2 comments)

Comments on Calculate Center of Thrust

Not sure you can based on only that data?
Canina‭ wrote 2 months ago:

Wouldn't calculating the center of thrust for a set of engines also require knowledge of the origin of the thrust vector of each respective engine, in relation to the others? Suppose that you have 11 engines of exactly equal thrust, 10 clustered close together and one far away from the others; the center of thrust of such a configuration would be quite different from that of one where all of the engines are distributed evenly. Once you have that, though, it seems to me that this should be a relatively straightforward vector calculation.

Josh Hyatt‭ wrote 2 months ago:

Canina‭a Origin of thrust for the $n$'th engine is denoted $r_n$ in my scenario. It's also not quite as simple as it looks at first. Consider identical engines pointed the same direction. Easy to see the effective center of thrust is right between the two. Now throttle one of those engines down to 50%. Where is the center of thrust now? It can't be in the middle. My intuition tells me it's probably the sum of each thrust origin times the thrust magnitude, but I'm looking for a mathematically sound answer, and I'm having trouble arriving to it myself.

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