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I understand that the the center of gravity can be calculated by making a 3D model of the rocket or launch vehicle when it is completely filled and stationary.

But in case of continuous ascent (i.e. mass continuously varying) how center of gravity position is computed?

Can this be modeled in any software?

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Typical liquid rocket stages stack the fuel and oxidizer vertically in separate tanks. If all you need is the center of gravity and don't need to be extremely precise, you can model this as three point masses: one for the dry structure, one for the center of the fuel volume, and one for the center of the oxidizer volume. As fuel is consumed, the fuel mass decreases towards zero and the fuel volume's center of mass moves downward from the center of the fuel tank to the bottom of the fuel tank; likewise for the oxidizer.

That model in effect treats the propellant tanks as cylinders. Real propellant tanks are more often ellipsoid-ended capsules than simple cylinders, so for a better estimate you need to break down the tanks into multiple sections.

Solid stages or boosters generally burn from the inside out along their entire length, so the fuel grain center of mass doesn't move as much (though the grain cross-section likely varies along the length of the booster, so it does shift somewhat). For rough purposes you can model this as a fixed point mass for the casing and a non-moving, but reducing, point mass for the grain.

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  • $\begingroup$ Would there be a tendency for the CM of liquid fuel rockets to move "downwards" along the axis as propellant is consumed, while for solids, if at all, the CM might move "upwards"? $\endgroup$ – uhoh Sep 8 '18 at 15:20
  • $\begingroup$ Fun fact: a full shuttle external tank's propellant tank CG is pretty much at its geometrical center, and so is an empty one's. So during launch there is a minimum longitudinal CG that then jumps back up. I remember calculating where this inflection point was, long ago. $\endgroup$ – Organic Marble Sep 8 '18 at 15:42
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    $\begingroup$ @uhoh Liquid stage CM moves downward; overall rocket CM tends upward (because of upper stages and payload). Solid boosters have some extra weight at the base (nozzle) that I imagine outweighs the nosecone, so their CM should also move down very slightly. $\endgroup$ – Russell Borogove Sep 8 '18 at 16:10
  • $\begingroup$ @uhoh, solids burn from the inside out, not so much bottom-up. You want the outside to remain covered in propellant until burnout. $\endgroup$ – Hobbes Sep 12 '18 at 8:34
  • $\begingroup$ @Hobbes there are several designs for the way solids burn and it's not necessarily 100% one or the other. However only the longitudinal difference makes any difference in this context. $\endgroup$ – uhoh Sep 12 '18 at 11:25

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