Rocket mass is changing due to burning of the propellant and this means that moment of inertia is changing too. Moment of inertia is mass X radius of gyration squared. I currently have a simulink model that caters for the varying mass of the engine and rocket. However, I am still having difficulties in determining the changing moment of inertia. I already have the moment of inertia of the rocket without the propellant using my CAD model. Questions are
1.Is there a mathematical formula of determining moment of inertia of the solid propellant?
2. Is radius of gyration constant or it keeps changing? (Assumption is that rocket body axes originate from the center of gravity which coincides with the center of mass)
Sorry my question is long but I would like to hear your views and answers. Thank you
Following formula for “Cylinder” could be used for determining moment of inertia of the solid propellant.
Length of the cylinder = l, Radius of cylinder = r. Radius of gyration = k.
Case 1: Axis, diameter at mid length.
l keeps decreasing as the solid propellant is consumed. Axis keeps shifting and is always at l/2. k keeps changing.
k2 = (l2/12) + (r2/4)
in this case the axis is passing through the center of gravity of solid propellent, hence the radius of gyration k0 with respect to a parallel axis (rocket axis) at a distance d from solid propellent gravity axis is given by
k02 = k2 + d2
Case 2: Axis, diameter at end.
l keeps decreasing as the solid propellant is consumed. Axis is fixed at the base. k keeps changing.
k2 = (l2/3) + (r2/4)
You will have to integrate one of the above formula with the moment of inertia of the rocket without the propellant.
If u are using solidworks..then...u can make configuration and set the level of burning fule and evluate moi from evaluation toolbar
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