How this calculator works
Energy depends on the rotor mass distribution and speed squared. Geometry mode uses a simple ideal solid body; measured-inertia mode is useful for assembled rotors. Usable energy is the difference between upper and lower speed energies. Material mode estimates K times allowable stress divided by density, with a separate stress shape factor that is not the inertia coefficient. Losses and generator efficiency reduce electrical delivery.
Formula
I = C m r²; E = I omega²/2; E_usable = I(omega_high² - omega_low²)/2; E_limit/m = K sigma/rho.
Worked example
A 4 kg solid disk of radius 2 m has I = 8 kg m². At 3 rad/s it stores 36 J. With K = 0.5, stress 1 GPa and density 2000 kg/m³, the ideal specific energy is 250000 J/kg.
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Frequently asked questions
Is tensile strength a safe operating stress?
Use an allowable stress that already includes an appropriate safety margin. This ideal estimate does not validate a rotor design.
Are the two shape factors the same?
No. C describes moment of inertia, while K describes material stress utilisation.
Does stopping extract all stored energy?
The mechanical energy difference is available in principle, but operating limits, losses and conversion efficiency constrain delivery.