Power Loop for SusTech Notes
Flywheel Scaling
The fastest possible non-magnetic flywheel is a thin hoop of material at maximum stress. Assume a thin flywheel hoop rotating around a vertical axis, with radius rA
rA
If the flywheel rotates at angular frequency r
r3A
2
Consider a small element 2
d
)(
2r)
=r2A
2
d
2
At maximum stress, 2=S
E = \pi r A \rho ( r^2 \omega^2 ) = \pi r A \rho ( S_{max} / \rho ) = \pi r A S_{max}
\large { E = \frac{1}{2} V S_{max} }
Real flywheels will have rotating structure that does not contribute to this strength, and flywheels thicker than a thin shell will have inner material at less than maximum stress and storing less than maximum energy. So the simple energy equation above is overoptimistic; if you include the container, the empty volume, the axial motor, the magnetic bearings, a decent safety factor, etc, then the maximum stored energy may be a small fra