The Flywheel Rotor Burst Bound: Maximum Specific Energy Set by Tensile Strength and Density, and What a Practical Rotor Retains

A flywheel rotor's maximum specific energy is E/m = K sigma/rho, with shape factor K = 0.500 for a thin rim, 0.606 for a solid disc (Poisson ratio 0.3), and 1 only for the ideal constant-stress disc. Evaluated with published material values for high-strength steel, E-glass composite, and carbon-fibre composite (T700/epoxy), the burst bound spans 17.9 to 219.5 Wh/kg for realistic geometries. With a safety factor of 2 on stress and discharge to half speed, a practical carbon-fibre rim rotor delivers 82.3 Wh/kg usable and requires 12.15 kg of rotor per usable kWh; commercial system figures near 11 Wh/kg sit about twenty times below the material bound. All results are analytical calculations (simulated, not measured) and are reproduced by the accompanying compute script.