Flywheel Energy Calculator Formula

Understand the math behind the flywheel energy calculator. Each variable explained with a worked example.

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Formulas Used

Moment of Inertia (solid disc)

moment_inertia = inertia

Stored Kinetic Energy

energy_j = 0.5 * inertia * pow(omega, 2)

Energy in kWh

energy_kwh = 0.5 * inertia * pow(omega, 2) / 3600000

Variables

VariableDescriptionDefault
massFlywheel Mass (m)(kg)50
outer_radiusOuter Radius (R)(mm)200
rpmRotational Speed(RPM)3000
r_mDerived value= outer_radius / 1000calculated
inertiaDerived value= 0.5 * mass * pow(r_m, 2)calculated
omegaDerived value= 2 * pi * rpm / 60calculated

How It Works

Flywheel Rotational Energy

A flywheel stores kinetic energy in its rotating mass.

Formulas

I = 0.5 m R^2 (moment of inertia for a solid disc)

E = 0.5 I omega^2 (rotational kinetic energy)

where m is mass, R is outer radius, and omega = 2 pi N / 60 is angular velocity. The usable energy is the difference between energy at maximum and minimum operating speeds.

Worked Example

A 50 kg solid disc flywheel, 200 mm radius, spinning at 3000 RPM.

mass = 50outer_radius = 200rpm = 3000
  1. 01R = 0.2 m
  2. 02I = 0.5 x 50 x 0.04 = 1.0 kg-m^2
  3. 03omega = 2 x pi x 3000 / 60 = 314.16 rad/s
  4. 04E = 0.5 x 1.0 x 314.16^2 = 49,348 J = 49.3 kJ

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