Storing energy in a spinning wheel

A flywheel is a battery made of motion: spin a heavy wheel up to store energy, let it spin down to get it back. What stops you spinning it faster is not the motor. It is the wheel tearing itself apart.

What a flywheel does

A flywheel is a rotor on bearings, driven by an electric machine that works both ways. Fed electricity, it acts as a motor and speeds the wheel up; asked for electricity, it acts as a generator and slows the wheel down. In between, the energy is stored as rotation. Nothing is burned and nothing chemical happens, so the wheel can cycle hundreds of thousands of times, and its state of charge is simply its speed.

Why anyone bothers

Most grid faults are short. Amiryar and Pullen's review reports that more than 80% of power outages last under a second, and that flywheels return 90–95% of the energy put in per round trip. A battery asked to bridge such gaps thousands of times a year wears out; a flywheel does not care how often it cycles. So flywheels sit beside data centres and steady grid frequency: the review describes a plant in Stephentown, New York, with 200 flywheels of 100 kW each.

Where the energy is, and where the limit is

The stored energy is E = ½ I ω², where ω is the spin rate and I is the moment of inertia: how much mass the wheel has and how far from the axle it sits. The square on ω is the whole design: double the speed and you store four times the energy, while doubling the mass only doubles it.

So why not spin every wheel faster? Because spinning material feels a pull outward, and the rim has to hold itself together against it. For a thin ring the review gives the stress as σ = ρ r² ω²: density times the square of the rim speed. It grows with the same square as the energy. Every material has a tensile strength, the stress at which it fails, and that fixes the top speed. Spin past it and the rim bursts.

Put the two formulas together and the mass drops out. The most energy a wheel can hold per kilogram is E/m = K σ_max/ρ, with K a shape factor set by the rotor's geometry. A heavier wheel does not raise this ceiling; strength, lightness or shape does. Hence the review's two families: steel rotors up to about 10,000 rpm, and lighter composite rotors up to about 100,000 rpm, dearer but holding more per kilogram.

Two things the formula does not say. Energy is not power: how fast it comes out is set by the motor-generator and its electronics, not the rotor. And a spinning wheel leaks. Drag in air rises with the cube of speed, so rotors run in a vacuum, and the review puts bearing loss at about 5% of stored energy per hour for mechanical bearings against about 1% for magnetic ones. Flywheels are for seconds to minutes, not for keeping summer sunshine until winter.

In short

A flywheel stores energy as rotation, and that energy grows with the square of the spin rate. The outward pull on the rim grows with the same square, so the material's strength, not the wheel's mass, sets how fast it may go and how much it holds per kilogram. Within that ceiling it cycles almost endlessly and answers in seconds, which is what short grid faults need.