Flywheels and Governors

A reciprocating engine produces torque in pulses while the load wants a steady value, so something must store the surplus and return it during the deficit. A flywheel does that by speeding up and slowing down.

It does not eliminate the fluctuation — it makes it small. The permitted coefficient of fluctuation sizes the wheel, from a few per cent for a pump down to a fraction of one for a generator.

The turning moment diagram plots torque against crank angle, and the largest area between the curve and the mean line is the energy to be absorbed in one cycle. I = ΔE/(C_s·ω²) then gives the inertia directly.

I = mr², so radius is worth far more than mass — doubling it quadruples the inertia at the same weight, which is why a flywheel is a heavy rim on light spokes. The limit is hoop stress σ = ρv².

A flywheel stores nothing over seconds, so if the load falls away the engine accelerates and keeps accelerating. A governor acts on that timescale by reducing the fuel supply itself.

Flyballs swing outward as speed rises, lifting a sleeve that closes the throttle — a mechanical proportional controller predating electronics by a century and a half. Maxwell's 1868 analysis of why governors hunt is generally taken as the beginning of control theory.

Being proportional, a governor needs an error to hold the throttle where it is — so speed falls as load rises. That droop is deliberate: without it, two engines on the same load would fight for it.

It is exactly the argument that reappears in power-system frequency control, where droop lets thousands of machines share load without communicating.

• A punch press uses a small motor and a large flywheel, restoring over a full cycle what the punch takes in a second.
• Grid inertia is the same principle at national scale — which is exactly what replacing turbines with inverters removed.
• Flywheel storage in composite rotors stores megajoules for frequency response and uninterruptible supplies.