HEÚREMA · the workbench of inventions · a law, put to work · kept by THE INVENTOR

THE WATT GOVERNOR ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP

The first machine that ruled itself. Two heavy balls spin on arms off the engine’s shaft; spin faster and they fly outward, and rising, they close the steam valve that feeds the engine — so speeding up throttles itself down. A loop with no brain, holding a steady speed. Slide the speed and watch the balls set their own limit.

◆ LIT▲ AMBER
◧ THE MEASURE · 2D
◍ THE FLYBALLS · 3D · faster = wider
◆ THE FOURTH · 4D · a tesseract turns
◐ THE SHADOW · one dimension down
👶 THE TODDLER CORNER — one fat tap
ω (rad/s)
ball angle θ
cosθ = g/ω²L
throttle

◆ LIT — exact / checkable

At steady spin each ball sits where gravity and centrifugal force balance: cosθ = g/(ω²L), so faster ω lifts the balls (θ grows) until, past √(g/L), they swing out. That rise mechanically closes the throttle, cutting the power that drives ω — negative feedback that pins the speed with no sensor or computer. A fail-loud self-check throws unless θ increases monotonically with ω AND the equilibrium ω² = g/(L·cosθ) holds exactly at the computed angle — the 1788 loop Maxwell later analysed to found control theory.

▲ AMBER — the figure

A static-equilibrium model — the real governor has mass, damping, and can HUNT (oscillate) if tuned badly, which is precisely what Maxwell’s 1868 ‘On Governors’ studied. The cosθ = g/(ω²L) balance and the feedback direction are exact.

HEÚREMA: an invention is a physical law cornered into doing work.  — THE INVENTOR
David Lee Wise / ROOT0 / TriPod LLC  ·  the workbench, with AVAN