Presets
Playback
Governor and engine
Faster rotation throws the balls outward and lifts the sleeve; a heavier sleeve raises the speed needed for the same angle.
Mode
Model checks
The science
What is modelled
Two flyballs on arms hinged at a small offset from the spinning shaft, with links to a sliding sleeve. In the frame rotating with the shaft each ball feels gravity and a centrifugal force. The arm angle is found where the total potential energy (gravity of balls and sleeve minus the centrifugal term) is stationary, which is the principle of virtual work.
Equations
U(θ) = 2 m g zb + M g zs - m ω2 rb2, equilibriumdU/dθ = 0.- With no sleeve mass this reduces to the conical pendulum
ω2 = g tanθ / (a + L sinθ). - Dynamics
I θ'' = -dU/dθ - c θ'withI = 2 m L2; in closed loop the throttle falls as the arms spread, and engine speed obeysJ ω' = Tengine - Tload.
Honest limits
The ball mass is lumped at the arm end, links and arms are massless, friction is a simple damper. The 3D page animates a stylised rpm-to-angle map; this page solves the physical balance with the same linkage dimensions, so angles differ in detail. A proportional governor always has some speed droop under load.
What to try
- Choose Porter governor: with a heavy sleeve the balls need much more speed to spread the same angle.
- Switch to closed loop and raise the load torque: the speed droops a little, and a higher governor gain reduces the droop.
- Choose On the Moon: the balls spread at much lower speed because gravity pulls them back less.