Presets
Playback
Apparatus
Model checks
The science
What is modelled
Two flyweights hang on arms of length L from a pivot on a spinning spindle. Gravity pulls them down, the needed centripetal force swings them out. Rigid lower links tie them to a sleeve that slides on the spindle; in a steam engine the sleeve moves the throttle.
Equations
- Conical pendulum equilibrium
cosθ = g / (L ω2)(the simplification used by the 3D page: the small pivot offset is ignored). - Weight radius
r = r0 + L sinθ, heightz = ztop - L cosθ. - Sleeve height from the rigid lower link of length L2:
zs = z - √(L22 - (r - rs)2). - Response: a damped second-order servo
θ'' = k(θeq - θ) - c θ'with k = 28 s-2.
Checks run in the page
- A long run at constant speed settles on the analytic angle.
- The speed at which the weights leave the lower stop equals
ω = √(g / (L cosθmin)). - The lower-link length stays constant over the whole range of angles.
- Sleeve lift rises monotonically with speed.
Honest simplifications
The dynamics is a fitted servo rather than a full rigid-body model with sleeve mass, spring load and friction; the engine and throttle loop is not modelled. Not a safety-rated simulation.
What to try
- Raise the speed: the weights swing out until they hit the upper stop at 54 degrees.
- Drop to the Moon preset: with weak gravity the weights lift at a much lower speed.
- Lower the damping and change the speed: the arms overshoot and oscillate before settling.