Three coupled real models drive this side-view kick wheel:
Flywheel: I·domega/dt = tau_kick − b·omega
Centering: x'' = −(k/m)x − 2*zeta*sqrt(k/m)*x' (damped oscillator)
Pulling: r(h)·t(h)·dh ~= const (clay volume conserved as wall rises)
The wheel is a rotational-inertia flywheel: each kick applies an angular impulse tau_kick, and between kicks angular momentum L = I·omega only bleeds off through bearing friction b·omega, so a heavier flywheel (larger I) coasts longer and smoother — the real reason kick wheels use a heavy stone or iron disc.
The clay lump's radial center-of-mass offset x obeys a damped harmonic oscillator: the potter's centering force supplies the spring term k (pulling the mass back to the spindle axis) and viscous hand contact supplies damping zeta. Too little centering force and the wobble decays slowly (or not at all, visible as a persistent shiver); strong centering with critical-ish damping collapses the wobble fastest.
Once you pull the wall, clay volume is conserved: as wall height h grows, radius x thickness must shrink to keep r·t·dh roughly constant, so thickness thins visibly as the vessel grows tall — pull too fast and the wall thins faster than it can support itself.
- Left view — side cross-section: flywheel base, spinning clay mass with a wobble marker, and the growing vessel wall profile.
- RPM / angular momentum — read directly off I·omega each frame.
- Wobble amplitude — the live |x| of the damped-oscillator centering model, in millimeters.