Simulation Lab

Experiment with the mechanisms

Simplified physical models for learning. They illustrate principles; they are not engineering tools.

Pendulum

A 'seconds pendulum' (≈0.994 m) beats once per second. Larger swings run slower — circular error — which the anchor escapement reduced by allowing small arcs.

Length: 0.994 mAmplitude: 10°Length error (temperature/regulation): 0.1 mm

Period	2.0042 s
Beat (half-period)	1.0021 s
Rate change from length error	-4.3 s/day

Balance wheel & hairspring

Frequency f = (1/2π)·√(k/I). Animation slowed 4×. Typical modern watches: 4 Hz (28,800 vph); vintage: 2.5 Hz (18,000 vph).

Moment of inertia: 12 mg·cm²Hairspring stiffness: 0.76 µN·m/rad

Frequency: 4.01 Hz · 28,838 vph

Anchor escapement

Each beat the pallet releases the escape wheel by half a tooth. A 30-tooth wheel on a seconds pendulum turns once a minute — so it can carry the seconds hand.

Beats per hour: 3600Escape-wheel teeth: 30

Beat: 1.000 s · Wheel revolution: 1.00 min

Gear train

Centre wheel turns once per hour. Enter wheel and pinion teeth from centre to escape pinion. The default 80·75·70 over 10·10·7 with a 15-tooth escape wheel gives the classic 18,000 vph.

Wheel teeth (comma separated)Pinion leavesEscape-wheel teeth: 15

Escape wheel turns per hour: 600.0 · Resulting beat rate: 18,000 vph (2.50 Hz)