Presets
Playback
Balance, train and operator
Each vibration of the balance moves the escape wheel by half a tooth; the wheel train must turn that into exactly one turn of the seconds hand per minute.
Model checks
The science
What is modelled
The balance beats at a fixed rate; the escape wheel (15 teeth) advances half a tooth per vibration; two gear stages with 8-leaf pinions reduce the escape wheel speed to the seconds hand. A chronograph hand moves only on a beat, so its reading is quantised.
Equations
- Escape wheel speed
(vph / 3600) x 60 / (2 x 15)turns per minute. - Hand speed
= escape rpm / ((z4 / 8)(z3 / 8)); matched when it equals 1. - Rate error
(hand rpm - 1) x 86400seconds per day. - Reading error of start and stop
sqrt(2 b^2 / 12 + 2 s^2)for beat period b and operator jitter s.
Checks run in the page
- Counted escape pulses through the train give the hand turns.
- Vibrations counted in an hour.
- Dial angle plus counter reconstructs time within one beat.
- Random start and stop errors against the formula.
- Rate error of the chosen train over 24 h.
Honest simplifications
A simplified three-wheel train with 15 escape teeth and 8-leaf pinions; real calibres have more stages, a clutch and a fifth-wheel layout, and the balance itself adds its own rate error which is not modelled here.
What to try
- Press 28 800 vph, one tooth off: the displayed time gains thousands of seconds a day.
- Compare 18 000 and 36 000 vph presets: the beat quantisation shrinks as the beat speeds up.
- Raise the operator jitter and see it dominate every beat rate.