Watch Escapement Beat Error
The time asymmetry between the clockwise (tick) and counter-clockwise (tock) swings of the balance wheel, occurring when the impulse pin is not centered between pallet banking pins at rest.
\[ \Delta t_{beat} = |t_{clockwise} - t_{counter\_clockwise}| \]
Plain Text Formula:
Beat_Error = |t_clockwise - t_counter_clockwise|
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ \Delta t_{beat} \] | Beat Error | milliseconds (ms) | Time asymmetry between half-cycles |
| \[ t_{clockwise} \] | Clockwise Half-Period | ms | Duration of clockwise oscillation |
| \[ t_{counter\_clockwise} \] | Counter-Clockwise Half-Period | ms | Duration of counter-clockwise oscillation |
💡 Worked Engineering Example
Problem Statement:
A 28,800 BPH balance wheel has a clockwise half-period of 124.8 ms and counter-clockwise half-period of 125.2 ms. Find beat error.
Step-by-Step Solution:
- Calculate absolute difference: |124.8 - 125.2| ms
- Delta = 0.4 ms
🎯 Result: Beat error is 0.4 ms, which is well within the acceptable chronometer standard of <0.6 ms.