Balance Poise Error & Isochronism
Calculates the daily rate disturbance caused by an eccentric center of mass on a watch balance wheel resting in vertical positions (Crown Up, Crown Down, Dial Up).
\[ \Delta R_{poise} = \frac{m \cdot r_{cg} \cdot g}{2 \cdot C_{hairspring}} \cdot \cos(\phi) \]
Plain Text Formula:
Delta_Rate = (m * r_cg * g) / (2 * C_hairspring) * cos(phi)
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ \Delta R_{poise} \] | Daily Rate Poise Shift | s/day | Position-dependent acceleration or retardation |
| \[ m \] | Balance Wheel Mass | grams (g) | Total mass of the rim and arms |
| \[ r_{cg} \] | Center of Gravity Eccentricity | micrometers (µm) | Displacement of mass center from true rotational pivot |
| \[ g \] | Gravitational Acceleration | 9.81 m/s² | Local gravity vector |
| \[ \phi \] | Orientation Angle | degrees | Angle of heavy point relative to gravity vector at dead point |
💡 Worked Engineering Example
Problem Statement:
Why does dynamic balance poising eliminate positional variance between 3H, 6H, and 9H?
Step-by-Step Solution:
- Gravity pulls on the heavy spot, speeding up swing when falling and slowing it when rising
- Dynamic poising mills or undercuts the heavy spot to bring r_cg -> 0
- When r_cg = 0, Delta R_poise drops to 0 seconds per day across all positions
🎯 Result: Poise compensation eliminates positional rate delta down to ±1 s/day.