Watch Balance Frequency & BPH
Relates the vibrational frequency in Hertz (cycles per second) to beats per hour (BPH), determined by hairspring rotational elasticity and balance wheel moment of inertia.
\[ f_{Hz} = \frac{BPH}{7200} = \frac{1}{2\pi} \sqrt{\frac{C_{hairspring}}{I_{balance}}} \]
Plain Text Formula:
f_Hz = BPH / 7200 = (1 / (2 * pi)) * sqrt(C_hairspring / I_balance)
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ f_{Hz} \] | Frequency | Hertz (Hz) | Complete balance oscillation cycles per second |
| \[ BPH \] | Beats Per Hour | vph | Number of pallet jewel ticks per hour (2 ticks per cycle) |
| \[ C_{hairspring} \] | Spring Elastic Torque Factor | N·m/rad | Torsional stiffness of the balance spring |
| \[ I_{balance} \] | Moment of Inertia | kg·m² | Rotational inertia of the balance rim and screws |
💡 Worked Engineering Example
Problem Statement:
Convert 28,800 BPH to operational frequency in Hertz.
Step-by-Step Solution:
- Each cycle contains 2 vibrations / beats
- Cycles per hour = 28,800 / 2 = 14,400
- Divide by 3,600 seconds/hr: 14,400 / 3,600 = 4.0 Hz
🎯 Result: A 28,800 BPH caliber operates at exactly 4 Hz (4 full oscillations per second).