Watch Balance Wheel Amplitude
Measures the maximum angular displacement of a mechanical watch balance wheel from its neutral equilibrium position in one half-oscillation. Typical healthy amplitudes range from 270° to 315° in horizontal positions.
\[ \theta_{amp} = \frac{1}{2} \cdot \theta_{total} = \frac{\omega_{max} \cdot T}{2 \pi} \]
Plain Text Formula:
Amplitude = 0.5 * Total_Rotation = (omega_max * T) / (2 * pi)
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ \theta_{amp} \] | Balance Amplitude | degrees (°) | Maximum angular displacement from dead center |
| \[ \theta_{total} \] | Total Arc of Oscillation | degrees (°) | Peak-to-peak total swing arc |
| \[ T \] | Period of Oscillation | seconds (s) | Time duration of one full oscillation cycle |
| \[ \omega_{max} \] | Max Angular Velocity | rad/s | Angular speed when passing through equilibrium |
💡 Worked Engineering Example
Problem Statement:
Calculate the amplitude of an ETA 2824-2 caliber oscillating through a total peak-to-peak arc of 560°.
Step-by-Step Solution:
- Identify total swing arc: 560°
- Divide total swing by 2: 560° / 2 = 280°
🎯 Result: Amplitude is 280°, which indicates optimal lubrication and mainspring torque transmission.