Watch Power Reserve Calculation
Determines the operating autonomous runtime in hours of a fully wound mechanical watch based on mainspring barrel revolutions and center pinion tooth ratios.
\[ t_{reserve} = N_{turns} \cdot \frac{Z_{barrel}}{Z_{center\_pinion}} \]
Plain Text Formula:
Power_Reserve_Hours = Barrel_Turns * (Barrel_Teeth / Center_Pinion_Leaves)
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ t_{reserve} \] | Power Reserve | hours (h) | Total running time from full wind to stop |
| \[ N_{turns} \] | Effective Barrel Turns | revolutions | Number of active unwinding turns inside the barrel drum |
| \[ Z_{barrel} \] | Barrel Tooth Count | teeth | Number of outer teeth on the mainspring barrel |
| \[ Z_{center\_pinion} \] | Center Pinion Leaves | leaves | Number of leaves on the center wheel pinion (turns once per hour) |
💡 Worked Engineering Example
Problem Statement:
A barrel has 84 teeth, driving a center pinion with 12 leaves. The mainspring unwinds 5.5 turns. Calculate power reserve.
Step-by-Step Solution:
- Teeth ratio = 84 / 12 = 7.0 hours per barrel turn
- Total power reserve = 5.5 turns * 7.0 h/turn = 38.5 hours
🎯 Result: The watch delivers 38.5 hours of autonomous power reserve (typical ETA 2824-2 rating).