Mainspring Torque and Barrel Power
Computes the elastic restoring torque output of a coiled horological mainspring based on Young's modulus, strip width, strip thickness cubed, active length, and wind angle.
\[ M_{spring} = \frac{E \cdot b \cdot e^3}{12 \cdot L} \cdot \theta_{wind} \]
Plain Text Formula:
Torque = (E * b * e^3 / (12 * L)) * theta_wind
📐 Variable Definitions & Parameters
| Symbol | Variable Name | Standard Unit | Physical Definition |
|---|---|---|---|
| \[ M_{spring} \] | Delivered Torque | N·m or N·mm | Torque exerted by the spring onto the mainspring barrel |
| \[ E \] | Young's Modulus | GPa | Elastic modulus of spring alloy (Nivarox / Nivaflex ~205 GPa) |
| \[ b \] | Spring Width | mm | Height of the spring strip inside barrel arbor |
| \[ e \] | Spring Thickness | mm | Blade thickness (governs torque to the 3rd power) |
| \[ L \] | Active Spring Length | mm | Total unwound strip length |
| \[ \theta_{wind} \] | Angular Deflection | radians | Angle of winding rotation |
💡 Worked Engineering Example
Problem Statement:
Calculate the impact on mainspring torque if the spring thickness e is increased by 10% (1.10x).
Step-by-Step Solution:
- Torque is proportional to thickness cubed: e^3
- Multiplier = (1.10)^3 = 1.331
🎯 Result: A 10% increase in mainspring thickness increases delivered torque by 33.1%.