Belt Capstan (Friction) Tension
Belt Capstan (Friction) Tension
Friction lets a belt or rope hold a much larger tension on one side than the other — the capstan effect used in winches and belt drives.
The capstan equation gives T_1 = T_2·e^(μθ). where T_2 is the slack-side tension, μ the friction coefficient and θ the wrap angle in radians.
Inputs
T_2 := 0.5 kN=500 N
mu := 0.3=0.3
theta := 3.1416=3.14
Apply the capstan (Euler–Eytelwein) equation.
T_1 := T_2·exp(mu·theta)=1283.17 N
Results
The tension ratio grows exponentially with wrap angle and friction, which is why a few turns around a post can hold a heavy load with a small grip.
Assumptions & limitations
- Belt/rope on the point of slipping.
- Constant friction coefficient.
- Wrap angle in radians.