Capstan Equation — Rope Friction

Coefficient of Friction μ: 0.30 Wrap Angle θ: 180° Hold Force T_hold: 10 N

Mechanical advantage: -

Load force T_load: -

Wrap turns: -

T_load = T_hold · e^(μθ)
where θ is in radians.

Discovered by Euler (1747). A small hold force can support enormous loads with enough wraps.

Drag the animation to change wrap angle. Used in sailing, rock climbing belays, and capstan winches.