# Capstan equation ( belt friction equation)

## Description

The capstan equation or belt friction equation, also known as Eytelwein’s formula, relates the hold-force to the load-force if a flexible line is wound around a cylinder (a bollard, a winch or a capstan. Because of the interaction of frictional forces and tension, the tension on a line wrapped around a capstan may be different on either side of the capstan. A small holding force exerted on one side can carry a much larger loading force on the other side; this is the principle by which a capstan-type device operates.

Related formulas## Variables

T_{load} | The applied tension on the line (N) |

T_{hold} | The resulting force exerted at the other side of the capstan (N) |

μ | The coefficient of friction between the rope and capstan materials (dimensionless) |

ϕ | The total angle swept by all turns of the rope (radians) |