Capstan equation
The capstan equation or belt friction equation, also known as the Euler-Eytelwein formula describes the tension required to cause slippage of a flexible line (such as a rope, wire rope, or a belt) that is wound around a cylinder and tensioned on its opposite side. Flexible lines tensioned on curved surfaces create normal forces and corresponding friction forces, resulting in a greater load required to cause slip than the load holding it taut. The capstan equation applies to multiple rope windings around the circumference of the cylinder, and for fractions of one revolution as is the case in applications such as rope drives or band brakes. It also applies to both static cylinders, such as bollards and capstans, and dynamic cylinders that can rotate such as pulleys and winches. There are multiple applications, especially in marine operations, where the effects are used to multiply human pulling capacity, such as the tensioning of rigging used for sails, and in the mooring of vessels. In mechanical systems, friction between belts and rotating pulleys also enables greater torque to be transmitted, especially in pre-tensioned systems that increase traction and grip.