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

TloadThe applied tension on the line (N)
TholdThe resulting force exerted at the other side of the capstan (N)
μThe coefficient of friction between the rope and capstan materials (dimensionless)
ϕThe total angle swept by all turns of the rope (radians)