The belt friction calculator is based on the Euler-Eytelwein equation and can be used to calculate the pulling force, holding force, the coefficient of friction or the wrap angle online.

Enter three known sizes and the missing size will be calculated. Basically, the following applies:

- the holding force is always smaller than the pulling force,
- the wrap angle is always positive,
- the coefficient of friction is always positive and
- the coefficient of friction is usually less than 1.

## About the math

The tool calculates the values based on the following equations.

Equation for pulling force

\[ F_2 = F_1 \cdot e^{µ \alpha}\]

Equation for holding force

\[ F_1 = F_2 \cdot e^{-µ \alpha}\]

Equation for the coefficient of friction

\[ µ = \frac{ln \frac{F_2}{F_1}}{\alpha} \]

Equation for the wrap angle

\[ \alpha = \frac{ln \frac{F_2}{F_1}}{ µ} \]

Please note that the angle must be given in radians.

## An expample

A rope is wrapped around a bollard. The rope is pulled with a force F_{2} of 1000 N. How big must the wrap angle α be so that the holding force F_{1} is only 50 N with a coefficient of friction of µ = 0.3?

The values can be entered directly into the calculation tool. In order to be able to calculate the wrap angle online, the corresponding input field is simply left blank.

The result for the wrap angle is 572 °, i.e. the rope must be wrapped around the pile a little more than 1.5 times.

Exercises on the subject of friction can be found under the keyword friction.