# Traction Around a Cylinder

I have been trying to figure out the formula for maximum load held by traction of a band or strip wrapped around a cylinder where there is a given force holding the other end of the strip.

Suppose the strip is wrapped 180 degrees around a horizontally positioned cylinder so that the strip is vertical as as it comes onto and leaves contact with the cylinder. The load is on the left and a holding force is applied downward on the right hand end of the strip. The load would be a larger force than the holding force. From experience, a rope around a tree can resist slipping in the face of tons of load force if the rope is wrapped a few times around the tree and a man holds the end of the rope with only a few pounds of force. It seems to me that the ratio of the two forces is an exponential function of the angle through which the wrapping is done. Of course, the coefficient of static friction between the strip and the cylinder must be known.

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#### kjohnson

I believe what you are looking for is called belt friction. Here is the wiki link that has the basic formula:

http://en.wikipedia.org/wiki/Belt_friction

There are some other sites & videos you could find if you want a full derivation.

I believe what you are looking for is called belt friction. Here is the wiki link that has the basic formula:

http://en.wikipedia.org/wiki/Belt_friction

There are some other sites & videos you could find if you want a full derivation.
kjohnson,

This information completely solves the problem. It even led to a PDF of a derivation.