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Climbing Capstans | Seek n' Geek IX

Capstans are commonly used in climbing to secure a rope to a tree to create a top rope anchor. Top rope climbing is when the rope is secured at the top and runs down through the anchor to the climber and the belayer below, as shown in the center image.

How much force is necessary to hold a climber? From FUNdaMENTALS the capstan equation is:

Figure 1: Capstan climbing anchors for top rope climbing

It was difficult to find a value for the coefficient of static friction of rope on a tree, so as a proxy I used a calculated value for hemp rope on wood. Then I used the equation to calculate the Fhold possible with an Fpull of 5kg with 3 wraps around the tree as drawn below. To validate that this is indeed the correct capstan equation I derived the equation from the drawings on the left, and the calculations are shown below.

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