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The capstan equation [1] or belt friction equation, also known as Euler–Eytelwein formula [2] (after Leonhard Euler and Johann Albert Eytelwein), [3] relates the hold-force to the load-force if a flexible line is wound around a cylinder (a bollard, a winch or a capstan).
The equation used to model belt friction is, assuming the belt has no mass and its material is a fixed composition: [2] = where is the tension of the pulling side, is the tension of the resisting side, is the static friction coefficient, which has no units, and is the angle, in radians, formed by the first and last spots the belt touches the pulley, with the vertex at the center of the pulley.
This does cause frictional shear stresses in the contact area. In the final situation the bollard exercises a friction force on the rope such that a static situation occurs. The tension distribution in the rope in this final situation is described by the capstan equation, with solution:
Frictional contact mechanics emphasizes the effect of friction forces. Contact mechanics is part of mechanical engineering. The physical and mathematical formulation of the subject is built upon the mechanics of materials and continuum mechanics and focuses on computations involving elastic, viscoelastic, and plastic bodies in static or dynamic ...
Added arrowhead in order to make clear that the curved line shows an angle and not direction of rotation. Shifted "Capstan". 22:16, 27 April 2015: 512 × 539 (1 KB) Krishnavedala: optimized: 03:19, 5 July 2012: 512 × 548 (1 KB) Krishnavedala: corrected "title" element: 03:16, 5 July 2012: 512 × 548 (1 KB) Krishnavedala
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Capstan equation; Metadata. This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.