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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).
Belt friction is a term describing the friction forces between a belt and a surface, such as a belt wrapped around a bollard.When a force applies a tension to one end of a belt or rope wrapped around a curved surface, the frictional force between the two surfaces increases with the amount of wrap about the curved surface, and only part of that force (or resultant belt tension) is transmitted ...
Examples of rope and pulley systems illustrating mechanical advantage. Consider lifting a weight with rope and pulleys. A rope looped through a pulley attached to a fixed spot, e.g. a barn roof rafter, and attached to the weight is called a single pulley. It has a mechanical advantage (MA) = 1 (assuming frictionless bearings in the pulley ...
By this the rope is stretched a bit and an internal tension is induced (= on every position along the rope). The rope is wrapped around a fixed item such as a bollard; it is bent and makes contact to the item's surface over a contact angle (e.g., ). Normal pressure comes into being between the rope and bollard, but no friction occurs yet.
V belts (also style V-belts, vee belts, or, less commonly, wedge rope) solved the slippage and alignment problem. It is now the basic belt for power transmission. They provide the best combination of traction, speed of movement, load of the bearings, and long service life.
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With belts and pulleys, friction is one of the most important forces. Some uses for belts and pulleys involve peculiar angles (leading to bad belt tracking and possibly slipping the belt off the pulley) or low belt-tension environments, causing unnecessary slippage of the belt and hence extra wear to the belt.
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