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The maximum value of static friction, ... the theoretical tension acting on the belt or rope calculated by the belt friction equation can be compared to the maximum ...
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).
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 ...
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:
The left hand side is the maximum frictional force, which equals the coefficient of friction multiplied by the normal force. Rearranging the maximum cornering speed is <. Note that can be the coefficient for static or dynamic friction. In the latter case, where the vehicle is skidding around a bend, the friction is at its limit and the ...
The overall effect can be seen as closely analogous to static friction, i.e., a minimal amount of work per unit distance is required to move the contact line. [ 6 ] The advancing contact angle can be described as a measure of the liquid-solid cohesion while the receding contact angle is a measure of liquid-solid adhesion.
Assuming the Fanning friction factor is a constant along the duct wall, the differential equation can be solved easily. [2] [3] One must keep in mind, however, that the value of the Fanning friction factor can be difficult to determine for supersonic and especially hypersonic flow velocities.