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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:
Lubricated friction is a case of fluid friction where a lubricant fluid separates two solid surfaces. [9] [10] [11] Skin friction is a component of drag, the force resisting the motion of a fluid across the surface of a body. Internal friction is the force resisting motion between the elements making up a solid material while it undergoes ...
Net indicated mean effective pressure (IMEP) is calculated using the indicated power; i.e., the pressure volume integral in the work per cycle equation. Sometimes the term FMEP (friction mean effective pressure) is used as an indicator of the mean effective pressure lost to friction (or friction torque) and is just the difference between IMEP ...
The equation above can be used to plot the Fanno line, which represents a locus of states for given Fanno flow conditions on an H-ΔS diagram. In the diagram, the Fanno line reaches maximum entropy at H = 0.833 and the flow is choked. According to the Second law of thermodynamics, entropy must always increase for Fanno flow. This means that a ...
A toothed belt-pulley design provides improved efficiency for mechanical power transmission using a tractrix catenary shape for its teeth. [9] This shape minimizes the friction of the belt teeth engaging the pulley, because the moving teeth engage and disengage with minimal sliding contact.
Hersey's original formula uses the rotational speed (revolutions per unit time) for N and the load per projected area (i.e. the product of a journal bearing's length and diameter) for P. Alternatively, the Hersey number is the dimensionless number obtained from the velocity (m/s) times the dynamic viscosity (Pa∙s = N∙s/m2), divided by the ...