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Capstan / Belt Friction

A rope or belt wrapped around a fixed drum multiplies tension by e^(µθ) (the capstan or Euler-Eytelwein equation). A small holding force restrains a large load — the reason a few turns around a bollard hold a ship. θ is the total wrap angle in radians.

Inputs

Friction coefficient µ

Wrap angle

Wrap unit

Known tension / load (N)

Tension ratio e^(µθ)

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Tight side (load × ratio)

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Hold force (load ÷ ratio)

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Rigid drum, uniform µ, no slip. A helper, not a substitute for engineering judgment.