# Winches

## Effort force to raise a load

A winch is a mechanical device that is used to wind up or wind out a rope or wire rope.

### Velocity Ratio

The velocity ratio can be expressed as

*VR = R / r (1)*

*where *

*VR = velocity ratio*

*R = effort force radius (m)*

*r = load radius (m)*

### Effort Force

The force to raise a load can be expressed as

*F = W / μ VR *

* = W r /** μ ** R *

* = m a _{g} r /*

*μ*

*R (2)*

*where *

*F = force (N)*

* μ = mechanical efficiency of the system (equal to one for an ideal friction-less system, a fraction less than one for real-world systems with energy losses due to friction)*

*m = mass (kg)*

*a _{g} = acceleration of gravity (9.81 m/s^{2})*

*W = weight (N)*

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