# Fall Impact Force

## Description

In lead climbing using a dynamic rope, the fall factor (f) is the ratio of the height (h) a climber falls before the climber’s rope begins to stretch and the rope length (L) available to absorb the energy of the fall.

The impact force is defined as the maximum tension in the rope when a climber falls. Using the common rope model of an undamped harmonic oscillator (HO) the impact force Fmax in the rope is given by the formula shown here.

Related formulas## Variables

F_{max} | fall impact force (N) |

m | climber's mass (kg) |

g | Standard gravity |

h | fall height (m) |

k | spring constant of the rope (N/m) |