Fall factor

As soon as the climber clips the rope into protection above the belay, the fall factor drops below 2.

[1] The impact force is defined as the maximum tension in the rope when a climber falls.

We first state an equation for this quantity and describe its interpretation, and then show its derivation and how it can be put into a more convenient form.

Eventually they come to a stop and at that instant the rope is at maximum tension pulling upward on the climber by a force of 2mg.

The yo-yo'ing will eventually stop when the fall energy has all dissipated by frictional forces between (and within) the rope, the protection pieces and the harness.

It is convenient to express things in terms of the elastic modulus E = k L/q which is a property of the material that the rope is constructed from.

Solution of the quadratic gives Other than fixed properties of the system, this form of the equation shows that the impact force depends only on the fall factor.

Using these values to eliminate the unknown quantity E leads to an expression of the impact force as a function of arbitrary fall heights h, arbitrary fall factors f, and arbitrary gravity g of the form: Note that keeping g0 from the derivation of "Eq" based on UIAA test into the above Fmax formula assures that the transformation will continue to be valid for different gravity fields, as over a slope making less than 90 degrees with the horizontal.