I put together this little calculator that estimates the maximum tension in a rope arresting a falling mass, given the rope type, fall factor, and the mass of the falling object. It should be self-explanatory - there are annotations.
It also estimates the rope’MBS for comparison, if not measured.
Maybe somebody will find it useful as well…
This is another version of the above calculator using the UIAA EN892 (dynamic) and EN1891 (low stretch) tests reporting the peak shock load (impact force) to calculate the rope modulus rather than guestimating the rope parameters as in the previous version.
As not all ropes and cordage have peak shock load and MBS data available (and also, the reported values need to be taken with a grain of salt as the standards only call for the thresholds not to be exceeded hence the actual values may not be properly reported), the original calculator still has some uses.
An interesting experiment by Petzl on impact forces during falls. It more or less validates the model used in the calculator above.
To see it, as they use Volta 9.2mm EN892 rope, set U=8.6kN, M=80kg, and R=1.7 to characterise the rope elasticity.
To compare the model predictions with Petzl measured shock forces on the anchor, set fall factor f to 0.3, 0.7, and 1.0 and read the maximum shock force for 80kg mass off the plot.
Just wanted to add that the calculator is technically limited to approximating peak shock forces in a rope with a fixed anchor point, similar to the way EN drop tests are conducted, not with a movable belayer being lifted off the ground, which has the net effect of further softening the fall.
It is probably still sufficient as a first approximation of impact forces even in this scenario (the practical reduction of peak impact force due to the belayer lift is roughly 20% in common scenarios), possibly reducing the rope modulus to account for the belayer lift (or comparing the predictions with the impact force on the anchor as I did). For a modified model that explicitly accounts for the belayer lift, see this paper.