Analysis of a test fall

Force v.s. time data for drop tests using climbing rope has been collected and made available on the net by Hal Murray ( I find analyzing this data is fascinating, even though it has little relevance to my use of rope in climbing. The fact is that the UIAA and some newer organizations have developed practical tests that provide a high level of confidence that ropes, as used in climbing, will do their part help heep us alive and healthy - understanding why ropes behave this way is not necessary for climbers.

Still, I'm a nerd and can't resist fiddling with data. So here goes...

Data for several experiments are available. Most of these include prusiks, force limiters, or other devices that mask the rope's properties. I've picked the first data set for analysis. The commentary supplied with this data reads:

	SamplesPerSecond 2500
	DateTime 2/12/89 11-04
	NumberOfSamples 5000
	Peak 1450
	Info 10 ft, fall factor 1, old climbing rope, good condition
This data is graphed in green below with force in pounds on the y axis plotted against sample number on the x axis. Total elapsed time is 2 seconds.

The red line is position data computed by estimating the mass, m, of the dropped object, and the time when it was dropped, t0=0, then updating its position, yt, and velocity, vt, each 1/2500th of a second with the rule:

	an = fn/m + g
	vn = vn-1 + an / 2500
	yn = yn-1 + vn / 2500
where fn is the nth force (shifted depending on starting time). Ignore the units for the position graph - distances were scaled to fit on the same graph as force. The total distance shown is approximately 1.5 meters and roughly corresponds to rope stretch.

Very nice, so far. The forces look reasonable, and we see a nicely damped oscillation as the mass comes to rest. The force curve is a bit noisy along the initial rise and we could speculate about the cause (is it knot tightening or other internal rope-friction releasing?).

To learn more, I plotted force vs. distance fallen (rope stretch). Force in pounds is on the y axis, and distance in meters on the x axis.

I think this plot is way cool, but keep in mind that the position of the inner spirals can be moved by assuming alternate initial conditions. I chose initial conditions that resulted in a sensible position vs. time plot. Unfortunately, I don't have a record of the initial conditions used to generate the position plots.

Anyway, I think it is fair to conclude that this plot is reasonably close to reality for our purposes. Here are some observations:

Comments, discussion, etc. are welcome, but not spam! I can be reached at

Ken Cline