Must I point out that after you fall and the rope catches you you start swing? Only after you stop yourself against the rock do you stop moving... there we go, the source of this magical critical damping

Sure there is some damping in the rope but most of it comes from friction between rope, quickdraws, and you hitting the rock

Clews is more correct than most others here.

Most of the energy goes into a number of places. Bouncing around after the fall, elongating the spring of the rope, permanetly deformation of the core of the rope, and the friction between the rope and the carabiners/rock (especially the carabiner that is actually catching you).

Let's say for one moment we look at the top most carabiner. Let's assume that you hit 8kN of force during a decent fall and the sliding coefficient of friction for the rope's sheath and the aluminium is .2.

At this moment, that carabiner would be resisting with 1.6 kN of force. This is equal to a 360 lbs of dampaning force. This is why you do not bounce a LOT when you fall on a climbing rope. There is a ton of friction in your system.

The internal friction in the rope itself absorbs very little of the actual energy of a fall.

Most of the energy goes into a number of places. Bouncing around after the fall, elongating the spring of the rope, permanetly deformation of the core of the rope, and the friction between the rope and the carabiners/rock (especially the carabiner that is actually catching you).

Let's say for one moment we look at the top most carabiner. Let's assume that you hit 8kN of force during a decent fall and the sliding coefficient of friction for the rope's sheath and the aluminium is .2.

At this moment, that carabiner would be resisting with 1.6 kN of force. This is equal to a 360 lbs of dampaning force. This is why you do not bounce a LOT when you fall on a climbing rope. There is a ton of friction in your system.

The internal friction in the rope itself absorbs very little of the actual energy of a fall.

So, kinetic energy has been converted to strain energy

Jay Tanzman has fleshed out a model for ropes that includes the friction in the top carabiner. We can calculate this frictional energy, based on Jay's model, and compare it to the fall energy, for a UIAA drop test.

Let's start with a real rope, say, the Blue Water Lightning Pro 9.7mm. It has a maximum impact force of 7.8 kN and a dynamic elongation of 32.2%.

Using Jay's model, and assuming a frictional coefficient of 0.33, we can calculate the rope modulus and from that determine the rope elongation and the carabiner frictional energy.

According to this model, the energy dissipated by the carabiner is 0.12 kJ, less than 3% of the fall energy.

Or course Jay's model isn't accurate. It overestimates the elongation of the rope by nearly 40%. But it doesn't come close to suggesting that the top carabiner is responsible for very much of the fall energy.

Jay's primary contention is that at the bottom of the fall virtually all of the energy is in the form of strain energy. But if you calculate this energy based on his model it accounts for only about 52% of the fall energy. Even adding in the 3% frictional loss due to the carabiner leaves a large amount of energy unaccounted for.

So the simple answer that Jay Young was apparently looking for is that the rope absorbs energy, not force. But it doesn't simply convert it to strain energy like a simple spring model suggests.

So, what you need to do is design an aparatus where you can do various drop tests of masses/drop heights that have energies that do not cause the rope to elongate past its elastic limit.

Then use masses which greatly excede the elastic portion of the stress strain curve and push it into the plastic portion.

Observe the velocity/position with a high speed camera and the forces with a meter.

Do this drop with the rope connected directly to an anchor. Then do the same drop height/weight and rope length with a carabiner absorbing the forces.

You should be able to come up with some decent formulas which predict the energy absorbed by the rope.

And don't forget, the energy absorbed by the plastic deformation in the rope is rather large too. Separating the energy absorbed by plastic deformation and internal friction is very difficult without embeded temperature sensors, etc.

Also, do not forget that the rope itself is not a homogenous body which behaves according to a simple spring/harmonics equation. Under the most simple modeling to even remotely accurately model the situation, you would need essentially THREE separate equations to model the different elements of the rope.

You start to get into a really neat/interesting differential equation at that point :)

In a UIAA drop test there is very little rope that slides over the top carabiner. And yet damping is still observed in the system, with roughly half the energy dissipated with each bounce (including the first).

Jay is right that the rope absorbs energy, not force. But he is wrong in suggesting that nearly all of it is in the form of strain energy.


[edited for brevity]

And don't forget, the energy absorbed by the plastic deformation in the rope is rather large too. Separating the energy absorbed by plastic deformation and internal friction is very difficult without embeded temperature sensors, etc.

Wait, what? Very little rope that "slides over the top carabiner"? Is the rope fixed to a point on top or is it running through a carabiner? If it is running through a carabiner, it does not matter "how much" is actually running over it or not. The friction is calculated based on the normal force, not the surface area.

You're making a distinction that I wasn't bothering with, namely between plastic deformation (which generally involves the release of a lot of heat) and "internal friction". My point was that strain energy and carabiner frictional loss cannot fully account for the fall energy. Rope damping, whatever the exact mechanism, is quite significant. No need for fancy experiments, the evidence is readily available.

We're talking about frictional ENERGY loss, not just the force. In a high fall factor drop very little rope slips over the carabiner and the frictional loss is relatively small.

The distinction however is huge. Especially when we're talking about the energy involved :p

Ahh, I misread what you wrote then. I thought you were talking about surface area, heh. What kind of length are we talking about here? Also, do you know what the sliding coefficient of friction between the rope and carabiner is?

Show the data and I'll believe it, hehe.

All of this is to say that I don't think that the work done by the damping in the rope is insignificant. I wish that Pavier had done a comparison of his model to simpler models to show that his numerical approach is much better. It would have shown the modification to the expected peak force due to the damping of the rope.

Jay is right that the rope absorbs energy, not force. But he is wrong in suggesting that nearly all of it is in the form of strain energy.

That's pretty much what I was looking for.
J