I'm probably about to show my ignorance of all things physics, but things being equal, I would expect it not to change at all. Curious to hear an actual answer.

Ideally, it shouldn't. But, life being less than ideal...

Has anyone seen any data on how the maximum impact force changes (or doesn't change) as fall length increases for a constant fall factor?

The climber's speed will be greater with the longer falls, so I would assume that would raise the force. However, the longer the amount of rope, the greater effect the dynamic properties of the rope will have.

However, for a fall on static gear the distance would make a huge amount of difference. For a fall on static gear, there is nothing to absorb the extra distance/speed. Farther fall = faster fall = harder impact.

Yes, all other things being equal, the longer fall will have a slightly higher peak force.

The reason for that is simple.

Aside from the rope, there are a lot of other things that can "absorb" some energy, such as the sling on the top piece, the climber's body, and most importantly, the knot tightening.

But each of these can absorb a set amount of energy, and unlike the rope, they don't scale with the length of fall.

A small fall will have a smaller amount of kinetic energy that must be "absorbed", and a larger fraction of that will be absorbed by those various other items, leaving a smaller fraction for the rope, and thus a smaller impact force on the top piece. In a large fall, the overall percent of the energy they can convert to heat is much smaller relative to the total amount of kinetic energy, so the rope must absorb essentially all of the energy, putting a higher force on the top piece of gear.

I've only seen one study that looked at how much energy the knot could absorb. Practically speaking, for falls over say ten or fifteen feet, I don't think it made much difference, but if you like I can try to track down that study for you.

GO

You bring up some practical points that I hadn't considered though I'm still interested in the case where those factors are negligible (lab case). I was asking this question because of the thread about Screamers. It linked to some BD research on Screamers that did some test falls of two different fall factors onto different types of slings, screamers, etc. They didn't vary the fall length within the same fall factor though.

You bring up some practical points that I hadn't considered though I'm still interested in the case where those factors are negligible (lab case). I was asking this question because of the thread about Screamers. It linked to some BD research on Screamers that did some test falls of two different fall factors onto different types of slings, screamers, etc. They didn't vary the fall length within the same fall factor though.

Let me put it another way.

The kinetic energy of a falling body is the force of gravity on that object times the distance it falls. IOW, kinetic energy is directly proportional to fall distance.

IOW, you can say that for any object, the energy is equal to the fall distance times a constant.

So, if FF is fall distance / rope, then for a given FF, the rope is always proportional to the fall distance, which is proportional to the energy.

So if you agree that any given section of rope should be able to absorb X amount of energy in the same way that double the amount of rope would absorb double the energy, then, ignoring air resistance and friction and all that jazz, the rope puts the same peak force on your gear for any given FF.

Make sense?

GO

I would still like to see some data on a case where these other factors aren't involved.

I understand most of what you're saying. I would still like to see some data on a case where these other factors aren't involved.

Strictly speaking you're confusing potential energy (mgh) with kinetic energy (.5mv^2).

This I don't understand "the rope is always proportional to the fall distance, which is proportional to the energy."

This statement

"So if you agree that any given section of rope should be able to absorb X amount of energy in the same way that double the amount of rope would absorb double the energy, then, ..."

seems only to lead to this conclusion

"the rope puts the same peak force on your gear for any given FF."

if the rope is in a linear force vs. distance relationship. I suspect that breaks down with greater fall factors, but I don't know for sure.

These data are taken from a paper by Martyn Pavier. The selected drops were performed with a 70kg steel mass and the belay was tied off. It appears that with the "other factors" removed the length of fall has no significant effect on maximum tension, at least over this limited range.



For real life falls I would wonder about the effects of belay device and belayer behavior.

I am? How so? The kinetic energy, ignoring air resistance, is exactly related to distance fallen.

Okay, let's take FF = 1. If we double the distance fallen, we double the amount of rope, right? With me so far? And would you agree that for every other FF that holds true? That takes care of the first two thirds of that sentence: "the rope is always proportional to the fall distance".

Then if you also agree that that the kinetic energy is equal to the fall distance times a constant.... It must be that "the rope is always proportional to the fall distance, which is proportional to the energy."

IOW, as long as you don't change gravity, the springiness of the rope, the fall factor, or the mass of the climber, the energy of the climber will always vary in exact proportion to the amount of rope available to catch the fall.

Kinetic energy is the energy of motion - it starts out as zero when the fall begins and grows as the climber's speed of fall increases. The maximum kinetic energy will not be equal to the original potential energy because the climber starts to slow down as the rope begins to get tight. There is gravity pulling down and the rope pulling up at the same time while the climber is slowing to a stop. I think what you mean to say is correct, that the total energy for the rope to absorb or dissipate is the potential energy which is determined by total fall length.

The springiness of the rope - I was talking about if it changes due to being overstretched. I don't know if all ropes stay in the linear regime up through factor two falls for all amounts of falling mass. If not, your argument breaks down.

The linear spring model (force=constant*change in length) for a rope only works for a certain percentage of stretch of the rope. So long as this model holds then for every additional foot of stretch there is the same additional amount of associated tension in the rope. Beyond the linear range (hard fall), for the same amount of stretch, the added tension in the rope grows non-linearly - maybe like force=constant*(change in length)^2. This means each additional foot of stretch incurs a greater additional tension than the last foot.

The springiness of the rope - I was talking about if it changes due to being overstretched. I don't know if all ropes stay in the linear regime up through factor two falls for all amounts of falling mass. If not, your argument breaks down.

The linear spring model (force=constant*change in length) for a rope only works for a certain percentage of stretch of the rope. So long as this model holds then for every additional foot of stretch there is the same additional amount of associated tension in the rope. Beyond the linear range (hard fall), for the same amount of stretch, the added tension in the rope grows non-linearly - maybe like force=constant*(change in length)^2. This means each additional foot of stretch incurs a greater additional tension than the last foot.

Maybe I'm missing something, but that chart of the Pavier data doesn't seem to address the original question—what is the relationship between the fall length and the maximum impact force for a given fall factor—very well.

Edit: Is the impact force in the chart for the "climber's" side of the rope? Have you compared the Pavier data to that predicted by the "standard" model? Do you know the rope modulus or impact force rating of the rope?

You're right, it doesn't demonstrate it very well. But I was reasoning that because the data show a linear relationship between fall factor and maximum tension, regardless of fall length, they support the notion that fall length doesn't matter (in this circumstance). The fact that longer fall lengths appear for both higher and lower fall factors bolsters the argument. But it is still somewhat weak.