simul climbing

While I have enjoyed following this thread (except for the flames) with avid interest and have learned some things, even about a vodka martini ('cept it's gin for me), perhaps when I check in tomorrow maybe you can explain, Kevin, how a fall on a dynamic rope can be "basically static" and the pro NOT pulling "will most likely result in death."

Should I not take this too literally, like the flaming, or is it that my physics education is too far in the past and clouded by gin-soaked web surfing?

Cheers!
Keith

edit: changed "static rope" to "dynamic"

If we assume that the two climbers have the same mass, the derivation of the impact force in case of a second's fall that pulls down the leader is still fairly simple. I'll spare you the details: Those who remember a little high-school physics can find them by themselves from the energy balance equation. In sum, it is as if the fall factor of the leader were amplified by an additional factor of 2+s/h, where s is the slack in the rope when the second fell, and h is the height of the leader above the highest pro. This more than doubling is bad, but keep in mind that all the rope is stretched between the two climbers, which means that the fall factor tends to be low. As an example, if the rope is 30 m long, the leader is 3 m above the last pro, and the second has a slack of 1 m when (s)he falls, the resulting effective fall factor is 0.233.

So far, we have ignored friction. Accounting for it will increase the effective fall factor for the leader. In our example, it will go up to something like 0.4. A bomber piece of pro will not fail.

I've seen the doom-and-gloom theory before, even in an otherwise excellent book like Florine and Wright's Speed Climbing, but it's just plain wrong.

Yessir! My point exactly; greater forces generated by two falling climbers as compared to one falling climber in the classic scenario of a roped climbing fall, but the forces are spread over the whole rope, "basically." And nothing static about it.

Now back to the martini, ever so slightly shaken by the fall.

Hmmm, interesting. I hadn't thought about a fall from the second depleting the "dynamicism" (feel free to use that anytime, I haven't copyrighted it yet) of the rope so that the leader's fall could be more serious. I have always just thought the biggest risks were from excess slack in the system which could extend a fall, and the second possibly being pulled around unexpectedly, hitting his head on a rock outcropping, etc. Hadn't thought of these force issues.

Actually the rope has nothing to do with it. Consider the second falling off the rock, the leader holding off until pulled from the rock. Now instead of the leader falling past the last piece of pro the leader falls into the last piece of pro as the rope continues to zip through it. The rope now only absorbs a small ammount of force as it is the leaders belay loop pulling into the carabiner of the piece that takes the fall, similar to a fall on via ferrata but without shock absorbers.

Of course for this to happen the terrain has to be near vertical and the second needs to not impact anything to slow his descent. But as he started to fall first his velocity will be greater than the leader until they both hit terminal thus the leader would not be able to fall past the piece and have the rope absorb the shock.

Certainly makes a guy want to go out and buy a cup!

Don't fall #2, please!! I'm a tenor not soprano; don't fall!!

Hmmm, now I am beginning to see why you might want to employ a microascender based system to protect the leader. I must confess at first I thought all that was just an unnecessary complication to an otherwise intuitively simple process. I still feel that way for the way I use simul-climbing, which is just for fast movement over easy terrain where there the risk of falling is nil, or just to give the leader a bit of extra rope to get to a better belay, etc. But if I were to really push it on vertical, I can see the advantage of such a system better now.

Kevin -

Thanks for explaining yourself. I understand the scenario you envision and the reason the leader's fall would not be absorbed by the rope. An ugly scene gets uglier.

While I won't debate the odds of this happening, it is a great example of the nightmarish visions we have to deal with to keep getting out on the sharp end, either end in this case. Your avatar says a lot.

While not exactly applicable to simul-climbing, I offer what Rich Goldstone has to say about such theorizing vs. experience over on supertopo.

Look for rgold

Again, thanks for bringing your experience to the discussion in such a rational manner.

Mark Nelson wrote:Certainly makes a guy want to go out and buy a cup! Don't fall #2, please!! I'm a tenor not soprano; don't fall!!

I've heard that the deft use of Tiblocs could protect you from this, Mark.

Kevin Stricker wrote:Actually the rope has nothing to do with it. Consider the second falling off the rock, the leader holding off until pulled from the rock. Now instead of the leader falling past the last piece of pro the leader falls into the last piece of pro as the rope continues to zip through it. The rope now only absorbs a small ammount of force as it is the leaders belay loop pulling into the carabiner of the piece that takes the fall, similar to a fall on via ferrata but without shock absorbers. Of course for this to happen the terrain has to be near vertical and the second needs to not impact anything to slow his descent. But as he started to fall first his velocity will be greater than the leader until they both hit terminal thus the leader would not be able to fall past the piece and have the rope absorb the shock.

Kevin, this is not correct. Consider what happens when a leader falls while normally belayed by the second. Suppose the second is able to pull in all the slack at prodigious speed, so that when the leader's harness reaches the height of the highest piece of pro there is no slack in the system. Suppose the distance between that piece of pro and the belayer is l and the height above it from which the leader fell is h. The fall factor is f1 = h/l. (Without any slack taken in, the fall factor is f2 = 2h/(h+l), which is worse if and only if h < l. BTW, this condition (h < l) determines whether one should try to pull in or pay out rope regardless of how much rope is pulled in or paid out.)

Back to our problem: What I mean by saying that f1 = h/l is that in first approximation the force on the climber can be computed by the classic impact force equation by substituting f1 for the fall factor f. When the falling climber passes by the highest anchor, the rope starts stretching and flowing over the biner. If you marked a point in the rope between belayer and biner, you'd see this mark move up and, if close enough to it, through the biner as the rope stretches and the climber comes to a halt.

This stretching and flowing happens also when the simulclimbing second is falling instead of belaying. The main difference is that only part of the rope moves up, because there's a falling mass at the other end. Suppose you had two marks on the rope--one closer to the leader and one closer to the second. You'd see the former move up and possibly through the biner, while the latter would move down. There's a point, roughly half-way along the rope, that does not move, in the sense that its final position is the same as it was when the leader hit the upper biner.

One way to interpret all this is that when both climbers fall together, each has roughly half the rope to stop him/her. Hence, the amplifying factor of 2 in my previous post. (The other component accounts for the slack.) The effect of friction is to lengthen the stretch of rope that stops the second at the expense of the leader.

Kevin Stricker wrote:But as he started to fall first his velocity will be greater than the leader until they both hit terminal

Kevin, draw free body diagrams for both climbers and you'll see how this claim is false. The downward acceleration on the leader initially exceeds g. For the second, it's the other way around.

Assume no air drag. The rope will stretch until the two speeds are the same. At that point the rope will start contracting, further accelerating the leader at the expense of the second until it is not stretched. It will then stop exerting any force until the leader has overtaken the second by a rope's length. The process will then repeat with roles reversed. That, of course, requires a very long fall.

Brenta...consider it as if you were climbing a multipitch route and your belayer was at a poor anchor that failed while you were climbing above him. Initially the second would fall until his locked off belay device started generating pull on the rope, that force would increase until he pulled off the leader. Now the leader is in freefall as well as the second BUT the rope is sliding down through the protection as fast as the second is falling. If this speed is greater than the speed of the leader falling then hypothetically the leader could impact with the last piece before falling past it.

Like I said...worst case...the chances of this actually happening is next to zero as rope drag in the system would slow the seconds descent while the leader would be in true freefall.

As the second was already falling before the leader looses his grip he has already accelerated to a good speed, the slingshot effect could not cause the leader to accelerate fast enough to overcome his speed in the seconds we are talking about that the fall could take.
Also wouldn't the contraction of the rope further exasperate the condition as most of the rope in the simulclimbing fall would be located below the last piece.

If you want to break out equations I would ask you to interpret the possibilities from a quantum view. Such as, would the outcome of the fall change if it was observed by a third party?

(edit to add: BTW this is not my theory, I stole it from Bill Wright and Hans's book. I personally do not think the likelyhood of this actually happening in real life to be very good. I just thought I would point out what I would consider to be the true worst case scenario)

Kevin Stricker wrote:If you want to break out equations I would ask you to interpret the possibilities from a quantum view. Such as, would the outcome of the fall change if it was observed by a third party?

For that, we just need to reinterpret the height h as Planck's constant. Just kidding, of course. Thanks for adding a dose of humor to an otherwise dry discussion.

I think I see what you are trying to describe, and I've read the same theory in Speed Climbing:

Florine and Wright wrote:But when a second falls while simul-climbing, the leader is pulled directly into the last piece of gear. If this piece holds, the leader will stop immediately, with no stretch in the rope--or anything else--to reduce the force.

I don't object to the claim that the leader is pulled toward the last piece of gear. That is definitely possible and potentially hurtful, insofar as it causes the leader to hit the rock. I object to the claim that the leader will stop immediately. That would take something like a biner on the leader's harness accidentally clipping the anchor as it flies by.

Kevin Stricker wrote:Actually Josh the worst case scenario is that the piece does not pull when the leader impacts it thus taking a basically static fall onto a piece which would most likely result in death. One of the few situations where you falling would kill your partner and not yourself.

Kevin,

I agree with you entirely.....but think this to be the "worst case" of the situation I described.

So basically the same, only with your description the leader is completely "sucked into" the system.

Scary shit!!!!

josh

So, are there any real world data out there? Any simul accidents that can be picked apart?

(BTW, the date should be 1865, not 1965.)