Falling on a roof

Having a bit more of a play, and it gets rather more interesting if you consider what you do when you realise you're going to fall.

Simulated fall when pushing out from wall (empirical rope model)

Pushing out from the wall as you fall seems to increase the speed of impact.

Simulated fall when pushing off towards wall (empirical rope)

But launching yourself towards the wall as you fall drastically decreases the peak lateral velocities (and stops you from hitting the wall at all in this case). Although this seems counterintuitive at first, it does make sense as the rope will now be pulling you outwards as it comes taught. I did a quick real-life experiment with a short piece of rope, and it does seem to hold true. So the best (if not necessarily most reassuring) answer to the OPs question might be to launch yourself towards the wall when you realize that you're going to fall. By corollary, you might want to jump sideways towards the fall line if you're taking a pendulum. I'd probably want to run a few more real life tests in a controlled situation before doing it in the wild.

PS - for my quick tests, I held the rope in one hand and released/threw the other end. Although the thrown end did not swing nearly as much, the impact force on the holding hand seemed higher. This would make sense, as jumping into the fall line will mean that it takes longer for the rope to come taught.

David, while I appreciate the use of many different colors for your graph, I find the lack of stick figures to be disappointing, and frankly it makes it hard for me to find your results credible.

Ryan M Moore wrote:David, while I appreciate the use of many different colors for your graph, I find the lack of stick figures to be disappointing, and frankly it makes it hard for me to find your results credible.

This is one of the best examples of peer review I've seen.

Ryan M Moore wrote:David, while I appreciate the use of many different colors for your graph, I find the lack of stick figures to be disappointing, and frankly it makes it hard for me to find your results credible.

Yes. It makes no sense without the stick people. I mean, go ahead, just ask jim.

Jim knows best.

Nerdy stuff, so I have to comment. The assumptions made for David's model and the interpretations people are making based on have the potential to mislead.

Using a model with a 2m roof with pro at the 1 m mark, where you assume collision occurs at +1.0 mark on your graph is an odd choice, because with a static rope and zero slack in this model, you hit the wall with... zero velocity! (Oddly, I think this could be one of the only falling scenarios in climbing that you could safely take on a static.)

However, the OP was climbing out a roof feet first, and hitting his head. So, he won't be colliding at x=1, he'll be colliding closer to x=0, unless you assume his head is in his... you know (it could be after the collision). The lateral speed without slack out is around 3 m/s at x=0. That would be like getting dropped on your head from 50 cm. Spinal board anyone? The around 1.5 m/s lateral velocity imparted with slack out would be like getting dropped on your head from 10 cm (I'm not a physicist or engineer, so you may want to double check this). I wouldn't want to take either fall head first. Neither fall would be too bad if you could cleanly absorb the lateral impact feet first; without slack out you not only have a higher lateral velocity, you have less time to set for impact.

So, I think slack is a good idea for the type of fall the OP is talking about. It might even give him enough time to not take the fall head first. If you disagree based on the math, you might want to try again with a model for a roof that would seriously scare/wreck you. For fun how about crunch the numbers on a 3 or 4 m roof with gear at 1 m (I'd be scared), you may reach a different conclusion.

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I used a stick figure to generate my argument.

Nerd out.

Stick figures and models ....

And no whippers yet

;)

Mark E Dixon wrote: This is one of the best examples of peer review I've seen.

^^^ This.

Fantastic model, David. Quick request, could you possibly extend your model to show the horizontal speed out farther along the x axis, such as to +2m (i.e. the point at which the pendulum stops swinging forward and starts swinging back)? It would make it viable to use this to look at the resulting relative horizontal speed for any ratio of distance between the climber and the protection vs the protection and the wall, such as if the protection is farther than halfway along the roof (it's already useful for showing that if the protection is much less than halfway, then the horizontal speed is proportionally greater/more dangerous for less slack).

One of the more fascinating aspects of the left-side panels in this model is that you can definitely see how the greater slack ultimately results in a pendulum that potentially carries you much farther past the point of protection compared to less slack, translating a greater amount of energy to horizontal motion, and a greater arc-length to potentially swing through. As your last piece of pro gets farther along the roof, less slack ultimately means less energy in the system is directed to swing you farther along the positive side (the impact side) of the pendulum, so you're more likely to come to a stop before hitting the wall. As the pro gets closer to the wall (or the climber gets farther from the pro), the opposite holds true. With less slack, you get a shorter pendulum with a faster period of swing resulting in a greater speed at the point directly under the protection given the same initial horizontal displacement. As your point of impact gets farther in the opposite direction from the pro as the start of the fall, this speed drops off more dramatically for systems with less slack compared to systems with more slack.

BUT, without any stick figure tests to corroborate these in silico results, this reviewer cannot recommend this for publication at this time.

Anyways, just my rantings that helped me (and hopefully help you guys) understand this.

Takeaway message for the belayer: it's all situational, but if the climber's farther out from the last piece (and not in any danger of decking), more slack is more likely to do good than harm.

Takeaway message for the climber: if at all possible, throw yourself towards the last piece of pro if you fall on a roof. And wear a helmet, or yer gonna die.

bigger takeaway message for the climber: Avoid all roofs anytime soon if you're a stick-figure.

Wow, the stick figures would be so much better!
I would love to throw some math out, but it is just too hard :(

Impact against the wall is hard due to the speed at which body slams against it. Impact along the wall can be ignored in absence of inconveniently placed ledges, ground included. The worst one can get from it is some wall rash. So, it would appear logical to take that complex motion and examine what happens to vertical and horizontal components.

Horizontal component would, basically, be a pendulum swinging around to top bolt with initial velocity, as the gentleman above quite astutely noted.
Vertical is governed by friction, tension, and gravity.

What is somewhat interesting, is that objects subjected to "swinging" motion, is some circles known as angular motion, experience the conservation of angular momentum law. Figure skating aficionados definitely know this - as soon as skater starts rotation and brings her arms in, she starts rotating as if wanting to initiate projectile vomiting in spectators. Of course, is she were to bring those arms out, the spin would slow down.

Vertical speed will be reduced due to friction and rope stretch. But what happens to the horizontal component? Well, I am so delighted you asked! Due to conservation of angular momentum, L*V is constant ( V - is the slamming speed, and L length of rope from last bolt), so if one were to magically lengthen L, the V will be reduced. And, 10% reduction in speed will reduce energy that your body needs to dissipate by 20%.

So, from this comes the short recipe for soft catch -
- climber free falls, acquired vertical speed and removing slack from the system.
- tension appearing in the system due to friction will initiate swinging motion around the top bolt.
- at that point, if belayer were to sit down, the climber would slam into the wall with a given horizontal speed. If math is done correctly, that speed will already be reduced by accounting for rope stretch and conservation of angular momentum. But, if belayer can somehow lengthen the distance between the climber and top bolt beyond what comes from rope stretch, due to conservation of angular momentum speed against the wall will be reduced even further.

If one were to give slack during the fall, the climber accumulates more speed, slams quite probably harder.
If one were to do nothing, and lock off, the slam is going to be determined by simple math, possibly complicated to some.
If one were to hop/jump after starting to feel tension in the system, the slam is likely to be reduced.

The way I see it, more slack allows for a vertical trajectory to increase in velocity, when combined with a dynamic belay (belayer jumps when rope becomes tight) that's timed correctly, the speed that picked up during the lengthy fall will put enough force on the dynamic system to maintain the vertical movement. Parallel with the wall means less force making contact with the wall ;) I wouldn't wanna be a newbie Spider-Man pendulum-swinging into a wall because I didn't let go to redirect my movement downward, with gravity.

Edit: O>-< (Tilt head to the left) (Love this thread)

Wow. Climbers are nerds. Love it, lol. I also love how someone cited a reputable climbing book that directly answered the question, yet the models continue. I am curious about the long runner vs extra slack claim. I've always heard (and generally practice) using an extra long draw (or extended runner) on roofs, although this also has to do with rope drag/wear. Would you still want extra slack if you extended the draw?

It depends.