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Hypothetical maths-y question?

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 ClimberGirl 14 Apr 2016

Imagine you were lead climbing on an indoor wall, got to about 4/5 clips up and then fell off with bolt at about knee-height. Assume belayer was entirely useless and failed to hold on to dead end of rope. With the friction created by rope rubbing against itself (going through an ATC), the belay device and the quickdraws, how fast would you expect to be falling when you hit the ground? Would the friction in the system be sufficient to slow you down enough to experience an okay (if rather sudden and hard) landing, or would serious injuries result?
No particular reason for asking (and I'm not planning on trying it out!) but I was just curious.... Anyone have any ideas?
Post edited at 09:39
Lusk 14 Apr 2016
In reply to ClimberGirl:

Fast-y nough, I reckon!
In reply to ClimberGirl:

Depends on thickness of rope obviously however you'd not be healthy when you reached the bottom. (Source: personal experience of a friend losing control of a belay plate during a lower off and catching me a meter or so from the ground.)
 jkarran 14 Apr 2016
In reply to ClimberGirl:

Assuming the rope isn't super fat and furry you deck hard enough to get seriously hurt, the rope does very little for you.
jk
 Dandan 14 Apr 2016
In reply to ClimberGirl:

You say 4/5 clips up, but then are very specific about the bolt being at knee height, so I'm not sure exactly how high you want to be, I've gone for 2.5m to first clip and 1m to each subsequent clip, if your knee is level with the 4th clip that puts your feet at a nice convenient 5 metres up.
The velocity if you hit the ground feet first (without taking in air resistance which I think is fair over a 5 metre distance) is just shy of 10m/s which is 22 mph.

That doesn't sound super fast and I imagine that if you jumped off something that high onto a rubber floor with good form and a controlled landing you could probably walk away quite comfortably.
Falling backward from a wall is certainly not a controlled fall so I'm guessing falling in that way would be more likely to result in some bruising, sprains or even a broken bone or two.
Add in a rope potentially pulling you off balance but doing, I imagine, very little in the way of actually slowing your descent, then it could be reasonably nasty.
I'd say you would still hit the ground pretty close to 10m/s, and the result could be anything from laughing it off to going home in an ambulance.
 Martin Hore 14 Apr 2016
In reply to ClimberGirl:

I'm aware of one instance at least where a climber fell on a top rope indoors from a similar height with the belayer not controlling the dead rope while using a standard belay device. It should never happen, but occasionally it will. There were some injuries.

The friction in the belay device and over karabiners will slow you down significantly I guess (so you won't hit the ground at quite the speed DanDan suggests) but still fast enough to do some damage.

I witnessed a similar instance when a lead climber fell from about that sort of height with the belayer using a GriGri that failed to lock. So a similar scenario. On that occasion the climber walked away unscathed (and the belayer re-considered the "fail-safe" nature of the GriGri).

Not the sort of thing to try out too often!

Martin
 Robert Durran 14 Apr 2016
In reply to ClimberGirl:

I witnessed such a fall (maybe a little higher) onto rubbery matting which resulted in a compound fracture of the lower leg. A lot of screaming went on.
1
ultrabumbly 14 Apr 2016
In reply to ClimberGirl:

It would perhaps make a huge difference as to where all the dead rope was. If well behind the "belayer" it would probably partially arrest to some significant degree as that rope would approximate the correct orientation to arrest and slow the fall as it would run up along their thigh or arse . If in front it would whip through very slickly. A component here might then be their height. As the weight of rope from ground to device on the dead side will contribute a little to the stopping power.
 remus Global Crag Moderator 14 Apr 2016
In reply to ClimberGirl:

Too many variables to give an accurate and realistic answer.

Anecdotally, I was dropped from 6 or 7 clips up a steepish overhang and landed very gently, presumably due to friction through the plate etc.
 Dave Todd 14 Apr 2016
In reply to ClimberGirl:

These things are just too random / variable to give you a definitive answer. How well / badly / luckily you land is probably the major factor in determining how injured you'd be. I know people who've fallen from a couple of meters onto mats and broken ankles, but I've also seen someone dropped the full height of the Foundry main wall and then get up and go bouldering!
 hms 14 Apr 2016
In reply to ClimberGirl:

I saw a fall from possibly a little higher than this a few eyars ago at my normal wall. The belayer must have turned his brain totally off, he was pretty much asleep on his feet, as he didn't take any action what-so-ever until visibly startled by the thump of his climber hitting the floor next to him. The floor was sprung wood, the guy landed on his back as I recall. Although deeply shocked and probably badly bruised, after several minutes he managed to get to his feet and walk away - never ever to climb with that belayer again I would sincerely hope. It was all deeply spooky to witness - not nice!
 olliehales 14 Apr 2016
In reply to ClimberGirl:

Just musings,

Gravity can be assumed as an acceleration of 9.81m/s^2. So you can first work out the velocity with which you would hit the deck if you fell off while solo'ing.

This may help http://www.wikihow.com/Calculate-Terminal-Velocity

Though the climber would not likely reach terminal velocity from the heights we are looking at, thus you would need to solve using the height person falls from (in metres).

You could then re-calculate by adding in all the frictional losses from each item in the system.

These however I can see being very difficult to quantify. I suppose you could start by looking at the contact surface area of each item, and the co-efficient of friction for each.

But then you would have to consider angular changes in the rope path and the effect this would have on the frictional losses - how you arrive at a semi accurate figure I have no idea



1
In reply to olliehales:

I think an easier way would be to have two ropes. A lead rope and a top rope. Have someone belay you properly on the lead rope and have someone tied in with a belay plate to the top rope but with their hands well away from rope/plate. Climb above clip of lead rope then jump off and see what happens

1
 riff156 14 Apr 2016
In reply to ClimberGirl:

Funny you should ask that as that's exactly what happened to me once, I was about 20-22 foot up not sure how many clips that was but enough, it was on an overhang and I hadn't been climbing for long and was struggling to make the clip, consequently I fell the guy belaying me unfortunately let go of the rope and down I came fortunately for me, but not for him I landed on him before hitting the ground, this was at a wall by the way, then I landed on the rubber floor, first thing I would say is there was defiantly a fair bit of friction in the system maybe due to it being a double overhang if you get my meaning so the rope had bends in it and I guess the fact I hit him and the floor was rubberised it didn't turn out to bad, I was ok but had a very sore back for a few days, the strange thing is that it all seemed to go in slow motion, hope this quells any desire you might have to test your question out

S
 stp 14 Apr 2016
In reply to ClimberGirl:

Well the only conclusion I can draw from all these tales of decking out is to always use an auto locking belay device.
1
 antdav 15 Apr 2016
Best case scenario of a light climber, not straight clips, fat and fluffy rope, high friction device would probably end up with a bit of a shock and panic and some sore feet and knees.

The opposite would probably be some serious breakage or worse.
 Chris Murray 15 Apr 2016
In reply to stp:

> Well the only conclusion I can draw from all these tales of decking out is to always use an auto locking belay device.

Personally I wouldn't climb with someone who I could only trust with an auto-locking device. If you need an idiot proof device, you're climbing with an idiot.
1
 Greasy Prusiks 15 Apr 2016
In reply to Le Chevalier Mal Fet:

Brilliant. I'm remembering that last sentence for future use.
1
 stp 15 Apr 2016
In reply to Le Chevalier Mal Fet:

But given the choice would you prefer to climb with someone using a safer belay device or a less safe one?
3
 Brass Nipples 16 Apr 2016
In reply to ClimberGirl:

I'd probably be slowed down by deliberately landing on the belayers head.
 marsbar 16 Apr 2016
In reply to stp:

Didn't you see the post above where the auto lock didn't?
 marsbar 16 Apr 2016

Martin's post for stp


> I'm aware of one instance at least where a climber fell on a top rope indoors from a similar height with the belayer not controlling the dead rope while using a standard belay device.

> I witnessed a similar instance when a lead climber fell from about that sort of height with the belayer using a GriGri that failed to lock. So a similar scenario. On that occasion the climber walked away unscathed (and the belayer re-considered the "fail-safe" nature of the GriGri).

I'd prefer to climb with someone who isn't an idiot. The device is less relevant than the person in charge of it.

I've also seen someone fail an assessment by putting the rope the wrong way in the gri gri. Immediately after being shown the little picture, and told how important it is to use the equipment correctly.
Post edited at 10:14
 Martin Hore 16 Apr 2016
In reply to marsbar:
> I'm aware of one instance at least where a climber fell on a top rope indoors from a similar height with the belayer not controlling the dead rope while using a standard belay device.

> I witnessed a similar instance when a lead climber fell from about that sort of height with the belayer using a GriGri that failed to lock. So a similar scenario. On that occasion the climber walked away unscathed (and the belayer re-considered the "fail-safe" nature of the GriGri).> Martin's post for stp

-----------------

> I'd prefer to climb with someone who isn't an idiot. The device is less relevant than the person in charge of it.

Neither of the belayers involved was in any way an idiot. In the first case it was a young person under instruction. The instructor may have made a mistake in over-estimating the belayer's ability and not sufficiently closely supervising the belaying - the belayer herself was as I understand it blameless - just insufficiently trained.

In the second case the belayer was fairly new to the GriGri. He was following pretty exactly the belaying procedure used by other more experienced GriGri users at the wall, and in my experience many GriGri users everywhere, at least at that time which was quite a few years ago - ie thumbing the device to facilitate quick paying out to a leader clipping a quickdraw. The leader fell back gently after having clipped, and the GriGri didn't lock.

Martin
Post edited at 14:30
 stp 16 Apr 2016
In reply to marsbar:

> Didn't you see the post above where the auto lock didn't?

A very unusual case. I've never had that happen and never seen that happen to anyone else. I've have used a Grigri since they first came out.

But a non-autolocking device of course will never lock. And the best belayer in the world can make a mistake. I think human error is far more likely than device error because a human is so much more complex than a simple belay device.

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