UKC

Little people lead climbing

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 Oceanrower 03 Dec 2013

Hypothetically, can a child be lead belayed safely on a standard dynamic rope?

Logic would say yes but will the rope stretch enough to dissipate the force of the fall?

E.g. an 90kg person will stretch a rope x metres.

A 30kg child will stretch the same rope x/3 metres.

Will there be enough elasticity to prevent harm? In fact, will there be enough deceleration or will the rope act more like a static rope?

And will it matter if it does, due to the lower forces involved?

I'm assuming the answer is something to do with Hooke's law but I'm not sure.
Post edited at 22:03
Removed User 03 Dec 2013
In reply to Oceanrower:

Yes the rope will stretch less. Combine that with strength-to-weight ratio and things like Gaia should be piss for the nippers.
 lowersharpnose 03 Dec 2013
In reply to Oceanrower:
Oceanrower,of course it is safe.

Lower mass --> lower forces --> less stretch.

Those idiots don't know what they are talking about (that wall safety guy with an Italian name and the plummy ex-Guardsman)

extension is proportional to force.

The lower the force, the lower the extension,

Idiots I tell you.
Post edited at 23:19
 fil 03 Dec 2013
In reply to Oceanrower:

Lead belaying kids is just about technique. Just learn to be dynamic, and it is perfectly safe.
I see so many people belaying indoors who just don't understand the concept of dynamic belaying and every time I hear the thud as someone else slams into the wall it hurts me!
 Robert Durran 04 Dec 2013
In reply to Oceanrower:

The forces are smaller with a child - try belaying a small child and then a fat bastard adult taking the same fall for confirmation.

The question is whether a given force is more liely to damage a small person that a fat bastard. I suspect so - imagine a small child and a fat bastard lying on the floor; I'd happily stand on the fat bastard but hesitate to stand on the small child.
 AlanLittle 04 Dec 2013
In reply to fil:

Well yes, but it is rather a lot harder to catch a 30kg faller dynamically if you weigh 80kg.

Thinking about it, an 8mm half rope should do the job quite nicely with a suitable belay device. I always just use my normal fat fuzzy wall rope though rope though.
 winhill 04 Dec 2013
In reply to fil:

> Lead belaying kids is just about technique. Just learn to be dynamic, and it is perfectly safe.

You'd need the reactions of a cat to make much difference at all, reaction time would trump technique every time.

I think you're probably setting some unreasonable (and highly dubious) standard for learning if you think 'Just learn to be dynamic' is the answer.
 mchonofsky 04 Dec 2013
In reply to Oceanrower:

Hi, physicist here. The salient quantity is the acceleration of the child, which will uniquely determine the internal forces on the child's organs.

The simplest model of a fall considers the rope as an damped harmonic oscillator. There doesn't seem to be much 'bounce' in the rope in the hard falls I've seen, i.e., the situation is overdamped. I threw together a noddy simulation in Matlab and the peak acceleration seems to go roughly as 1/m^b (consistent with my back-of-the-envelope figuring) for some rational 1/2 <= b <= 2. (It's quite late at night, so I'm not too confident in my figuring of what b is for a useful model, but would welcome any commentary! I think b = 1, but I might wake up tomorrow and decide that's totally wrong. I haven't done the fit quantitatively in Matlab.)

TL;DR: yes, light people ought to get more acceleration in falls.

The relationship is something like half the weight -> twice the acceleration (roughly equivalent to 4x the fall height -- measured from the fall to the moment when the rope goes taught -- for constant mass).

Hope this is useful to people. Apologies for any maths errors -- quite late at night -- they're bound to happen! Obviously this neglects any human or biological factors in safety, and I think the general conclusion we can extract from this analysis is that the dynamic properties of one's rope are generally not safety-critical in falls. (Otherwise, large and small people would not be able to climb on the same ropes.)
 Jonny2vests 04 Dec 2013
In reply to mchonofsky:

> TL;DR: yes, light people ought to get more acceleration in falls.

> The relationship is something like half the weight -> twice the acceleration (roughly equivalent to 4x the fall height -- measured from the fall to the moment when the rope goes taught -- for constant mass).

That seems to defy common sense. Ants must have incredible acceleration.
 krikoman 04 Dec 2013
In reply to Oceanrower:

isn't acceleration the same regardless of mass.

Didn't some bloke in Pisa demonstrate this with his different sized balls?
 Yanis Nayu 04 Dec 2013
In reply to krikoman:

> isn't acceleration the same regardless of mass.

> Didn't some bloke in Pisa demonstrate this with his different sized balls?

That's just unnecessarily personal!
 fil 04 Dec 2013
In reply to winhill:

> You'd need the reactions of a cat to make much difference at all, reaction time would trump technique every time.

You don't need the reactions of a cat at all, you just need to be paying attention. Something that many belayers don't seem to bother with.
 Trangia 04 Dec 2013
In reply to fil:

> You don't need the reactions of a cat at all, you just need to be paying attention. Something that many belayers don't seem to bother with.

Plus 1

You shouldn't have to shout "watch me here" as you make the crux move, it should be a forgone conclusion ALL the time you are climbing! There seem to be too many seconds out there who ignore this fundamental "rule".....
Shearwater 04 Dec 2013
In reply to Jonny2vests:

> That seems to defy common sense. Ants must have incredible acceleration.

This isn't about acceleration due to gravity, it is about acceleration due to reaching the end of your rope and stopping. That'll be a factor of how stretchy the rope is, and the mass of the tethered object.

Given the same rope, a lighter weight will cause it to stretch less, and so the weight will be brought to a halt in a shorter period of time. Assuming the heavy weight and light weight are falling at the same speed, this implies the lighter weight will experience a greater acceleration. Doesn't seem unreasonable to me, but I Am Not A Physicist.
 lowersharpnose 04 Dec 2013
In reply to lowersharpnose:

Get a G-Force App and measure the acceleration.

e.g.
https://play.google.com/store/apps/details?id=com.example.gForce&hl=en

Tie the phone to a rope and give it a 2m fall (a very low mass)

Then put it in your pocket and do the same (you are being the high mass here).
In reply to krikoman:
> (In reply to Oceanrower)
>
> isn't acceleration the same regardless of mass.
>
> Didn't some bloke in Pisa demonstrate this with his different sized balls?

Yes.
 mchonofsky 04 Dec 2013
In reply to Shearwater:

> This isn't about acceleration due to gravity, it is about acceleration due to reaching the end of your rope and stopping. That'll be a factor of how stretchy the rope is, and the mass of the tethered object.

> Given the same rope, a lighter weight will cause it to stretch less, and so the weight will be brought to a halt in a shorter period of time. Assuming the heavy weight and light weight are falling at the same speed, this implies the lighter weight will experience a greater acceleration.

Shearwater's explanation is exactly right. The acceleration here is a balance of gravity (constant for all masses) and rope stretch (inversely proportional to mass, or something like that).

In the case of the ant -- yes, an ant attached to a climbing rope would hardly stretch the rope at all, and so, yes, it would be brought to a stop almost immediately. Would this fall be dangerous to the ant? Our intuition says no, and that might be right, but it's actually because insects are known to routinely endure accelerations of tens to hundreds of g, where free fall is 1 g (see Burrows and Wolf, J Exp Biol 205, 2002).

But obviously this has no bearing on how dynamic the belay is, or indeed whether a child can put in adequate protection with good judgment, etc. Since most (?) lead-climbing kids weigh at least 60 lbs (I'd guess, from what I've seen) and I weigh about twice that, it's equivalent in terms of acceleration to them taking about four-fold larger falls than me over equivalent fall distance. My intuition says that's fine, but I defer to the judgment of others more knowledgeable than me (and the finer details of any child-lead-climbing situation) on this point.
In reply to mchonofsky:

F = ma

It's the force that does the damage. With a child mass is smaller so acceleration can be larger without imposing dangerous forces.

From what I've seen < 25kg competition climbing kids enjoy lead fall practice.
 teflonpete 04 Dec 2013
In reply to Shearwater:

Wouldn't having lighter internal organs result in them having less momentum and being less stressed inside the body despite the more abrupt acceleration?
In reply to krikoman:

In a vacuum that would be the case. But the effect of the air resistance is greater for a child than an adult because surface area/volume (dimensionally, 1/length) decreases with increasing size. The air resistance is proportional to surface area. Air resistance is one of the reasons a cat can fall a long way without hurting itself - cat's instinctively enhance the air resistance by spreading out their legs and their tail as much as possible. Which is probably not a good idea for a falling rock-climbing (even one lacking a tail!). Small objects are also stronger than large objects, given the same construction and materials (also because of 1/length scaling). So all in all I would expect falls to be less serious for a child than an adult. However, children may not be so thick-headed as their parents, so they should wear helmets.
Shearwater 04 Dec 2013
In reply to teflonpete:
No idea See Tom's comment above you.

Anyway, regarding the original question... possibly this is the sort of information gear manufacturers might already have, if someone felt like dropping them a line?

It is probably reasonable to assume that the forces experienced by a child taking a fall arrested by a dynamic rope are within the safety margins of a human body, given that you'd probably hear about a child who had been injured by working safety equipment, but who knows.
Post edited at 13:35
 Robert Durran 04 Dec 2013
In reply to tom_in_edinburgh:

> F = ma

> It's the force that does the damage. With a child mass is smaller so acceleration can be larger without imposing dangerous forces.

No. It's the acceleration. A kg of soft tissue doesn't "know" whether it is part of a heavy or of a light body when it accelerates.

A smaller body with a smaller harness might be an issue (same force spread over a smaller area).

In reply to Robert Durran:

> No. It's the acceleration. A kg of soft tissue doesn't "know" whether it is part of a heavy or of a light body when it accelerates.

But the body isn't an amorphous bag of soft tissue. Injuries will happen at critical points like the neck as a result of movement of the head relative to the body. From the point of view of forces on the neck it will matter how much the head weighs.
In reply to tom_in_edinburgh:

Actually the most obvious thing being missed here is that there would be warning stickers over everything telling you not to allow children to lead if it was a problem.
In reply to Robert Durran:
> (In reply to tom_in_edinburgh)
>
> [...]
>
> [...]
>
> No. It's the acceleration. A kg of soft tissue doesn't "know" whether it is part of a heavy or of a light body when it accelerates.
>
> A smaller body with a smaller harness might be an issue (same force spread over a smaller area).

Actually it's deceleration and the force applied to the body that could cause damage.
 Neil Williams 04 Dec 2013
In reply to DubyaJamesDubya:
That's probably because most indoor/sport or easy, well-protected trad lead falls aren't very long, and so the forces involved are well below what is likely to cause injury purely from the catch.

And I'm not convinced young kids should be climbing bold, run-out trad, so that isn't too much of a concern.

Not saying they are negligible, as they aren't really, but 2*negligible is still negligible, say.

Neil
Post edited at 14:45
 Neil Williams 04 Dec 2013
In reply to tom_in_edinburgh:

And if you smash into the rock/wall (the cause of far more injuries than the rope itself), it will matter how much the body weighs as that's what is being decelerated.

Neil
In reply to Robert Durran:

> A smaller body with a smaller harness might be an issue (same force spread over a smaller area).

I'd have thought the force on the harness was less. Hooke's Law F = k x

The distance the rope stretches x is less for a child than an adult. k is the same because it's a property of the rope. So F is less i.e. the upward force applied by the rope to the harness at the point of maximum rope stretch is less in the case of a child.

 Robert Durran 04 Dec 2013
In reply to tom_in_edinburgh:
> But the body isn't an amorphous bag of soft tissue. Injuries will happen at critical points like the neck as a result of movement of the head relative to the body. From the point of view of forces on the neck it will matter how much the head weighs.

Fair enough!
My quick calculations show that (usual elastic, non friction assumptions!), for a fall factor 0.5 and a rope which stretched by 5% under an adult's weight, then a child half the adult's weight will experience about a 32% greater deceleration than the adult but about a 34% smaller force. Then using scale factors and looking at pressures (as from the harness) and stresses (neck?) suggest not much difference between adult and child.
Post edited at 15:07
 Robert Durran 04 Dec 2013
In reply to Neil Williams:

> And if you smash into the rock/wall (the cause of far more injuries than the rope itself), it will matter how much the body weighs as that's what is being decelerated.

Children come off better? A bit like babies better surviving falling out of windows.
In reply to tom_in_edinburgh:
Isn't the rope designed to apply a maximum force to the object it arrests.
I can't see a lighter object being exposed to more fore than a heavier object.
Taking a slightly different tack: It seems to me it's the elasticity of the rope that is the most important factor here. Is it not fair to say the further you stretch a rope the more force it requires to stretch it even further (surely we've all leant back on a rope and felt it give a bit then sat on a rope to stretch it further and so on)also the force required to stretch the rope the same distance increases as it runs out of elasticity (?)
A lighter object is being arrested in the 'softer' part of the rope stretch so, if anything, would be more gently cushioned against any impact/deceleration forces than a heavier object that might be reaching the elastic limit of the rope.
Post edited at 15:29
 Neil Williams 04 Dec 2013
In reply to Robert Durran:

"Children come off better? A bit like babies better surviving falling out of windows."

On F=ma yes, and it is a case of that if they hit the wall. But I suppose someone receiving a very dynamic catch is less likely to hit the wall. That said, that situation is not a lot different from the situation of me at 17.5 stone belaying someone half my weight, which I do every week. It's hard to do a proper dynamic catch because they aren't heavy enough to pull me up even if I bounce a bit, all I can manage is a step in.

Neil
In reply to Robert Durran:

> My quick calculations show that (usual elastic, non friction assumptions!), for a fall factor 0.5 and a rope which stretched by 5% under an adult's weight, then a child half the adult's weight will experience about a 32% greater deceleration than the adult but about a 34% smaller force. Then using scale factors and looking at pressures (as from the harness) and stresses (neck?) suggest not much difference between adult and child.

That is consistent with what you see when the smaller competition climbing kids take lead falls. Lead falls in a practice situation (as opposed to unintentional falls trying to get a move) seem like fun for them even when they go quite a long way.

M0nkey 04 Dec 2013
In reply to Oceanrower:

Kids are made of rubber. This is well known. They'll be fine.
 Robert Durran 04 Dec 2013
In reply to tom_in_edinburgh:

> That is consistent with what you see when the smaller competition climbing kids take lead falls. Lead falls in a practice situation (as opposed to unintentional falls trying to get a move) seem like fun for them even when they go quite a long way.

I've always assumed that was due to learning to fall before learning to feel scared.....
 Ian W 04 Dec 2013
In reply to Neil Williams:
> (In reply to Robert Durran)
>
> "Children come off better? A bit like babies better surviving falling out of windows."
>
> On F=ma yes, and it is a case of that if they hit the wall. But I suppose someone receiving a very dynamic catch is less likely to hit the wall. That said, that situation is not a lot different from the situation of me at 17.5 stone belaying someone half my weight, which I do every week. It's hard to do a proper dynamic catch because they aren't heavy enough to pull me up even if I bounce a bit, all I can manage is a step in.
>
> Neil

Dynamic belaying doesn't involve jumping / bouncing on the part of the belayer; it involves using and CONTROLLING slack in the system to bring the faller to a more gradual stop than just locking the belay device. This may or may not involve the belayer physically stepping in towards the climber.
Back to the original q. The deceleration forces on a 25kg child will be greater than on me (marginally >25kg. ahem..) for the same drop belayed in the same way. It is unlikely to involve injury inducing forces unless you are getting really high fall factors (virtually impossible in a wall situation, for example), but a belayer should be aware of this and belay accordingly, i.e try to belay more dynamically for the young'uns.
 Neil Williams 04 Dec 2013
In reply to Ian W:

"Dynamic belaying doesn't involve jumping / bouncing on the part of the belayer; it involves using and CONTROLLING slack in the system to bring the faller to a more gradual stop than just locking the belay device. This may or may not involve the belayer physically stepping in towards the climber."

It involves all of those things in different measures. The point is that the climber doesn't just get a hard catch on rope stretch only.

Neil
 Robert Durran 04 Dec 2013
In reply to Ian W:
> The deceleration forces on a 25kg child will be greater than on me.

The deceleration will be greater, but the forces less.
Which, if either do you mean?

 winhill 04 Dec 2013
In reply to Trangia:


> You don't need the reactions of a cat at all, you just need to be paying attention. Something that many belayers don't seem to bother with.

> Plus 1

> You shouldn't have to shout "watch me here" as you make the crux move, it should be a forgone conclusion ALL the time you are climbing! There seem to be too many seconds out there who ignore this fundamental "rule".....

But the point is that the time you have to react when 30kgs tries to stretch the rope is far shorter than when 90kgs hits the rope.

I seem to remember Adrian Berry saying that moving in to provide a dynamic belay takes place as the rope stretches because reacting and moving is so slow compared to falling, obviously a longer fall gives slightly more time, but the idea that dynamically belaying 30kgs of rope stretch is the same as 90kgs is totally flawed.

For a wide number of reasons, I doubt that more than a handlful of a percent of those falls that take place every week are successfully belayed dynamically so the impact of dynamic belaying on children's falls is very small and little or no help to the OP.
 Ian W 05 Dec 2013
In reply to Robert Durran:

Sorry, I meant the rate of deceleration will be greater.
 Ian W 05 Dec 2013
In reply to Neil Williams:

Exactly. Well put.
 krikoman 06 Dec 2013
In reply to John Stainforth:

> In a vacuum that would be the case. But the effect of the air resistance is greater for a child than an adult because surface area/volume (dimensionally, 1/length) decreases with increasing size.

You really think air resistance would have a major effect in someone falling 10m ??

Might do if you were a flying squirrel!!
In reply to krikoman:

Or wearing a cape!

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