UKC

I have read with interest the various recent threads on falling practice, and it struck me how much the emphasis is on the leader's issues, with very little discussion of good, safe belaying technique.

I recently watched a climber taking repeated falls; the belayer seemed to be trying to give a "soft belay" by allowing rope initially to slip through the (ATC-type) device. All well and good; but at the crucial moments his brake hand on the dead rope was not in the downward, lock-off position, which seemed dangerous to me.

It seems safer to me to hold the rope locked off downward, and let the rope run a little through the device in that position, while maintaining a good fist grip on the dead rope, but also use body movements (move in towards the wall, etc) to help cushion the fall.

In reply to bpmclimb:

Does it really matter unless they are on trad gear which might rip out? The rope should have enough elasticity for falling practice, assuming you are doing it on bolts.

Chris

In reply to bpmclimb:

I think a soft belay is one where the rope is absolutely locked in the proper way but that the belayer hops or jumps at the last minute so as to give a softer fall. As far as I know this is also called dynamic belaying.

If your partner is a small person this happens automatically and makes for a really chilled fall (if such a thing is possible - which it is.)

In reply to Chris Ellyatt:

Yes. Good dynamic belaying gives a nice soft gentle catch and is a pleasant experience in slow deceleration, bad belaying gives a sharp jarring clattering halt which just isnt very pleasant and increases risk of you hitting things hard if you swing in. It's not just the forces on the gear that matter.

Very few climbers are good at dynamic belaying, although light climbers have the inbuilt advantage of not needing to try so hard!

In reply to Chris Ellyatt:

Yes it does matter, as the chance of hitting the wall hard are very much higher with an unforgiving belay.

In terms of effectiveness, belayer movement is very much more effective - and usually safer too - than plate slippage. At a wall it's usually easy to provide 1m of 'give' by the belayer allowing him/herself to be pulled in and/or up some way. And 2m or more is certainly possible. The maximum safe plate slippage will usually be no more than a foot or so, as rope slippage through the brake hand too is a much more refined technique and not one to recommend to anyone other than perhaps competition belayers using a figure of eight. This helps explain why gri-gris are common among good sport climbers, for whom dynamic belaying is usually second nature - the plate choice is of little help compared to belayer movement.

In reply to bpmclimb:

Climb with your wife who's half your body weight, you get a great dynamic belay then.

In reply to bpmclimb: yeah a little jump/stepping forward makes the fall a bit softer for the leader, letting rope run through the device intentionally is bad belaying if you ask me. I wouldn't ever belay like that and wouldn't trust a belay that slipped rope on purpose...

In reply to bpmclimb:

There was me think good belaying stops you hitting the floor, bad belaying doesn't.

In reply to JoshOvki:

.. and there was me thinking that it was worth going looking into the matter in a bit more detail than that. Perhaps I just like analysing things

In reply to bpmclimb:

There is your problem, over analysing things :p

In reply to JoshOvki:

Not quite sure why you say "over analysing". I hardly went into great detail - just noticed someone's belaying hand up in the air, holding the rope in the position of least friction, while his mate took repeated lobs, which didn't look safe to me. Yes, he managed to arrest a few falls, but it looked touch and go.

Do you mean that any further analysis of belaying technique, beyond the scope of your simplistic statement, is pointless?

Trouble is, there's the sort of belaying that stops you hitting the floor 99 times, but because it's inherently a bit flawed, you hit the ground on the 100th. Personally, I'm not comfortable with that sort of belaying.

In reply to bpmclimb:
To me good belaying should be a subconscious act when someone takes a fall, be it a practice fall or a pushing as hard as they can and pop off fall. If someone is consciously allowing rope slip to give a softer fall, this atleast in my mind could well end in an accident.
Luckly most of the people I belay are heavier than me so I give a softer fall due to being lighter. When they belay me, they normally step into the wall to give a softer fall.

In reply to bpmclimb:

Have a read of this: VIDEO: A Fear of Falling - Clip-Drop Technique

The Dynamic Belay For Climbing Walls and Sport Routes

When you fall off a sport or wall route, no one wants to come to an abrupt stop that will shock your internal organs, jolt your back and slam your feet into the wall.

To achieve the above, climb with a well used, furry old rope that lacks any stretch and that has just been fallen on, use an auto-locking belay device, be quite a bit lighter than your belayer and make sure that your belayer stands tight against the wall, stays rooted to the spot or uses a ground anchor and better still jumps backwards in the event of a fall.

This will ensure that when you fall you come to an abrupt stop and slam into the wall. The result of such a static fall can be at the least discomfort or worse injury.

What we want from a belayer on sport and wall routes is a soft catch, or cushioned catch, using a dynamic belay. You fly through the air and gradually come to a stop, like falling on a bungie cord without the rebound. The falling leader decelerates rather than coming to an abrupt stop.

John Arran has come up with a good analogy,

"If you catch a cricket ball with your hands dead still it will hurt, as the ball will stop dead as all the energy has got to go somewhere fast. If you let your hands give and move with the ball a little so that the ball comes to a stop more slowly, the energy will be absorbed more slowly and there won't be any painful impact force."

Catching an egg without it breaking is another good analogy, says Adrian Berry.

More: http://www.ukclimbing.com/articles/page.php?id=1838

In reply to JoshOvki:

Definitely a worthwhile topic. And for what its worth, in my experience slippage is usually something that 'occurs' rather than something you provide in a pre-meditated way.

In reply to bpmclimb:

As Adrian Berry: http://www.ukclimbing.com/articles/page.php?id=1844 says

"Dynamic belaying is about letting the rope slide through the belay device a bit - FALSE! Arresting a fall requires an almost instinctive response, there isn't enough time for the fine motor skill required to allow for controlled rope slippage, the risk is you will drop them altogether (note: this can be done but requires gloves, a figure of eight as a belay device, and preferably a back-up belayer.)"

In reply to JoshOvki:

Knob

In reply to alooker:

I think any talking of jumping is poor coaching. The knack is to yield to the force rather than trying to time a jump. A mistimed jump, slightly late jump has the potential to see both belayer and climber coming onto the tight rope whilst "falling" and increasing the forces involved. If we talk of yielding to the forces you encompass all the elements of a dynamic catch including minor slippage at the belay device.

I would dispute this, I've been using this technique for the last few years, and to my mind once it's well practiced it's as safe as any other dymanic belaying technique. Probably safer in some circumstances. I also prefer to climb with partners who know how to belay this way - it gives you more control than jumping up towards the first clip (once your feet leave the ground, you're just going along for the ride). It's particularly useful when you've got a climber on a slab above a roof - you can make sure they're past the lip before you stop them so they are swinging into space. One particular incident in spain pops into mind, where my partner had initially locked off, but I was swinging in towards some tufas head first so he just dropped me another few meters and caught again, saving me a potentially very nasty collision. You can't do that instinctively without a lot of practice.

In reply to timjones:

I think it depends on the scenario - a couple of the guys I climb with are about half again my bodyweight, and if I yield to the force, I won't stop yeilding until I hit the wall anyway, so better to jump towards the wall in a controlled manner as I feel the force coming on to the rope, or keep my feet planted securely and use th atc to control the fall

In reply to Ciro:

I'd define a movement as you feel the force as yielding, rather than jumping. It's the talk of a timing a jump that bothers me.

In reply to timjones:

Fair enough - in that case yes I agree with you, it's important to let the rope initiate the movement.

In reply to Ciro:

I prefer to climb with partners who stand close in and just lock of the plate. I would rather slam into the wall a little occasionally than risk my belayer being lifted off their feet slamming into the wall themselves, knocking themselves unconscious, letting go of the rope, dropping me and ending up dead myself. The amount of dangerous dynamic belaying I see at the wall where this seems like a real risk horrifies me.

In reply to Robert Durran:

Fair enough, each to their own and all that. But for me, this is where catching practice comes in. I don't want an extended period out of climbing with a badly broken ankle, or a fractured skull from slamming the wall in an inverted fall, so I want my belayers to learn how to control a fall dynamically, without getting thrown around and risking the scenario you describe above. It's not that hard, it just takes practice to make it instinctive (and a willing crash test dummy).

In reply to timjones: Yes, perhaps I didn't make myself clear - I was aiming more for being light-footed that a full on high jump, but fair enough someone could make a wrong assumption

In reply to Ciro:

Fair enough if you are happy that the people belaying you can do it safely. However, I think a lot of people see experienced belayers standing miles out and copy them without realising that it does need practice (these will be the same people who stand miles out when the climber is only at the second or third clip - they clearly havn't thought things through!)

In reply to Robert Durran:


Yes, that's certainly an issue. However I'm not prepared to modify my own behavior (and compromise my climber's safety) just so that others won't copy me and get it wrong. Unfortunately, I find if you approach a stranger and try to suggest some changes to make things safer, they tend to get very defensive and won't listen - often to the point of becoming abusive. So at the wall I think it's down to the floor walkers to point these things out, and at the crag it's down to the individual to make his own risk assessment.

In reply to bpmclimb:

Thanks for the replies. It seems that there's quite a bit of difference of opinion about this.

My take on it is that it goes back to basic belaying skills, and how they are originally learned. The most dangerous scenario, to my mind, is when the belay hand on the dead rope is up in the air (making a U-shape in the rope rather than an N-shape) at the precise moment that the climber's weight comes on the rope. Climbers who habitually pause in the rope-up position while belaying, even momentarily, are courting disaster. Teaching belaying by putting together five separate movements is, I think, flawed in this respect. I prefer two phases, the first being taking in or paying out rope while keeping any departure from the N-shape to an absolute minimum, and the second being changing position of the hands on the dead rope while maintaining a fist grip with at least one hand.

This may all sound obvious, but one only has to take a stroll around a busy climbing centre to see plenty of ingrained bad habits. Climbers are often in a hurry to get away from bottom roping and into the whole glamorous world of leading, falling, etc., taking their bad habits with them.

I think that safe belaying of a lead climber, including the providing of "soft belaying" allows for some variation in style, provided that the basic belaying is sound. I don't mind the idea of a small amount of rope slippage through the device, provided that the rope is in the N-shape and held securely in a fist grip, although I think far more useful amounts of cushioning can be provided by body movements.

In reply to Ciro:

Quite right.


True, though worth doing so if it looks like a horrible accident is imminent.


Yes, it should happen far more often

In reply to bpmclimb:


With a large amount of rope slippage you can go directly from catch to lower-off without stopping the climber, so no shock loading of the system whatsoever - it's not possible to get "more useful amounts of cushioning" than that.

In reply to Ciro:

With enough rope slippage, you can get the ground to do all the work for you, so no inconvenient loading of your expensive rope at all!

In reply to bpmclimb:

One other point that I think is worth making - there seems to be a general consensus on this thread that a dynamic catch is a good thing, but rope slippage is bad. That's all well and good when the belayer is able to move around, but how else would you introduce a dynamic element at a hanging belay?

In reply to Robert Durran:

??

I thought we were having a sensible discussion here.

In reply to Ciro:

Is it confusion over how to give said slippage that is people's concern? Obviously holding the dead rope high is bad, but you don't need to do this to give some slippage - hold the rope 8inches or so from the belay plate and it naturally feeds through a bit during the catch.

In reply to Calder:

If you intend to give several meters of slippage, it depends totally on the situation, but you want to change the angle the rope comes through the device progressively to prevent it locking up till you want it to. With a 40kg climber and a lot of rope drag, the device will probably lock immediately unless your brake hand is quite high, and you'll stop the climber before the brake rope reaches the vertical... with a 90kg climber you'll want to start pretty much from a vertical position and then bring your hand round behind your arse to stop them.

In reply to bpmclimb:

Anyone here think additional slack in the system contributes to a softer fall?

I recently had partner complain about a hard fall due to me having too little slack in the system! Personally I think he was talking bUllock but hey ho.

Unless you're on very steep stuff I think dynamic belaying is one of those things that, you're damned if you do and damned if you don't. The time you get that yeilding to the force just right will be the time the extra fall distance means your climber catches his ankle on a ledge.

In reply to JLS:

Absolutely! Assuming you've fallen out from the wall, the further you are below the top quickdraw when the rope comes tight the more acute the angle between the rope from the draw to the climber, and the vertical. The more acute this angle is, the more of your momentum will be absorbed by the system, and the less will be swung round the fulcrum (the draw) into the horizontal plane.


Yes, what sort of catch is required is very much terrain dependant. There is no one technique that will be a "best fit" for all scenarios, which is why good belaying is something we can be learning till the day we hang our rock shoes up.

In reply to Ciro:

There is not really any such thing as shock loading. Just that some forces are bigger than others. There is not anything special in terms of forces of the climber coming to rest. Sorry, I should have given this reply befire rather than resorting to humour!

In reply to bpmclimb:

Personally I'd never let rope 'slip' through the belay device. In my mind that carries too high a risk of losing adequate control.

I'd always try to provide dynamic balaying by body positioning and movement and allowing some slack in the system before the fall. In general I only have the rope tight when the climber has either asked me to take, or there is some other reason I definitely don't want slack in the system (e.g. if they're on the the first or second clip).

In reply to JLS:

Yes.


<cough>

There's never a soft fall when there is no slack in the system.

I think Saturday's catch by E was as soft as I'd confortably go. Much softer and it might have been very hard!

In reply to Ciro:

I think this is probably waffle. It is a common myth that slack in the system somehow decreases the fall factor. Cetainly more slack in the system (not the same as using the balayer dynamically) will result in greater maximum tension (ie less soft fall) if the fall is vertical. Extra slack may stop you swinging into the wall in a non vertical fall as you describe, but will not decrease the maximum tension in the rope.

In reply to Robert Durran:


There certainly is! There's a certain amount of kinetic energy that needs to be absorbed to arrest a falling climber. The force on the component parts of the system will vary over the time from the point where the rope begins to come tight, till the point where the climber stops. The shorter the time frame over which this occurs, the higher the peak force will be.

If you want to test this out for yourself (and I don't recommend you do!) try doing a bungee jump with a regular bungee cord attached to your ankles, then do the same with a semi-static abseil rope - see if there's any difference on the shock load on your hip sockets

In reply to Robert Durran:

It's basic mechanics.

In reply to Fraser:

NO


Wrong. Slack in the system will make the fall harder. Slack is not part of dynamic belaying; dynamic belaying is provided by the "give" of a moving belayer. The only reason to have slack in the system is to allow easy clipping and/or stop the climber swinging into the rock.

In reply to Robert Durran:

I never suggested it would decrease the maximum tension in the rope.

In reply to Fraser:

Granted! :-D It made me reconsider using a helmet for sport climbing but on reflection I think a rucksack with rope and rack strapped to my back would be much more useful!

In reply to Robert Durran:


Exactly! First you need to do is allow enough slack in the system to stop the climber being immediately swung into the wall, and *then* you need to absorb the momentum that's been generated with a soft catch.

In reply to Ciro:

No. You mean higher average force.

Of course there will be a higher maximum force with the static rope, but it is all relative. A thick steel cable will give an even higher maximum force; by your logic this would mean there was no "shock" loading with the static rope. If you want to talk about shock loading without waffling, you need to arbitrarily define how many Newtons constitutes shock loading.

In reply to Ciro:

In which case "soft catch" is a misnomer - extra slack actually makes it a harder catch (as opposed to the belayer stepping in which will, as discussed earlier, make it softer).

In reply to JLS:
Absolutely! My right foot hit the wall on a fall recently and the knee is quite uncomfortable because the impact was quite high due to the lack of slack in the rope. This of course is no-one's fault but my own since I was screaming like a girl to 'take, take, TAKE!!' but please goodness I've now learnt my lesson!

Agreed. It all depends on where you are. No dynamic belaying near ledges or sticky out stuff.

In reply to Ciro:

>"Absolutely!"

So you are saying that the increased velocity of the climber when the rope goes tight is not significant?

I was thinking that shortening the fall will, by a function of acceleration due to gravity, decreases the absolute amount of energy in the fall. You can then by use of dynamic belaying disapate that energy.

I'm still finding it hard to imaging how having more energy to disapate is an advantage...

So if a partner is 1m above a bolt how much slack is correct 0.5m or 1m or 2m... why not 5m?

In reply to Ciro:

It's actually quite tricky mechanics - poresumably why you have resorted to waffling!

In reply to Robert Durran:

No, I mean higher peak force.

Think of it this way. If you're going down the road at 60mph on your motorbike and you're highsided, and thrown off into a bridge, you'll stop very quickly and the peak force will likely be high enough to kill you as your organs pass through each other. If you were instead thrown into a huge drift of powder snow, you'll stop over a much longer period of time so the peak force will be much less, and you'll probably live.


Why?

In reply to JLS: Is it not the case that the extra rope paid out allows more of the energy generated to be absorbed? So you may fall further but before you impact the wall a lot of energy has been dissipated by the stretching rope.

In reply to JLS:

It is significant - it increases the maximum tension in the rope.


Yes. Remembering that dynamic belaying has nothing at all to do with having extra slack in the system.


That's because it's not an advantage!

Only enough to stop the climber swinging into the rock. ie none on steep enough ground.

In reply to Robert Durran:


It's high school stuff, although agreed I don't appear to be able to explain it very well as you seem to keep getting the wrong end of what I'm trying to say. Perhaps someone with science teaching experience can explain it better than I can.

In reply to Ciro:

Velocity vectors. By introducing a downwards velocity vector the resultant velocity is no longer normal to the wall. How big this downwards vector should be is, of course, open to debate...

In reply to eve_b:

>"extra rope paid out allows more of the energy generated to be absorbed"

E=mc'2 so is it not the case the energy being generated a square function whereas the rope absorbtion thing is a liner function...

In reply to Ciro:

Obviously a situation in which the average force is higher will tend to have a higher maximum force, but they are not the same thing. You are using them interchangeably and this confuses the issue.

In reply to JLS:


Yes, it's a balance between the two - if there's not enough slack in the system you'll find it very hard to add enough dynamic element into the catch to prevent the climber hitting the wall. Adding more slack than is neccessary rarely causes a problem unless there's something to hit on the way down.

Obviously all this only applies well above the ground. 6m above the ground, slamming the wall is very much the order of the day.

In reply to Ciro:

A stretchy rope with a fall and a swing is quite tricky high school stuff! I am a maths teacher who teaches this stuff up to A level standard. I do know what I am talking about.

In reply to JLS:

It'd be a hell of a fall if you were getting to anything like c!

E=1/2mv^2 maybe?

Extra slack gets you out away from the wall on steep ground. The rope never hits hard, when I think of a 'hard' catch it's the terrain that does damage so it makes sense to drop clear if you can do so safely.

jk

In reply to Robert Durran:


Well I'm pretty sure all of the concepts I'm talking about were covered in higher physics... I could be wrong though, it's all so long ago I might be getting confused with first year mechanics.

In reply to Robert Durran:

Lets get some perspective, even tricky high school mechanics is basic mechanics.

In reply to JLS:

"linear function"

In reply to Ciro:

On the other hand, if you're only going at 20mph, then you're going to hit the bridge a lot less hard, it might only mangle you and you'll need less depth of snow on the theortical bank before you are not injured at all.

Having lots of extra slack in the system is essentially just deliberately increasing the speed of the the motorcyle. If you have 4m of extra slack in the system, then the climber falls 4m further before any braking begins to happen (ie a 3 meter fall becomes a 7m fall) and is undisputably going faster at the point of imapct. Why people think extra slack = lower impact force is totally beyond me. It's what happens after the rope comes tight that has a chance to reduce the peak forces, accelerating further before that happens can not possibly reduce anything.

In reply to Calder:

Ok, like the "shock load" it's all relative!

In reply to hexcentric: The intention is not to accelerate, but to decelerate more slowly.

In reply to hexcentric:
Having no Physics etc. I tend to agree - more rope = bigger fall BEFORE the slowing begins, thus more speed and presumably more energy - the extra amount of rope thus run out may stretch more and help give some reduction, but would it compensate for the greater force?
A further point - all very well when the leader doesn't hit the deck, but I see a fair bit of indoors belaying with plenty of slack when the leader is only at the second clip - ankle breaking stuff. I'd argue that you could employ two belaying techniques - one up to the third clip, another beyond that.

In reply to JLS:

Hopefully.......(and I really do mean hopefully!)....I'll not be travelling at the speed of light!

In reply to Jim at Work:
In short: energy absorbed by the rope will go up with the square of it's length, while energy generated in the fall will go up linearly with the distance fallen.
In more detail:
By falling further, more potential energy will be released which is E = mgh*, so all in all linear. Whereas the energy absorbed by a spring E = 0.5kd^2**, (note, quadratic relationship to displacement). Also note the spring equation: d = F/k***. Adding slack to the system is equivalent to adding springs in parallel. Two equivalent springs in parallel will have half the spring constant of one (k_both = k1*k2/(k1+k2)). Meaning that loaded with the same force two springs will stretch double the distance of one (as d=F/k). Now note, that potential energy absorbed by the spring goes up with the square of the displacement, while the potential energy of the fall increases linearly with the distance fallen.

Hence, given double the rope length in the system, the climber will fall a bit further than twice as far (the actual extra rope, plus rope stretch, which let's say is 30% making the total distance 2.6), releasing more than twice (let's say 2.6 tiems) the amount of potential energy, however 4 times more energy will be absorbed by the additional spring. Hence, more slack in the system results in a softer catch (assuming of course, that the climber does not hit the ground).

*where m is mass, g acceleration constant, h distance fallen
**where k is the spring constant, d displacement of the spring's end from equilibrium
***where k is the spring constant, d displacement of the spring's end from equilibrium as before and F is the force acting on the spring.

In reply to freyja: You mean series, not parallel.

In reply to Calder:
yes, I meant series, thanks! The argument that follows and the maths are for springs in series, it was just a major typo.

In reply to freyja: I spotted it because it's the kind of thing I'd do!

In reply to Jim at Work:

No

In reply to freyja:

To pick out just one obvious flaw in your argument, the energy absorbed by the rope must equal the potential energy released when the climber is stationary at maximum rope extension and tension. 2.6 does not equal 4.

Your argument and conclusion are wrong.

In reply to Robert Durran:

I am not sure whether you are being pedantic or ignorant. The energy will be used up to stretch the rope, and slow you down, once the rope stops stretching you come to an abrupt halt, the speed which you are travelling at this time, will depend on how much energy was wasted for stretching the rope, and slowly decelerating you, the change in acceleration (called jerk) is what hurts, the lower the acceleration at the time you come to an abrupt halt, the lower the jerk, the less it hurts. The rope capacity to absorb energy also doesn't have to be used up, it will just stretch less given less energy.

at the end of the day, you can always trying jumping off the same point with the rope being tight, and with the belayer having just paid out lots of slack, and see for yourself which scenario you prefer. (Obviously, if do try this, try it high up the wall...)

In reply to freyja:

"at the end of the day, you can always trying jumping off the same point with the rope being tight, and with the belayer having just paid out lots of slack, and see for yourself which scenario you prefer"

Scenario - your knot is 1m above the last bolt...

2m fall with 8m rope = 2/8 = 0.25 fall factor

Now add 2m of slack...

4m fall with 10m rope = 4/10 = 0.4 fall factor

So is the widely used fall factor theory wrong?

The really issue is whether the additional slack in some way alleviates a sling shot effect.

I think not. I think you can only alleviate the sling shot effect if the slack can be added to the system AFTER the rope goes tight and NOT before but I not up to proving it with physics...

Dear Mick

Please can we have a Mechanics forum so we can talk about rope dynamics and belay forces late into the night?

Kind regards,

Graham.

;p

In reply to JLS:

We've somehow digressed from discussing how to give a dynamic belay to achieve a 'soft catch', to having extra slack in the system - which would surely serve a different purpose altogether.

Whatever. I'm out...

In reply to Robert Durran:
YES.

Wrong.

I've experienced freyja's suggestion exactly as described very recently and I know which I prefer. In case you'd missed it and to state the bleeding obvious, I prefer lots of slack. Anyone belaying me with none will only do so once.

And with that, I too am out.

In reply to JLS:

Ahem, temporarily back in...the fall factor theory isn't calculated in the way you have in your example.

Now I really am out!

In reply to freyja:

The energy in a falling body is kinetic energy (not potential) and increases by the square of its velocity. E=1/2mv²

In reply to Fraser:

>"Wrong."

It's not as black and white as that.

Perhaps I have been guilty of thinking about straight down falls on routes near the vertical and not thinking about falling away like when your feet stick and you hands blow which adds a big horizontal component to the fall but still... I think a yard of slack is asking for trouble unless you're climbing in 45deg caves.

In reply to Robert Durran:

This thread is very amusing. Everyone using basic high school physics to solve what it essentially a slightly complex problem (what's the peak force exerted by a rope with complex elastic properties in a fall of varying lengths).

However, I think you've spent most of the day arguing about the wrong thing - especially when it comes to extra slack in the system. The point you should be arguing about is the *angle* the rope is at when it comes taught.

With a tight rope this angle will be closer to horizontal, thus exerting a horizontal force on the climber and potentially slamming them into the wall. By contrast, when more slack is added, the rope is at a more vertical angle and that reduces the *horizontal* component of the force. I guess that's why most people who fall a lot don't like tight ropes.

In reply to midgets of the world unite:


I see what you're saying and I agree with the sentiment, but the horizontal component of the fall force will be the same regardless of the way it is absorbed. What is more correct is that the horizontal component will become relatively small compared to the vertical component and therefore of less relevance to the fall trajectory.

In reply to jimtitt:

Yes, kinetic energy is square in velocity. Spring energy absorption though is given as E=0.5kd^2, from Hooke's law (spring equation), quadratic in distance. You cannot compare the order of the two, because the variables are different, therefore it makes more sense to compare potential energies in both cases, or manipulate the equations until you can compare like for like.

Pretty much all of the potential energy will be converted into kinetic energy during the fall, the two energies being equal. So it is possible to use them interchangeably up until the point when the rope goes taut. As the breaking starts, some of the energy will go into extending the spring component in the rope, some into heat (touch the belay device), some of it can go to stretch the spring components in your body (this hurts!)

In reply to midgets of the world unite:
As for the angle, the cushioning effect of slack would be felt even when climbing an overhang with the belayer standing directly below you, although, obviously, the angle is important when it comes to potential wall slamming.

Anyway, this is not a physics forum, I just couldn't stop myself from chipping in when I saw quantum physics being proposed as a framework to understand the belay dynamics.. Happy and safe climbing to everyone!

In reply to john arran:

Now we're arguing about the right stuff! Not sure how you reach your conclusion "the horizontal component of the fall force will be the same regardless of the way it is absorbed". The issue is I don't really understand what you mean by the term "the fall force".

A fall is predominantly vertical. The rope pulls on the climber, accelerating them upwards and also into the wall. The horizontal velocity the climber has when they hit the wall depends on the amount of force the rope exerts, and the angle of the rope during this force. Since all of these quantities change with time during the fall, and in complex ways, it's not clear to me that the horizontal force produced is the same in each case.

In reply to freyja:
<nerd mode>
You're totally right about the potential energy, but something funky has happened to your maths*. When you treat the rope as a spring**, you're best assuming that the elastic modulus is a constant for the rope. Doing this properly, if x is the max rope stretch experienced, you get

mgh + mgx = 0.5 * k* x * x

So, assume that the max force on the climber comes at the moment of maximum rope stretch, sort out the maths, and assume constant elastic modulus (E = kL/w, where L is the length of rope and w the rope width) you get to the fall factor equation, which states that, for the same climber and rope, the maximum force on the climber depends only on the ratio of fall height (h) to the rope length, L.

The quantity h/L clearly goes up if you pay out slack (imagine doubling a 1m fall by paying out 1m of rope when 20m is already out), so under your own model, there is no "cushioning effect of slack". Sorry.

*i think it goes pear-shaped when you treat an extra bit of rope as a totally independent spring.
**this is actually a bad way of modelling ropes (when you fall, you don't bounce up and down for ever) but does an OK job for our purposes.

</nerd mode>

In reply to Formerly Known as Pylon King:

Takes one to know one

In reply to midgets of the world unite:

I was (mistakenly, it seems) thinking you were referring to a climber falling in an arc away from the rock, as often happens when failing on undercut or layback moves - hence the horizontal component of the fall to be arrested by the rope. I agree that any horizontal component introduced during the fall arrest (due to the bolt not being in the same vertical plane as the vertically falling climber) is a different issue, although not unrelated. I suppose it's safe to say that in any case the horizontal distance still needs to be covered but that the rate of this happening will differ, notably due to the time over which the fall is arrested.

In reply to freyja and others:

The standard modelling used to prove that max force is proportional to the square root of the fall factor (fall factor = length of fall (including rope stretch) divided by rope payed out) assumes an elastic rope obeying Hooke's law, no additional slack in the system and a frictionless krab on bolt fallen on. If you modify this to include additional slack in the system, it can be shown that any additional slack increases the max force (and therefore max deceleration).

Freya has used all the same assumptions, but her argument is riddled, I am afraid, with nonsense and reaches a wrong conclusion.

If, as Fraser and others argue, actual experience suggests that addditional slack decreases the maximum force (and I would be very surprised and prepared to humbly eat my hat if they are right) then it must be because the assumptions made depart suffuciently far from reality to give a completely contrary result.

To those who say that the argument is irrelevant to practice: Yes, bolts and ropes don't (hopefully!) break, so the max force is not related to safety, so the overriding cosiderations when deciding whether to give extra slack are concerned with swinging into the rock, hitting the ground and easing clipping. Obviously the max force on some trad gear is highly relevant to safety!

There also seems to be some confusion between increasing the length of a fall by giving extra slack (as above) and cushioning a fall by a belayer stepping in towards the rock.

In reply to Robert Durran:

Also note that doing the maths for a non vertical fal with a resulting swing in is actually really quite hard and either I can't or havn't tried hard enough to do it! There have been various waffly arguments above to try to show that extra slack decreases the speed at which the climber swings into the rock. It may well be true, but I don't think anyone has correctly argued why!

In reply to Robert Durran:

I have just rechecked my maths (yes, sad at 1.30 am.....):

Climber mass m
Acceleration due to gravity g
Climber height h above belay and runout r above bolt
Length of slack in system s
Modulus of rope k (so that force F = kx/l where x is extension (stretch) of rope and l is length of rope unstretched)

Max force = mg+((m^2)(g^2)+2kmg(1-(h-2r)/(h+s)))^0.5

It is easy to show that this increases as s increases when h>2r.
Note that h>2r is neatly the condition for the climber not to hit the ground before the slack starts whipping out; obviously if this condition is not met other more important and painful factors come into affect.

Interestingly the max force actually decreases as s increases if h<2r, but in this case the slack starts whipping out just as the climber falls past the belayer (assume a hanging belay with a clean drop below!) so it might be worth paying out as much slack as possible if the climber is above poor gear and is already looking at a massive fall past the belay (anyone fancy testing this out?!)

In reply to Calder:

I already seem to be talking to myself on here late into the night.....

In reply to Fraser:

I strongly suspect that your perceived softer fall with lots of slack is actually because, with more slack, your belayer is pulled more in and/or up, thus effectively creating a dynamic belay system - if you had a massively heavy belayer who never budged an inch, you would perceive a harder fall with more slack.

In reply to Robert Durran:

Good man! For anyone interested the derivation of this can be found here:- http://www.rockclimbing.com/cgi-bin/forum/gforum.cgi?do=post_attachment;pos...
Interestingly in practice the maximum force on the climber is not felt at the end of his fall but early in the arrest.

In reply to Robert Durran:

You can conduct a little experiment to prove it at home using a weight, rope and chinup bar. Drop the weight from a fixed position above the bar and vary the amount of slack. Observe the velocity of the weight as it swings under the bar.

In reply to Robert Durran:

I think the main reason you percieve a softer fall with more slack is that the dynamic rope takes care of the vertical component of the load, whilst the decidedly un-dynamic rock is often what arrests the swing. If the rock wasn't in the way you might percieve a harder fall with more slack.

In reply to Robert Durran:

All this arguing about max force is a total red herring. Midgets of the World Unite painstakingly explained it at 20.32.

When you fall off, assuming you are lobbing onto bolts and not marginal trad gear (which given the context of the OP is not an unreasonable assumption) you don't particularly care what the peak tension in the rope is. What you care about is not swinging in at the end of the fall - ie. the horizontal component of the force. - as this is what slams you into the rock and causes injury. It's all vectors innit, the more rope you have out, the closer the angle of the rope between you and the top runner, will be to the vertical.

This is why you want either slack in the system, or an actively dynamic belay, or a bit of both - and a belayer experienced enough with giving dynamic catches to judge what is appropriate in what context.

In reply to everyone:

I think this whole debate has resulted in complete over-analysis, frequently typical among academics. It's like scientists trying to analyse a joke.

Give me an example of one semi-decent climber whose belayer gives no slack and I'll eat my rope.


In reply to JLS:


Surely you're not serious?! I'd want and expect a yard of slack after 4-5m climbing on pretty much any terrain.

In reply to Quiddity:

Yes, and I acknowledged exactly this in my post of Thursday 23.31 above.


I think this is a waffly explanation (note that I am not denying that more slack helps prevent slamming into the rock, just that this like other explanations given, is waffle).

In reply to Robert Durran:


That and on steeper routes you drop clear of the terrain or at the very least give your legs more room to work cushioning the impact with the rock. Maybe I'm in a minority here, maybe I just have a numb bum but it's not the rope/harness I feel in a 'hard' fall it's whichever bit of me slams into the wall!

jk

In reply to Robert Durran:


'it's all vectors innit' - waffly - no shit.

Midgets has explained it far better than I can so I don't see the point in going through it again. My point is that you don't need a complex numerical analysis to understand this.

In reply to Fraser:

Well, I'm glad that the design of the plane I flew to Kalymnos on at Easter was subjected to extremely thorough analysis by academic experts in their fields.


No, it's scientists analysing science.


Me! (Ok, can we stretch to quarter-decent....). Obviously I actually want just enough slack to allow movement and clipping without the rope going tight - not excess slack which is what we are talking about.

In reply to Robert Durran:

How much does your belayer weigh relative to you?

In reply to Ciro:

There has been a lot of surprising confusion between a hardness of a fall (ie max tension in rope) and swinging into the rock (obviously hard in a different way). They are two very separate issues. At last you seem to be acknowledging this, and agreeing with me that extra slack gives a harder fall!

In reply to Quiddity:

Depends who is belaying me obviously. I always feel happier with a heavier belayer - yes, I know this tends to give a less dynamic belay, but I hate my belayer being lifted off their feet and into the wall with resulting possible loss of control.

In reply to Robert Durran:


Yikes. Well they're your ankles.

In reply to Quiddity:

This thread is ace.

It's good to see that others value the dynamic aspect of belaying as much as I do as I thought initially I was being a fussy bugger.

Since I've been sport climbing more and hence falling off more I've gone from simply wanting a safe belayer to wanting a safe belayer who I trust implicitly to arrest a fall gently. Being belayed by someone new (but still safe) who hasn't had lots of experience of catching people lighter and heavier than themselves makes me nervous and less likely to push myself to my personal limit when climbing.

I hope that hasn't distracted people from the force calculation discussions above which have been delightfully geeky.

In reply to JLS: Re fall factors and slack.

How about: right hand side of el cap, 2m above belay, no gear, looking at a fall factor of 2. Belayer forgets to put belay plate on, so now 60m of slack, fall factor is reduced to just over 1.

In reply to Fraser:

Yes, but for balance (and for our less experienced readers) it might be worth pointing out that this is a highly sport/wall-based discussion, particularly where there is a high fall factor.

Outside in the real (trad) world, my more usual version of dynamic belaying is noting suitable holes to jump into to dynamically take is as much slack as possible to prevent a ground fall. I find that supplying an extra metre of slack in these circumstances is somewhat frowned upon.

The exception is where you are trying to arrange for a falling leader to avoid the lip of a roof or big swing, but I wouldn't want inexperienced belayers to read this and run away with the idea that they are always obliged to allow metres of rope to run out before they start holding onto it.

In reply to jimtitt:

That is exactly how I derived it. Here, extra slack in the system was not considered (the point of this debate). However, it is easy to see from the algebra that both H and L are simply increased by the amount of extra slack giving H+s and L+s. I rewrote (H+s)/(L+s) as 1-(L-H)/(L+s) to make the effect of varying the slack s transparent. (in my analysis 2r is substituted for H and h is substituted for L).


I lay awake last night worrying about this! The climber in reality does not spring back up but comes to rest at the lowest point, so the deceleration at the end of the fall must be zero. Does this mean that the elastic model is bollocks and those who claim that extra slack gives a softer fall might be correct in practice after all (now where did I put my edible hat?) The reference above claims that actual ropes do obey Hooke's law pretty closely - how is this reconciled withthe maximum force being felt earky in the arrest?

Am I right in thinking that your work involves testing/analysing this sort of thing? Do you have a better model than the elastic one for analysing falls? Can you give us a definitive answer as to whether extra slack does or does not in reality give a harder or softer fall?

In reply to Dave Garnett:

I actually think this is a genuine problem. I am increasingly seeing obviously wall bred novice trad climbers belaying standing well out from the rock and often with excess slack - accidents waiting to happen with unzipping lower wires and failing upper wires.

In reply to David Coley:


To quote my own post of 01.29 this morning:

"Interestingly the max force actually decreases as s increases if h<2r, but in this case the slack starts whipping out just as the climber falls past the belayer (assume a hanging belay with a clean drop below!) so it might be worth paying out as much slack as possible if the climber is above poor gear and is already looking at a massive fall past the belay (anyone fancy testing this out?!)"

So the situation you describe actually is optimally favourable to a soft fall since the climber is falling past the belayer with maximum slack in the system. It might not, hoiwever, be very favourable where psychological trauma is concerned....

In reply to Dave Garnett:

I think it's more a "well off the ground" discussion than a "sport/wall" discussion. I certainly wouldn't want my belayer to dive into a hole when I took a fall onto a vertical wire placement 20m above the deck. First of all, I'd want to fall far enough that the load came onto the wire with a reasonably low horizontal component to prevent it getting ripped out sideways, secondly I'd want the dynamic properties of the rope to be absorbing the force of my fall only, not that of my belayers fall too, and finally I'd want them to be in control of themselves so they can give me a dynamic catch.

Hopefully what inexperienced belayers will take away from this is that it's a pretty complex subject, that they should think a lot about, not just consider once they've passed the belay test at the wall they know what they're doing.

In reply to Ciro:

Oh, potential ground falls can come into the 'well off the ground" category too!


I understand that (and you would need to communicate this to the belayer) but how do you calculate whether the longer fall will result in the wire ripping anyway? In the end, the biggest factor determining how much energy needs to be absorbed is how long you have been falling (increases as a square of velocity, which is increasing constantly). Perhaps you should be extending the draw appropriately and relying on the the rope to absorb the shock. If there's a fair bit of rope out (and 20m is plenty, particularly 9mm) coming to a sudden halt isn't an issue in my experience (unless you run out of space to do it in, of course).

> Hopefully what inexperienced belayers will take away from this is that it's a pretty complex subject, that they should think a lot about, not just consider once they've passed the belay test at the wall they know what they're doing.

That I do agree with.

In reply to Quiddity:

Ahem, You'll find I mentioned vectors about 24 hours ago. And you'll not get a clear and concise explanation without a diagram. As I tell my students...

Draw a f*cking diagram!

In reply to Robert Durran:


Yes, and no respectively. The elastic model is bollocks but it still gives a reasonable description of the relative increase in force with extra rope elongation. It overestimates the amount of the force, and completely gets the timing wrong, but it's OK to start with.

With the maths you've done so far, you're 2/3rds of the way to proving why extra slack means slamming into the wall with less violence*. Simply assume the climber is dropping a horizontal distance x from the wall. Add a small amount of extra rope, dl; this will increase the fall distance and hence the magnitude of the max force, but a greater component of this is directed vertically. A diagram and a bit of trig easily shows that the horizontal force goes down.

*most people would describe this as "a less hard fall", regardless of any semantics you wish to pursue.

In reply to Robert Durran:

Your dedication is commendable.

In reply to Dave Garnett:

Indeed, with trad placements the whole thing becomes much more complicated, and it's something I've only just started thinking about. Interestingly, I just did a quick back-of-the-fag-packet calculation that seems to disprove my logic about the horizontal forces on the gear... however I did make an awful lot of assumptions to simplify the calculation, so I'll have to look at it in a bit more detail later.

In reply to Calder:

Just mentioning vectors proves nothing - they've got to be the right vectors analysed correctly.


One of the problems of internet forums!




If I told my students that, I would at least get a written warning....

In reply to Robert Durran:

To quote myself:

"Velocity vectors. By introducing a downwards velocity vector the resultant velocity is no longer normal to the wall."

I was obviously assuming overhanging terrain where you are not vertically above the bolt/gear, but are above and out from it. Calculating the magnitude of the velocities by some means or other - whether crudely or accurately - is interesting, but ultimately unnecessary.

However, finding a safe and consistent method of giving the soft catch is very worthwhile.




My students are older, and they can take it because they'll have been told 100 times before.

In reply to midgets of the world unite:

But does its prediction that giving extra slack produces a harder fall (greater max tension in the rope) correspond with reality?

Sorry, this is wrong. When swinging into a vertical wall, what matters is the horizontal component of the momentum with which one hits the wall.
The force on the climber has two components:
(1) a radial force in the direction of the rope contributed to by the whole of the tension in the rope and a component of the climber's weight.
(2) a tangential force perpendicular to the rope only contributed to by a component of the climber's weight.
The horizontal momentum at the moment of impact is entirely tangential. This tangential velocity is only affected by the tangential force on the climber (integrated over the time of swing plus a starting value from the free fall before the rope starts going tight). Thus it is not contributed to by the (radial) tension in the rope.

My calculations suggest that more slack generally gives a smaller initial tangential momentum as the rope starts to go tight as well as a smaller tangential component of the climber's weight, so yes, it does follow that the impact with the wall is decreased by giving more slack. This ties in with everyone's experience of less "slamming" into the wall with more slack. But it has nothing to do with the direction of the tension in the rope as you and others have wafflingly and incorrectly argued.


It should be quite clear to anyone following this thread that there is a clear distiction between the hardness of fall (max tension in rope) and the speed with which a climber slams into the wall. They are separate issues. The first increases with more slack, the second decreases with more slack. It has nothing to do with semantics, so please do not try to confuse things.

In reply to Calder:

Sorry, no idea what you are arguing or what points you are trying to make here.

Entertaining mathematical shenanigans. Regardless of all that, I would want to keep it simple in my requests of a belayer. The key ones are:

1. Give me what you think is the right amount of rope so that I don’t hit anything (whether that is stopping short or falling past) and can move/clip without being pulled off. The things to avoid are swinging into things, slamming into things, hitting the ground. This is something that will be changing constantly and so will require continuous attention and adjustment. If it’s steeply overhanging sport climbing and I am well off the deck, that extra bit of slack is cool with me. If there is anything in particular I want you to be aware of I will say before I set off or when I am up there – or both.

2. If neither of us is going to get hurt by hitting stuff, feel free to move with the pull of the rope when it comes tight.

3. If you’re using an ATC-type belay plate, lock off - don’t try to let some rope slip through the belay plate as you might lose control of the rope. I can think up scenarios of exceptions but they are unlikely to arise.

I won’t be asking you do to any fancy-pants jumping off belay ledges to take in enough rope to prevent me hitting the ground. If it turns out that is the choice for you, I’ll not blame you whatever choice you make. Nor will I be doing any fancy-pants leading above marginal gear that requires you to jump up as the rope comes tight to reduce the impact force on my gear: feel free to try (just don’t jump outwards) but I doubt it will help.

So
- right amount of rope to not hit stuff or be pulled off
- no belay device rope slip: lock off please
- move with the pull if safe for you and me.

Anyway, back to all the fun with complexities...

In reply to Robert Durran:

Who defined the hardness of the fall as the max tension in the rope? The hardness of the fall relates to the greatest stopping force you experience - if there's a wall within hitting distance, in most cases it will be determined by the speed at which you hit the wall, not by the force with which you stretch the rope. I've yet to experience a fall of any length into space on a dynamic rope that felt anywhere near as hard as a 1m fall into a wall.

In reply to all:

Perhaps the matter could be approached by side-stepping the technicalities of mechanics for the time being, and simply looking at what the "experts" do in various situations. This does beg the question: who are the trustworthy experts?

I have seen instructors in charge of advanced youth groups belaying young climbers and encouraging them to take falls. The catch that the instructor gives is often very soft indeed, with a great deal of rope slippage, such that the catch merges smoothly into the lower. Obviously there is usually a large weight differential in this scenario. It seems reasonable to me to see the rope slippage element as increasingly risky as the climber's weight increases relative to that of the belayer.

I would like to know what the top sport climbers/coaches do as default, particularly when not using a Grigri, and in what way they modify their belaying technique (especially the rope slippage element) as the climber's weight increases.

Regarding the question of deliberately introducing slack: I think a lot depends on where the climber is in relation to the last bolt. If I fell from steep ground just above a bolt I can imagine being grateful for a little extra slack, to avoid a tight arc of inward swing and possibly rapidly hitting the wall with feet/knees. On the other hand, if I've climbed up 3 metres above a bolt (and perhaps pulled up some slack to make the next clip) then I would feel that there was already plently of slack, and wouldn't feel too happy about my belayer introducing even more!

In reply to Ciro:

Well I just have in order to clear up any confusion and discussion at cross purposes that may have been going on earlier in the thread. There were two separate issues being discussed and someone had to point this out and draw a clear distinction to stop a lot of time being wasted.

In reply to Robert Durran:

Ha Ha. Good one Robert.

Oh wait. I've read the thread. Jokes on me!

In reply to metal arms:

pmsl

In reply to Quiddity:

What does that mean?

In reply to Robert Durran:

I found his contribution jolly humorous.

In reply to bpmclimb:


From the videos I have seen the top sport climbers get belayed by really cute women. Chris Sharma's belayer jumped about 5m in the air when she caught him.

Perhaps the optimal belay solution is to marry a ballet dancer with her own GriGri.

In reply to Robert Durran:

It's not two separate issues, it's two components of the same issue - each worthy of discussion in their own right, but both of which must be taken into account when considering the original question.

Your definition of hardness of fall being the max tension on the rope is unfortunately flawed - to take the extreme case, if I hit a ledge on the way down, breaking both my legs and absorbing a lot of the momentum in the process, I'd consider that a hard fall, regardless of the fact that the max tension in the rope was quite low compared to what it would have been if I'd missed the ledge.

In reply to Ciro:

Well obviously they are related.


Which is precisely why I repeatedly tried to make a clear distinction so that we all knew which was being discussed in its own right at any on time.


Well, you could have defined the hardness of the fall as the maximum force of any type on the climber, but that would not have separated the two issues. To do so was the whole point of my sensible distinction.
I think you are being rather silly here!

In reply to Quiddity:

How come pmsl means that?

In reply to Robert Durran:

Yes, as the text you quoted from me implies, if you think about it.


It's hard to know what you're on about since you mix radial and tangential with horizontal so confusingly - e.g. "The horizontal momentum at the moment of impact is entirely tangential"? I'm impressed you can accuse me of waffling whilst writing stuff like this. Nevertheless, I think I see what you're getting at. Also, your tone is pretty strident for someone who's arguing with a physics lecturer about physics (and is wrong). The reason you are struggling is that your 'radial' and 'tangential' co-ordinate system is non-inertial - your co-ordinate system itself accelerates as the climber falls and failure to account for this will cause all sorts of problems.

Instead, consider the following, basic scenario. We've got a vertical wall. We'll define horizontal and vertical coordinates perpendicular to and parallel to the wall, respectively. The climber is falling, vertically. The rope comes tight. Now, read your own statement 1. Your radial force in the rope can be resolved into two components. A vertical force and a horizontal force. The size of the horizontal component depends upon the magnitude of the tension in the rope, *and the angle of the rope*.

If a climber, falling vertically, experiences a large horizontal force, they're going to end up hitting the wall, and hard. Simple. If a climber, falling vertically, experiences a zero horizontal force, they will not hit the wall at all. This is not hard.



The distinction is quite clear, but only you have insisted on defining the 'hardness of fall' as the max tension in the rope, and did so without informing anyone else for a large part of the thread. Everyone else seems to be using a sensible, though vague, definition of fall hardness as "did that fall feel unpleasant". This, of course, has everything to do with semantics, that being the study of meaning. I suggest you take a fair share of the blame for confusion yourself.

In reply to midgets of the world unite: I wasn't. I'd take "how hard the fall is" to mean how much impact is placed on the top runner, as opppsed to "how pleasant the fall is" which is a completely seperate issue.

I think a number of people futher up thread were arguing (though I could have misread this) that having extra slack out lowered the impact force on the runner you were falling onto, which seemed patent nonsense to me. I wouldn't dispute that a longer fall might be less of a slam for the climber but that didn't seem to be their point at all.

In reply to Robert Durran:

I thought that was rather implicit - we were after all talking about falling practice... I would hope the climber would have selected a top runner that was up to the task of holding the fall, so the main problem becomes what happens to the climber, not the runner.

In reply to hexcentric:

you're right in all senses. In fact, I corrected someone above who thought they'd shown the impact force went down with extra slack.

this has all got horribly technical because "someone is wrong on the internet", but basically you want three things out of a fall

1) minimal impact force, so runners don't rip and bones don't bruise
2) not to swing violently into the rock
3) not to hit anything on the way down.

criterion 3 is somewhat at odds with the other two. However, if there's no chance of hitting anything, then a dynamic belay will ensure criterion 1, whilst a little bit of extra slack will greatly help criterion 2. Right?

In reply to midgets of the world unite:

So to summarise what we need is - Good belaying for falling practice.

Conveniently in the thread title!

In reply to midgets of the world unite:


Not horribly wrong, just a useful bit of scientific peer review

It's made me think a bit more about how I evaluate the risks of different fall scenarios on trad gear.


In the context of falling practice, criterion 3) should be fulfilled by the climber choosing the correct place to fall and popping off the correct distance.

However 1) and 2) are also somewhat at odds... giving slack to avoid the swing means more energy to be dissapated in the catch - again in the context of falling practice with a bomber top runner this is easily dealt with via a dynamic catch.

In reply to midgets of the world unite: Right.

In reply to Ciro:


yeah, I think that's exactly the point. With decent belaying a dynamic catch will easily offset the increased force from a big fall - you just need a clean enough fall-out zone!

In reply to bpmclimb:

The catch merging into the lower is exactly what I was talking about earlier - I cannot profess to be a top sport climber or coach, but I regularly catch partners from significantly less than my own bodyweight to about 20-odd kg more in this manner at the wall, when they're doing falling practice from the chains. On rock, it's not something I'd usually do, but it's useful to have that technique in the bag if it looks like the climber is about to take a big swing into something injurous. Obviously the heavier the climber, the more friction is required to keep control of the fall, so the lower your brake hand has to be to start with and the faster you have to progress it, but with a bit of practice it becomes quite instictive. At the end of the day, if it feels like it's getting out of control you can always lock off at any point... that just requires whipping your hand round behind you.

In reply to Ciro:

Oh, and indeed the instructors of advanced youth groups was indeed where we got the idea to experiment with this technique. It's certainly not a beginners technique, and not one I'd recommend using with a heavy climber until you've practiced on a light one... we used my mate's super skinny wife as a crash test dummy under the guise of helping her get over her fear of falling...

In reply to midgets of the world unite:

I don't necessarily think it does imply that. Since the whole debate is about whether the max tension does increase with the amount of slack in the system, I think I could have reasonably expected an explicit answer as to whether the elastic model correctly predicts whether this is the case.


On a vertical wall, the horizontal component of momentum at the moment of impact will be equal to the tangential component of momentum. What is wrong with that? Obviously this is not the case if the wall is not vertical.


The only claim I made relevant to the conclusion of my argument was that The tangential force is equal to mass x rate of change of tangential speed. I now see that this was an error ignoring the extra term mass x radial speed x angular speed (my claim only holds true if the rope is not stretching).


Sorry. I should not have said you were wrong to work with horizontal and vertical components rather than radial and tangential components. However, I chose (without success due to the above error I have admitted to!) radial and tangential for the following reason which I think your argument overlooks:
Yes, the force on the climber towards the wall is precisely the horizontal component of the tension in the rope and for a given tension this will be smaller for a smaller angle of the rope with the vertical as produced by having more slack in the system. BUT, having more slack in the system will also increase the magnitude of the tension in the rope (as you agreed the elastic model shows). This, of course, increases the horizontal component of the tension and it is not clear therefore whether these two competing factors actually do decrease the horizontal component of the tension. I think your argument is therefore inconclusive.

The reason I attempted to work with the tangential component of the force on the climber is that this is independent of the tension in the rope - it is the tangential component of his unchanging weight which clearly decrerases with the angle the rope makes with the vertical.

So, I think the jury is still out on this one (though experience suggests that extra slack does indeed decrease the speed with which the climber hits the wall). I think a solution of the full equations of motion are needed to see whether the elastic model predicts this and my initial jottings suggest that these are pretty messy!

I admit I initially assumed that "hardness" meant max tension in rope and when I realised that different people were talking at cross purposes I thought I had made an honest attempt to separate and clarify the two issues of max tension and force of swinging into the wall. It seems I failed to do so. I hope things are clear now.


Sensible, arguably, but, as you say, vague, and this was the problem which I tried to clear up by clearly separating the two issues.

In reply to Robert Durran:

Well I'm glad we got to the bottom of that. Good effort for hanging in there..

In reply to midgets of the world unite:


I have just had another go at this and I really can't see how it can be done "easily". In fact I tend to be confirmed in my opinion that a full solution of the equations of motion (which, incidentally look far less intimidating in radius/angle rather than x/y form!) is required unless you have come up with something really clever. (Then again, maybe I am just being thick!). Either way, I would love to see your argument.

This thread is great. It combines three of the finest things in life: climbing, mathematics and a good row on UKC.....)

Eric in Bristol summed the whole thing up perfectly, closely followed by metalarms. Good job guys. And jolly humorous - awesome!!!

In reply to midgets of the world unite:

I'm learning so much here. Dr Stu of midget fame, may I commend you on your logic.

I've been thinking about this non-inertial frame of reference thing.
Just choosing to work with radius/angle polar coordinates rather than x/y coordinates does not mean I am working in a non-inertial rotating frame of reference; I can derive planetary orbits in polar form (and remember doing this for A-level Further Maths at school) without introducing a rotating frame of reference (indeed I can't see why I might want to do so!), and I certainly didn't come across or use rotating frames of reference until well into first year at university.

But yes, I did mess up my tangential acceleration....

In reply to Robert Durran:

Yes, there's nothing intrinsically wrong with polar co-ordinates, it's the fact that the rope defines your radial axis, and this rotates during the fall.

As far as my 'simple' proof goes, maybe I was having a bit of fun at your expense! As you say, you have to integrate over the equations of motion to work out the final speed of the climber in the horizontal direction. I made this simpler by changing my dependent variable from the time, t, to the amount of strain in the rope, e. This way the equations are the same for both cases, except that the case with a little extra slack has a smaller angle at all e (dtheta/dl = -1/x/cos(theta), where x is the distance from the wall, dl is the extra slack).

You also have to integrate the case with more slack to a slightly higher limit in strain, as the fall is longer. Why my integration works is that this extra bit of the integration comes at the end of the fall, when the force is nearly vertical. Thus, my 'proof' depends quite a lot on the spring model of a rope, which as discussed earlier, is not very accurate, particularly in the timing of maximum force.

I have a hunch you will get a similar answer, but for very different reasons, with a more accurate model of a rope. In this case the maximum force comes early in the fall, making the angle of the rope when first loaded more critical, not less. Without a decent model of how the tension in the rope changes with time (which I don't have), one can't be certain, though.

In reply to bpmclimb: Just a quick point. Jumping into a hole as the climber falls has been mentioned a couple of times but the only time I can think that would be a good thing would be to avoid a ground fall.

Surely if the climber is falling and the belayer is effectively falling in the opposite direction isn't that going to drastically increase the forces on the rope despite the reduction in the distance the climber falls?

In reply to BruceWee:

Quite possibly but that is better than hitting the ground.

In reply to BruceWee:

No* (although I can see why this is counterintuitive!) It is similar to the principle of lowering off putting twice the force on a runner as abseiling off it; There is the same tension everywhere in the rope, so if there is enough tension in the rope to stop one climber, it will also stop the other one.

*making all the usual assunptions about elastic ropes, lack of friction etc.

In reply to Robert Durran:

I can see why the total energy to be absorbed would be the same (assuming climber and belayer are of equal weight), but in a real world fall where friction will slow the motion of the rope through the top runner, obviously the tension in the climbers side will be greater than the tension in the belayers side if the belayer remains stationary. Is it not the case that by deliberately creating more tension in the belayer's side, you're going to inhibit the action of the rope through the runner, reducing the capacity of the rope to act dynamically? You're certainly going to reduce your own ability to add any further dynamic element to the catch.

Since the total energy to be absorbed will be the same, it seems to me that in terms of load on the top runner there's nothing to be gained by jumping down, and something to be lost in terms of dynamism.

Where there would be an advantage of course, would be that if the top runner is going to fail anyway, by jumping down you're reducing the length of the fall onto the second one... but then again the whole thing gets very murky (excuse me if I waffle , as by causing the initial piece to fail earlier, you may have caused the falling climber to carry much more energy into the second stage of the fall than the would otherwise have done.

In reply to Ciro:

I maybe posted too hurriedly and I'm now wondering whether I am actually correct. Certainly friction will change things, as it will in a normal belay situation. Oh no, I can see another late night coming up scribbling equations.........

Preliminary thoughts: Same length of rope to absorb energy. Same amount of gravitational energy converted into kinetic energy at the moment the rope goes tight (if one climber is lower, the other is correspondingly higher (assume equal masses)), so stretch in rope the same (if climbers stop at same moment) so same force. Of course, the two climbers may not stop at the same moment.......

In reply to Robert Durran:

My thinking was that decreasing the tension differential between the two sides of the rope means less force to overcome the friction, meaning the climbers side of the rope has to absorb a greater percentage of the climber's momentum.

But now that I come to think of it on the other hand, the climber will be moving with less energy.

Another factor I hadn't really considered - although the total force will be the same, loading some of it onto the belayers side of the rope will actually decrease the horizontal component of the overall force on the runner, which is presumably going to be a good thing most of the time.

In reply to Robert Durran:

Ok, I've done the maths (elastic, frictionless model) for the situation for two climbers of equal mass, and the belayer, with lightning reflexes, jumps into the hole or off the ledge at the same instant as his partner falls off*. It turns out that the maximum tension in the rope is indeed exactly the same as if the belayer just locked off the plate. So my initial thoughts were correct! So it's worth jumping down a hole to stop your partner decking out - the top runner is no more likely to fail!

*This keeps the scenario symmetrical - both will always have equal velocity and will come to rest at the same instant. In an asymmetrical situation the maths is much harder and they won't come to rest at the same time (awkward differential equations needed rather than a simple energy equation), one bouncing back up while the other is still going down, which doesn't happen in practice and the elastic model struggles to cope......

In reply to Ciro:

As I have shown, the tension and therefore friction at the krab is approximately the same, but with the situation more symmetrical, less rope might run through the krab so less energy is dissipated as heat. Therefore more energy to be absorbed by the rope, so increasing the extension and therefore tension. Hopefully it is a second order affect not spoiling the rather satisfactory frictionless approximation too much!

In reply to JLS:
Does this argument not add weight (so to speak) to Freya's hypothesis? The fall factor is used to describe the effect on the rope and therefore a higher fall factor means more energy has been absorbed by the rope and less has to be absorbed by the climber.

I'm too tired to do the whole maths/physics thing right now but people doing bungee jumps fall from a very great height and seem to do okay.....with plenty of slack.

In reply to eve_b:

No, the higher the fall factor, the more energy there will be in the fall per meter of rope available to cushion the fall, so the greater the forces on the climber, belayer and runner.


Yes, all that slack generates a large amount of energy in the fall, but an extremely dynamic rope allows that energy to absorbed without creating the sort of forces that would detach your legs at the hip. Which is the same effect you're trying to re-create when you give a dynamic catch.

In reply to Robert Durran:

However, I *think* when you start to try to take account of friction the model changes completely. This seems really counter-intuitive but I can't yet see a flaw in the logic:

As you mentioned previously, in a frictionless system, the load on the anchor when lowering the climber is actually double the weight of the climber. However, in the real world, the belayer exerts much less force than the climber (otherwise a 40kg belayer could never belay a 70kg climber without a ground anchor), so friction must be actually reducing the overall load on the anchor. I've belayed someone 95kg to my 62kg without leaving the ground whilst lowering, so I have to assume the load on the belayers side will be less than 2/3 of the load it's opposing on the climber's side. So total load will be (say) 1.6 * force generated by the climber rather than 2 * the force. If the belayer loads the rope from the other side, this advantage is lost.

Am I missing something?

In reply to Ciro:


The capstan equation: http://en.wikipedia.org/wiki/Capstan_equation

In reply to eve_b:

No. It is nonsense.

I refer to the (correct) formula I presented a couple of days ago:

Climber mass m
Acceleration due to gravity g
Climber height h above belay and runout r above bolt
Length of slack in system s
Modulus of rope k (so that force F = kx/l where x is extension (stretch) of rope and l is length of rope unstretched)

Max force = mg+((m^2)(g^2)+2kmg(1-(h-2r)/(h+s)))^0.5

As I pointed out earlier, once 2r>h (ie the climber falls past the belay - obviously a very bad idea on single pitch climbs...), the formula shows that the max. tension actually does increase with more slack. In the special case bunjee jump situation (r=h=0) it can be seen that Max force is independent of the length of slack (the whole rope in this case) ie the jumper experiences th same force no matter how long the rope is!

Note that bunjee jump ropes appear to actually behave more closely according to the elastic model (with rebound) than climbing.

In reply to Ciro:


It certainly changes, but hopefully not catastrophically!


As I described, I suspect this more symmetrical situation might actually behave closer to the model. If this is what you are saying.

In reply to Ciro:

>"so I have to assume the load on the belayers side will be less than 2/3 of the load it's opposing on the climber's side"

You may be missing that some of the load is being transferred into to rock by the runners and doesn't extend all the way down the rope to the bit you are holding. If say there are five runners in then, any that cause the rope to change angle will shed load. The rope above each will be more heavily loaded than the rope below. So what may feel like 2/3 at the bottom will be a good bit closer to 100% after the fourth runner... though I dare say a fair bit will be lost at the bend around the top crab.

In reply to midgets of the world unite:

I'll have another go at the weekend if it rains...


Some light reading?:

http://www.sigmadewe.com/fileadmin/user_upload/pdf-Dateien/Physics_of_climb...

In reply to tom_in_edinburgh:

A few simple tests will show you that the capstan equation is worthless in a climbing context and gives completely incorrect results.

In reply to Robert Durran:

Indeed that's what I'm saying, and since approaching the model leads to higher overall gear ripping force, we're back to the conclusion that a belayer in free fall with his climber (of equal weight) increases the chances of the runner failing

In reply to jimtitt:

Care to expound?

In reply to Ciro:

The model shows that a belayer jumping down hole does not increase the force on the runner, so surely approaching the model actually suggests that this might be close to the case in reality.

In reply to Robert Durran:

Now that's basic mechanics!

Interesting, will have a more intent read some other time and maybe a play with the help of matlab. Do these SigmaDeWe folk have some credentials?

Jeez, there's a much simpler solution to this discussion guys:

Get on a rope and jump off above the last bolt, once with a good bit of slack and a second time but without any. See which feels softer - that's what it's all about after all, not theoretical calculations and musings, where, for the sake of your calcs, you make assumptions and ignore real-world experience.

End of story - it's not frickin' rocket science.

In reply to Fraser:

Absolute party pooper.

In reply to Fraser:

The elastic model (and there seems to be some concensus that it is adequate to make broadly correct predictions in this matter - actually somewhat to my own surprise!) predicts that adding extra slack will result in a harder fall. Yes, it would be a good idea to test the model in practice, but I think that relying on people's perceptions might be unreliable - the length of fall, the swing, etc. might cloud their judgement. A properly conducted test with objective measurement using an instrument like a big spring balance incorporated into the system is what is needed. I think jimtitt (who posted earlier today on the thread might well be the person to ask about this - maybe the results of such a test are available)


Correct. It's frickin' rope science.

In reply to Fraser:

When it comes to bolts that is indeed pretty much the end of the story (although it's still interesting to work out why), but when it comes to working out what sort of loading is going to rip your gear out of the wall the easiest, I'm not so sure I want to just "suck it and see"...

In reply to Ciro:


No, I think Fraser is still not accepting that extra slack gives a harder fall (higher max tension in rope). He understandably wants evidence in practice (as would I, because I admit to niggling doubts that the elastic model is good enough myself!) but that should be properly measured evidence, not just his subjective "perception" which could be affected by other factors.

If you mean that max tension is not of practical importance in sport climbing anyway, then yes, that is true in the sense that even a hard fall will not produce a max tension that is dangerous for the climber (or even uncomfortable) or risk breaking a rope, bolt, krab or quickdraw.

In reply to Robert Durran:

But if in the real world a coefficient of friction of say 0.69 for a standard (static belayer) fall through a single karabiner in a top runner(a figure I saw attributed to petzl somewhere last night, but the link was dead so I couldn't veryfy it) means that the total force at the anchor is 1.39 * F (the force generated by the climber) rather than the 2 * F predicted by the frictionless model, and if your frictionless model showing the forces to be the same whether the belayer jumps downwards or not is correct, it follows that if the belayer jumps downwards the total force on the anchor is going to be somewhere between 1.39F and 2F - the sooner the belayer reacts and jumps, the closer to the theoretical 2F limit it's going to get.

In reply to Robert Durran:

I have actually been wondering how you'd go about creating a strain guage quickdraw to go generate some data...

In reply to Ciro:

Yes, I see what you are getting at now and it makes sense. However I think (and will need to think some more......) that in the situation that the belayer doesn't jump into the hole, the tension in the climber's side of the rope is greater with friction than without (consider the extreme case of "infinite" friction which would effectively be a factor 2 fall directly onto the runner, with therefore a very big tension in the climber's side and none in the belayer's side!). So this effect will tend to cancel out the effect you describe. Whether it partially, wholly, or more than wholly cancels it out is not obvious.....

In reply to Robert Durran:

Yes, my brain is hurting trying to visualise all this... you wouldn't think I had a degree in engineering the way I'm floundering around here... I seem to have forgotten pretty much the lot in the intervening years. :-D.

In reply to Robert Durran:

No, that's not what he wants. What he wants is for you to forget your theoretical calculations and hypotheses and realise you're omitting real-world experience which tells everyone who's ever tried it, that more slack gives a softer fall. You should try getting some "evidence in practice" and you'll very quickly see your calculations proved wrong.

That's what he wants.

In reply to Fraser:


I would definitely like to see some properly, scientifically collected evidence in practice (ie not subjective perceptions, possibly affected by other factors and even prejudices). I am perfectly prepared to be proved wrong. All that would mean is that the elastic model is not close enough to reality to provide the correct prediction. That is how science works; come up with a model, use it to make a prediction, test the prediction with a proper experiment and, if the prediction is wrong, discard or refine the model and try again). The elastic model predicts that more slack give a harder fall. This may or may not be true in reality. I have slight doubts myself. Without a suitable strain gauge, I can't conduct the experiment. Maybe somebody else can or can show us the results of such an experiment. I might try some more googling.

In reply to Robert Durran:

Why not just try it for yourself in practice and see how you think it feels?



Now you really are stretching things beyond the believable!




No, try some more falling!

In reply to Fraser:

I might do so (it would be good for my climbuing anyway!) but I shall not take it as proof either way - I too might be subject to subconscious prejudices.

In reply to Robert Durran:

Good on you - I'll be at Ratho next week watching with interest. And a clip-board, calculator and white coat

In reply to Fraser:

He's trying to work out how hard the fall is on the top runner, not how hard it is on the climber... short of using himself as the sling in a very long extender, I'm not sure how he can find out how this feels...

With regard to the original question of belaying for falling practice, how hard the fall is on the top runner shouldn't be a concern, but it doesn't mean it's not worthwhile figuring it out to see if any of your pre-conceived notions of how to best to catch a trad fall onto poor gear are wrong.

In reply to Ciro:

No, I'm actually trying to work out the maximum tension in the rope and therefore on the climber. If there is no friction at the krab on the runner, this will be precisely half the force on the runner (elastic rope or not). The two things are closely related but not always the same.

In reply to Fraser:

Don't hold your breath. I might bottle it. It's scary up there......

In reply to Robert Durran:

Ah, in that case I would have to join Fraser in questioning it's usefulness as anything other than an academic exercise...

In reply to Ciro:

The capstan equation (which as far as I know was first introduced to the climbing world in Stephen Attaway´s paper on belay devices and friction ) unfortunately requires conditions which do not occur in our application. At the time the theory was formulated by Amonton the need was for a method of calculating the power transmission ability of the typical flat belts used then and it assumes an infinitely flexible material bending around an effectively infinite radius. In a climbing application however the rope has considerable bending resistance (properly called moment of inertia or area moment of inertia) and the radii involved are relatively small.
The resistance of a rope (or tape) running over a karabiner or other pieces of equipment such as a belay plate is made up from this bending resistance and the friction between the two surfaces. Generally the bending resistance is the dominant effect which led to Attaways paper being flawed.
Since the capstan theory has no way of taking this into account it gives completely incorrect results, as you can easily see by comparing Attaways theoretical values (or calculate your own) against test results.
I looked into this in some detail in a paper I wrote some years ago (somewhere down one of my jumbled webpages;- http://www.bolt-products.com/Glue-inBoltDesign.htm) though perhaps I wasn´t as clear as I could have been about how inapplicable capstan theory is, assuming that readers would realise that since the other factors which effect the resistance cannot be put into the formula it would is obvious it could not give correct results.

For your problem with slamming into the wall one could probably usefully look at spring pendulums though how to account for the initial free drop is yet to be resolved. This is something Richard Gold might work on in the summer in connection with something different we are playing with (he´s the maths professor not me).

The "jumping into the hole" scenario is academically interesting but in real life not particularly so, not hitting the ground being the overriding concern and potential failure of the gear of secondary interest. I´ll see if one can do a reasonable test but it will be unlikely to reflect reality, getting the timing right to cope with the delays in the maximum forces experienced due to frictional hysterises is going to be difficult let alone the reaction time of the jumper.

The standard rope model even with friction correction has its drawbacks in real-life scenarios since the belayer/device plays the dominant role in the forces generated and is not included in the model. With small FF´s the results are not far off reality as belay plate slip is relatively small but with larger falls the standard model gives results vastly different to those generally experienced in the field which is where the mathematicians opinion of what defines a model starts to move away from my idea of what one should expect from modelling.

Not falling is always the better choice!

In reply to jimtitt:

Thanks for the very thorough reply! Looks like some good stuff on your site, I'll give it a good read at a later date... for now it's time to get sorted for the weekend's climbing

With regard to the slamming the wall, I'm not so concerned as I know from practical experience what works and what doesn't - I do a lot of falling and catching practice. However I've just started out in trad after a lot of bolt clipping, so I'm interested in how gear changes how the belayer should behave. The jumping into a hole thing interested me, as I'd already been thinking about a hypothetical scenario where the leader is facing a big fall onto a single piece of gear, and if that gear holds they'll be fine but if it rips they're decking, so your only concern is to try to limit the force on the runner. If you've got time to jump back off the ledge and shorten their fall at the expense of losing dynamism in the catch is there a benefit to doing so, or would you be best to stand and prepare to make the catch as softly as possible. My instinct would be the latter - cushion the fall rather than minimising it.

In reply to Ciro:

Well I have tried the jumping in the hole thing, as often the case doing an apparently simple experiment throws up all sorts of issues. If both faller and belayer fall/jump at the same time the knot on the faller side goes into the runner karabiner and gives disastrously high impact force on the runner, around 6 or 7 times the force compared to a simple fall. The standard model seems to have missed this bit out!
In reality there will be a delay on the belayer side because of the belayers reflexes which we don´t know but this makes it very hard to test in practice because this delay allows the faller to travel a fair distance which in turn means you need a much higher drop-test facility than is generally available.
Someone would have to make a double load-release hook with a time delay mechanism as well!