UKH

So I've just been walking the dog (the actual dog rather than a yoyo trick) and I was pondering as you do, the important things in life. My focus dropped onto belays constructed from rope and I questioned whether the conventional wisdom actually is right or whether it's a bit of an urban myth. 

My thinking is that when you use rope, you generally go back and forth from your harness to the piece until you've built your anchor. Hach leg consists of two strands, and these two strands resist an elongation underload. 2 strands will elongate less than 1 as there there is double the resistive force. Looking at the stats for a 9mm rope it's somewhere around 7% elongation for a single strand under an 80 kg load, and I'm going to hazard a guess that having two strands will halve the stretch, there or there abouts. Ignoring knots this means that you are in the ball park of trhe stretch of a single strand of 9mm semi static caving rope, i.e. you've lost a substantial amount of the benefit of having the rope. 

Now consider a different situation at the same belay, you link pieces together with a sling and then tie into this sling with your climbing rope. The climbing rope is one strand and retains the higher level of stretch of a single strand because you've tied in with a fig 8/clove hitch/ BFK/whatever takes your fancy. 

Which is going to be more protective of the belay? Will the longer strands of rope and extra knots be more beneficial than I think they will be? Or is the efficacy of a rope belay at attenuating the impact on the belay vastly overstated? I really can't see how the rope is going to be THAT much more effective at absorbing impact when you compare it to the rope going 20-30m off to you buddy climbing.

Answers on the back of a fag packet/thumb in the breeze?

In reply to beardy mike:

Belays made using the rope only is for when the anchor points are far and apart. If the anchor points are far back but close to each other you can use a sling between them and extend with the rope. Then come all the other combinations including clipping in directly to a cam (and another anchor). 

In reply to Stefan Jacobsen:

I understand all of that. But during a certain training, it was very explicitly said that a rope belay puts less impact onto a belay. I'm merely questioning whether that accepted wisdom is actually wisdom or maybe some thinking which is flawed. 

In reply to beardy mike:

I think this is one of those "how long is a piece of rope" things.

Sorry, had to get that in there.

There are a lot of variables in setting up a trad belay and the reality is that it might depend a lot more on the equipment you have with you and where the anchors are located than your personal preference for sling vs rope in your belay.

On thing I would mention for situations where the belay is a long way back from the cliff edge at the top is that putting the belay device a distance back from the edge helps prevent it, and possibly you also, going pyoing over the edge of the cliff if the second falls and there is too much stretch between anchor and belay plate. Personally I like to set up in guide mode with the plate loaded directly on the belay and me personally having a couple of metres of slack so I can move around/peer over the edge/escape the system/etc easily enough, no matter what the 2nd is doing.

In reply to beardy mike:

The main reason we used lots of rope in trad belays, in the old days, is we usually had bags of spare rope, particularly when using double ropes. The typical nest of ropes made a tremendously resilient belay that was able to absorb lots of energy - through rope stretch and knot tightening, etc. Only as pitches tended to become longer (particularly elsewhere in the world) and use of single ropes became more common, did we start using more and more slings in belays. When done right, the old fashioned belays, using lots of rope, were very safe.

In reply to John Stainforth:

Well that is precisely what I'm questioning. Why does it make it safer? Logically the more legs you have, the less stretch you will get although the load will be spread more.  Maybe knots contribute lots but I'm dubious about that. If you have three points, share the load between two of them with a sling and then tie into the sling and the third point with rope with a single strand, then logically you will see more stretch and impact absorption than if you double the rope back to your harness...

In reply to beardy mike:

My observations are purely empirical, having tested most types of belay many times, the hard way! Bear in mind that the more ropes you have, each one is subjected to less stretch (maybe), but the overall absorption of energy is spread amongst all those ropes, so each has to do less.

In reply to beardy mike:

I wonder if DMM or someone has some numbers on this?!

I think if you belayed directly to two anchors using 1m of rope to each (so 4m of rope used in total) I would suggest that you would get more benefit from having the two pieces equalised with a sling and then attaching yourself with one rope strand which is 1m long as the one single strand will stretch more than the 4 combined. 

In reply to beardy mike:

If you’re bringing up a second, the most effective way to ‘protect the belay’ is your body position, friction over the edge and limiting the length of fall by not having loads of slack out. It’s quite feasible to put no load on the anchors at all when someone slumps on the rope.

If it’s multi-pitch, the choice of rope over slings & master point is really a question of whether people are alternate or block leads. Block leads are a pain using the rope ends. 
 

The danger time is FF2 falls on the belay leaving a multipitch stance. Avoid at all cost, get some gear in. FF1 falls above a stance are going to load the belay in the opposite direction to what most people build for anyway. More likely to lift gear out than load it.

In reply to John Stainforth:

Less stretch is plainly the physics of it, of that I am 100% certain. I guess my pondering is really about whether the advantage is overstated and is it a case of this is what someone thought of 50 years ago so therefore it's now accepted as a universal truth rather than having actual physics behind it? Comparing the numbers on a dynamic rope to a static rope, was interesting to me as the difference when doubled closes up. I mean if a static rope is doubled and sees an elongation stat of 3.6% and you halve that to 1.8, and a dynamic rope goes from 6.5 to 3.25, the change is actually greater for the dynamic rope. I guess my point is that I can see knots making a bigger difference than the rope, and IF that's the case, surely just having a single strand and some knots is going to be preferable, regardless of how many points you have?

In reply to beardy mike:

I've not read the above responses but the training context is probably meant something more along the lines of building a rope belay is more dynamic than a sling belay where the climber clips their harness directly into the sling. Obviously if the harness is connected to the sling via a rope then it's all a bit academic Vs just with a rope, both are perfectly dynamic.

In reply to Alex Riley:

Yep, I can see that. But then surely the fact that the leading climber is connected to the belay via a massive long shock absorber is going to attenuate the force of a fall onto the belay more than knots etc? I'm questioning it because during the aforementioned training, belays with ropes were sold as the single best way to build a belay unless you happen to be leading in blocks. But somehow to my engineering brain something doesn't quite ring true about it, especially when the point I just made is taken into consideration.

In reply to beardy mike:

It probably either wasn't explained very well or was dogmatic opinion rather than fact. There is unfortunately a fair amount of that knocking around on training courses.

In reality whatever suits the situation better is the best option. Knowing which is best and building it robustly and efficiently is the key.

In reply to beardy mike:

You're definitely right to question this.

Belays where you're out of the system can be far better (think, simple - complex problem solving scenarios) and use less rope, can be simpler/quicker to rig. Obvs having some rope in the system, ie the rope connected to a sling that is equalising the anchors will give a good amount of dynamism and if the thought for a particular anchor set up is 'I need more dynamism due to dodgy anchors', more anchors are almost certainly required. 

In reply to beardy mike:

I don't particularly believe that rope in the belay does very much to attenuate forces, not in comparison to many metres of stretchy rope between you and the climber.  It helps a little, perhaps.

But if the choice is between linking multiple natural anchors with a sling to form a powerpoint and then attaching to that powerpoint with a single strand of rope, and forming a belay with multiple strands of rope, then I see two significant advantages. 

Firstly, the chance of (roughly) equally loading the points is much better if connected to each one with extendible rope.  If you have a single strand of rope loading the sling powerpoint, then unless you've placed it pretty perfectly in 3D space, it will load one or perhaps two points only.  By comparison, the action of rope stretch in a rope-built system allows all the points to take at least some load.  Not important if all the points are good, but significant if they're individually not that great.

Secondly, if you have to take the weight of the second, distance you'll move under rope stretch will be much lower with multiple strands, and that might be the difference between being pulled off the stance or not.

In reply to beardy mike:

I think you are confusing elongation as experienced by the belayer with elongation as experienced by the rope. It is the latter which approximates to energy absorption, not the former.

In reply to Wicamoi:

The absorption of the energy by the belay is very important in fall factor 2 falls, which luckily are pretty uncommon nowadays.

In reply to beardy mike:

Yes, a rope belay is more stretchy, and thus putting more stress on the anchor points, than when using slings. But the current wisdom is, that the belay shall be able to hold any force, a fall might produce, and that can be achieved using slings provided the anchor points are solid. The days of protecting the belay are over. It has to be safe. Period. 

Then comes the exceptions where you have to use judgement. Understanding the difference in seriousness of a top belay on a snow slope with friction over the lip versus a steep multi pitch lead belay from a hanging stance and with a possible high fall factor and thus impact force on the belay. 

To put it into perspective, a rope has to be able to endure a fall factor 1,77 leading an impact force not higher than 12 kN. This means that your lead belay has to be able to hold that kind of forces.

On the other hand, a falling follower on that snow slope will not produce more than half a kN.

In reply to Stefan Jacobsen:

A rope belay is MORE stretchy, putting more stress on the belay? Surely more stretch = more force absorbed by the rope and less force at the anchors? I would expect another thing to help or rope belay is all the knots tightening up. There will be a lot of knots in there. I’d imagine clove hitches don’t absorb force like a fig8 on a bight (which you can tie straight in to your harness loop)?

In reply to Stefan Jacobsen:

A rope belay is MORE stretchy, putting more stress on the belay? Surely more stretch = more force absorbed by the rope and less force at the anchors? I would expect another thing to help or rope belay is all the knots tightening up. There will be a lot of knots in there. I’d imagine clove hitches don’t absorb force like a fig8 on a bight (which you can tie straight in to your harness loop)?

In reply to Jamie Wakeham:

I think Jamie wakeham's reply hits the nail on the head. To explain another way, While op is right about the amount of rope stretch you get overall, there's a difference in how that rope stretch is benefitting you. The good thing about having it connect the anchor points (rather than sling doing that) is that the stretch (even though there's if less of it overall) helps to equalise those points better. 

Thats my understanding. Also they do need to keep things simple in training courses to prevent information overload. 

In reply to beardy mike:

OK, I'll ask a slightly different question. Has anybody ever heard of or seen a belay falling apart because of the impact experienced during a fall? I certainly haven't. I've worked on and off in the outdoor industry since 2012, been climbing for 31 years, and I've never heard of anything like it. I'm moving on to hopefully teaching in a professional context and I want to make sure that I place emphasis in the correct place, and I'm thinking that what's important (in this sort of order) is:

Placing really solid pieces

Ensuring that 1 or more of your best pieces has a locking biner as a fail safe

Using some rope in between you and your anchors involving knots which can tighten

Producing a cone to help stabilise your position is helpful

Protecting your belay with a piece soon after the leader steps off the belay

Protecting your second by ensuring that you are tight to the anchor and aren't pulled off balance by a sudden loading

Using appropriate methods of building the belay which equalise it reasonably well in the knowledge that all your pieces are good and placing emphasis on positioning yourself in the best spot for line of sight and communication.

Seem fair?

In reply to Stefan Jacobsen:

I take it you don't winter climb then?

Quite a few winter delays are bomb proof.  Most are ok.  Many are very poor!

In reply to George_Surf:

Of course, my mistake

Yes, knots will absorb energy too. 

In reply to top cat:

Every winter. Did you read through the rest of my post? The judgement part?

In reply to top cat:

I have to admit I'm talking about in a rock climbing scenario. In winter all bets are off and the game changes dramatically.

In reply to beardy mike:

I think it all comes down to context.  And I don't just mean the context of the belay you're building (clearly we're going to choose differently if we have two shiny bolts or five crappy micro wires) but also the context of the teaching.

If I'm working outside with someone doing their first leads, they're probably quite overwhelmed with the whole situation and it'll be a case of talking them through the most straightforward belay system for that scenario.  I'll probably add a caveat that 'there are lots of other ways of doing this so don't get hung up on always doing exactly what I show you today'.

On the other hand, I often teach a fairly academic ropework class that I've developed with local mountaineering clubs.  It takes nine hours over three sessions, and we're indoors and warm.  So we can go over a wide range of if-this-then-think-about-that decisions, and really drill into the physics of why we might make a certain decision.

In reply to beardy mike:

Lockers are needed in points if catastrophic failure only. Our national climbing organisation has recently been assessed by the UIAA, and I deliberately used non-lockers in two piece anchors, and then asked the assessor explicitly if that would be acceptable. It is, and even the “new” girth hitched locker in the master point is accepted by the UIAA. So from now on, that is what we will teach as an acceptable anchor system. Your organisation may differ of course. 

In reply to Stefan Jacobsen:

Yes, I use the girth hitched masterpoint lots, IMO a great technique as it akes the masterpoint visually extremely clear.

In reply to beardy mike:

I dont have anything to add on the stretch / impact force issues but often it is easier to obtain a narrow angle between the individual points when using rope - simply because rope is typically longer than slings and often when looking for 3 trad points they may be more widely spaced.  This of course means the load on each point is less.  

My point being that the belay is protected by having narrower angles and that often this is more easily achieved using rope and hence this may be a part of / one of the reasons behind the ' traditional advice' 

Well - its a thought anyway........

In reply to beardy mike:

I don't think it makes much difference due to rope elasticity but knot tightening could be significant in giving some release of energy.

In reply to martin09:

I actually have no real bone to pick with the traditional method other than wondering whether the reality of impact absorption is different to the professed advantage. It's obvious to me that many times it will be absolutely appropriate when anchors are a way back. Much like people bang on about how double ropes reduce impact which is a load of cobblers in many situations - unless pieces share the load, there's virtually no difference. Anyway, I think I've got it a bit straighter in my head now...

In reply to beardy mike:

Earlier in the year I was leading Britomartis (HVS 4c) where there is a bit of a rubbish hanging belay after pitch one involving a rusty peg and some peenut placements of what I thought were dubious quality. There were 2 seconds to bring up and I wasn't 100% happy.

I used a 4m sling as I often do from 3 wires and a rusty peg with a short section of rope back to me from a masterpoint.

I decided that the dynamic rope might absorb some of the tension but could also create bounce a bit as I was working to bring in the second and third climbers. I opted to use the sling as I figured a static would distribute the load more evenly.

Turned out the 3 pieces placed were great, who knows how good the peg was. Nobody got dead but this thread was interesting to read as it brought the climb back to mind.

In reply to beardy mike:

I think there are various good reasons for rigging with the rope when it makes sense (so not for guided parties or people leading multipitch routes in blocks), and I usually rig with just the rope, the main exception being when the anchor is a long way from the belaying position I want. I almost never use double-strand arms--except very occasionally on purpose to distribute a load to a distant anchor point a bit better---so one answer is that if you are doubling the arm-strands in your rope anchor, you're doing it wrong, (You are also using up too much rope.) That said, in all but a very small number of unusual circumstances, my guess is that the "protective" benefits of dynamic rope vs. static materials are inconsequential, either because there is literally only a small difference in the peak load outcome, given that most of the fall energy is being absorbed elsewhere, or else because there are so many confounding factors that we can't discern how much the rope rigging itself contributes.

I'm not sure we're getting a good picture if we just talk about rope stretch.  Ultimately, the load applied to an anchor is given by the tension in the material connecting the load to the anchor, and that tension, within the elastic limits of the material, is proportional to the percentage stretch, with a constant of proportionality often called the rope modulus.  If we have two strands of rope supporting a load, a given amount of stretch will produce, say, a certain tension in each strand, and so double the single-strand tension in the combined strands.  That means the modulus of a two-strand arm is double the modulus of an individual strand and so, in some sense, the two strands are twice as "stiff."

So far so good, but when your leader comes rocketing straight down onto the belay, the double stiffness of the rigging strands (which shouldn't be an issue because the rigging shouldn't have been done that way) does not mean double the peak load to the anchor points, it is more like a 40% increase (which is less than 100% but of course could still be catastrophic). The reason for this is that the peak load to the anchor is determined by how much fall energy has to be absorbed, and the energy absorbed by stretching the rope is, via the miracle of basic integration, proportional to the square of the percentage stretch.  The result of this, when you slog through the details, is that the doubled modulus shows up under a square root sign and so, very roughly, only multiplies the peak by the square root of 2 (about 1.414) rather than by 2.  So the hypothetical question becomes whether increasing the peak dynamic rope-anchor load by 40% is better or worse than rigging with static material.  I don't know the answer, or whether the answer is significant, but my suspicion is that the static material is still worse. In any case, it is worse if the rope anchor is built properly with each arm being only one strand.

I mention all this because climbing ropes are engineered to have good elastic properties for a range of loads expected from climbing falls.  I think the engineering considerations for static ropes are different, making the energy-absorbing properties different, and so making comparisons of the imparted peak load, based only on comparing rope stretch, might turn out to be misleading.

Since most of the leader's fall energy is going to be absorbed by stretch in the climbing rope, knot-tightening, and body-deformation, the contribution of the rigging isn't likely to matter much except, perhaps, in case the belayer gets flung off the stance by the fall impact.  In that case, the climbing rope has no role in absorbing the belayer's fall energy and the job falls entirely to the rigging and the belayer's attachment to the rigging. The worst-case scenario would be some kind of Dyneema rigging and the belayer attached with a Dyneema tether.  In this case, I think catastrophic loads are possible, enough to actually break metal climbing gear.

Horses for courses

In reply to rgold:

---so one answer is that if you are doubling the arm-strands in your rope anchor, you're doing it wrong, (You are also using up too much rope.)

In that case, and if I've understood your point correctly, all the UK mountain training and other courses are teaching it wrong, since the default recommendation for out-of-reach anchors is to clip the ropes into the anchor points and bring them back to clove hitches at the harness, making double arm-strands.

Re using too much rope: not usually, and on the occasions when it is, it tends to be immediately apparent that a different method is called for

In reply to beardy mike:

A lot has to go wrong to cause a total anchor failure, so examples are going to be extremely few and far between. This can't be taken as evidence that most anchors are adequate.  I've been climbing for 66 going on 67 years and have read of four or five total belay anchor failures caused, as far as we know, by leader falls. All of these are in the US, so I have no idea what European statistics might add.

This is hardly a statistic, but over the years I've seen---and occasionally had to use---anchors I doubt would withstand a factor 2 fall.  It wouldn't surprise me at all if someone found that 10% of all anchors are inadequate for the maximum possible loads.

In reply to rgold:

Thanks. In interesting response. Going to digest that one for a while...

In reply to bpmclimb:

Well, yes, sorry, I'd say they're teaching it wrong.  Force of tradition perhaps? Short pitches and long ropes in the UK?

Maybe I'm being a bit harsh.  The advantage of bringing everything back to the belayer is that all the adjustments can be managed from the stance.  If you have the basics of clovehitchology down, it is no problem to rig the clove hitches in their proper position on remote anchor points, but maybe this is expecting too much of beginners?  I don't know.

I agree that if the anchors are quite far from the stance, then building a rope-only anchor isn't the best idea. I don't know what metrics are in place for "not usually," but speaking just logically rather than situationally, why does it make sense the double the amount of rope consumed (two belays could be involved) when there at best one minor advantage to doing that and, returning to beardy mike's original point, there may actually be disadvantages?

In reply to beardy mike:

Almost certainly makes little difference. The rope between the belayer and the climber is the bit doing the stretching.

We can both imagine a factor 2 fall on a multi pitch climb with a short amount of rope out, and in that instance there may be a marginal benefit to using rope in the stance over a static sling. But in the majority of cases, where a couple of pieces have been placed, lowering the fall factor, and most importantly adding lots of friction as the rope is redirected around the biker, it’s the live rope that does the stretching.

think of it this way, when sport climbing, with people who are lobbing off, the belayer may be lifted a couple of feet, and if a third person wanted to they could hold onto them so the belayer stays on ground. The forces transferred to the belayer are in the order of a human’s weight (700ish N). In a multi pitch setting are they really going to be reduced by a significant amount when transferred to the anchor by a couple of m of rope, like you said, often in parallel?

You can snap a sling by doing a ff2 on it with a steel mass, but a steel mass and a human being in a harness are very different things…

In reply to bpmclimb:

Well, I'm getting lots of downvotes---ya can't win 'em all.  In case it isn't clear what I'm speaking about, here's picture of what I think of (and teach) as the standard way to rig anchor with a rope.  The extra loop used as a redirection point is a strictly optional addition.  It is a somewhat useful option that isn't available if one brings all the strands back to the belayer as described by beardy mike.  https://mountainproject.com/assets/forum/346013.jpg

Note that the method I described incorporates a power point that can be used for upper belays with a plaquette.  A possible problem with bringing all arms back to the belayer occurs, as is often recommended, if the carabiner holding all the clove hitches is clipped to the belayer's tie-in loop.  If this is the case, the belayer will not be able to escape the belay without a fair amount of totally avoidable faffing.  So even if you are going to bring everything back to the belayer, it is sensible to tie a power point loop and clip all the strands to that rather than to the tie-in loop.

Another perhaps minor advantage of the method I described is that you don't load up a carabiner with clove hitches or have to supply multiple carabiners to accomodate the clove hitches.  An ordinary three-point anchor rigged with everything brought back to the belayer requires three clove hitches at the belayer's attachment point.  You might need a dedicated big carabiner for this and in any case would end up with some part of the load applied a long way from the spine, which is known to weaken the carabiner.

If anyone thinks all this is just some idiosyncratic nonsense from across the pond, you'll also find the same rigging set-up here https://people.bath.ac.uk/dac33/high/6TheBelay.htm#dil on the exceptionally useful site by David Coley.

In reply to beardy mike:

great topic & good replies folks!

the scenario i envisioned: bommer 3 point anchor to masterpoint on a dyneema sling.

a) 8' rope to belayer's harness, b) 8' sling to belayer's harness (hung belay)

leader of next pitch pings off whilst placing gear at anchor height ie 16' fall.

a = factor one fall, b = factor two fall.

does this help outline 'more rope in system = less shock on anchor?'

------

saw a brilliant article with scenario: pitch 2 had a nails start, to reduce risk of a factor 2 fall on p2, p1 leader climbs beyond end of p1 (aka p2 belay stance) and places next 1st piece of gear ready for p2 whilst max rope is in the system. thought that was quite inspired (pre-rigged jezus piece)

:-j

In reply to sbc23:

I couldn't agree more. I think the growing trend among some climbers to belay directly on the anchors as the default option is downright dangerous and I am not happy climbing with people who do this. A direct belay should be the exception for when belaying off bolted anchors or other utterly bomb-proof ones. Yes, direct belaying makes escaping from the system easier, but, if this is a concern, then building a central point rather than using the ropes should be the preferred default.

In reply to Robert Durran:

Personally, I use a plaquette belay only rarely, so I'm very sympathetic to this perspective, which I think comes partially from considerable experience with braced stances that is typical of an older generation of climbers.   I think it is fair to say that most contemporary climbers know very little, if anything, about such niceties.

On the other hand, holding an upper-belayed fall puts a relatively small load on the anchor.  If plaquette belays are dangerous because of anchor loads, it would have to be because most anchors are too weak to, say, rappel off.  I don't think that's a realistic appraisal of contemporary anchor-building skills and gear capabilities, and considering how ubiquitous plaquette belays have become, we'd expect bodies to be raining down the cliffs.

Perhaps I'm missing the point and it is some of the other features of plaquette belays that make them "dangerous" in Robert's eyes.  There are configurations in which the anchors are too low or the belay has to be extended from the anchors in which a plaquette is increasingly suboptimal.  The encouragement and even the promotion of belayer inattention (under the banner of multitasking) adds both the immediate prospect of danger (accumulation of slack while the belayer is otherwise occupied) and may have longer-term consequences in terms of belayer complacency. And finally, there is a constellation of problems stemming from the difficulties and dangers of paying out slack.  I'm thinking not only of lowering catastrophes, which we read about periodically, but also the fact that the belay rope is continually tensioned and so stepping down or back may be impossible in situations in which the second desperately needs to do this. 

Finally, the number of guides with elbow tendonitis from the day-to-day effort of hauling ropes through a plaquette is quite considerable.  If you use the device a lot, there's a decent chance of overuse syndromes.

Whatever the drawbacks, I think that direct anchor belays are the wave of the future and that when it comes to plaquette belays for the second, that ship, to some extent fueled by the bolting of belays on formerly trad climbs, has already sailed in the US and Europe.

In reply to rgold:

I don't think it's idiosyncratic nonsense, I can understand the advantages you're describing it having. But it is a lot more complicated than any of the options that might be considered "standard" in the UK, which is its own disadvantage, especially for beginners. Escaping the system is so rarely needed that building every anchor around the possibility could reasonably be considered overkill*. And given that you first brought this up in response to people talking about pieces that were out of reach, I don't see how it's at all feasible to create this anchor without lots of back and forth to get all the lengths correct as you can't adjust them from the edge.

There are advantages and disadvantages to every system. I don't think anyone would disagree that your "standard" is a valid option, albeit not appropriate in every circumstance. But as someone with a wide range of experience and a recognition of a variety of options, it seems odd for you to have described using double stands to bring the clove hitches back to the belayer as "wrong" rather than just not the system you use.

*And as you've hinted, it's trivial to modify the common UK practice of doubled strands running back to the belayer by adding an isolation loop next to the belayer, so escaping the system would be a reason to tweak the standard rather than throw it out altogether.

Surely in the realm of technically correct but not really relevant with decent modern gear.

In reply to beardy mike:

One thought is that in the belay you don't want stretch. You want stretch in the bit between the belayer and the climber (if they fall off).

Case in point: when starting out I fell and nearly decked as my belayer had not accounted for rope stretch in the belay anchor and got pulled off the stance.

I did have a climbing partner once who took groups out as part of his job and would always belay using a sling on single pitche climbs as it meant that in the event of one of the group getting into trouble he could escape the system to help (tying the climber off of course)

On multipitch climbs (using two ropes) it is often quicker/easier to use the rope than slings and obviously it depends on the availiblity of anchors at the top of the cliff.

In reply to beardy mike: OK, lots of complication but basically your question is about having one rope connection point between the climber belay pieces, or many.  Given that rate vs. degree of stretch isn't linear as force is applied, I think the single rope might stretch more in a satisfying way, but the distribution of force across many, meaning the individual ropes stay 'further up the stretch curve' means actual transmitted force is lower.

Any dynamic piece is far more preferable than a sling, or a misused daisy chain,  

In reply to beardy mike:

I think, Mike, that this has gone over the heads over a number of commentors...

I suppose there are a few scenarios in which the belay will be loaded. One is someone attached directly to the belay falls off, including from slightly above the belay. Here, clearly, the worst scenario is that they take a factor 2 onto a sling or chain belay that they are attached to by a sling, meaning their body absorbs most of the force.

Better in this scenario is that they are attached by rope to a sling/chain belay or else that the whole belay is built from rope, because either gives a modicum of force absorption. It might still be unpleasant to very unpleasant! But, I doubt anyone can say for sure whether being at the master point of a rope belay or being attached to a sling masterpoint by a short length of rope is better, because of the amount of variables in a realistic situation - including types of anchor, complexity of the system, slack, knots, absorption by bodies, etc.

As for a leader fall, there are even more variables, as you already know. E.g. if the belayer is belaying off their harness, a fair amount of the force will be absorbed via the belayer getting pulled - either up into or down onto the belay (depending on the situation). I wonder, consequently, whether the material the anchor is built of is the decisive factor.

I think you are right to question the orthodoxy, but I think the teaching point contains within it some wisdom, buried under pseudo-rationalisation, including the importance of keeping belays simple and of avoiding falling off whilst clipped by a sling to whatever set up.

In reply to Luke90:

Is it? It's surely the "standard" option - with the addition of an extra knot and a difference of everything being clipped to this new loop and not the convenient permanent one on your harness?

In reply to Robert Durran:

Yes, the body is a tremendous shock absorber when one’s belaying standing on a good ledge. I’ve held at least four leader falls directly onto a waist belay, with no intervening runners. The impact was enormous (body bruising) but it worked. The first two were not even with a belay device, but with the rope round the waist and a twist round the wrist on the ‘dead’ hand, using leather gardening gloves.

In reply to tehmarks:

Depends which link you're looking at, and which variation if you look at his second one. And also how you interpret his contention that if your rope strands to your out of reach pieces are doubled up then you're doing it wrong.

In reply to beardy mike:

Horses for courses.

If the situation means the leader will lead 2 or more pitches in a row, a rope belay is a pain.

Isn't the stiffness of the belay a good thing anyway, so you (or the belay device if direct) don't get moved much when the second weights the rope. The rope to the climber and the slip in the belay device should be the dynamic element.

If it's so marginal you really need the dynamic element of the belay rigging itself, you probably are in different territory needing different discussion anyway.

As others have said rope belay is great for anchors far apart or far from the belay stance. If it's all simple and you have a spare sling... then why not.

I reckon we're overthinking this

Edit, with regards to comments about belaying directly from anchors there are some situations where that is safest. This excellent video changed my mind on a couple of points

https://youtu.be/eqZQnCGl24A?si=fmgUlLAEIoRiMu-x

In reply to rgold:

Trying to get a nice position with the second in view while belaying but where the anchors are out of reach (let's say 10ft away) for example. This would mean having to 'guess' the amount of rope needed (including some stretch) and then guessing exactly the same again fo the second and possibly third strands. If this is something that only beginners struggle with, I'm definitely a beginner. If you get it wrong, then you're not load balancing on your belays pieces well. 

If you're got enough rope then it's not a problem, if you don't then you won't use this technique. 

The big advantage, in my mind, is that using the rope gives you more flexibility in direction of load on the pieces in the anchor. If my belay is 'static' then you have a very small angle of useful load sharing.

With a rope based anchor, you have a much larger angle where load balancing is still happening (it might not be perfect but lets say you were 5% out on one leg, static belay legs would have the force as 0% and 100%, dynamic ropes in the belay would probably give you 70:30% or possibly better? (dependingon stretch). 

If you rig with the rope as single strands (called 'in reach' in the UK) then you may gain in stretch but you lose in getting a good balance across your pieces because of guessing lengths. 
 

Happy to be proven wrong but I'm not sure what you're suggesting for an out of reach anchor.

In reply to beardy mike:

So much of this discussion is almost irrelevant unless you are:

• either belaying in the middle of a multi-pitch route with less than bombproof belays
• or belaying at the top of a cliff where the belays are less than bombproof AND the top slopes in such a way that merely tripping over could have a serious outcome (i.e. a cliff top you might be unhappy to wander about on un-roped)

If you're belaying in the middle of a multi-pitch with bombproof belays then as long as you've taken steps to avoid a FF2 and you've protected against upward pull as well, dynamic differences due to belay configuration will be so marginal as to be irrelevant because there's enough "spare load capacity" however you rig it.

Even more so if you're belaying at the top of a cliff with bombproof belays, because seconding should never produce forces anywhere near those possible from leader falls.

If you're belaying on a "flat" clifftop then different setups might have advantages like being able to easily observe and communicate with your second, but just walking 10m back and bracing against any suitable slope or boulder will be secure enough even without any attachment to the rock to avoid being pulled off the top. I'm not suggesting we all do this at the top of Stanage but any rigging differences will surely not make a relevant difference.

In the situations I mention where the rigging may make a difference, I suspect it will rarely be the most important action to make things as safe as possible; e.g. avoiding possible FF2 by 1st pitch climbing past belay to put 1st piece of gear in on 2nd pitch and then coming down to belay point will make a bigger difference to the potential forces than how the belay is rigged.

In reply to timparkin:

Thanks for responding Tim.  It is weird to get a bunch of downvotes but no one contests the points I made or suggests alternatives. (Edit: that is starting to change...)  Of course, I'm paying a price for my pejorative use of "doing it wrong."  A better choice of words might have been "suboptimal," but that's water under the dam at this point; I'm stuck with the consequences of my immoderate usage.

As for your comment,  there is no guesswork whatsoever in the single-strand method if you know how to install clove hitches on remote anchor points. I teach folks how to do this all the time.   Meanwhile, if you double everything up on a three-piece anchor ten feet back, you consume 60 feet of rope, which is absurd in a multipitch context. (Nonetheless, you can find videos in which a guide or instructor (or maybe a self-appointed expert) does exactly this!)  With the single-strand method, you still use up a bit more than 30 feet of rope, which is still too much in most cases.

The point is that the single-strand method, in addition to providing possibly better energy absorption (the original point of the thread) and keeping a host of clove hitches off the carabiner and providing a power point for a plaquette if you like such things and a possible redirect off of two anchor points, consumes half the rope in all situations, not just the remote ones.  What if your three anchor points are five feet away; that's not what I'd call "remote."  Then the double-strand method is going to consume 30 feet of rope whereas the single-strand method only a bit more than 15 feet.  If you have to do this at both belays, which isn't an extreme hypothesis, the double-strand method requires that you have 60 feet of rope to spare.  So the single-strand method is going to make a lot more rope belays practical, as well as being better in all the other ways, in a substantial number of quite plausible multipitch scenarios.

Yup.

Yup.

Once again, this is wrong.  There is no guessing of lengths and everything can be adjusted to keep loads aligned.

The only way I could clarify any more would be to make a video, which maybe I should do, although right now isn't a good moment for me.  The reality of anchoring is that the anchor points tend to be at least a bit out of reach most of the time, so any good method absolutely has to deal with what you are calling an out-of-reach anchor. 

Now if the anchor points are really remote (let's say more than ten feet away from the belayer's stance) then the all-rope anchor is no longer practical.  You rig the anchor with slings or a cordelette in a way that provides a power point and the belayer clips the power point and walks/lowers to their stance and ties off.

In reply to rgold:

You install the clove at the anchor point, grab the middle of the clove and wander back to where you want your stance, then tighten the clove by pulling on the strand not connected to your harness?

In reply to Stefan Jacobsen:

No, you clip the rope to the anchor carabiner, walk back to the belay location, adjust to the desired tension, and then, holding that setting, walk your hands back up the rope and convert the already-clipped bight to a clove hitch. I think knowing how to do that is common knowledge but maybe not?

That's the first clove (referring to the diagram I posted).  The second one you do while standing at the anchor.  The third one is back at the belayer position and is cloved to the power point and adjusted there.  The fourth clove is done the same way the first one was.  This is assuming three anchor points and a single rope.

I already know there will be responses about how much faffing this is.  It isn't, it takes longer to describe than to do.  I've actually timed it against the standard cordelette installation and the times are the same.

In reply to rgold:

Sounds simple enough. No vid needed. Thanks!

In reply to rgold:

It's slower than big loops hitched back and if it isn't perfect or you decide to change your stance position it's more of a faff to adjust. 

When I use out of reach anchors I'm usually only going to them once, then to the edge to tie the clovehitches. 

In reply to beardy mike:

In response to your original question, the main advocate for rope belays I've come across is the hugely experienced Pete Hill. You can find the rationale (which is more or less what you've laid out) in some of his instructional books. I suspect he will have done some testing of the various options to arrive at his conclusions, but I don't know of any specific experiments or data. Personally, I don't use this technique unless I've run out of carabiners.

In reply to sbc23:

If you’re bringing up a second, the most effective way to ‘protect the belay’ is your body position, friction over the edge and limiting the length of fall by not having loads of slack out. It’s quite feasible to put no load on the anchors at all when someone slumps on the rope.

- Only if your partner is lighter or you're able to wedge or brace against something, no? Sat on the flat edge (assuming it doesn't slant down as it goes back from the lip, have a nice groove to wedge in etc), so I can see my second, I'm not sure that's going to work (NB most partners are heavier or at least not lighter than me, mind).

​​​

In reply to rgold:

Arr yes your second is tied off like you say, no problem. You get to the next pitch and attach yourself to the rock, shout climb when ready. Your belaying and the rope is tight. Your second set off but falls getting to the out of reach clove hitch and gets hurt. They were never 'top roped' when they were climbing to the anchor and now they are between you and the still attached anchor lessoning your options. This is why we teach if the anchor is out of reach attach the rope to the harness. When it is time to climb they undo the clove hitch from their harness and you take in so the rope is snug before they actually set off. There are other advantages too but out of scope for this thread.

In reply to Mr Messy:

An excellent point if you have a second who might fall off getting back to the anchors, and you also have enough rope to build that extended anchor and still allow the leader to reach the next stance.

When we use all-rope anchors on multipitch climbs, the second would be the person who led the previous pitch and built the anchor.  I don't see them falling off trying to undo their own handiwork and so this is a concern I don't have for my climbing.

Except: if I'm climbing with an inexperienced second and so am leading all the pitches, I use a cordelette or slings at the anchor, partially to avoid rebuilding a rope anchor for the second and partially to keep things as simple as possible, for various reasons, one of which you've identified.

In reply to rgold:

Thanks for responding! And I agree - and I like your single rope adjustment method (perfectly well explained. 

In reply to CantClimbTom:

Absolutely.

I've been building belays for quite some time and don't have any preferred way of doing it, it entirely depends on the circumstances.  If I think about it I generally use a combination of rope-based and slings.  If I'm at the top or on a big ledge I'll run one rope up to a belay well back from the edge and back, and then have one or more pieces close to me clipped in with slings.  Or the other rope. Or whatever works as long as it's tight.

In reply to beardy mike:

Totally but when teaching something technical and critical you need to know your audience. IIRC you're a professional engineer with the mental tools to analyse the problem almost instinctively, it's understandable the perhaps over-simplified, sub-optimal solution and explanation irritates you slightly but the key point still came across simply, rope good, even if the why wasn't as clear. Not everyone has the maths background to get the why or work out the value of the alternatives, simple, safe, hard to get wrong makes sense when teaching a mixed audience. By all means expand if you can clearly when someone is interested and getting it but only then.

I almost always used the rope, whether swinging leads or doing blocks, it works fine. Never paid much heed to exactly how I used it, whatever worked for the kit I had to hand but like you, I'm pretty comfortable thinking it through in real time.

Jk

In reply to Dave Garnett:

Your description sums up perfectly how I think most climbers operate, inc. self.

In reply to beardy mike:

Most of the rest of the thread has gone off into arguments of minutiae but this needs challenging. Double ropes should reduce the impact on the top piece, but reducing the drag. This is a lot more critical than the load distribution which is often minimal.

In reply to jkarran:

Guilty as charged, engineer and at times gear designer so even worse. I guess my main issue is I want to make sure I emphasise the most important parts of building an anchor which is bombproof pieces. How it's all connected together as far as I can work out is largely irrelevant as long as you've connected yourself to it using dynamic rope.

In reply to galpinos:

Can I clarify, do you agree that double ropes don't reduce impact? There's typo which is confusing me...

In reply to beardy mike:

Sorry, quick typing in a truncated lunch break.

Double ropes do generally reduce impact compared to a single, because, used properly, they would generally reduce the drag compared to a single.

In reply to beardy mike:

I don't even think the dynamic rope bit matters really, it must hold you in a position that allows you to hold a fall, even if part of it fails, which it shouldn't but plan for if it does.

Basically, can one reasonably credible failure (placement, piece, unclipping) drop or swing you any distance? If not and the loads are shared out reasonably and not multiplied unreasonably then it's good enough IMO.

Stretchy stuff in the belay protects the person assembling the belay from slips and trips, after that the live rope, plate slippage and the floppy meat at the end of it is good enough. Rope in the belay is nice and really helps with good equalisation and getting comfortably positioned but whatever gets the job done.

jk

In reply to galpinos:

I mean OK, but that is going to be marginal at best. I see plenty of climbers (myself included) not placing pieces perfectly parallel to another, which means you are effectively climbing on a single rope. I'd say the rope you use will have more of an affect of the impact you see than the drag. And bearing in mind that many climbers use 9.2mm ropes as singles these days, versus an 8.5mm double, is the drag difference really going to be very significant? I doubt it...

In reply to beardy mike:

I think the drag difference will be from beautiful looking straight runs of double rope v not extended enough ugly zig-zaggy single rope rather than what diameter rope is being used.

I always used to say that properly extended double rope runs that kept apart and where they both smoothed out the line of the route were a thing of beauty.

In reply to Michael Hood:

It's only an ugly zigzag if you make it an ugly zigzag. Us brits have a monofocus on single ropes, and don't get me wrong, there are times when 100% they are the right thing to use, but much of the time you just don't need them. Besides I believe Galapinos point was more that the friction at the top anchor will cause the impact at the top anchor to vary due to the difference in diameter of rope used, hence DMM producing the Revolver...

In reply to beardy mike:

No doubt Galpinos will clarify themselves, but I think you've got the wrong end of the stick. I think they're talking about the fact that in a leader fall the peak impact force (on either the leader or top piece of gear) is influenced by the 'drag' of the rope up to that point.

This is independent of single vs double, but Galpinos point is that there is likely to be less drag when using doubles than a single (though obviously this is not always the case).

Attempt at an example:

Given the same falling mass, falling from the same distance above the top piece, same amount of rope between belayer and leader.

If the rope zig zags between pieces on the way up to the top piece (the 'draggy' scenario) the peak impact force will be higher than if the rope does not zig zag, but goes in a straight line.

Edit to add. Some information from Petzl: https://www.petzl.com/US/EN/Sport/Fall-factor-and-impact-force---theory?Act... the section titled Actual Fall Factor 

In reply to beardy mike:

Petzl reckon about 25% increase in impact force on top piece from ideal scenario to bad drag  (slight increase in load on climber and obviously a decrease at the belayer). Rope becomes less important the higher the drag, as the drag decreases the effective length of rope the force can be absorbed over.

Off topic but diameter is not a good indicator of the energy absorption of a rope due to:

• the standard allows the ticket diameter to be +/-2mm on the rounded (to one decimal place) measured diameter. Your 9.2mm single could be 8.95mm and and you 8.5mm half could be 8.74mm.
• more importantly, rope construction is the key. A magic springy Beal is going to give you a softer catch than a strong Edelrid aramid woven wire!

In reply to Fellover:

Galpinos doesn't need to claify himself becasue you've done a very good job for me:

This.

In reply to galpinos:

OK, the off topic bit was what I was alluding to in my post in the first place. Given that in probably 50% of scenarios people are clipping the rope alternately rather than in parallel, you're effectively falling on a single strand, making your double rope fall actually a single rope fall. The impact is higher because of this and basically at similar levels to a thin single rope configured in a single rope type usage. As youve pointed out fatter singles generally have a better impact absorption characteristic so its not all that clear. I know some of the time you're placing well staggered gear, but much of the time you're not, and that was what I was getting at rather than a drag related scenario. And as I said previously to Michael, much of the time you can avoid the dreaded zigzag by extending well. I know that's not all the time and doubles have their place for sure, but seeing people climbing VDiffs with 60m doubles begs me to question why. Again, are they putting in such poor gear that they genuinely need double ropes and the benefits they afford? And of that's they case, why is their gear so bad... 

In reply to beardy mike:

The main benefit of using your rope is reaching the anchors conveniently without carrying a load of other crap!

In reply to gravy:

A couple of 120/240 slings don't constitute a load of other crap, especially if it's dyneema.

In reply to slawrence1001:

That 40g a sling makes all the difference to topping out on your VS.

In reply to beardy mike:

Bit late to this debate, but my two pence worth is that when using ropes to belay anchors well back from the edge, the biggest challenge is trying to pull all the stretch out of the rope to prevent me being pulled over the edge on rope stretch !

In reply to GrahamD:

My experience too. Especially when BITD having to tie the rope to a distant fencepost, and untie and reattach nearer the edge for communication and reducing friction while taking in.

In reply to Queen of the Traverse:

As I said, it totally depends on how you are sat. If you’re back from the edge a bit and sat on the ground then the force is already about 50% of the second’s weight due to friction at the edge. Then you’ve got the static friction of you being sat on the ground. This varies a lot with the surface, but could be 100% of your own weight. 

This does work. If you watch that film of Dave Mac doing the Long Hope route, he abseils off a rope wrapped around a small pile of rocks and friction over the edge.

If you’re in a hanging stance or leaning over a gritstone edge, then it’s obviously not going to work. But in that situation you don’t want to be worrying about ‘protecting the belay’ anyway - it needs to be bombproof. A bit of dynamic load absorption or equalisation is great but do you want to be relying on it? I wouldn’t. If there’s any doubt and no other options then I’m sitting down and avoiding loading the belay at all.  

In reply to Stefan Jacobsen:

Ropes stretching absorb energy and reduce the force applied to the individual anchors.

If a seconding climber of 80kg mass on a tight rope falls 2m (i.e. the rope stretches 2m under the load of the falling climber) the system of the rope and the anchors is required to absorb the following amount of energy:

80kg*9.81m/s^2*2m=Mass*Gravitational Acceleration*Distance Fallen=1567J

Work done (i.e. energy dissipation due to rope stretch)=Force (Applied to rope)*Distance (the length by which the rope stretches)

This can be rearranged to give:

Work Done/ Distance=Force=1567J/2m=783.5N

At the end of the fall the system is in equilibrium with no part of the system accelerating relative to any other part (i.e. the anchor is still in place and the climber is no longer falling/ swinging). Following Newton's Second Law, the sum of the forces on the rope must equal 0N. As such the load applied to the master point of the anchor is 783.5N

If you halve the distance over which the energy of the fall occurs you double the force applied to the master point of the anchor.

A forum like UKC is a horrible format for trying to explain the mathematics in a clear fashion so if anything is unclear please feel free to pop me a message and I'll write it up in word's equation editor.

In reply to sbc23:

Ok thanks. I think we're basically talking about the same thing then.

In reply to beardy mike:

The strands of rope will act as springs in parallel, as such the "spring constants" for the two strands (presumably the same for both) would be summed together:

https://en.wikipedia.org/wiki/Series_and_parallel_springs#:~:text=Conversel....

So your assumption about having 2 strands halving the amount by which the rope stretches is correct, however half of the energy goes into one strand, and half into the other so while the length of rope stretch is halved, the force applied to individual strand while absorbing the energy of the fall is also halved so the amount of force transferred to the master point of the anchor is the same as what is applied if you only have a single strand of rope. If you are connected directly to a sling used to build an anchor it won't be able to stretch very much and will instead transfer much higher loads to the anchor. In terms of holding a seconding fall with 30m of rope out the energy absorption of the anchor is going to be largely irrelevant, if they fall 1m from the top the energy absorption of the rope would significantly reduce the load on the anchors.

When belaying from above, tightening of knots, friction of your bum on the top of the crag and rope drag all add extra complexity to this, albeit they all absorb energy and reduce the load applied to the master point of the anchor.

In reply to spenser:

Grand. You're right, I forgot to halve the energy! It'd still be some interesting maths to work out what the difference is in the three different scenarios, one with all rope, one with some rope and one with no rope at all...

In reply to beardy mike:

I will leave that to someone else!

In reply to spenser:

Not sure that's quite right. If rope stretch is halved, deceleration distance is halved and hence force goes up. If you extrapolate to an infinite amount of ropes, there would be no stretch and very high forces. 

In reply to timparkin:

I've really been trying to stop myself from posting on this thread because discussing rope maths on forum threads is always carnage, but I agree with you here. Slightly disconcerting to be going up against the head of the BMC Technical Committee and UKC's premier cam designer, but here goes

I think we all agree that we're talking about a fall scenario.

I also think that from a maths/physics pov, we're all currently thinking about a rope as being a Hooke's law following spring (which they are not, but it's by far and away the easiest thing to do).

Spenser is totally correct that the two ropes/springs in parallel effectively add their spring constants. This means that with two ropes in parallel to the anchor, rather than one rope to the anchor, we effectively have a twice as stiff spring between the falling mass and the anchor point.

A stiffer spring will mean that there is a larger peak force on the anchor than a less stiff spring. We know this without any maths, because we know that if we attach the falling mass to the anchor with a steel cable (effectively a very high stiffness spring) then the peak force will be very high.

I'm sure I've made an error that someone will point out

In reply to Fellover:

I'm in full agreement.  If I were in the position of wanting to protect my belay anchors as much as possible then I'd choose the 'single strand to each piece' system to allow for maximum rope stretch and minimum force.

But if I am somehow in a position where I feel the need to protect my belay anchors that badly, then today has already gone very very wrong.

(incidentally, if protecting the belay was that important I think I'd still choose to rig with a single strand to each piece, as opposed to equalising them with a sling and then using one strand to that powerpoint.  I'd get more rope stretch with the latter system but I think the improved equalisation that comes from stretchy rope going to each individual piece is probably a more significant factor)

In reply to timparkin:

You halve the distance each strand stretches, however each strand absorbs half of the energy of the fall (as opposed to a single strand configuration which absorbs all of the energy).

When someone falls off seconding they have gravitational potential energy (GPE) equal to:

mass* gravitational acceleration* height

If there is no rope involved almost all of this will be converted to kinetic energy (small amounts of heat and sound will be generated too, but these will be negligible). When the person hits the ground this is dissipated by the person's muscular structure and compression of bones.

When a rope is involved the GPE lost due to the change in height will be dissipated by the rope, the remaining GPE will stay as GPE.

Work is done on the rope by stretching it, the energy expended by this is equal to the kinetic energy associated with the fall. Work done is directly proportional to the product of force and distance over which the force acts. So if you halve the energy which a strand absorbs and you halve the distance the force acts over you keep the force the same.

W=Fd=2*0.5*W=F*2*0.5*d

In reply to rgold:

Ah - I had been hoping that there was some brilliant way of doing this that I'd never seen before - but it's simply the hand-over-hand way.  Fair enough.

I agree, it's not very different time-wise to the 'two strand and adjust at the harness' method, but I think the latter is faster (and easier to fine tune) if the anchors are a significant way off.  If I have plenty or rope I'll probably default to two strands, but if I know I'm short I'll switch to one.

In reply to spenser:

Thank you for the lecture. As I mentioned before, I accidentally wrote the wrong term and I can’t correct it. 
Being a mathematician, maybe you would be interested in reading this paper by rgold: The Standard Equation For Impact Force? Google it!

edit: I see others who may be interested. 

In reply to Fellover:

Absolutely assuming a spring obeying Hooke's Law, my brain would melt doing the calculation without that assumption!

Certainly don't feel intimidated by having a technical discussion with me, my field of expertise is more functional safety and thermodynamics, it's nice to play about with some maths that doesn't involve a steam table!

I have drawn out a diagram and got myself into a maths circle but need to go back to work on my day job so haven't got time to figure out where I am going wrong, I will hopefully get some time to figure it out this evening.

In reply to spenser:

"the force applied to individual strand while absorbing the energy of the fall is also halved"

I think (I'm an electrical engineer) you can only say that the energy absorbed by each strand is halved. But force is energy over distance. so the force on each strand is the same (half the force, half the distance). Just instinct telling me this so I may be wrong.. 

In reply to spenser:

Not at all - was just a cheeky joke (fwiw I think that you and BeardyMike provide some of the best climbing-engineering comments on here, alongside others like Galpinos). Fortunately, all that's needed to understand ropes modelled as springs is GCSE physics.

I too have drawn a diagram, though not a very clear one. It's supposed to show a top roping scenario (belayer at the top), using a rope of length L, with stiffness K, with a slack length of S, climber of mass M. However, I think it's generalisable to other scenarios e.g. leading.

I'm sure people have done this maths countless times before. I'm also sure someone will let me know if I've made any mistakes

I think the most important thing to take from it is probably the idea that the tension in the rope in a fall situation is not linearly related to any of the variables (mass of the climber, the stiffness of the spring, the amount of slack out) and as such is going to be hard to just intuitively understand.

In reply to spenser:

Spenser, the bold statement is where your analysis goes wrong.

This statement would only be true for the rope (modeled as an idealized spring) if the tension in the rope (called the "force" in the bold statement) remained constant as the rope stretches, and further under the assumption that the "force," which is the tension in the rope, is always equal to the weight of the falling leader.  A few seconds with a rubber band indicates this isn't the case.  In fact, the tension in the rope starts out at zero and increases to a peak load way past the leader's weight.

In the idealized spring model, rope tension is proportional to rope stretch, with the maximum tension occurring at the instant of maximum elongation.  The constant of proportionality is called the rope modulus or spring constant, which appears in the charts you referenced.  The tension in the rope is not constant but is rather an ever-changing function of the amount of stretch (technically, the relative stretch, say as a percentage of the total rope length).  We do want to compute force times distance, but the force is always changing as the distance changes, and this requires (very simple) integration technique which shows that the energy absorbed by stretching the rope (spring) is proportional  to the square of the elongation. The result is that parallel strands double the rope modulus but do not double the peak force, as I mentioned in my original response to beardy mike some time ago

Quite a few years ago, I wrote up the details of the analysis for some undergraduate math and engineering majors who were interested in the topic.  That account has somehow found its way onto the web and is available at https://4sport.ua/_upl/2/1404/StandardEqn.pdf.

In reply to beardy mike:

I don't think anyone answered this but I've heard of a number of accidents where belays have been ripped leading to both climbers falling. I definitely remember two deaths in the early 90s from IIRC Minus 1 Gully. That was the first time people realized the dangers of placing cams in icy cracks, as those were the runners found on the rope. I don't remember exactly but I don't think they belay was cams though. 

Wasn't there a horrible case just last year when a second falling off at Stanage pulled the belayer off the top of the cliff? I think both survived which is great, but obviously something went very wrong with the belay. 

In reply to rgold:

Thanks, I got to a W=k*deltaL^2 expression earlier, I had an interview this afternoon which wound up curtailing my ability to play around with maths and I hadn't figured out where I was going wrong before reading your post.

In reply to Fellover:

Galpinos gets the really geeky stuff involving standards as he's the UK's UIAA SafeCom/ CEN representative for mountaineering related equipment etc. I just chair the meetings and write the odd article!

Mike used to work for an equipment manufacturer (we've not met before though).

My background is all rail and nuclear stuff, I can go a bit overboard and start info dumping about stuff if someone gets me started (it's great when someone wants a brain download about something, less great when they want a Yes/ No answer!)

In reply to TobyA:

What I'm particularly interested in though is, is there any real life examples of belays which ripped due to the method of belay construction. Without wishing to pas comment on your incidents, we're they caused by the sling belay or by poor runner placement? Sounds like the first was and possibly the second too? I know of an anchor failure near me too, at Fairy Cave Quarry with both climbers falling down a slab, one of them for 35m, but we have no data on that, but we suspect anchor failure?

In reply to spenser:

Worked for a few. But this stuff is really not my specialist topic...

In reply to beardy mike:

I don't know how we could determine, after the fact, that it was the rigging method that caused a belay anchor to fail.  Perhaps someone could do some laboratory testing in which the only variable is the rigging method, but I think it would be challenging even in that environment to get useful results. 

I think we're stuck with the theoretical calculations, where we can control everything but the variables in question, and then further stuck with whether or how the results of such analyses should inform practical judgments, especially since the catastrophic outcomes representing systemic failure are so very rare. The vast majority of belay anchors (excluding big wall anchors) typically get little more than double body weight  The only situation that really tests a belay anchor is a factor 2 fall onto the anchor and such falls are very rare.  The Jim Titt comment, "place good pieces and tie them together" is going to be good enough advice almost all the time, and so we are faced with the question of how much time and effort we want to expend on guarding against a hypothetical outcome which is highly unlikely to occur in practice.

My general reaction to the conundrum is this.  Time may matter, and depending on how much it matters, adding time to the belay construction process brings with it another set of dangers. On the other hand, a procedure that addresses theoretically bad outcomes without sucking up a lot of extra time is worth doing even if the outcome to be mitigated is most likely not ever going to occur. On the other hand, it isn't smart to climb on a crag the way you'd climb in Patagonia.  If time is not a significant factor, then spending a bit more of a commodity that isn't precious makes sense, even if the expenditures are directed at unlikely outcomes.

Where we draw the line in these matters is very much a personal decision based on our risk tolerance, so I haven't tried to give examples.  But here's one: I'll usually content myself with two-point anchors on mountain routes but mostly use three-point anchors when cragging.

In reply to rgold:

I reckon it's very possible to have a belay which would survive a big fall if it were rigged with a well equalised system (regardless of the method of equalisation) but which would fail if it were poorly equalised with a sling so that each piece was loaded one after the other.  Three tenuous pieces which could each hold 1/3 of a fall, but which would each rip if loaded fully one after the other. 

(again, if I'm using this belay in real life then something's gone horribly wrong)

Is it possible to imagine a belay where the difference between holding and failing is solely the rigging method?  I'd say yes, but the window where that happens is going to be far narrower. 

Specifically I think it's a narrow gap between 'using a sling to equalise and then attaching with a rope to the powerpoint', and 'equalising with the rope', but the fact that the sling doesn't stretch to accommodate better equalisation means I think this is possible, if very unlikely.   

It's an even narrower gap between using the one strand and two strand systems to rig with a rope.

Fully agree with everything you say about risk tolerance in a given situation.  Sometimes one good nut is the best answer.

In reply to BeardyMike:

As a slight aside from this discussion, I remember reading an article on the cows tails used for caving SRT.  Due to the short length of the (dynamic) rope,  it was found that knot slippage was more important in reducing peak load stretch of the cow's tail.  So a key finding was "if you fall on your cow's tail, make sure you loosen it immediately, to safeguard yourself until you can change it".

So in our hypothetical dodgy belay situation, it might be worth tying in with loose knots.  Especially so if the rope goes from your waist to the belay and back.

In reply to TobyA:

I know of an incident (involving someone you've met) on the Ben (Zero or Point Five gully, can't remember which) where a leader fell from the second pitch, resulting in the peg belay failing and both climbers falling to the bottom.  Fortunately, both survived, but it was pretty serious.

In reply to Dave Cun

Then would it be logical to put extra knots into a dubious belay setup eg overhand in a sling? Would weaken the sling but reduce effects of impact. Perhaps reminiscent of the (very) debated advantages of screamers.

In reply to Dave Garnett:

+1 for this.

The problem with having favourite or default procedures is that they are likely to be based on the belay situations which predominate in one's own particular climbing area. This thread is full of posts from experienced climbers using similar terms and descriptions, but I suspect the belay scenarios they are picturing are very different.

For example, many of my local trad routes have at their tops vegetated 45-degree scrambles to reach large trees, which are often well separated as well as set well back. Having a default procedure involving repeat backwards/forwards/sideways scrambles in order to convert runners to clove hitches, just to get single strands of rope to anchors, would be ridiculous. 

In reply to bpmclimb:

FWIW, I totally agree with this and do the same thing (if enough rope is available) when faced with analogous situations, which as you discerned can be rare in other locales.  Of course, any default procedure has to give way to diverse other options when circumstances dictate it---we shouldn't have to add that disclaimer to every comment!  That said, as the discussion went on, I found a slew of internet videos in which the pieces were not a 45-degree scramble away but just a foot or two out of reach, and yet the instructor consumed double the amount of rope and created a 40% stiffer anchor anyway (here's one of several examples youtube.com/watch?v=bAQRIbQQgs4&), so your certainly apt observation about default procedures being suboptimal in fact cuts both ways:  we don't have to rig on an ordinary multipitch belay stance the way we would rig at the sloping top of a climb with only very remote anchors available.

In reply to beardy mike:

This discussion seems to have got entangled in the detail of slings v 1 v 2 rope strand attachment.

Fwiw, whilst I am usually the Jim Titt, good pieces good knots mindset , I invariably belay  with a doubled back ropes from out of reach anchors together with close anchors.

On multi pitch especially , high anchors mean the load will align close to the rock, ie not outwards, and will be less affected if the belayer is moved under load . They also allow a quick runner for the leader of the next pitch to avoid a ff2. Doubling back also means the belayer is in control of the knots and if neccessary on a long pitch above the belay  give the leader more rope to reach the next stance by releasing the rope to the high anchors . ( not ideal on hard moves as a readjustment of the belay plate is needed )

My observations of the sling belay brigade is that the temptation is to belay too close to the anchor points.

In reply to rgold:

This latter scenario is actually a really important one for me. As we are so keen on double ropes it really makes sense to me to use slings to bring pairs of anchors to a point and then connect to those using a single strand clovehitched to the point. The sling gives you equalisationish, and extends the point closer to you so more likely to be easily in reach it and retaining lower impact with the single strand, uses a minimum of rope and is more easily adjustable. I use this method in my personal climbing loads but as I have said a few times, to me it seems so much more important to get good anchors...

In reply to Rick Graham:

Hey Rick! Thing is that this is an analogue world with so many variations between the rowdy ropers and the sling saloon... sometimes I like Curry, and sometimes I like Noodles, and sometimes I like Singapore Noodles...

In reply to beardy mike:

I deliberately used " invariably"

In reply to rgold:

I'm not sure that "consuming double the amount of rope" is as much of a penalty as you're making it out to be. Firstly, if the anchors aren't much out of reach the doubling isn't very significant or if the anchors are a long way out of reach, getting the clove hitches in the right place without doubling becomes a faff. Secondly, the rope you potentially "saved" from use in the belay still isn't much use to you because it has to come back to you from the clove hitch anyway to go through your belay device. I guess in those hopefully rare situations that the leader on the next pitch is using up every last inch of rope to get to a belay you could potentially take them off belay to give them that extra rope you cunningly avoided using but that shouldn't be common enough to be worth giving all that much consideration to.

You have a perfectly reasonable system that works for you most of the time. You don't need to keep portraying other valid alternatives as inferior.

The video you posted is clearly aimed at beginners, so it's offering a simple system that's easy to learn and works adequately almost all of the time.

In reply to Luke90:

Your points are well-taken.  I think I've said rather more than I should have said already, and am happy to leave this particular field of contention.

In reply to bpmclimb:

Speaking of large trees: there’s no point being connected to more than one large tree for redundancy reasons. In the unlikely event of one large tree falling, it will rip everything apart anyway. 

In reply to Luke90:

This is true. At the end of the day all of these anchor systems are realistically good enough for any British trad climbing. It all just comes down to personal preference.

I personally like using slings because you can block lead much more easily on multipitch, and they are much more suitable for alpine terrain or any situation where you need to move fast.

However, there are clearly benefits to using a rope anchor and being able to use both proficiently is a more useful skill than sticking to one.

In reply to Stefan Jacobsen:

That assumes it's the tree which fails, and not the sling / krab / knot...

In reply to Stefan Jacobsen:

Yes, if you are lucky enough to have the solid tree (more or less) in line with the climb.

Aside from the redundancy issue, you often want a "triangulated" position at the crag top for lateral stability; also, it's quite common to need to get to the most suitable tree for abseil descent, which can be done more safely if there's already a rope running up to it.

In reply to sbc23:

I have to say that my strong preference is to belay from a point where I can see my second.  This means that I tend to sit right on the edge and therefore don't want any significant extra 'give' in my belay set up.