## / Half Ropes as Twin Ropes - Impact force?

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Sitting at work, bored and skiving and thinking about ropes.

So, using half ropes as twin ropes (ie. clipping BOTH ropes into ONE piece of gear). If you fall, the impact force will be absorbed by double the cross-sectional area than it would if you fell on one rope alone. Does this double the impact force?

Been trying to do the maths (underworked engineer) but am unsure how to approach it.

I've always been told that using halves as twins was a bad idea for this reason but haven't seen the proof. It also doesn't explain how triple rated ropes are possible.

Is anyone able to shed light?
In reply to RKernan: Yes, it will theoretically double the impact force on the gear compared to having a single half rope clipped.

It's not very rigorous, but the way I think about it is in terms of how quickly you'll be decelerated. With one rope that rope has to do all the work so it'll take longer for you to be decelerated. If you've got two ropes clipped you'll decelerate faster, with 3 ropes faster still. F = ma tells us that greater deceleration means a greater force if mass is constant, so having more ropes clipped means greater deceleration which means a greater force on the gear.

The reason triple rated ropes are possible is because the tests only specify an upper limit on impact force but no lower limit (though i think there is a limit on how elastic the rope can be.) This means your half rope can have a low impact force which when doubled is still low enough to pass the twin rope test.

I always thought that using halves as twins was okay as long as you always clip both strands into each piece of gear. Perhaps not the case?

I've no idea about the maths, but if you look at the test stats of something like the Beal Joker you'd get an idea of how the different tests affect the same rope, maybe.

Some useful info on the Beal website

http://bealplanet.com/sport/anglais/typecorde.php#choix

Clipping 2 ropes to the same piece only increases the peak force by roughly 10%.

Any rope rated for single use would pass the tests for doubles and twins if the resultant force on a single is <11kn. Any double ropes will pass the test for twins. Hence triple rating is not the holy grail is sold as.

Companies just won't spend the money to certify them as there would be little selling point to market a fat rope as triple, so the trick is to get the thinnest rope possible which will pass the tests for a single and triple certify that.

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> Clipping 2 ropes to the same piece only increases the peak force by roughly 10%.

Have you got a source? I don't mean to be confrontational, it just seems quite counter intuitive to me.

The easy way, just look at all the testing results from triple rated ropes and see the relationship.

The not so easy way, look at the formula for impact force and how different ropes relate.

The formula for impact force involves:

The weight of the climber (m)
Gravity (g)
The fall factor (f)
And the one we want to look at, the Modulus of elasticity (k). This, to simplify it, is what determines how 'elastic' the rope is.

The formula is F(impact force)=mg+mg&#8730;((1+(2fk/mg))

You can already see that K doesn't multiply linearly the impact force. i.e. is not in the form F=k*(xxxxxx)

If you play with the formula you'll find out that for values relevant to climbing the resultant F is around 10% when doubling up on k

That &#8730; in the formula is meant to be a square root symbol. It took me 5 minutes to figure out how to put it on and it doesn't even work... Boooo...

Sooo, it it ok then to double, or triple up my 11mm single, and use it to tow my car?

Steve

What color is the car?

> Is anyone able to shed light?

I'm not able to. I'm no engineer and I'm simply speculating.

However... it seems to me that in the 'real world' the are a couple of things that tend to increase frictional forces and, as a consequence, actual impact forces when clipping both half-ropes to each piece of gear.

1. There is going to be greater frictional force in the top piece of gear's karabiner. Remember we would have two ropes going through it.

2. The belayer will now have two ropes which he/she can now grip onto. Possibly there will be less 'slip' through the belay device and consequent higher impact forces on the top piece of protection.

On what do you base your assumption that doubling the rope would double the modulus of elasticity (k in your equation)?

- Having two ropes instead of one means that each rope would have to absorb half the energy in order to bring the climber to a stop.

- Kinetic energy is linearly dependent on mass, so the impact force on each rope can be calculated by the above formula with half the climber's mass.

- To get the total impact force on the climber, we would then add the impact force on the two ropes.

Nb. I'm no physicist. In the past I have been known to be totally wrong in similar matters. I may very well be in this as well.

BTW, i'm not condoning for anyone to go out and use their ropes in a manner they are not certified for.

When it comes to saving your neck follow manufacturers guidelines and ignore what some random guy is saying in an internet forum.

You been told
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> 1. There is going to be greater frictional force in the top piece of gear's karabiner. Remember we would have two ropes going through it.
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> 2. The belayer will now have two ropes which he/she can now grip onto. Possibly there will be less 'slip' through the belay device and consequent higher impact forces on the top piece of protection.

These are exactly the thoughts that occurred to me as well.
In reply to supos: I wondered about that as well. The numbers support Mr Lopez's point though.

Using the figures from this UKC review: http://www.ukclimbing.com/gear/review.php?id=3765 there is an average increase in impact force of 16% between testing as a single rope and testing as a twin rope.

Note that the tests for single and twin ropes are the same (same mass etc.)

> Using the figures from this UKC review: http://www.ukclimbing.com/gear/review.php?id=3765 there is an average increase in impact force of 16% between testing as a single rope and testing as a twin rope.

These figures are meaningless unless we know something about the testing regime. Otherwise how do we know how these results relate use in the 'real-world'?

I'm guessing that the standard UIAA test rig was used.
In reply to Skyhook: Yes, the UIAA rig was used.

That's the equation I was looking for - thanks!

supos:
With 2 ropes (modelled as springs) in parallel Kxy = Kx+Ky

http://scienceworld.wolfram.com/physics/SpringsTwoSpringsinParallel.html

I suppose since you're modelling the 2 ropes together as one, you're not looking at the impact force on one but rather on both, meaning you keep m the same.

Feeling rusty at this now...

Bottom line - it should be OK to use half ropes as twin ropes (for sport climbing etc) depending on the rating of the ropes?

How significant is the frictional force on the top krab?

"The belayer will now have two ropes which he/she can now grip onto. Possibly there will be less 'slip' through the belay device and consequent higher impact forces on the top piece of protection."

I assume tests are carried out assuming no slip?

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> On what do you base your assumption that doubling the rope would double the modulus of elasticity (k in your equation)?

No, doubling up the ropes won't double up k, it is much more complicated than that. All the above 'assumptions' are approximations to illustrate why happens what is happening. If you'd like a more detailed explanation with 3 page long equations to back it up and exact results may i suggest you join a mathematics forum?

;-)

> - Having two ropes instead of one means that each rope would have to absorb half the energy in order to bring the climber to a stop.

> - To get the total impact force on the climber, we would then add the impact force on the two ropes.

So you have just discovered that if you have 2 ropes they share the load equally. Nobel prize on the way
Running the numbers on my Tendon half ropes (max impact force of 5.5kN), assuming the equation is right, gives an impact of 7.45kN when used doubled.

This is still less than the 8kN max impact of a Tendon 10.2mm single.

Not taking account of friction though, but I can't see how that would be any different to twin ropes?
> Bottom line - it should be OK to use half ropes as twin ropes (for sport climbing etc) depending on the rating of the ropes?

Yes. It is routinely done in at large sport crags where you then abseil the routes.

> How significant is the frictional force on the top krab?

Again... I'm neither physicist nor engineer.

Think about it. In order for the rope to absorb as much of the kinetic energy of the fall as possible, the rope should be available to stretch equally along it's entire length from climber to belay device.

Friction on the top karabiner (and to a lesser extent lower karabiners) will (in my un-informed opinion) reduce the amount of kinetic energy able to be transferred to the rope below the top crab.

You could think of it this way. If the frictional forces on the top karabiner were huge and there was no 'slip' of the rope over the karabiner, then the only bit of rope to stretch (absorb energy) would be to piece of rope between climber and top karabiner.

> I assume tests are carried out assuming no slip?

Yes I and that's why it's difficult to say how differently the different ropes will perform in the real world.

Indeed.

If I had bothered to do the math I would have seen that what Mr Lopez and I propose is actually identical. Doubling k has the same effect as halving m and calculating the force of each rope, then adding the forces of the two ropes.

As is often the case, we came to the same conclusion using different approaches.
> Running the numbers on my Tendon half ropes (max impact force of 5.5kN), assuming the equation is right, gives an impact of 7.45kN when used doubled.

Remember that quoted impact forces on double ropes are obtained drop testing 55kg as opposed to 80kgs on singles and twins
Good point. Working back to find k then rerunning the equation with m=80 gives a peak force of 11kN with halves as twins.

Seems quite high!

Skyhook:

"You could think of it this way. If the frictional forces on the top karabiner were huge and there was no 'slip' of the rope over the karabiner, then the only bit of rope to stretch (absorb energy) would be to piece of rope between climber and top karabiner."

Is that not taken into account by the fall factor?
^should mention, that's assuming a factor 2 fall.

UIAA tests are made with fall factor 1.77

There's a formula to derive the modulus of elasticity from the quoted UIAA impact forces, i'll have a look see if i can find it.

Here K=F(F-2mg)/(2fmg)

THanks, that gives the same result as what I found working backwards.

I should do my research better.

With f = 1.77, F = 9.23kN for m = 80kg.

SOmewhat more reasonable. I think I'd be happy enough using my halves as twins.

> So you have just discovered that if you have 2 ropes they share the load equally. Nobel prize on the way

Hey, no need to be rude! You explained the phenomenon using a pretty non-trivial assumption in your reasoning. I used a different approach to reach the same conclusion, but I included the reasoning behind it.

I never said you were wrong, just that your reasoning was incomplete. And I never claimed I was going for the Nobel Prize.

That's tongue in cheek dude. Relax, it's only a joke.
going back to the other thread regarding can clipping one rope in to two bits of equalised gear reduce the impact force on the gear (as opposed to clipping one bit in to each rope assuming they would also get loaded equally), it would seem the answer is yes! Something I wouldn't have known before!
Interesting point, there's quite a difference - on the order of 25% more force on an individual piece of gear when you clip one rope into each piece.

>> "You could think of it this way. If the frictional forces on the top karabiner were huge and there was no 'slip' of the rope over the karabiner, then the only bit of rope to stretch (absorb energy) would be to piece of rope between climber and top karabiner."

> Is that not taken into account by the fall factor?

Well that's what, in effect, happens on the UIAA test rig.

Where there is <strong>no</strong> friction on the top karabiner (or lower ones) all the kinetic energy of the fall will transferred to the rope between the climber and belayer (also the belaying device).

> (In reply to RKernan) Yes, it will theoretically double the impact force on the gear compared to having a single half rope clipped.

Only if your theory is wrong.

Mammut doubles are fine to use as twins.

If, as is customary for the simplest analyses, the rope is modeled as a spring with no damping, then doubling the ropes multiplies the impact force by the square root of 2 and so produces a 40% increase in the load.

Testing suggests the actual increase is often rather less than that. It may be pretty hard in reality to get both ropes to share the load equally, or the model itself may be inadequate, or a combination of both.
It would be best to think of the problem in terms of impuse: Force x Time = change in momentum, as due to the elacticity of each indiviual rope the event time will change, e.g short time = low elacticity = greater force
longer time = high eleactisity = less force. The change in momentum will allways be constant.

Or perhaps the integral of the force X time since force X time is momentum.
> (In reply to Mr Lopez)
> going back to the other thread regarding can clipping one rope in to two bits of equalised gear reduce the impact force on the gear (as opposed to clipping one bit in to each rope assuming they would also get loaded equally), it would seem the answer is yes! Something I wouldn't have known before!

I wonder if The Ex Engineer has any further comment. When we were talking about it this the other thread, he seemed to think that as soon as the runners aren't perfectly level, the cons can quickly outweigh the pros.

Personally, I think its quite easy to tell by eye if that is the case though.
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> Or perhaps the integral of the force X time since force X time is momentum.

It is true that impulse is the intergral of force with respect to time, but it is not true that force x time = momentum.
Force x time = m(u-v) the change in momentum.

This change in momentum will be constant in a lab situation so the only factor to affect the force is time : Force = constant / t.

It is safe to moddel a rope as a spring so in this sittuation of clipping both ropes into the one bit of gear we have 2 springs in parallel.

Hokes law states Force = -kx [ k is the spring constant and x is the ammoun tof stretch in the rope]

For parrallel springs this becomes Force = -2kx.

By combining equations we get constant / t = -2kx

rearrange to get t: time = - constant / 2kx.

In conclusion this means that due to both ropes being cliped into the one piece of gear stoping time has halfed and as such force theoretically doubles.

This is a simplised theoretical situation all donations wellcome to fund a full investigation

[very bored physics graduate, with climbing background]

So what about 2 pieces of parallel gear clipped to one rope vs. clipped to a rope each?
> I wonder if The Ex Engineer has any further comment.

Yes, I've posted one.

> When we were talking about it this the other thread, he seemed to think that as soon as the runners aren't perfectly level, the cons can quickly outweigh the pros.

That's a decent summary of my position

> Personally, I think its quite easy to tell by eye if that is the case though.

I don't think you can really 'tell by eye', but the UKC expert on equalisation is probably Jim Titt who posted above. I'd be very happy to defer to his opinion about how likely it is going to be to get better than an a 1:2 equalisation in the real world.
Apart from the most simplistic rope models we stopped using an undamped spring about 40 years ago, a cursory glance at an impact force curve shows that there is a huge element of damping going on in the system. Martin Pavier probably did the definitive initial work on this.
In a fall involving intermediate protection straight away there is the energy lost running the rope over the top karabiner which is roughly around 40% without even bothering with friction in the rope itself and the energy used to provide semi-permanent stretch which is probably around 10%.
The better models use a value of k taken from experimental results and its fairly clear that using a value of 2k for two strands doesnīt work, as Richard says the models give an increase of 40% but testing doesnīt.

The part which isnīt clear is exactly how accurately the two strands are equally loaded in the certification tests and so how accurate the values given are, I could ask someone I know but itīs getting a bit nerdy for me since it would be impossible to reproduce in a real fall!
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> That's a decent summary of my position
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> I don't think you can really 'tell by eye', but the UKC expert on equalisation is probably Jim Titt who posted above. I'd be very happy to defer to his opinion about how likely it is going to be to get better than an a 1:2 equalisation in the real world.

Hmmm, depends I guess!
Presuming we are talking about climbing on two half-ropes and the choice is clipping each strand into one piece or one strand into two equalised pieces then the one strand should always be better. Irespective of the equalisation the belayers ability to brake one strand of a double rope system is considerably reduced (40% less according to the CAI) and the rope impact force is also lower.
But if itīs the only strand keeping you off the deck then one might start to think about whether itīs the one running over that sharp edge.
That said I wouldnīt hang around trying to equalise anything since Iīd probably get pumped and fall off!

I wouldn't equalise anything either. Putting 2 adjacent cams in might happen though. Then you have a krab in front and one behind and it's been suggested that they're not really equalised because of some complicated friction consequences.
In reply to jimtitt: Hi Jim,

As you surmised, the debate is about how to best to minimize the impact force on two (or more) runners placed at the same level, e.g. two cams in a flared horizontal break on gritstone.

Using both ropes will obviously lead to a very effective splitting of the forces between both runners.

Using one rope will lead to a lower impact force overall but that force may well end up loading just one runner. (Hence the question about equalisation)

A complication is obviously what happens if one runner rips.

A second complication, as you have now reminded us, is the effect of the dynamic belaying introduced from trying to hold just one rope.

My thinking is that unless you can get a reasonable amount of equalization between the runners (using one rope) then the two rope option would be preferable. That is mainly based on the fact that as discussed here, twin rope impact forces are only slightly increased and that this result MAY translate to falls using double rope technique with runners on both ropes.

However, this is based on a major assumption, so if you know of any useful test results on double ropes with runners on both ropes, it would be great to hear of them.

As a climber whose local crag has lots of horizontals, I deal with this issue all the time. Regardless of the potential for getting a lower anchor load with one rope clipped to an "equalized" pair, the realities of efficient climbing, the very finite endurance resources of my aging forearms, and the extra security afforded by having both ropes engaged lead me to clip one half rope to each piece almost every time.

Apart from the somewhat vague comments by the CAI I donīt know of any realistic tests ever done. The whole issue has so many variables that one would either have a painstakingly complex lab experiment which wouldnīt reflect reality at all or you could pick a scenario to test which backed up whatever theory one wanted.

If you used static equalisation you almost certainly wonīt achieve anything like a reasonable load split especially doing it hanging on with one hand, the more likely option is a sliding dynamic equalisation. Using a standard 10mm Dyneema hybrid sling you would get a load split of 58%/42% but this is only if you used a system with limiter knots and a single karabiner on one strand, use a sliding X and youīll be around 65%/35%.
BUT!!!! Youīve increased the overall load on the two pieces because you made a triangle of forces, for a 90° angle on the sling each piece gets a little over 20% more so on piece is taking 65+20% so 85% of the total force which strikes me as getting so near it takes all the load anyway that it wasnīt worth the effort. Of course you could use a much longer equalising sling to reduce the angle but you then lower the protection point still further and increase the fall distance and thus the fall factor and chance of hitting the ground.
Then there is the problem of extension if one piece fails, with the two strand method there are the questions of how accurately one can get the tension equal if you are belaying with two seperate strands, the difference in the belayers force with one strand taking all or only a proportion of the force and so on!

Bit too many unknowns and variables to make a realistic recommendation I reckon, personally Iīd think using one strand in each piece but allowing slightly more slack in one would give the best result overall and itīs the easiest.

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