Self Belay Top Rope Devices – Static Ropes – Math

New Topic
This topic has been archived, and won't accept reply postings.
Removed User 18 Mar 2021

Hi,

I have been researching self belay devices for top roping (I accept that in principle it is more dangerous than top roping with a partner), I wanted to understand the figures written on the devices to understand the margins being discussed. I also found a review where the reviewer implied that a 400Kg load was somehow much less than 4KN (where as in fact they are almost the same). This lack of understanding made me try and understand the science behind the figures and how they relate to climbing.

It’s been a long time since I have had to use the maths below and associated principles so please correct me If I have things wrong.

There tends to be 2 sets of figures quoted on ascenders that are used for top rope belaying. I will use the CT rocknlock as an example. 

There is the maxim force that can be applied across the whole devices (as if a crab was connected to each end and a load applied across these) These figures are 20KN ( which is 20000N, divide it by 10 (approximate value of gravity acceleration) which equates to a mass of 2000KG or 2 metric tons. This is not really relevant for the use being discussed here.

1) The figure I am interested in is the “grab” force of the cam on the rope for the rocknlock that is 4KN or 4000N or mass of 400KG.

2) So when I fall on a rope the cam will take my weight if I am less than 400KG? No… not that simple.

3) If I weigh 100KG, if I fall on the device I apply a downward force of 100kg x 10 N or 1000N or 1KN to the device. If this was the only force in play I would keep on falling!

4) So what stops me… the rope. Let’s assume I am on a dynamic rope as this makes sense to me and the maths easier.

5) If I fell 30cm before the rope/device caught and then I am brought to a stop in another 30cm (I am assuming the decelerating force is consistent as the rope stretches).

6) As the stopping distance is the same as the free fall I can assume the negative acceleration is the same as gravity in this case.

So the net force to achieve this would be the same as my weight in the opposite direction…. -1KN.  

7) If the net force is -1KN, then the force applied by the dynamic rope is -2KN as the 1KN is subtracted to allow for my weight. So the total force applied through the cam is 3KN ….

8) Now this is when I doubt my maths…. This figure is really close to the 4KN limit of the rocknlock and more than the 2.5KN of the microtraction (a popular choice for self belay top roping).
 

So either my maths is wrong or these devices are not designed to catch a fall, but simply hold you, in which case there should be no slack in the system so no falling just holding.

Now – what would make this safer…. 2 ropes with two devices as the forces will be reduced by a factor of 2.

9) What about static ropes? Now I am confused because these seem to be recommended for self belaying. I assume so you don’t hit the ground if you have an early fall as a dynamic rope would extend too much. That said when you start any climb the first section is sketchy anyway.

10) If we consider my attempted lesson in mechanics (6) and swap a static rope for the dynamic rope the forces become huge. If the static rope arrests the fall in 3cm rather than 30cm (my laws of motions knowledge is a bit sketchy here) then assume that the negative acceleration is 10 times greater. So the net force applied to arrest your fall would be -10KN (that is a ton!), so the force across the cam is 11KN 

In summary I would like someone to shoot this down because the maths here makes it look as if these devices cannot take a fall, especially on a static rope. With the microtraction you are 4 times over the stated maxims on a 30cm drop.

Thanks for reading this...

This is just my opinion and I hope someone can show me why I am wrong

5
 George_Surf 18 Mar 2021
In reply to Removed UserNick Murphy:

I dont know about the maths but they must be wrong! I think unless youre really 'falling' on a traxion (and I dont mean the slack accumulated between having it hang on a locker at the bottom of your belay loop compared with the distance it takes for it to move to the top of your belay loop) youve got nothing to worry about (dont every let any slack rope accumulate, if youre doing it right it won't, the traxion runs like silk once you get going).

Static I think is better, it wears less on edges, it stretches less when you fall/sit on the rope. if youre really worried you can wear a thin bungee around a chest harness and this keeps the traxion always in the up orientation. what you need to be more worried about is redundancy; backup knots, possibility of 2 ropes, protecting edges etc. sorry it doesn't really answer the question...

 john arran 18 Mar 2021
In reply to Removed UserNick Murphy:

There's a good reason why nobody is allowed to retail genuinely static ropes, or even close to properly static. The terms I'm familiar with are semi-static and low-stretch, but these may no longer be current terminology. In any case, you can expect a stretch in the order of a few percent from any climbing rope available, which should make an enormous difference to your figures.

 petegunn 18 Mar 2021
In reply to Removed UserNick Murphy:

Are you worried about the equipment failing or just interested in the numbers?

Most equipment is tested under static load so by the time you've added your rope, crabs, slings, harness, even yourself etc. the actual load applied to any singular device in far less. 

FWIW I use a (semi) static rope and a shunt and have done so for 20+ years and I weigh about 80kg. 

Post edited at 12:41
1
 nikoid 18 Mar 2021
In reply to Removed UserNick Murphy:

https://www.hse.gov.uk/research/crr_pdf/2001/crr01364.pdf

This may be of interest if you want a bit more "science", in particular the section on back up devices, eg shunts etc.

Removed User 18 Mar 2021
In reply to Removed UserNick Murphy:

Hi,

Many thanks for the feedback. 

1) The reason I started the thread was to help me decide which device to buy. rocknlock or microtraction, as I mentioned the rocknlock has a higher grab load value and I wanted to understand if this was significant.

2) I also read a review where the kongduck was discarded because it only had a 400kg grab load value ... which in fact is quite high in at 4KN.

3) Interesting the link to the HSE document that is a few replies back does show that the tension in the rope when ascending vigorously can get above 1.5KN .... so I think my figures are in the right ball park - I can only assume that the way the forces are distributed by the CAM is more significant than I thought.

4) Thank you for the insights on "static" ropes, this is very helpful.

5) I also wanted reassurance that the devices won't fail if I use a well thought through method.... I think I got that too 

 sbc23 18 Mar 2021
In reply to Removed UserNick Murphy:

I think your logic in step 7 is wrong. Consider the forces on the falling human. You've (quite reasonably) assumed he is decelerating at g. The net force on him needs to be mg upwards. He has mg weight, therefore there needs to be 2mg upwards in his connection to the rope. So the cam needs to grab at 2kN.

In reality, things are different. The upwards force isn't constant. The rope is elastic. The force increases with increased strain (stretch) in the rope. Hooks Law. It will be zero initially and highest just before you stop. This is why you 'bounce'. The force in the rope is higher than your weight until you stop, then the force drops to just your weight and the rope has to reduce length to get back in elastic equilibrium. 

Depending on the cam design, it can slip and then subsequently hold. It's not going to just fail and fall apart at 4kN, although it may damage your rope if it has teeth. This happens all the time and by design with belay devices.

Also, unlike the steel weight in the DMM Dyneema video, a human isn't a solid mass. The body can bend and distort. If you fall on a static rope your waist may come to an almost instant stop, but a large amount of your mass in your torso, arms & head may carry on going for a period of time. For a given fall, falling momentum is fixed (mass x velocity). Hence the impulse (force x time) required to reduce the velocity to zero is fixed. Increasing the impact time reduces the required decelerating force. 

Post edited at 20:38
 Osiris 18 Mar 2021
In reply to Removed UserNick Murphy:

Seems an incredibly complicated way of deciding what device to use. Just use a shunt and static rope. Dave MacLeod has for years. I use this set up. It works and has no teeth to cut the rope (ropeman, microtraxion, rollnlock - i would wish to avoid falling on these at any cost).

https://www.andy-kirkpatrick.com/blog/view/self-lining

2
 MischaHY 19 Mar 2021
In reply to Removed UserNick Murphy:

I appreciate that you've tried to science the shit out of this and I love that energy but honestly if you're actually interested in toprope solo then just bang a traxion on literally any rope, stick a backup knot in a few metres off the deck so you can't deck out, and then crack on. You'll be 'reet 👍

 MischaHY 19 Mar 2021
In reply to Osiris:

> Seems an incredibly complicated way of deciding what device to use. Just use a shunt and static rope. Dave MacLeod has for years. I use this set up. It works and has no teeth to cut the rope (ropeman, microtraxion, rollnlock - i would wish to avoid falling on these at any cost).

I've fallen on toothed devices multiple times and haven't even had moderate sheath scuffing. Most climbers massively over emphasise the actual danger of damage here because with a suitable setup (trax on an oval biner with a chest rig to keep it oriented) you will never fall more than a few centimetres onto the device. 

 mal_meech 19 Mar 2021
In reply to Osiris:

> Just use a shunt and static rope. Dave MacLeod has for years. I use this set up. It works and has no teeth to cut the rope (ropeman, microtraxion, rollnlock - i would wish to avoid falling on these at any cost).

^^^ this a thousand times this^^^

Using a Shunt on a semi-static is by far the most common and is "safest" for both you and your gear.

I used several systems before going to a shunt and wish I'd just bought one sooner.

Post edited at 09:38
1
 Ceiriog Chris 19 Mar 2021
In reply to MischaHY:

Exactly

> I appreciate that you've tried to science the shit out of this and I love that energy but honestly if you're actually interested in toprope solo then just bang a traxion on literally any rope, stick a backup knot in a few metres off the deck so you can't deck out, and then crack on. You'll be 'reet 👍

Exactly


New Topic
This topic has been archived, and won't accept reply postings.
Loading Notifications...