# Thread: Mathletes: Dare ye enter?

1. ## Mathletes: Dare ye enter?

Okay...so an older thread (and my carabiners) got me wondering...

If 25kN = 5620lbf directional holding force with gate closed along the long axis of a carabiner and 7kN = 1573lbf directional holding force with gate closed along the short axis of a carabiner then what is the directional holding force with gate closed of said carabiner attached to webbing when it's looped around a tree and clipped to the webbing? (For reference: http://www.tothewoods.net/HomemadeGe...eSupports.html)

The forces exerted on the carabiner, when used in the manner on Just Jeff's website, are neither perfectly directional along it's long or short axis. There is somewhat of an angle using this method. Difficult to measure and probably wouldn't be consistent due to different circumferences of trees...but logic would dictate the the directional holding force of the carabiner with gate closed would be somewhere between 7kN and 25kN, yes? Maybe not?

Since climbing carabiner strengths are measured along it's long and short axis, does a force exerted at an angle negate the force ratings since the carabiner isn't being used in a way in which it was designed for maximum protection?

2. Although I'm not an engineer, and although I have been known to be rather handy with numbers, I think I can poffer (I believe that's a word) some thoughts.

The force of 7kN is the measurment of a pull between the spine of the carabiner and the gate itself. This strength is lower because the force is being held by the pins that hold the gate in position. This is still quite strong, but noticibly weaker than the normal loading of a carabiner. The reason that such a carabiner can withstand as much force as it can, is due to the shape. The "D" shape places most of the load along the spine of the carabiner placing as little froce as possible on the weakest part of the 'biner: the gate. The example from Jeff's wonderful webpage describes a direct pull on the spine of the 'biner. Although the load seems to be pulling at an angle, the truth is that the angle load is on the webbing, the pull on the 'biner is in a straight line (summed vectors). Not only that, but the pull is in a straight line with the spine.

The forces exerted on the webbing is another matter for discussion. I can't remember where right now, but there was a discussion regarding the forces exerted on the support system given different angles of sag. That same mulitplication of forces is in effect on the webbing as it passes throught the biner. Not the end with the loop, but the part that passes though. I suppose the question should be, will that multiplication of forces due to acute angles overload the 'biner?

Dave

3. Originally Posted by Doftya
<snip> I suppose the question should be, will that multiplication of forces due to acute angles overload the 'biner?

Dave
Fair enough, and I'd like to know the answer to the question you pose.
Anyone?

Your explanation was well thought out and made perfect sense: in essense, the load is still borne by the long axis of the carabiner.

Still has to be better than not using a carabiner and threading the webbing through its own loop. I understand that, over time and due to friction on the webbing, this may not be the best solution...and by that I mean when using webbing sans the carabiner.

4. i think in that picture it's hanging slack and lose. once it's weighted it will align differently and be mostly loaded along it's major axis. webbing is wider than the 11mm rope that's intended to be used, but it should still be loaded mostly along the major axis.

5. Originally Posted by Alan
The forces exerted on the carabiner, when used in the manner on Just Jeff's website, are neither perfectly directional along it's long or short axis. There is somewhat of an angle using this method. Difficult to measure and probably wouldn't be consistent due to different circumferences of trees...but logic would dictate the the directional holding force of the carabiner with gate closed would be somewhere between 7kN and 25kN, yes? Maybe not?
It looks to be like the carabiner is only touching the webbing and it is not touching the post. Therefore, the load on the carabiner is along the long axis. There could be a slight sideways loading because of friction between the webbing and the carabiner but this should be trivial compared to the total force on the carabiner.

If the force weren't along the long axis the webbing would bend (it's very flexible) until the force was along the long axis.

If the carabiner were subject to a side load, (i.e. a force trying to bend it orthogonal to both the long and short axes), I think it would be much weaker.

For the load on the webbing, if θ is the angle between the webbing and the horizontal ridgeline, then the force on the webbing is the weight of the hammock and occupant divided by 2sin θ

So, if your webbing breaks at exactly 1,000 lbs and you and your hammock weigh exactly 200 lbs then the smallest θ you can have is about 5.7°.

200 / 2sin 5.7 ≅ 1,007

6. While using this method, I typically pull the webbing tight so that the carabiner is cinched up against the tree pretty well. If the trees are close enough, I double-wrap my webbing before I apply the carabiner, thus putting much of the force on the two webbing wraps (wrap and a half?) around the tree. But for the sake of arguement...lets stick with a single wrap (or is it really a half wrap?)

Once a weight is applied, and I agree with others in that the brunt of the force is applied along the long axis, how much torque/twist is applied to the carabiner due to the downward angle and weight of the occupant?

Anyone familiar with torque/twist kN breaking rates of carabiners?

7. Originally Posted by Alan
While using this method, I typically pull the webbing tight so that the carabiner is cinched up against the tree pretty well. If the trees are close enough, I double-wrap my webbing before I apply the carabiner, thus putting much of the force on the two webbing wraps (wrap and a half?) around the tree. But for the sake of arguement...lets stick with a single wrap (or is it really a half wrap?)

Once a weight is applied, and I agree with others in that the brunt of the force is applied along the long axis, how much torque/twist is applied to the carabiner due to the downward angle and weight of the occupant?

Anyone familiar with torque/twist kN breaking rates of carabiners?
I think you see different things happen with small diameter trees and large diameter trees.

With small diameter trees you have more of a torque/twist on the carabiner because there is more of a curve to follow. But the angle isn't as severe so the vector force isn't as big to start with as with a large diameter tree.

With a large diameter tree, if the force gets large enough because of the vector angle, I think the carabiner might slide along the webbing it is looped around and reduce the force on it or the webbing where the carabiner is looped around might be the weak point sense there is a severe bend in the webbing? I haven't tried it so that is just something to think about.

At any rate, I personally would want a pretty strong carabiner for that application.

8. Originally Posted by Youngblood

At any rate, I personally would want a pretty strong carabiner for that application.
How strong, would you say?

9. Originally Posted by NCPatrick
How strong, would you say?
I don't know off the top of my head how to figure it out for myself.

10. Oh. Well would you think that the 22-23 kN carabiners commonly used for this application are about right? I haven't heard of one failing yet, so I'm guessing it would be within a safe range.

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