Stoppers in Horizontal Cracks

OK, so we might be a *little* biased here....

but yes, TRICAM EVOs!

Eric Moss wrote: This is a very unsound nut placement for catching a fall. When fallen on, the wires will cinch together, thus creating a near 180 degree angle in the connection and producing overwhelming force on the nuts. It is for this very reason that we always want to minimize the angle in the connection between two pieces. There are several variations of this deadly setup, one involving a sling as seen here: climbing.com/skills/nuts-101/ The correct version of this placement can be found in Climbing Anchors by John Long and Bob Gaines. It requires connecting the two pieces with clove hitches to maintain a safe angle by preventing cinching.

Great idea - but sometimes in practice you get far less than optimal, like when the wires on opposing stoppers in a horizontal overlap each other and putting in a clove hitch won't allow the stoppers to hold each other in the crack. The cinched arrangement in the photo is better than nothing.

BTW, I've taken a factor 0.75ish 20'er on exactly such an arrangement. It held fine despite the dire warning in your post. Yeah, shocking, I know - I should have died. Climbing gear is often stronger than people think it is and maybe not nearly so "deadly [a] setup".

Here's the math:

Assuming the angle in these cables is 160 degrees (a generous assumption as the angle is probably even greater), the force on each nut is

1/2*sec(80)*F

Where F is the force exerted on the anchor (which, by the way, is greater than the force of the falling person, due to the pulley effect in a lead fall)

Thus, the force on each nut is approximately 2.88*F, almost 3 times F!

F can be calculated for various situations here as "peak force on protection": junkfunnel.com/fallforce/

Be safe...or not, I don't care.

Junkfunnel is well-named; it is junk. It performs a calculation based on the static elongation of the rope; this is guaranteed to be off.

And the proposed rigging math is wrong as well---and in two ways. First, the given formula is wrong; it should be (1/2)*F*sec(80) (not tan(80)), which would give an even higher anchor load in the situation considered. But because one nut is threaded through the other, we have a pulley situation and none of the fixed power-point calculations apply.

Because of the pulley effect (and ignoring friction), the left-hand piece gets the load applied to the anchor, and the right-hand piece gets up to 40% more than that. Neither of these is even remotely three times the load applied to the anchor, which is not to say that an extra 40% on the right-hand piece is not cause for concern. However, rigging in such a way that the angle at the power point is lower may not work at all for such placements, and then you have nothing, which hardly addresses the "be safe or not" challenge.

Moreover, if you can't use extensions to lessen the angle (because of the outward loading prohibition) and have to live with, say, a 160 angle, then you are far better off with the pulley rigging posted by the OP than with anything that makes a fixed power point and produces those near-triple loads. This means that Eric's argument is actually a strong argument in favor of, not against, the OP's set-up.

The set-up may or may not be ideal---this had already been covered before the recent posts---but it isn't necessarily the lurking catastrophe suggested either, and the potential utility of such arrangements is confirmed by folks like Mark---and he isn't the only one---who have actually tested them with real-world falls.

To recapitulate: the illustrated set-up, though not ideal, can be the only viable solution when the placements are close together and the rock configuration makes it imperative to minimize any outward loading. The piece you thread through the eye of the other piece should be the "weaker" one if you can tell, since it is the pulley piece that gets the (perhaps around 40%) higher load.

Now for the caveat: To the extent that friction of the threaded wires impedes the pulley effect, the loads on the pieces might turn out to be higher. If they are much much higher, Eric could be right. Only some actual testing could settle that issue.

You're right. It is secant. You're wrong about everything else.

Care to elaborate?

To give you more ammunition, here's my reasoning. You might have to enlarge the picture to read the math. (Click on picture, click "view full size," click to activate magnifying glass.) As you can see, the "40% larger" claim came from the square root of 2 multiplier.

I appreciate your analysis and I don't doubt its accuracy in a frictionless environment where the cables are long enough to allow equilibrium in tension in the right stand. However, as I'm sure you're aware, both friction and cable length impede this equilibrium, not to mention kinking of the cables.

You've shown that there is a possibility of a sound placement of the type in question. As a general practice, it's still a bad idea unless we can be sure that at the moment of peak force on the protection the tension in the right cable will be constant.

As to your criticism of the force fall calculator I linked to, I'll just say that I'd love to see a better estimate of fall force. To that end, here is perhaps a more useful estimate: blackdiamondequipment.com/e…

As I said, actual testing of pulley-type horizontal placements would be required to pin down the loading, but I don't think wire against wire friction will play a particularly significant role in modifying the results I suggested. That's just a hunch of course. Connecting with clove hitches as in the diagram in Long's book isn't practical when the pieces are closer together and are judged to be unable to resist outward loads, not to mention the fact that setting up something like that one-handed while hanging on for dear life is going to be challenging.

As for online fall force calcualtors, all the correct ones I've seen use the most elementary rope model that treats the rope like an ideal spring. You can find a pretty complete account of that at 4sport.ua/_upl/2/1404/Stand…. There's a boiled-down equation there that is easily used on a scientific or graphing calculator or inserted into a spreadsheet. Everything we know from testing, and what we would expect from the assumptions made, is that this equation typically overestimates the forces.

There used to be a calculator at myoan.net that was total garbage; I just checked and it (finally!) seems to have been taken down. There is also a spreadsheet at multipitchclimbing.com which, I'm sorry to say, doesn't seem to agree with the physics of the situation. Of course the Petzl calculator is long gone, and an accurate one by jt512 is gone as well.

I can't see what is under the hood at junkfunnel, but the fact that the calculation is based on static elongation is a red flag, because manufacturers engineer their ropes to have as small a static elongation at low loads as possible that will still be consistent with a relatively high dynamic elongation. These elongations are used in the force formulas to estimate the Hooke's Law constant (or rope modulus) and the static elongation is going to provide an inaccurate estimate.

In the referenced note, the manufacturer's UIAA impact force rating is used to get the rope modulus; is will be a better estimate for the (linear part of) the load curve.

If you want better estimates than the standard equation provides, there are various papers, mostly in engineering of sport journals, that describe models claimed to be more accurate. These all involve solving systems of differential equations and so typically require industrial-strength computer solvers.

Can Camp stop using MP forums to throw advertisement... seriously?

You say the force calculator should use the ideal spring model, but not use static elongation. This seems contradictory.

Also, you're not addressing the worst case scenario here. Are you seriously endorsing this stopper configuration as a general practice?

Eric Moss wrote:You say the force calculator should use the ideal spring model, but not use static elongation. This seems contradictory.

Not in the least---we know the rope doesn't behave like an ideal spring. The load/elongation curve isn't a straight line, it is S-shaped. But there is a significant portion, between the very low loads and the very high loads, that is much more nearly straight and so is better approximated by the spring model. In order to get that approximation to work, you want to sample a load/elongation point from the straight part of the "S." Using the static elongation samples the very bottomost part of the "S" and so will make the model even less accurate than it should be.

Eric Moss wrote: Also, you're not addressing the worst case scenario here. Are you seriously endorsing this stopper configuration as a general practice?

No, if you read back, I issued a warning about that configuration long before you did. Subsequently, I just said that there are circumstances in which it is reasonable choice---and in some cases might be the only choice---and that the loads you predicted were far bigger than one has any good reason to anticipate. And then finally, something I frankly hadn't thought of before that emerged from the calculation I posted is that in some cases, the pulley arrangement might be better than a hard connection.

What about using some bungee cord tension the opposed nuts together and clipping only clipping the downward force nut to the rope?
no pulley effect, no cloves, and you still have tension holding the nuts in opposition

I've stacked nut BITD but with tricams and small cams I don't bother with that anymore.
As for you won't snap a wire; you can. I've Snapped small wires in horizontals.

eli poss wrote:What about using some bungee cord tension the opposed nuts together and clipping only clipping the downward force nut to the rope? no pulley effect, no cloves, and you still have tension holding the nuts in opposition

Great, if there is indeed a "downward force nut". What we're talking about here is where the potential holding power results from the two nuts being pulled toward each other at the time of impact. In the less than ideal situation where the nuts are too close together and you wind up having to use the looped/pulley arrangement, yes, there will be more downward/outward force on the one nut, but most (we hope) will still be horizontal.

No one is saying this is ideal and a standard procedure. Sometimes you just have to deal with what the rock presents.

I realize now that peak force on the anchor only occurs after the rope has finished stretching. This implies that the force on the anchor and the friction between the cables will gradually build, allowing for the tension in each strand to equalize.

Given that there is length in the stands to equalize tension and barring binding that would prevent equalization, I think rgold's estimate will prove to be quite accurate.

Thank you, rgold.

I am 125 feet out from the belay and eight feet above my last piece looking at a horizontal which is the only protection around and will only support opposing stoppers at 180 degrees. The next 10 or 12 feet have holds but no protection. What am I going to do argue with myself about what is the best placement? While it is good to know what is optimal in reality you take what you can get.

I've been considering the implications of the capstan equation in this scenario. Granted, it doesn't apply directly to stiff wires such as nut wires, but it does apply to slung-together opposed horizontal nuts and it could elucidate the wire-through-wire situation as well.

According to the capstan equation (with a friction coefficient of .66), a sling with a 1/6 turn around a carabiner would not have equal tension throughout, but a 2:1 tension disparity.

What do you think of using the capstan equation to adjust the model for the opposite horizontal nuts?

Also, another thing that the current model overlooks is the effect of off-axis (likely including an outward component) loading of the nuts that occurs in this configuration. I don't expect any model to approach this contingency, but I think it's fair to assume that each nut will be loaded in a direction that undermines its steadfastness.

Eric Moss wrote:I've been considering the implications of the capstan equation in this scenario. Granted, it doesn't apply directly to stiff wires such as nut wires, but it does apply to slung-together opposed horizontal nuts and it could elucidate the wire-through-wire situation as well. According to the capstan equation (with a friction coefficient of .66), a sling with a 1/6 turn around a carabiner would not have equal tension throughout, but a 2:1 tension disparity. What do you think of using the capstan equation to adjust the model for the opposite horizontal nuts? Also, another thing that the current model overlooks is the effect of off-axis (likely including an outward component) loading of the nuts that occurs in this configuration. I don't expect any model to approach this contingency, but I think it's fair to assume that each nut will be loaded in a direction that undermines its steadfastness.

Whatever makes you happy to think about. But reread the post above yours - what does it matter? Here it is again:

beensandbagged wrote:I am 125 feet out from the belay and eight feet above my last piece looking at a horizontal which is the only protection around and will only support opposing stoppers at 180 degrees. The next 10 or 12 feet have holds but no protection. What am I going to do argue with myself about what is the best placement? While it is good to know what is optimal in reality you take what you can get.

Marc801 wrote: Whatever makes you happy to think about. But reread the post above yours - what does it matter? Here it is again:

You're right. Anchor strength doesn't matter. Science is stupid!

Eric Moss wrote: You're right. Anchor strength doesn't matter. Science is stupid!

We're not talking about anchors - the pic that started all this is a mid-pitch protection point.