American Death Triangle is a Myth

The Myth
01:11 Setting up
04:09 1st Test
06:15 2nd Test
07:23 3rd Test
10:25 4th Test
11:46 Testing Rappels Wide
16:35 Testing Rappels Normal
19:00 Giant Sliding X
20:56 Conclusion
23:24 How to build a proper anchor

[garychap]

Ahhh.... the good ol' 60-60-70 triangle! Buy yourself one today!

_(offer only good on convex surfaces)_

[jonnigs]

Great video as always!

The only way to get a perfect 50/50 load sharing is to have an angle of 0° between the bolts, in every other case the sum of the load on the bolts will be more than 100%.

The load multiplication of the death triangle has to do with the top strand being free and allowing the bolts to pull on each other. The numbers from the calculations assume no friction, to get similar results on the dynos as expected you will have to add pulleys on the top angles (not really a real world scenario though...).

[FerretyWeasel]

A good way to think about it is that the anchors must not only support the vertical load, but also the load against each other. One anchor is loading the other horizontally, hence the higher load than 50%

[nicktoozoff]

In Australia, I was always taught that the ADT was called such because there was no redundancy built in.

[MrJoebass]

Your opening comment about taking F2 falls on American Death Triangles on unsheathed ropes is literally something I think about every time I rig slacklines and then I just say to myself "hmmmm it seems like people have been doing this and been just fine for decades so its probably alright" but this episode is what I have been waiting for all along!!!

[bowins]

If you look up crane rigging deductions and theories, it explains in great detail how sling angle changes forces in relation to vertical load. 45 degree angle in sling multiplies force by 1.41 compared to a vertical force. So 1 kn vertical force will produce 1.41( barring strange friction forces in the rig) kn of force.

[NickDangerThirdGuy]

When I started climbing at Josh in the late 70's, I learned that the Death Triangle was the typical arrangement of 3 button head bolts, center being higher, with countless loops of sun bleached webbing threaded through them. Often so many webbing loops that you couldn't get anything more through the eye of the bolt. Bolts were commonly all within 2 ft and the webbing was looped in a triangle through all three. It was practice at the time to just connect through the webbing loops without equalizing the anchor at all ( (3:58) picture the loop of webbing around the piranha in the video). Pulling on the longest span of webbing often left the angle at less than 30 deg. which greatly increases the load on all angled legs of the "system". The basic idea being that it was very easy to exceed the ability of the system since all aspects of that system were pretty sketchy to begin with. Manky webbing (albeit a lot of webbing) and 1/4 button head bolts. This did not inspire a lot of confidence. So NOT a myth just a safety tip that has probably outlived its necessity.

[collinrottinghaus]

You guys are idols of mine. I appreciate how selfless, generous, & absorbed in the science you guys are. I appreciate that you guys live life for fun, but also work hard to improve the fun of others

[DHClapp]

Explanation of what's happening with belay setups, starting around @17:00:

(For clarity of language, imagine the setup on a wall or rock face instead of on the floor, so that we have a clear "up", "down", "left", and "right".)

In the up-down direction, each leg of the triangle IS supporting 1/2 of the force on the static line. But in addition to that, they are also experiencing force in the left-right direction. The belay device is pulling both chains down, but it's also pulling them toward each other. And the angle of the "legs" of the triangle determines exactly how much.

You can intuitively understand this if you think about a 50-lb. static load on the end of a rope hanging at your waist level in front of you from a point a few feet above you. If you want the rope to be at an angle instead of straight up-and-down, you can pull sideways on it. The harder you pull sideways, the more of an angle you can put in the rope. If you pull with just a couple of pounds, you will give the rope a slight angle. And if you pull with a whole bunch of force, you can make the rope almost horizontal. As we increase the angle of the rope, the up-down force remains the same — it's just the 50-lb weight. But the left-right force increases. Which means the total force being resisted by the rope is always at least 50-lb., and can be a lot more if we're really pulling it hard sideways.

It's the same any time a rope (or chain) is at an angle. It's always resisting force in the up-down direction, and force in the left-right direction. How much exactly is a little more complicated, because trigonometry.

If you're super curious and want a quick sanity check in a "death triangle" or anchor situation, you can use the formula below (or consult the cheat sheet at the end of this comment). In a two-anchor situation like at @17:00, the total force on each chain is

1/2 x F x sec(Ø ÷ 2)

where F is the force on the line and Ø is the angle the ropes or chains make where they meet. sec is the notation for secant (pronounced see-kuhnt), which is one of the trigonometric functions like sin and cos.

So if the angle at the belay device is 90°, the force on each chain is 1/2 x 1.83kN x sec(45°) = 1.294kN.

If the angle is 60° (a narrower triangle), then it's 1/2 x 1.83kN x sec(30°) = 1.057kN.

If the angle is 120° (a wider triangle), then it's 1/2 x 1.83kN x sec(60°) = 1.83kN. Which means with a wide, 30-30-120 triangle, the total force in each leg of an anchor should be exactly the same as the total load on the line!

If the angle is 133°, which is the angle in the setup at @20:42, then the force on each anchor should be 1/2 * 2.16kN * sec(66.5°) = 2.708kN, which is very close to what you found.

At 178° (meaning the chains are so far apart they're being pulled just 1° down from directly horizontal), the total force on each anchor would be 1/2 x 1.83kN x sec(89°) = So don't do that.

Obviously, the value of sec(Ø) increases a LOT between 133° and 178°, i.e., when the triangle is super-duper wide, but that's beyond the angle most people would try and get away with. However, this kind of multiple does come into play when calculating the total tension on a slack line.

Finally, here is a bit of a cheat sheet for equal-length dual-anchor setups with approximate values:

Angle Force on each Anchor

20° 0.5 x load
60° 0.6 x load
90° 0.7 x load
120° 1 x load
140° 1.5 x load
160° 3 x load
170° 6 x load
176° 15 x load (pretty close to horizontal, like a stiff slack line)
178° 30 x load (nearly horizontal, like hanging something from the middle of a very tight line or chain)

[jakepawlak]

This is obviously more of a warning about vector forces in anchors, but you can also use the vector force multiplication to your advantage. It's a rescue technique that is taught to tower climbers and I've used it when we rigged the 1km in Oregon to pull in just a bit of slack.

If you have a rope that is anchored at one end and a casualty on the other end that needs to be lifted slightly before being lowered, you can put your body weight on the tensioned rope and it will lift your casualty up slightly allowing you to detach them from whatever they are weighting before being lowered.

[alextemus]

Just a note that was never explained in the video: the top side of the triangle will always have lower force than the two other sides due to the friction of the rope/webbing going around the corners at the anchor dynamometers. Each of the readings that are on the top length of the triangle are probably around 70-80% of the force felt on the two sides that are directly pulled.

All the math problems we ever did in geometry classes are lies! They (thankfully) removed friction from the problems.

[runzombies]

Makes sense that the ADT performs worse than a sliding X with the same masterpoint angle. However, if you only have one sling, you can get a more acute masterpoint angle with the ADT than a sliding X. It would be interesting to compare the ADT to the sliding X if the same length of sling is used, rather than the same masterpoint angle.

[eddiec]

The vector chart assumes you have individual legs like a standard anchor. The ADT modifies the angle the anchor is pulling because horizontal leg at the top. When you have an equilateral triangle your strand is 60 degrees from horizontal but the anchor is pulled at 30 degrees (look at the angle the anchor is pulling). That means the anchor feels the force as if the master point is 120 degrees. This totally checks out with the test at 7:27. 2.9kn/2strands * tan(120/2)=2.5kn which is super close to 2.46kn.

[rogerpalin]

I’m a qualified mountaineer, and commercial rope technician and think your channel is awesome and has definitely added to my knowledge and understanding. At the moment I’m seeing so many American videos on YouTube or Instagram posted by “rock guides” or so called IFMGA guides, that are doing so many dodgy things and posting them as educational. Such as unequalized, unloaded systems, using dual fixed point bolt anchors but then putting the load on one bolt. Anchor points that include a triangle of death, but in a belaying scenario that could end up shock loaded. It seems, all in the name of speed, lightweight, “innovation”. What is going on with the climbing instructors?

[zu]

is it just me or is Bobby like the best Human being ever?

[ALRinaldi]

Is that a dynamometer in your pocket or are you happy to see me…

[topselftuning]

another good and informative video - thank you. Coming from industrial climbing (rope access) my experience is that no matter what you show it will always be picked apart for what is perceived as wrong... instead of oh thats a new way to solve this challenge. Having said that - be sure when building an anchor that you check that your locking carabiners are locked... thank you

[colinwatt]

This video reminded me of something I’ve wondered about (and also a possible video idea). I’ve seen AMGA certified YouTubers suggesting the use of dedicated top-roping quick-draws with locking carabiners. If you orient them with both spines against the rock will you compromise strength of the dogbone (which would have a 90deg twist)?

Note: I believe the benefit of using them in this orientation is to keep the rope away from the rock to prevent it from being pinched or rubbing, thus adding a lot of friction to the system and prematurely wearing your rope. Additionally, since they are both locking quick-draws the concern about the rope unclipping itself is eliminated (barring human error).

[jluwufj]

When you do the "regular" rappelling tests with the rope through the caribiners (with the caribiners touching) - you don't see the force multiplication because the sideways forces from when the regular death triangle has the bolts pull on themselves are "skipped" by the caribiners directly pushing on each other. The rope pulls them together and they transmit the side-to-side forces against each other metal against metal. So you are only left with the more direct vertical forces. The only way to rig the system so the caribiners don't touch is for either for the rappel rope to be rigid between the biners (not a thing) or for the bolts to be farther apart.

Essentially - the death triangle only "works" as a death triangle if your anchor legs/bolts can't touch each other

[davidtorres]

Great explanation of Kilonewtons! A lot of my friends ask me why climbing gear isn’t rated for pounds of force. Knowing that is only as good as knowing the forces you’re generating. Your videos are such a good resource for that! Thanks!