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%
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...).
Yeah, for more useless testing, I would love to see same tests with pulleys. I assume the reason the force on the top stand is consistently low is the friction at the top corners.
I don't think this is correct, in the triangle configuration I worked out the best case scenario was square root of 2 times half the supported force, or about 70% of the force at the master point, but never 50/50
@@robmckennie4203 Sqtr(F/2) means you have 90° at each anchor point, that means that the points have to be touching. If they are touching and the focal point is at 0°, then you don't have a death triangle any more. The "death" comes from the fact that the points are being pulled together as well as down. If the points are allready together then there is no triangle. So yes, my statement holds true. Even though I meant the first part for anchors in general.
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
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.
Friction doesn’t play apart unless there is movement. So yes, while they are pulling and the system is becoming more tight, the friction around those corners is going to have an affect. Once it’s static then the load is directly related to the angle from one anchor to the other. If you look at the top leg of the death triangle example and think of each of those top vertex angles as vector points between the primary attachment point and the opposite anchor point. You should see that load carried by each leg will be different, the shorter leg will be higher than the longer leg. Haha..😂 ..I hope that makes sense, rigging is difficult to put down in words alone. I need pictures….lots of pictures 😎✌🏼
@@maxwellmark Friction absolutely plays a role even in static systems. Static just means the sum of force vectors is zero, friction being one of those forces.
@@johnliungman1333 My reference to static is to imply it is not moving. In order for friction to be a component there needs to be movement. Since the sum of the vector points is zero than the friction component is also zero.
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.
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.
Only the last version shown is redundant regarding the sling, but by making a knot you also take some of the loadbalancing capabilities of the anchor version without the knot, Still I think I may use this anchor in the future cos I think that even with the knot the anchor is still well balanced specially if you tie the whole thing pointing into the direction of the climbers ascending below you in guide mode
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!!!
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.
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.
@@ethan3570 thanks for the masterpoint angle calculations. I was more interested in the forces on the bolts in those scenarios, though it shouldn’t be difficult to predict those given the masterpoint angles in each scenario.
I've climbed maybe 4 times in my life, but I'm addicted to this channel. The way I say to myself, "What I want to see next is..." pretty much as you cut to one of you saying, "We need to do this next..." I love it.
American caver. Was always taught that the issue was a lack of redundancy, not force multiplication. Pretty simple rule. If you have two anchor points have two independent loops in your rigging.
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
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.
This /\ I was just about to comment on it too. An anchor using the American Death Triangle is not a configuration that the force diagram in the video applies to. If you want to test the 180-degree-infinite-force thing you'd have to connect a sliding X to two opposing bolts so that the X ends up in the exact middle of them in a straight line (not possible in reality because the sling will always stretch a little but could get close enough). That will give you your "magical" extreme forces on the bolts.
You have to go pretty extreme to get cosine losses eating up much of your force. At a 30 degree angle (equilateral triangle), you are only weakening the whole thing by around 13.4% on paper. At 45 degrees, so a right triangle, you reduce the strength by 29.3%. That's significant but still allows a decent safety factor. At 60 degrees, you're basically reducing the strength in half. Keep in mind though, that is 120 degrees for the bottom angle on the triangle. In reality, harsh angles are needed for any severe loss of performance.
This video reminded me of something I’ve wondered about (and also a possible video idea). I’ve seen AMGA certified RUclipsrs 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).
The biggest issue is the direction of force vector in an ADT. Bolts or attachment points are usually designed to pulled toward the load, not horizontally toward each other. This can cause failure. Mathematically, force amplification won’t occur until the interior angles are greater than 120. 90 degrees is a good rule of thumb. The angle doesn’t matter on the chain when they are connected across the top. This was a rough one.
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
@@silvanmetz717 Just trying to dumb it down for lay-folk. You try to say "force vectors..." crap to regular people and they tune out. I'm trying to speak to their (incorrectly formed) intuition. Their confusion comes from building an incorrect intutition based on how the rope/sling runs rather than looking at the force angles. I was just saying that their intuition of force multiplication wasn't entirely wrong - that rope running that 180 through the biners pulls them together pretty hard - that's where some of their intuited force went.
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!
You guys rock! Just want to point out a practical application of the science here. Ever rap off an anchor with one bomber bolt and one really sketchy one? You might think that the sketchy one just carries half the load but now we know that isn't true. So, what if it fails, causing a sudden extension on the other. Hey! That would be a cool video idea! Chop one leg of the anchor and see how big the load is when you're tied in close then at increasing distances below the anchor. Keep up the good work!
Ok as a downrigger in the entertainment business for many years this was a brilliant demonstration of the loading forces. We generally love anything from a 30 to 60 degree angle in a two point hang (called a "bridle" in show vernacular) but may do up to a 90 degree angle if need be. I generally speaking don't like hanging angles above a 100 degrees as they begin to side-load roof trusses in a way that causes them to want to twist towards the direction of the force. Brilliant examination of this very showbusiness related subject. Great stuff! 👍
Interesting point. I would assume that the load on the second anchor would hit zero for a moment as the weight accelerated the very small distance to take up that little bit of slack and all of the textiles (rope, slings, harness, etc.) would start springing back (giving back any stretch they were giving up at the point of first anchor failure) and then the reloading and re-stretching in an instant and then put a little bit more load on the second anchor than what broke the first anchor. I would love to see the line graph of that one!
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 RUclips 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?
I like the way you California guys talk. Just the way you said, "Science!" at 16:45 made me think of "Bill & Ted's Excellent Adventure" starring a very young Keanu Reeves. LoL.
As a French guy who has been taught to use the "European death knot" I am curious about the result of the test with that one. And to add a comment on the ADT since that is the subject the death part is really the one you mentioned, there is no redudency and fi you break the sling due to a rock falling on it or rubbing against the rock you go all the way down.
@@joestevenson5568 I can think of a dozen different ways that could happen. All of which are likely in an accident situation. Rope in chipper, limb you’re on snaps, you accidentally cut the limb you’re on, limb you rope is on snaps, limb above falls and hits you. Some of these will also result in additional weight or force above your own body weight being applied. And while we are talking about typically 10-11mm static there is stretch to it as well. As many people travel from limb to limb (limb walking) there is the chance of a dynamic fall. But it’s not the rope that needs testing - it’s the knots… Some of which in recent years have been replaced by mechanical devices. Which also could use some testing. Since it’s no longer just a high line channel and now covers rope access sports and disciplines outside of just that - it makes perfect sense. “How not to” …. There are also people who climb trees for recreation as a hobby - as I have… It’s like a modified Trad/Aid climbing with a bunch of technical aspects that also fit well with canyoneering… And search and rescue rigging. There is a lot of cross over of rope access in many disciplines. And a lot to be learned from each. I’ve done SAR climbing work in the military and thought I knew a lot about rope work, I started climbing trees for fun a decade ago and found there was more to learn… SRT/DRT, a wide array of accent techniques, different knots and hitches - and a few that if you know them could save your ass alpine climbing… Since they are based on minimal or no equipment. eg I would be comfortable - and have rappelled on a Blake’s hitch. You can look into “recreational tree climbing” and ropes courses to learn more.
Hey! Try the death triangle combined with other common issue: carabiners with open gate. See how hard you need to pull to break an open carabiner on anchor with death triangle.
I would have really liked to see percentage numbers in addition to the raw values in KN. For example the lowest point always sees 100% of the load but the center point saw 40% in this configuration. You guys make such fantastic content. Please keep on keeping on!
I have fantasies of starting a climbing youtube channel where I explain the physics. I just really don't want to film and edit myself. I have offered myself to Ryan as a resource.
@@arnoldkotlyarevsky383 That would be pretty cool! I'd subscribe to that :) This one got me pretty confused though, How are both the anchors seeing almost the total force input at the same time? Is it not doing work at all?
1) By symmetry, the 2.47kN force is supported equally by both sides of the triangle. So each side takes 1.24kN - but that's vertical. The diagonal force must be 1.24 / cos(30 degrees) = 1.43kN 2) Account for friction. Typical pulley efficiency over a carabiner is 60%, but that's for a 180-degree bend. Here we have 120-degree bends, so en.wikipedia.org/wiki/Capstan_equation predicts pulley efficiency = 0.6 ^ (120/180) = 0.71. 3) 1.43 kN * 0.71 = 1.01 kN - predicted force on the horizontal line ("C"). 4) To get the force on the anchor points, we use 2 trig equations. The first equation figures out the angle at which the bolt is being pulled via equilibrium along the axis perpendicular to that. Probably needs a picture, but basically 1.01 * sin(a) = 1.43 * sin(b), where a + b = 60 degrees. This is a transcendental equation best solved by trial and error, giving a = 35.5 degrees and b = 24.5 degrees. Then the force on the anchor points is 1.43 * cos(24.5) + 1.01 * cos(35.5) = 2.1kN ("A" and "B"). For practical purposes, the transcendental equation in Step 4 can be avoided by pretending a = b = 30 degrees. The result - (1.43 + 1.01) * cos(30) - still rounds to 2.1kN. But apparently the pulley efficiency here turned out to be 0.9 / 1.43 = 0.63.
@@thiagoennes The response above is good. A possibly more intuitive way to interpret the measured forces is: [in the case of the ADT] If the anchor bolts were right next to each other, then all of the force would be going into them in roughly equal measure. Makes sense, right? As you separate the bolts, the applied force does not change but some additional amount of force is required to keep the bolts separated (this force is supplied by the rock the bolts are anchored to). The greater the separation, the greater the force. At 60 degrees of separation, the force required to keep the bolts separate is equal to the force applied by the climber. at 120 degrees, the force on each bolt is almost double the applied load from the climber. As you approach 180 degrees, the force required to keep the bolts separated approaches infinity. This is, of course a simplification since the anchor material stretches, and there is friction in the system which complicates the whole scenario. The math for the simple case is fairly trivial, but if you want to describe an asymmetric load, or if you want to add friction, or both, the maths gets weirdly hard. Im working on it!
Hey guys I have a few simple rules when setting anchors. I sure you already know this but just to say my thing. FYI I come from a climbing but predominantly industrial background. Anchors should be installed at a minimum of 10 x the diameter of the bolt apart, the further the better thus minimizing the conning effect. If you want to form an equilateral triangle of 60 degrees than all you need is three sides of the same length. Ryan how come you don’t use a jumar to tighten your pulley system instead of your hand? Have you guys come across the Harkin hand winch built for a rope access application? One side gives you a 3:1 mechanical advantage and the 2nd configuration gives you a 10:1 mechanical advantage. Bolts to the ground and is compact and great for compressed (small) mechanical advantage.
when you visualize the forces in your anchor, it helps to see the forces in between the two bolts, separately from the forces along the axis of pull. So you have a) the axial force through the master point and b) the force between the bolts. The Cosine of the angle, gives you the horizontal force between the two bolts. With that, you can easily see how all the forces add up.
Will be impossible to share the load between the two bolts as long as you loop through. Because you will always have the rope pulling towards eachother as well as pulling down.
These results are important, because if you watch to the angles of the forces, one can see that this is the same with those lifting loops - the purple one in the background on the mashine. The wider the angle the more multiplies the force on both ends. In this case the force mashuring devise is the climber and the other two ends are the ankers, if one want to compare with a crane lifting a load up with a rope which is in such a wide angle. In your experiment, if the rope was tide down on each chain sepearedly, the force onto the ankerpoints should be sharing the load by almost half, when these rings are still close together. Because the rope is going though, the effect is like those lifting loops used in a very wide angle. Sorry for my English, but it is not my first language. You guys are the best. Your topics are great and with the breaking test is so much to learn about "gear fear" and what to keep in mind, if one is using those equipment. Best wishes and be save. Jan v. Baumbach - Germany
NOTE!! What is shown at 12:00 is very different from the test setup. There are no force magnifying triangles at 12:00, but the test setup using 1 atc creates a triangle. Force wise the 12:00 setup is just fine.
Very good video. Confirms what I always suspected. ADT isn't so bad, Atleast on bolts. Trad gear a differnt story. Though on nasty alpine routes I've rappelled off many single nut anchors. Fixe rings are standard top anchors for sport routes around here.
From about 12:00 on, running a rappel rope through two rings that are separate does magnify the loads on each bolt. Ideally, the solution is to have chains long enough to hang down far enough to make a lesser angle - but not have two separate rings, at all. Instead, join the two chains with one or two links, and have the rope run just through that, eliminating the horizontal section of rope altogether. Visualize the chains as two lengths of webbing, and the idea is clear. There is no purpose served by creating rings apart. Once again, modern practices have arisen without thorough considerations of the various consequences, and just because bolts ordinarily are assumed "bombproof" does not mean one should routinely use them in ways that tend to multiply forces.
The reason the chains take less force is because you do not have the added force from the line between the two bolts. When you make the continuous line into a triangle the bolt points are acting as pulleys and directly loading each other along the top.
Would like to see 2 bolts with a tensioned steel cable between them, then put a carbiner in the middle of that span, clip a rope to it as a toprope point, seen this set up in some areas...
I feel that the ADT is a lot more concerning on ice or rock routes where you've placed your own protection as it can pull at less predictable angles as compared to other anchors. I've never been concerned when I'm on well bolted anchors of anything breaking. I have been concerned that trad gear might pop if pulled at an angle other than downward.
Not sure if I got it right, but here goes: Assume X is the master point force, Y is each bolt's force, and A is the angle between the lines coming from the master point and going to the bolts. Take the vertical components of the angled lines and add them together. That equals the downward force. 2*Y*cos(A/2)=X The force on each bolt Y = X / (2 * cos (A/2))
On rewatching, at 17:00 and 21:00, finally the realization that the top horizontal strand of the ADT is totally different from a single, taut strand weighted in the middle, where significant magnification of load is possible. If frictionless pulleys were substituted for biners(which add friction that reduces transfer of load), tension on a continuous strand will be equal all the way around; at each bend, both sides exert the same force, and the angle between determines the single resultant force on that point, as the dynamometers were set up to record. Practically, the triangle 1) makes the effective angle on each side shallower, hence slightly increasing their share of load; 2) the main risk is a cut sling, with no isolation to add redundancy, not so much the risk of the triangle causing failure; 3) the horizontal portion of the rappel rope as run directly through rings, will basically equal the applied load below, no matter what the setup involves; the angles at the respective bolts may change, which can increase the load there, but under rappelling loads, never to a dangerous level. A taut cable between bolts, with a ring midway, is about the only configuration which might magnify loads on the bolts beyond a safe level. Another aside, is that isolating loads from two bolts in a 30-45 degree Vee requires no extra "sliding X" because if one side fails, the shift onto the other side involves a very small pendulum of a foot or so, and drop of just inches; equalization tricks can actually increase the distances and shock, tho still negligible.
The reason the force on the bolts will never be half the force at the master point, in the triangle configuration, is because the bolts still have to support the tension on the rope twice. The best case scenario is having the bolts very close together and the master point very far away, and in that setup the tension on the rope will be half of the force at the master point, and the bolts will have that tension pulling in 2 directions 90 degrees apart. Because it's 90 degrees you can just use Pythagoras, square roof of 2 because the forces are equal, so the total force on the bolt is square root of 2 times half the force at the master point, so call it 70%. The angle at which the force on the each bolt is equal to the force at the master point is also a cool geometry problem, but i couldn't do that one in my head
just some formula, at 19:20, based on the way you measured angle, the 60 deg, i believe formula would be something like: Per sling load = main_load / ( 1 + cos(angle/2) )
This is first year classical mechanics, applications of newtons laws. If you vary the angle then the force of tension will be different. All you need to know to calculate the forces in terms of that tension is the angles and the kilo newton reading. You can decompose the forces acting on the angled straps summing the x and y components to zero assuming the system is at some point in equilibrium. Then you can set up a system of equations and substitute one of the angled forces in terms of another. Then with this A=T/(cos(theta)tan(theta)+sin(theta)) you can vary the angle and see mathematically what the forces will be without doing this experimentation. If you don't make that assumption then you would need to calculate the acceleration by using the 1D position equation in kinematics. Which is the approach I would use when you do those drop tests
Hey ! I'm 2 years late for commenting but I just discovered your channel 😅. Anyway, this stuff is kinda basic for me being a mechanical engineer but I love that you're taking the time to test it all ! I laughed a bit when you thought that when using chains and basically just moving your measurement point you'd get a different result with the same angle ! Anyway, keep it up !
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°) = 51.43kN!!!!!!! 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)
There's a reason that the tension in the ADT anchors at 60° angles doesn't match up with the sliding X at 60° angles. When you have the equilateral triangle tensioned, if you look at the angles that the anchor point load cells are being pulled at, they are NOT 60° with respect to the master point vertical line, even though the ADT angles themselves are. I suspect that if you set up a sliding X so that the pull angle of the anchor lines are the same as the pull angles of the ADT anchor lines, they would be a much closer match in tension numbers.
Since the corners can pivot on the linkage of parts, and the friction of the strap over the carabineer isn't that high, best case you would see only a small change in the values. Maybe a couple percent IMO. They could get the same effect by shaking the straps around to cause any uneven forces held back by friction to slide and disapate.
@@court2379 Gotta disagreee. I believe Friction is the only thing not accounted for in math, this would explain the huge discrepancy between measured results and calculated. Imagine the extreme, 100% friction, (clove hitched on) there would be zero tension in the center of the triangle. @mitchell - I agree, would love to spend about 30 episodes just on DMM revolvers.
Interesting video. I had never considered the vector forces at play here. I always though the American Death Triangle got its name because it has no redundancy.
I think you’re not taking into consideration that when you make the triangle you’re making two pulleys that are pulling towards each other multiplying the force. Look up an example where someone uses a winch to pull a vehicle that is stuck off road. If the winch is rated at 12,000 pounds that’s what it can pull. If you take the winch line and take it through a pulley back to the vehicle with the winch on it it pulls double because you’re reeling in 1’ of cable but only moving 6” with nearly twice the force.
:thinking: Huh, good point on “you almost may as well be using just one anchor” with the American Death Triangle, which I suppose is the whole point of avoiding it. It’s not that you’ll be absolutely overloading your anchors or slings, if it were that bad, no one would ever be using death triangles because they would just be so inherently dangerous that trying it even once would kill you. One can get lucky a whole bunch and manage to avoid injury just by using one anchor all the time as well, it’s all about preparing for that time when things _do_ go wrong, and in the death triangle, you just don’t have an redundancy, _and_ you’re loading your anchors more than 100% of the actual load.
The triangle basically turns the carabiners into opposing snatch blocks. The middle of the line between them will become the floating anchor point and they will then both multiply any force you put through them.
WRT Units: The US Customary/Imperial system is, as usual, confusing. Pounds (lb) are a unit of weight (mass * gravitational acceleration) instead of mass, except for the US customary pound which is defined as exactly 453.59237 grams (mass). Pounds-force (lbf) are a unit of force (mass * total acceleration). There are actually several different types of "pound", used for measuring the weight of different materials. For this, I'm considering only the Avoirdupois pound (the normal one). Otherwise you get weird effects like a (Troy) pound of gold weighing less than an (Avoirdupois) pound of feathers. Slugs are the Imperial unit of mass, but they're almost never used. Instead, the US defined pounds to be a unit of mass, instead of weight as was traditional. In this system Newton's second law isn't F=ma, it's F=ma/g_c, where g_c is 32.174 lb * ft / (lbf * s)^2 In US Civil Engineering there's also the unit kip (thousand pounds-force). 1 kip = 4.44822kN. This is mostly important if you're setting up a climbing gym or similar, since the rated forces the walls and other structural elements can withstand will likely be in kips. In the SI system kilograms are the unit of mass, Newtons are the unit of force (mass * acceleration), and there's no explicit unit of weight. In this system, Newton's second law IS F=ma.
TLDR: Still don't use the death triangle because it's stupid, but there are misunderstandings in this video. The only reason there is more force on those bolts is because of the mechanical advantage of having the rope go through both in series. If you connect the rope to each by threading it back to the main anchor like a tight V, it simply splits the force. The assistant guy mentions this at 18:00. It's because the ropes are going through the carabiners separately. There is also another difference which is the velocity of the force. The amount of force being put on the bolts in a death triangle is less velocity than in a V shape which does change the danger factor some. (in a 2:1 mechanical advantage the velocity will be half as much ish) It can't "share the load" unless it is connected to each bolt independently. The reason there is slight loss when doing a very acute angle is because of loss of force in the ropes themselves.
TLDR; the results you found were not at all surprising if you add the vector forces produced by each strand and use a bit of trigonometry. In your rappel example, even if you're very far below the anchor so that the angle goes to zero, the ropes make a 90* angle through both bolts, which means each bolt sees a factor of sqrt(2) (or cosin 45*) times the tension on the rope, which is half of the climbers weight. So in that case each bolt sees sqrt(2)/2 or 0.71 x the climbers weight. That's why the anchors don't "share the load", because the connecting segment across the top always adds another component of force that is perpendicular to gravitational pull. By contrast, if you have a very long sliding x (approaching 0 degree angle) both strands on each bolt pull down, so the vector forces are are parallel. In that case each strand carries 1/4 the climbers weight, and each bolt supports two strands, so each bolt supports half of the climbers weight, hence "sharing the load".
**So these measurements show that the endpoints of a ZIPLINE may be carrying DOUBLE the load of the weight of what is on the shuttle pulley. This helps to explain why there are so many zipline failures.**
The idea that the top of the triangle is experiencing some kind of force greater than the tension in either of the other legs is a bit odd. There's only two points acting on that part of the triangle - the tension in the sling pulling each end out until it's balanced. So the tension in that rope should only be about the same as the tension in any other point of the sling (otherwise, the sling would move through the karabiner at each end until it equalized.) It's only when there's some force acting on the middle of the rope or if a knot was jammed up against one of the points that it could change much. A tip: You can analyze a system of rope or chain *fairly* well by considering each bolt/piece of gear/pulley/karabiner as a point in space, then considering each point separately and drawing the forces on the ropes as vectors pointing in the directions that the ropes travel away from the point. This neglects friction and the weight of the ropes/gear, but in a lot of cases those are negligible (and when they're not, you can add those in, too). If you do this with any of the anchor systems you tested, you'd find that the force on each bolt is not just the force required to hold the climber up, but also some force pulling out to the side because of the angle. That's why you'll never see the load being shared all the way down to 50% unless the bolts are exactly in a vertical line.
"That's why you'll never see the load being shared all the way down to 50% unless the bolts are exactly in a vertical line" Could this explain why, as mentioned above in another comment, bolts in Europe tend to be placed one above the other?
To get 50% you'd need both bolts to be in line with each other (which isn't physically possible since they'd have to pass through each other). Having the extensions doesn't change anything.
Here's something to try. Put a line between 2 hitches of a 2 cars and pull it taught. Now put a biner and a rope to the middle. Pull the rope and you'll move the cars! Yhat's the force multiplier you are talking about. It's the tangent of the half angle and as it gets close to 180 degrees (a straight line) the half angle is 90 degrees. The tangent of 90 degrees is infininte.
This is assuming a static line. A dynamic line will comply and the angle will become less than 180 degrees drastically reducing the force multiplier. Look at the tangent of an angle and you will see that it drops off rapidly when you drop from 90 degrees towards zero. The tangent of the angle is the force multiplier. At least that's what I recall.
@HowNOTtoHighline if you did that last experiment (the 133 degree one), but with even higher angle (ideally 180 degrees) and with less stretchy material, you should see the forces on bolts to be multiples of your load.
American death triangle depending upon it being a V you have a equivalent weight lifting ability but when you do use it in a triangle 🔺️ connection you are adding a mechanical advantage to one side or the other. Mechanical Advantage look it up.
Dude Pythagoras. If Y is the direction of the load, then the y force on each bolt will be 50% of y. For a given angle away from Y the total force on each of the the bolts (along the hypothesis) would be (1/2* y)/cos(angle). Then use Pythagoras to work out the x portion of the force.
The more acute the angles the better, so don't drink while repelling or rock climbing because the beer goggles make the ugly angles look acute. Dad joke 101.
basic bridle math there, it starts adding up really quick the longer to make the base of that triangle, and can get really odd when you make it shift and start shortening one leg of it say with single legs rather than a looped sling
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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%
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...).
sohcahtoa!
and as we all know from thermodynamics zero friction is not a thing. funny side fact the english wikipedia didnt know that yet...
Yeah, for more useless testing, I would love to see same tests with pulleys. I assume the reason the force on the top stand is consistently low is the friction at the top corners.
I don't think this is correct, in the triangle configuration I worked out the best case scenario was square root of 2 times half the supported force, or about 70% of the force at the master point, but never 50/50
@@robmckennie4203 Sqtr(F/2) means you have 90° at each anchor point, that means that the points have to be touching. If they are touching and the focal point is at 0°, then you don't have a death triangle any more. The "death" comes from the fact that the points are being pulled together as well as down. If the points are allready together then there is no triangle.
So yes, my statement holds true. Even though I meant the first part for anchors in general.
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
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.
They could do it with Pulleys!! But I don’t think it would change too much… but what do I know LOL
Friction doesn’t play apart unless there is movement. So yes, while they are pulling and the system is becoming more tight, the friction around those corners is going to have an affect. Once it’s static then the load is directly related to the angle from one anchor to the other. If you look at the top leg of the death triangle example and think of each of those top vertex angles as vector points between the primary attachment point and the opposite anchor point. You should see that load carried by each leg will be different, the shorter leg will be higher than the longer leg. Haha..😂 ..I hope that makes sense, rigging is difficult to put down in words alone. I need pictures….lots of pictures 😎✌🏼
@@DJ-kg6zq You are absolutely correct….there is no friction in a static anchor. It’s all about the angles…👍🏼
@@maxwellmark Friction absolutely plays a role even in static systems. Static just means the sum of force vectors is zero, friction being one of those forces.
@@johnliungman1333 My reference to static is to imply it is not moving. In order for friction to be a component there needs to be movement. Since the sum of the vector points is zero than the friction component is also zero.
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.
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.
In Australia, I was always taught that the ADT was called such because there was no redundancy built in.
Only the last version shown is redundant regarding the sling, but by making a knot you also take some of the loadbalancing capabilities of the anchor version without the knot, Still I think I may use this anchor in the future cos I think that even with the knot the anchor is still well balanced specially if you tie the whole thing pointing into the direction of the climbers ascending below you in guide mode
As an American I was taught it was the lack of redundancy and the way lateral motion can cause abrasion to your sling.
Yes, that is why it is called that. Kiwi's know that too.
@@beyondthepale2023 you'd think you were sizing up to an Aussie, with that "Kiwi's too" comment.
@@smokingbluegrass we probably taught the Australians ...
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!!!
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.
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.
Ethan on paper a helicopter cannot do a backflip, in real life a helicopter can do a backflip. I did not read your comment, it is too long!
@@DJ-kg6zq The top 7 lines layout the approach, everything else is just repetitive text and a number.
@@ethan3570 thanks for the masterpoint angle calculations. I was more interested in the forces on the bolts in those scenarios, though it shouldn’t be difficult to predict those given the masterpoint angles in each scenario.
I've climbed maybe 4 times in my life, but I'm addicted to this channel. The way I say to myself, "What I want to see next is..." pretty much as you cut to one of you saying, "We need to do this next..." I love it.
American caver. Was always taught that the issue was a lack of redundancy, not force multiplication. Pretty simple rule. If you have two anchor points have two independent loops in your rigging.
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
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.
This /\
I was just about to comment on it too. An anchor using the American Death Triangle is not a configuration that the force diagram in the video applies to.
If you want to test the 180-degree-infinite-force thing you'd have to connect a sliding X to two opposing bolts so that the X ends up in the exact middle of them in a straight line (not possible in reality because the sling will always stretch a little but could get close enough). That will give you your "magical" extreme forces on the bolts.
I was about to point this out also. The free body diagram says it all.
Is that a dynamometer in your pocket or are you happy to see me…
Both😏
Weeeeell, we all remember how hilarious that was…about 25 years ago IIRC. GOOD ONE!!1!11!
You have to go pretty extreme to get cosine losses eating up much of your force. At a 30 degree angle (equilateral triangle), you are only weakening the whole thing by around 13.4% on paper.
At 45 degrees, so a right triangle, you reduce the strength by 29.3%. That's significant but still allows a decent safety factor.
At 60 degrees, you're basically reducing the strength in half. Keep in mind though, that is 120 degrees for the bottom angle on the triangle.
In reality, harsh angles are needed for any severe loss of performance.
Whoa whoa whoa. Don't mention sine, cosine, or tangent to these guys. They're doing backyard science, not designing nuclear reactors.
is it just me or is Bobby like the best Human being ever?
looks like it is just you and one other..... I forgot to add that Bobby is probably the first to think that.
This video reminded me of something I’ve wondered about (and also a possible video idea). I’ve seen AMGA certified RUclipsrs 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).
The biggest issue is the direction of force vector in an ADT. Bolts or attachment points are usually designed to pulled toward the load, not horizontally toward each other. This can cause failure. Mathematically, force amplification won’t occur until the interior angles are greater than 120. 90 degrees is a good rule of thumb. The angle doesn’t matter on the chain when they are connected across the top. This was a rough one.
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
This, sir, is total physics bullshit. No offence! But the real explanation are force vectors...
@@silvanmetz717 Just trying to dumb it down for lay-folk. You try to say "force vectors..." crap to regular people and they tune out. I'm trying to speak to their (incorrectly formed) intuition. Their confusion comes from building an incorrect intutition based on how the rope/sling runs rather than looking at the force angles. I was just saying that their intuition of force multiplication wasn't entirely wrong - that rope running that 180 through the biners pulls them together pretty hard - that's where some of their intuited force went.
Thanks for helping us be less obtuse about our anchors.
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!
This angle stuff is super important if using ice screws.
Not really. Ice screws are pretty multidirectional. Pitons and nuts, less so.
You guys rock! Just want to point out a practical application of the science here. Ever rap off an anchor with one bomber bolt and one really sketchy one? You might think that the sketchy one just carries half the load but now we know that isn't true. So, what if it fails, causing a sudden extension on the other. Hey! That would be a cool video idea! Chop one leg of the anchor and see how big the load is when you're tied in close then at increasing distances below the anchor. Keep up the good work!
Ok as a downrigger in the entertainment business for many years this was a brilliant demonstration of the loading forces. We generally love anything from a 30 to 60 degree angle in a two point hang (called a "bridle" in show vernacular) but may do up to a 90 degree angle if need be. I generally speaking don't like hanging angles above a 100 degrees as they begin to side-load roof trusses in a way that causes them to want to twist towards the direction of the force. Brilliant examination of this very showbusiness related subject. Great stuff! 👍
I think the scary part comes with is what happens in one anchor blows and how much force is applied to the remaining anchor
Interesting point. I would assume that the load on the second anchor would hit zero for a moment as the weight accelerated the very small distance to take up that little bit of slack and all of the textiles (rope, slings, harness, etc.) would start springing back (giving back any stretch they were giving up at the point of first anchor failure) and then the reloading and re-stretching in an instant and then put a little bit more load on the second anchor than what broke the first anchor. I would love to see the line graph of that one!
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 RUclips 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?
Ryan's oww makes him a human torque wrench.
That would be more like Gmnmnt - CLICK! But I guess he could BURP/BEEP!
I like the way you California guys talk. Just the way you said, "Science!" at 16:45 made me think of "Bill & Ted's Excellent Adventure" starring a very young Keanu Reeves. LoL.
As a French guy who has been taught to use the "European death knot" I am curious about the result of the test with that one. And to add a comment on the ADT since that is the subject the death part is really the one you mentioned, there is no redudency and fi you break the sling due to a rock falling on it or rubbing against the rock you go all the way down.
Fun fact: the flat eight kills more than the “European death knot”
Blake’s hitch drop test. As well as any other arborist climbing nots.
That would be sweet :)
How is a drop test appropriate for any arborist knot? You're supposed to keep static lines in tension always.
@@joestevenson5568 I can think of a dozen different ways that could happen. All of which are likely in an accident situation.
Rope in chipper, limb you’re on snaps, you accidentally cut the limb you’re on, limb you rope is on snaps, limb above falls and hits you. Some of these will also result in additional weight or force above your own body weight being applied.
And while we are talking about typically 10-11mm static there is stretch to it as well. As many people travel from limb to limb (limb walking) there is the chance of a dynamic fall.
But it’s not the rope that needs testing - it’s the knots… Some of which in recent years have been replaced by mechanical devices. Which also could use some testing.
Since it’s no longer just a high line channel and now covers rope access sports and disciplines outside of just that - it makes perfect sense. “How not to” ….
There are also people who climb trees for recreation as a hobby - as I have… It’s like a modified Trad/Aid climbing with a bunch of technical aspects that also fit well with canyoneering… And search and rescue rigging. There is a lot of cross over of rope access in many disciplines. And a lot to be learned from each. I’ve done SAR climbing work in the military and thought I knew a lot about rope work, I started climbing trees for fun a decade ago and found there was more to learn… SRT/DRT, a wide array of accent techniques, different knots and hitches - and a few that if you know them could save your ass alpine climbing… Since they are based on minimal or no equipment. eg I would be comfortable - and have rappelled on a Blake’s hitch.
You can look into “recreational tree climbing” and ropes courses to learn more.
Hey! Try the death triangle combined with other common issue: carabiners with open gate. See how hard you need to pull to break an open carabiner on anchor with death triangle.
I want Bobby to be 100% again!
We can rebuild him. We have the technology. We can make him better than he was. Better, stronger, faster.
6 million dollar man or Joe 90?
You could use a marlinspike hitch for when you need to pull on the line manually. Wrapping it around your hand and yarding on it is no fun!
Why is E.T. just hanging out in the background and not helping?
I would have really liked to see percentage numbers in addition to the raw values in KN. For example the lowest point always sees 100% of the load but the center point saw 40% in this configuration.
You guys make such fantastic content. Please keep on keeping on!
It would be pretty cool if you could get a physics teacher to explain the theory and compare it to the empirical data :)
I have fantasies of starting a climbing youtube channel where I explain the physics. I just really don't want to film and edit myself. I have offered myself to Ryan as a resource.
@@arnoldkotlyarevsky383 That would be pretty cool! I'd subscribe to that :) This one got me pretty confused though, How are both the anchors seeing almost the total force input at the same time? Is it not doing work at all?
1) By symmetry, the 2.47kN force is supported equally by both sides of the triangle. So each side takes 1.24kN - but that's vertical. The diagonal force must be 1.24 / cos(30 degrees) = 1.43kN
2) Account for friction. Typical pulley efficiency over a carabiner is 60%, but that's for a 180-degree bend. Here we have 120-degree bends, so en.wikipedia.org/wiki/Capstan_equation predicts pulley efficiency = 0.6 ^ (120/180) = 0.71.
3) 1.43 kN * 0.71 = 1.01 kN - predicted force on the horizontal line ("C").
4) To get the force on the anchor points, we use 2 trig equations. The first equation figures out the angle at which the bolt is being pulled via equilibrium along the axis perpendicular to that. Probably needs a picture, but basically 1.01 * sin(a) = 1.43 * sin(b), where a + b = 60 degrees. This is a transcendental equation best solved by trial and error, giving a = 35.5 degrees and b = 24.5 degrees. Then the force on the anchor points is 1.43 * cos(24.5) + 1.01 * cos(35.5) = 2.1kN ("A" and "B").
For practical purposes, the transcendental equation in Step 4 can be avoided by pretending a = b = 30 degrees. The result - (1.43 + 1.01) * cos(30) - still rounds to 2.1kN.
But apparently the pulley efficiency here turned out to be 0.9 / 1.43 = 0.63.
@@arnoldkotlyarevsky383 Please do this ^^ Ask students to film and edit, ^^ As a project..
@@thiagoennes The response above is good. A possibly more intuitive way to interpret the measured forces is:
[in the case of the ADT]
If the anchor bolts were right next to each other, then all of the force would be going into them in roughly equal measure. Makes sense, right?
As you separate the bolts, the applied force does not change but some additional amount of force is required to keep the bolts separated (this force is supplied by the rock the bolts are anchored to).
The greater the separation, the greater the force.
At 60 degrees of separation, the force required to keep the bolts separate is equal to the force applied by the climber. at 120 degrees, the force on each bolt is almost double the applied load from the climber. As you approach 180 degrees, the force required to keep the bolts separated approaches infinity. This is, of course a simplification since the anchor material stretches, and there is friction in the system which complicates the whole scenario.
The math for the simple case is fairly trivial, but if you want to describe an asymmetric load, or if you want to add friction, or both, the maths gets weirdly hard. Im working on it!
Hey guys I have a few simple rules when setting anchors. I sure you already know this but just to say my thing. FYI I come from a climbing but predominantly industrial background. Anchors should be installed at a minimum of 10 x the diameter of the bolt apart, the further the better thus minimizing the conning effect. If you want to form an equilateral triangle of 60 degrees than all you need is three sides of the same length. Ryan how come you don’t use a jumar to tighten your pulley system instead of your hand? Have you guys come across the Harkin hand winch built for a rope access application? One side gives you a 3:1 mechanical advantage and the 2nd configuration gives you a 10:1 mechanical advantage. Bolts to the ground and is compact and great for compressed (small) mechanical advantage.
when you visualize the forces in your anchor, it helps to see the forces in between the two bolts, separately from the forces along the axis of pull. So you have a) the axial force through the master point and b) the force between the bolts.
The Cosine of the angle, gives you the horizontal force between the two bolts. With that, you can easily see how all the forces add up.
Will be impossible to share the load between the two bolts as long as you loop through. Because you will always have the rope pulling towards eachother as well as pulling down.
These results are important, because if you watch to the angles of the forces, one can see that this is the same with those lifting loops - the purple one in the background on the mashine. The wider the angle the more multiplies the force on both ends. In this case the force mashuring devise is the climber and the other two ends are the ankers, if one want to compare with a crane lifting a load up with a rope which is in such a wide angle. In your experiment, if the rope was tide down on each chain sepearedly, the force onto the ankerpoints should be sharing the load by almost half, when these rings are still close together. Because the rope is going though, the effect is like those lifting loops used in a very wide angle. Sorry for my English, but it is not my first language. You guys are the best. Your topics are great and with the breaking test is so much to learn about "gear fear" and what to keep in mind, if one is using those equipment. Best wishes and be save. Jan v. Baumbach - Germany
15:25 lookits like a 5:1 ratio , fer every foot wide, youd want it at least five foot long
Thank you Bobby for talking about sliding x redundancy in the line itself. Hope you get better soon.
NOTE!!
What is shown at 12:00 is very different from the test setup. There are no force magnifying triangles at 12:00, but the test setup using 1 atc creates a triangle.
Force wise the 12:00 setup is just fine.
Very good video. Confirms what I always suspected. ADT isn't so bad, Atleast on bolts. Trad gear a differnt story. Though on nasty alpine routes I've rappelled off many single nut anchors.
Fixe rings are standard top anchors for sport routes around here.
From about 12:00 on, running a rappel rope through two rings that are separate does magnify the loads on each bolt. Ideally, the solution is to have chains long enough to hang down far enough to make a lesser angle - but not have two separate rings, at all. Instead, join the two chains with one or two links, and have the rope run just through that, eliminating the horizontal section of rope altogether. Visualize the chains as two lengths of webbing, and the idea is clear. There is no purpose served by creating rings apart. Once again, modern practices have arisen without thorough considerations of the various consequences, and just because bolts ordinarily are assumed "bombproof" does not mean one should routinely use them in ways that tend to multiply forces.
This video is super educational enough!
Congratulations, you have unlocked the "Trigonometry" perk!
The reason the chains take less force is because you do not have the added force from the line between the two bolts.
When you make the continuous line into a triangle the bolt points are acting as pulleys and directly loading each other along the top.
Would like to see 2 bolts with a tensioned steel cable between them, then put a carbiner in the middle of that span, clip a rope to it as a toprope point, seen this set up in some areas...
I feel that the ADT is a lot more concerning on ice or rock routes where you've placed your own protection as it can pull at less predictable angles as compared to other anchors. I've never been concerned when I'm on well bolted anchors of anything breaking. I have been concerned that trad gear might pop if pulled at an angle other than downward.
Not sure if I got it right, but here goes:
Assume X is the master point force, Y is each bolt's force, and A is the angle between the lines coming from the master point and going to the bolts.
Take the vertical components of the angled lines and add them together. That equals the downward force.
2*Y*cos(A/2)=X
The force on each bolt Y = X / (2 * cos (A/2))
On rewatching, at 17:00 and 21:00, finally the realization that the top horizontal strand of the ADT is totally different from a single, taut strand weighted in the middle, where significant magnification of load is possible. If frictionless pulleys were substituted for biners(which add friction that reduces transfer of load), tension on a continuous strand will be equal all the way around; at each bend, both sides exert the same force, and the angle between determines the single resultant force on that point, as the dynamometers were set up to record. Practically, the triangle 1) makes the effective angle on each side shallower, hence slightly increasing their share of load; 2) the main risk is a cut sling, with no isolation to add redundancy, not so much the risk of the triangle causing failure; 3) the horizontal portion of the rappel rope as run directly through rings, will basically equal the applied load below, no matter what the setup involves; the angles at the respective bolts may change, which can increase the load there, but under rappelling loads, never to a dangerous level. A taut cable between bolts, with a ring midway, is about the only configuration which might magnify loads on the bolts beyond a safe level.
Another aside, is that isolating loads from two bolts in a 30-45 degree Vee requires no extra "sliding X" because if one side fails, the shift onto the other side involves a very small pendulum of a foot or so, and drop of just inches; equalization tricks can actually increase the distances and shock, tho still negligible.
The reason the force on the bolts will never be half the force at the master point, in the triangle configuration, is because the bolts still have to support the tension on the rope twice. The best case scenario is having the bolts very close together and the master point very far away, and in that setup the tension on the rope will be half of the force at the master point, and the bolts will have that tension pulling in 2 directions 90 degrees apart. Because it's 90 degrees you can just use Pythagoras, square roof of 2 because the forces are equal, so the total force on the bolt is square root of 2 times half the force at the master point, so call it 70%.
The angle at which the force on the each bolt is equal to the force at the master point is also a cool geometry problem, but i couldn't do that one in my head
Ryan's ouch is now a unit of measurement 😃
@9:50 - I checked my local climbing store, but I couldn't find an alien like you've got.
just some formula, at 19:20, based on the way you measured angle, the 60 deg, i believe formula would be something like:
Per sling load = main_load / ( 1 + cos(angle/2) )
This is first year classical mechanics, applications of newtons laws. If you vary the angle then the force of tension will be different. All you need to know to calculate the forces in terms of that tension is the angles and the kilo newton reading. You can decompose the forces acting on the angled straps summing the x and y components to zero assuming the system is at some point in equilibrium. Then you can set up a system of equations and substitute one of the angled forces in terms of another. Then with this A=T/(cos(theta)tan(theta)+sin(theta)) you can vary the angle and see mathematically what the forces will be without doing this experimentation. If you don't make that assumption then you would need to calculate the acceleration by using the 1D position equation in kinematics. Which is the approach I would use when you do those drop tests
Hey ! I'm 2 years late for commenting but I just discovered your channel 😅. Anyway, this stuff is kinda basic for me being a mechanical engineer but I love that you're taking the time to test it all ! I laughed a bit when you thought that when using chains and basically just moving your measurement point you'd get a different result with the same angle ! Anyway, keep it up !
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°) = 51.43kN!!!!!!! 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)
Loved watching this video, but the book “ on rope” ( which has been around since the 80’s) has discussed this in thorough.
There's a reason that the tension in the ADT anchors at 60° angles doesn't match up with the sliding X at 60° angles. When you have the equilateral triangle tensioned, if you look at the angles that the anchor point load cells are being pulled at, they are NOT 60° with respect to the master point vertical line, even though the ADT angles themselves are. I suspect that if you set up a sliding X so that the pull angle of the anchor lines are the same as the pull angles of the ADT anchor lines, they would be a much closer match in tension numbers.
No jokes about sharing the load? The climbing community is apparently more grown up than me
Bridles are useful when you need to mount something somewhere where there is no way you could anchor exactly there.
Try testing Edelrid's "ADJUSTABLE BELAY STATION SLING", if you can get a hold on that. It should behave kinda like sliding-x.
Would love to see this with pulleys instead of carabiners at the corners of the triangle.
Since the corners can pivot on the linkage of parts, and the friction of the strap over the carabineer isn't that high, best case you would see only a small change in the values. Maybe a couple percent IMO. They could get the same effect by shaking the straps around to cause any uneven forces held back by friction to slide and disapate.
@@court2379 Gotta disagreee. I believe Friction is the only thing not accounted for in math, this would explain the huge discrepancy between measured results and calculated.
Imagine the extreme, 100% friction, (clove hitched on) there would be zero tension in the center of the triangle.
@mitchell - I agree, would love to spend about 30 episodes just on DMM revolvers.
Interesting video. I had never considered the vector forces at play here. I always though the American Death Triangle got its name because it has no redundancy.
I think you’re not taking into consideration that when you make the triangle you’re making two pulleys that are pulling towards each other multiplying the force. Look up an example where someone uses a winch to pull a vehicle that is stuck off road. If the winch is rated at 12,000 pounds that’s what it can pull. If you take the winch line and take it through a pulley back to the vehicle with the winch on it it pulls double because you’re reeling in 1’ of cable but only moving 6” with nearly twice the force.
:thinking: Huh, good point on “you almost may as well be using just one anchor” with the American Death Triangle, which I suppose is the whole point of avoiding it. It’s not that you’ll be absolutely overloading your anchors or slings, if it were that bad, no one would ever be using death triangles because they would just be so inherently dangerous that trying it even once would kill you. One can get lucky a whole bunch and manage to avoid injury just by using one anchor all the time as well, it’s all about preparing for that time when things _do_ go wrong, and in the death triangle, you just don’t have an redundancy, _and_ you’re loading your anchors more than 100% of the actual load.
20:48 hypothesis
The angle is relative to the percent of force?
The triangle basically turns the carabiners into opposing snatch blocks. The middle of the line between them will become the floating anchor point and they will then both multiply any force you put through them.
WRT Units:
The US Customary/Imperial system is, as usual, confusing.
Pounds (lb) are a unit of weight (mass * gravitational acceleration) instead of mass, except for the US customary pound which is defined as exactly 453.59237 grams (mass). Pounds-force (lbf) are a unit of force (mass * total acceleration). There are actually several different types of "pound", used for measuring the weight of different materials. For this, I'm considering only the Avoirdupois pound (the normal one). Otherwise you get weird effects like a (Troy) pound of gold weighing less than an (Avoirdupois) pound of feathers. Slugs are the Imperial unit of mass, but they're almost never used. Instead, the US defined pounds to be a unit of mass, instead of weight as was traditional. In this system Newton's second law isn't F=ma, it's F=ma/g_c, where g_c is 32.174 lb * ft / (lbf * s)^2
In US Civil Engineering there's also the unit kip (thousand pounds-force). 1 kip = 4.44822kN. This is mostly important if you're setting up a climbing gym or similar, since the rated forces the walls and other structural elements can withstand will likely be in kips.
In the SI system kilograms are the unit of mass, Newtons are the unit of force (mass * acceleration), and there's no explicit unit of weight. In this system, Newton's second law IS F=ma.
Just waiting for ET to turn to you and say 'Friend." And stick out his.... finger at you.
Dude such an 80's kid.
I don't know what I'm more impressed; your test, or the fact that you have 2 enforcers and 3 more dynamometers.
I’m a few months I will have 15 load cells 😂
That's a cute angle if I've ever seen one.
Trigonometry is one hell of a drug.
Que buen video. Por cierto, espero ver a E.T. volando como dummy de pruebas desde la torre jaja
TLDR: Still don't use the death triangle because it's stupid, but there are misunderstandings in this video.
The only reason there is more force on those bolts is because of the mechanical advantage of having the rope go through both in series. If you connect the rope to each by threading it back to the main anchor like a tight V, it simply splits the force.
The assistant guy mentions this at 18:00. It's because the ropes are going through the carabiners separately.
There is also another difference which is the velocity of the force. The amount of force being put on the bolts in a death triangle is less velocity than in a V shape which does change the danger factor some. (in a 2:1 mechanical advantage the velocity will be half as much ish)
It can't "share the load" unless it is connected to each bolt independently. The reason there is slight loss when doing a very acute angle is because of loss of force in the ropes themselves.
TLDR; the results you found were not at all surprising if you add the vector forces produced by each strand and use a bit of trigonometry. In your rappel example, even if you're very far below the anchor so that the angle goes to zero, the ropes make a 90* angle through both bolts, which means each bolt sees a factor of sqrt(2) (or cosin 45*) times the tension on the rope, which is half of the climbers weight. So in that case each bolt sees sqrt(2)/2 or 0.71 x the climbers weight. That's why the anchors don't "share the load", because the connecting segment across the top always adds another component of force that is perpendicular to gravitational pull. By contrast, if you have a very long sliding x (approaching 0 degree angle) both strands on each bolt pull down, so the vector forces are are parallel. In that case each strand carries 1/4 the climbers weight, and each bolt supports two strands, so each bolt supports half of the climbers weight, hence "sharing the load".
**So these measurements show that the endpoints of a ZIPLINE may be carrying DOUBLE the load of the weight of what is on the shuttle pulley.
This helps to explain why there are so many zipline failures.**
The idea that the top of the triangle is experiencing some kind of force greater than the tension in either of the other legs is a bit odd. There's only two points acting on that part of the triangle - the tension in the sling pulling each end out until it's balanced. So the tension in that rope should only be about the same as the tension in any other point of the sling (otherwise, the sling would move through the karabiner at each end until it equalized.) It's only when there's some force acting on the middle of the rope or if a knot was jammed up against one of the points that it could change much.
A tip: You can analyze a system of rope or chain *fairly* well by considering each bolt/piece of gear/pulley/karabiner as a point in space, then considering each point separately and drawing the forces on the ropes as vectors pointing in the directions that the ropes travel away from the point. This neglects friction and the weight of the ropes/gear, but in a lot of cases those are negligible (and when they're not, you can add those in, too).
If you do this with any of the anchor systems you tested, you'd find that the force on each bolt is not just the force required to hold the climber up, but also some force pulling out to the side because of the angle. That's why you'll never see the load being shared all the way down to 50% unless the bolts are exactly in a vertical line.
"That's why you'll never see the load being shared all the way down to 50% unless the bolts are exactly in a vertical line" Could this explain why, as mentioned above in another comment, bolts in Europe tend to be placed one above the other?
Do people not watch these all the way through? I love these videos.
Drop tower ideas - test fall factor more than 2
When you're climbing on an old route whose bolts are sketchier than poorly placed micro nuts, it surely deserves the name "Death Triangle".
To get 50% you'd need both bolts to be in line with each other (which isn't physically possible since they'd have to pass through each other). Having the extensions doesn't change anything.
Here's something to try. Put a line between 2 hitches of a 2 cars and pull it taught. Now put a biner and a rope to the middle. Pull the rope and you'll move the cars! Yhat's the force multiplier you are talking about. It's the tangent of the half angle and as it gets close to 180 degrees (a straight line) the half angle is 90 degrees. The tangent of 90 degrees is infininte.
This is assuming a static line. A dynamic line will comply and the angle will become less than 180 degrees drastically reducing the force multiplier. Look at the tangent of an angle and you will see that it drops off rapidly when you drop from 90 degrees towards zero. The tangent of the angle is the force multiplier. At least that's what I recall.
I think you and @TheBackyardScientist should make your own journal to rival Nature.
@HowNOTtoHighline if you did that last experiment (the 133 degree one), but with even higher angle (ideally 180 degrees) and with less stretchy material, you should see the forces on bolts to be multiples of your load.
American death triangle depending upon it being a V you have a equivalent weight lifting ability but when you do use it in a triangle 🔺️ connection you are adding a mechanical advantage to one side or the other. Mechanical Advantage look it up.
Can you just redo every single test you've ever done, but on the drop tower?
bobby hutton brand anglemometers
difference in forces on each chain is due to differences in flexibility of the chains.
Dude Pythagoras.
If Y is the direction of the load, then the y force on each bolt will be 50% of y.
For a given angle away from Y the total force on each of the the bolts (along the hypothesis) would be (1/2* y)/cos(angle). Then use Pythagoras to work out the x portion of the force.
The more acute the angles the better, so don't drink while repelling or rock climbing because the beer goggles make the ugly angles look acute. Dad joke 101.
basic bridle math there, it starts adding up really quick the longer to make the base of that triangle, and can get really odd when you make it shift and start shortening one leg of it say with single legs rather than a looped sling
Nich thing about the metric system: 1Kg generates about 10 newtons of force. The 10 comes from earths gravity.(~10m/s^2).
1N = 1kg*m/s²
I wonder what the forces would be for simul rappelling? You wouldn't have the triangle scenario, but rather a rectangle
You use two bolts instead of one because bolting material or even the rock could fail through damages from rockfall or vandalims