Demystifying Climbing Math and Avoiding the Death Triangle
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- Опубликовано: 3 окт 2024
- I have a confession to make. Apart from how much I love tying knots our Knot of the Week series (bit.ly/2eShWcW) I also geek out about the numbers behind them. That also goes for climbing and rigging things like top roping and rappelling. Contrary to popular belief, math is important in climbing, even though it’s not discussed as much as it should be.
Today I’d like to get into more of an advanced application for knots and really speak to the “why” behind what makes some knots better than others. I’ll also be discussing tubular webbing in detail and get into the pitfalls to avoid when rigging it during climbing, top roping, or rappelling applications. This includes the dreaded American Death Triangle.
I’ve never been a huge fan of math, but something about the numbers I discuss in the video really resonate with me and help me to understand what’s truly at play when I rig something that I’m literally putting my life on the line with. Hopefully this information resonates with you as well and you get a lot out of the information in this video.
As I mentioned, you’ll meet all kinds of differing opinions on “how” to rig things like a top rope or a rappel. However, the numbers I’ve stated here don’t lie and when it comes to those, there’s only one way to interpret them. I’d love to hear any comments and questions you might have in the comments below. I enjoy hearing others’ opinions on these principles as well.
As a machinist, this is my favorite explanation on forces related to climbing and climbing equipment. It covered a ton of information but kept it square enough for average people to generally understand the talking points. Knowing how to use your gear is one thing but knowing how your gear works is often another. Saved for reference!
I have 15 years of climbing experience (including a college class on it) and this was the best recap/summary I've seen.
Thanks James, I appreciate that. ~ Bryan
Agreed!
he could have said that everyone has a tool for measuring your death angle and thats your hand with the little finger and thumb hand sign :). if the angle of the sling is larger than that your setup isnt okay or needs more than basic attention to be safe. But anyway the video is golden and really well put together and thanks for making it !
One really important thing to mention, and i did not pick it up in your video is to be aware of the weakest link in your setup. There is no point of wrapping sling multiple times on anything and get WL of lets say 72kN if a carabiner you're using to hold that sling can only be safely used to 24kN.
If you're wrapping the sling around a natural anchor, ie rock or a tree, then double or triple wrapping can help as if reduces the force exerted on each strand, therefore reducing the chance of a strand breaking if laid over an abrasive part of the anchor.
Surprised this isn't the highest comment (not just because of content but because it's got the most up-votes...), I can't really fault him for not pointing-out something that should be a given/premise **but** it's just such an important concept (identifying the weakest-link in your set / your 'failure point' if the setup went) that 'it bears repeating'!!
To OP- THANK YOU so very much for this video, am a long-time amateur climber who's now getting-into rope and I have been trying to discern my "ideal first kit" for serious use (am using a weak setup now, over grass / ready for falls, to get a better feel for what kind of kit I want to order), have been very bothered by finding harnesses that aren't life-support rated (by major manufacturers, the idea of a "work positioning saddle" that isn't also life-support is just mind-blowing to me, maybe you just use a lifeline as primary help and the saddle is solely for comfort?), it actually had me online finding calculators for converting kN to "max weight capacity" to tensile strength as well as things like fall-calculators (I put ~1600lbs of force on a line if I take a 10' drop, iirc), am so happy to have found so much great math in onen url especially with you explaining it, and the knots!!!! I needed that SO badly (knot-strength-reduction #'s) but honestly it never even crossed my mind that there'd be a charrt like that anywhere, so again thank you so much your video here has been of IMMENSE value to me!!
“screw-it down so you don’t screw-it up”...thank you my man, that piece of info was awesome!
Good intro overview video but just a few things. The percentage a knot weakens the sling is also dependent on the material of the sling. This is related to the melting point of the material. The percentages listed are mainly based on nylon. Materials such as dyneema/spectra typically have a 50% decrease in strength when there is a knot.
With tubular webbing, the strength rating is based on single strand so when you tie a knot in it creating a loop you have doubled the strands (17.8kN x 2) and you lose strength for the knot. So (17.8 x 2) - 12.46 = 23.14 kN. That means that your tubular webbing is a strong as your sewn sling (typically 22kN).
talking about angles, I was always told give it the spock test. Live Long, and prosper. That is a good angle to shoot for. 45 degrees(ish) and that anchor should be bomber, as long as the gear is good.
I liked the Intro; Do not buy cheap rope! Know what you’re buying! I really like seeing civilians who know that simple things like a twist in your line can reduce the load it can handle. Informative and you’ed have done good as a Repel Master Instructor (after Air Assault School). You don’t get to Repel out of helicopters without knowing the ‘not so fun stuff too’. Awesome refresher course. Thanks.
"and I felt like that was a good way to tie that into all of these knots." Now that's punny. Excellent video, thanks for the explanation.
This is very informative. I am not an avid climber or rappel much, but this is great information to have on hand. I do some of this for work, but never had the break down to what item is capable of. Thanks much man.
Lots of good info! It is good to see some young folk are going the extra mile to explore fuller understanding of these sometimes critical issues.
2:15 An advantage of "Tubular" is that it distributes the load more evenly than "Tape" (flat) which tends to focus the load on the center as the edges more easily stretch. Tubular has no 'center' & no edges, so no focus of force.
(Sort of the opposite of the reason knots are weaker than straight rope because the load is focused on the outer bends).
3:40 no grapevine bend?
5:32 Most folk only use static or only use dynamic, depending on their main rope activity, and
. "Static is just for catching a 'Slip'" (2ft) as in lead rock climbing where you typically fall just before you think of putting in your next pro ;). If you fall 5-15ft before the rope catches you, it stretches so your body can absorb the impact gradually (unless you hit a ledge first).
6:00 He refers to the strength of the loops as if they are only 1 strand, but they are inherently doubled, but for comparative purposes, that's ok. (Count the strands in direct tension, times the load rating.)
10:24 "Trace" I would call follow back thru the knot.
12:15 Burrs or rust particles (like sand or dirt) can weaken your fabrics even after they are removed from the anchor.
19:35 I think some examples would help here:
@150deg, a 200# load puts 400# on each anchor (800# total).
@120deg, a 200# load puts 200# on each anchor (400# total). (This is the magical & symmetrical 2 anchor arrangement!)
@ 90deg, a 200# load puts 140# on each anchor (280# total).
@ 0deg, a 200# load puts 100# on each anchor (200# total). (Trees too close together might have weak roots, but one in-front of another a good distance works very well.)
I hope you guys appreciate what Bryan just did, this is a tech nerd level presentation that a place like REI would charge over $200.
The reason the info from REI is $200 is because the (life support!) info you get at REI would be from a certified professional, and would be correct. Unlike this bullshit. 🙄
Thanks for the great short lesson on the math of anchors. I haven't ever heard it explained quite so simply
Holy shit dude! 'Hopefully you learnt something', i swear you taught me more than atleast 5 of my proffessors at school. What a great video! Highly instructive and useful! Specially if you're theoretical and want to know 'why' like me!
Pretty good review of a very complicated system. lots of topics to cover in a very condensed package. Felt good to dust off the ol brain and do a bit of reviewing. Reminds me I should probably get the big ol book out and review as well. Thanks for putting this together.
Your Math would be so easy in the Metric System
Combining kN and imperial seems backwards to me xD
Fuck it, let's use stones.
murica fuck yea
I'd like to understand the physics of WHY a girth hitch cuts the weight rating in half. It's very counterintuitive because it looks like it should at-minimum be 100% still, and counterintuitive things are extra dangerous.
Good final zinger at the end. “I felt like thats a good way to tie that in to all these knots.” Haha
At around 15:30, you state that doubling up a sling will effectively double the rating of the sling (and then you show how to triple the strength rating). This is probably not quite accurate. Yes, it will most likely add to the rating, but not by 2x. Also remember if there is any uneven load on the sling, or the sling cuts (perhaps the sling is damaged?) the whole anchor will fail. It would be more beneficial to use two separate slings to get the desired rating, and perhaps use doubling up the sling like you do as a technique purely to half the length of the sling, while not negatively impacting the stated rating (as shorting the sling with a knot would do)
I don't know who you're fooling with saying that's 6 inches at 9:41 lol
Tanner Forrest ‘bout to say!
Shit my mind went to doing calculations on this aswell lol
Beautifully presented. One point on anchors that may be of use: Distance to focal point (knot) should at least equal the distance to the adjacent anchor - as long as the max distance from the focal to either anchor does not exceed 50% of the distance to the OTHER anchor (offset anchor points). This would keep within 60 degrees, but ALSO minimize offset tension. Thoughts?
Thanks for this. Good stuff. Would be nice to see *why* they reduce the strength by XX%
Because of the turn radius in each knot. Think of a sharp knife vs blunt knife vs smooth steel edge... each affect how much the rope can be cut by its own opposing strands. If you follow the strands in each knot you'll see weaker knots turn more sharply or around less of its own strands than a stronger knot.
The reductions and angles are important to know, also follow the basic rule of not turning any rope or cord more sharply than its own radius.
Great video, only criticism is that by doubling the sling it won't increase its safe working load. Its still reeved around the tree in a basket hitch situation. Its safe working load is still reduced from a straight pull situation. This is one of the most basic
principles taught in rigging. I do agree it is better than rigging it in a choke situation greatly though.
The triple clipping would not hold 96kN because the sling can slide on the anchor, it's not 3 individual slings on the anchor, it's one sling that can slide around so the tension is distributed throughout the whole sling. It would be significantly less than 96kN, but somewhat more than 24kN (I would guess 36-48kN in a triple wrap on a wood beam like that, and with a double wrap maybe 30-36kN), but it's not just 3x the strength.
The triple wrap would be closer to the full 48kN because of the additional friction isolating the strands forces - however in this example the sling was so tight there was a very bad angle and a biner would not have the two sling strands on it at the same point, meaning some amount of crossloading on the biner would be happening, which is always bad. You want a single area as close to the spine side of the basket of the carabiner loaded, and no wider.
This information is not bad, almost half the speed of reading the same transcript, if played at 1.5x. But a well written summary in text would take even half that time (ie 5 minutes).
Im terrified however because the mathematics presented were dead simple (very basic trig is middle school, grade 6-7-8) and if climbers cant understand that before they go out, there's bigger problems waiting to happen.
Great content and very informative. At 16:08 you mention the strength is tripled to 96kN. If 1 kN = 224 lbs, then 96 x 224 = 21,504. Just curious how you came to 384,155.52.
Yes, great vid, but you screwed the math up pretty bad at this point-Your numbers suggest that one sling could be used to hold 192 tons (384,155.52 lbs)!
Sick video - informative & well said. Thanks
LOL - where'd my comment go? It was here a couple weeks ago. Oh well. Love the diagrams and illustrations and enthusiasm and high-speed delivery with very few edits - great job! But your enthusiasm over-ran your math and some of your facts, as other commenters pointed out as well. "That angle is called the American death triangle." No, the American triangle is a triangle, NOT an angle. It is a triangle made by a single strand of webbing or cord connecting one anchor to the other anchor to the master point and back to the first anchor, then tied (or sewn) to complete a single loop, making a triangle shape. It would be great to add a third column to your Angle vs Resulting Tension chart and compare anchor forces for your V anchor system and for the American triangle for the same angles at the master point. See Wikipedia American death traingle here: en.wikipedia.org/wiki/American_death_triangle .
Thanks. But how does gravity open a screwgate carabiner? "Gravity" would have to turn the grip part say half a dozen turns. Don't get it.
You should also avoid the lesser known Slavic trauma rhombus and Nordic injury square.
Nice video but a bit difficult to understand using imperial why not just use kilograms and tonnes? Ie talking in kn and then flipping to pounds seems a bit complicated
Withstand is by definition "remain undamaged or unaffected by". So for this reason when discussing a strength rating of a material stating "this is how many pounds of force it can withstand" is not IMO a good idea, as its way to easy to confuse it with a working load rating. Other than that great video.
love the new intro, hopefully you keep it!
Thanks Nick, glad you like it! ~ Bryan
great vid, thanks for taking the time to put this together.
So does wrapping the webbing/rope around multiple times mean you can technically negate the drop in percentage from the knot? I mean, I know the knot will still have the drop in percentage, but if you double the strength by wrapping it, it should make the rope/webbing stronger then, correct? Or will the knot be "X"% of the overall strength of the rope/webbing?
Great principles for learning for the beginner that I am, thanks! However, being slightly OCD with numbers and just out of my head, aren't all the kN multiplications completely wrong??
Like, if 1kN=224lbs, there is no way 17.6=4001.62 precisely right? Slight error but... And more importantly 96kN is gonna be roughly 100*224, so something close to 22,000 and definitely not 400,000! Might just be errors, but mostly I'm afraid I might have misunderstood something?
Also, doubling a sling, would that really double its strength? I get that the weight is distributed along each strand, and that though the contact points on the carabiner hold half the weight, wouldn't the increase in contact surface reduce the strength to something slightly below 200%?
Don't want to be picky, just want to make sure I get the principles correctly. Numbers themselves I can figure out.
I did the same math and the tubular webbing would carry 3987.2 lbs of force not 4001.62, it's not massively off but I think it screwed up math later on and when it comes to climbing I think a small change makes a huge and unsafe difference
Crystal clear intro! Thanks
Pretty sure the gate strength measure is a measure of how much force the carabiner can take if the gate is open, not the strength of the gate itself
There are usually three tested ratings on a carabiner, the major axis with the gate closed, the major axis with the gate open and the minor axis, which is when the carabiner is loaded at 90 degrees from the spine with the gate closed. The major axis is when the carabiner is pulled from end to end along the spine of the carabiner
Great info. Well explained.
BEER KNOTS for webbing loops can't be beat. Little tricky but fool proof and tough.
Do you have the sources where you found your information? I want to keep a reference manual
Ooh, shiny new intro logo. it looks so serious. I loved the goofy intros though, it was a laugh in the tactical world of "IF YOU DON'T DO THIS HILLARY HIT SQAUDS WILL KILL YOU" seriousness.
While the video provides some useful information, (technical spec nerds eat your heart out) it seems to be devoid of basic application of this information. Most users; recreational climbers, rappellers, and outdoor enthusiasts are never going to need an anchor that is 96kn. To explain that further, it's really unnecessary to wrap your sling 4 times to achieve xyz strength when the carabiner you attach to it is rated for 22kn. (Your anchor is only as strong as the weakest link) But you want to have the strongest anchor possible always right? Seems like sound logic, but in reality you are missing the efficiency aspect of anchor building, the best anchor is the fastest, which takes the least amount of material, and is strong enough for the task at hand.
For climbers looking for more info on anchors, John Long and Craig Luebben both have fantastic books on the subject.
TLDR: Math and ratings are important but don't get too caught up on them.
Erik Kloeker you could always stack up carabiners as well to match you overkill sling. I'm all for this, climbing is problem solving. Do you want to bet your life on rules of thumb? Or do you want to understand it down to the numbers. You're right, you will probably never need that bomb proof sling, but for the sake of narrative, it was eye opening to see some possibilities. Also, this channel has a rescue audience. If you are setting up a big haul to roll a car up off of someone, you would tripple up slings.
depends on the anchor points but normaly for climbing 90° is not good enougth , the recomendation is 60° or less
Are there any drawbacks to using a dynamic rope for rappelling instead of static?
Yes, as you start to rappel and lean back over the obstacle, the rope will stretch instead of hold you and you can fall. Also the more line you get out, the more it stretches which you would have to adjust for while rappeling down the obstacle. Basically, you can move down the obstacle without letting out rope due to the stretch of the line, which means as the rappeler, you lose control.
climbers are pretty much always using their climbing rope to rappel at the off the top of their climbs but that's mostly due to necessity. if you want to go rappelling just for the sake of it go on a static it will be much more enjoyable.
Another problem is, if your rope is turning 90° over a rock edge, when a dynamic rope stretches it causes more abrasive wear at that contact point. A static rope minimizes the sawing action at that contact point every time the rope is loaded and unloaded .
(To James W's comment) Wait, what? Maybe in a cartoon. If you don't let out rope smoothly, a rappel on dynamic rope can be bouncy. LOL- "you can move down the obstacle without letting out rope?" Only if the rope is cut! Yes, there is more rope stretch (for the first rappeller) on a dynamic rope than on a static rope (which also has some stretch), but if you rappel with a qualified instructor, there should be no falling or adjusting or losing control.
Great info! Thanks.
You're welcome, Jeff. Glad you enjoyed it. ~ Bryan
I thought the American Death Triangle would be if you used one sling around both trees as your anchor.
It is. It's when a single sling used to form a triangle changes the angle the load comes form and thus increases the angle. This guy does NOT know his stuff. So many dangerous mistakes in every single video.
Awesome video. Thanks.
Thank you, glad you liked it. ~ Bryan
Great video!
Question: Knots in rope and webbing decrease the tensile strength to varying degrees, what does this mean in regards to safety knots (like the overhand knots after a water knot)? My assumption is that the safety knots do not affect the strenght because the safety knot is not the first knot engaged when the webbing is tightened.
Does anyone have any info on this?
This video, ruclips.net/video/Vrgadjo9niY/видео.html, by DMM illustrates various knot strengths.
Thank you, thank you, and one more time...thank you
WRONG
KN is not 224 lb of force. This is fundamental to understand. KN is a measure of force which is weight multiplied by the velocity. THe webbing may hold 224 lbs of weight but at a higher speed and acceleration it will definitely break.
The explanation and theory was great, but if your going to do any climbing, you probably should let someone else do the math for you. So many mistakes, I lost count, but the funniest is when you quadrupled Zero and came up with a 200% increase. :-)
why wouldn't it be 72 kN when tripled? 24x3 is 72. i dont see how you got 96
very informational. great job.
Thanks, appreciate the comment! ~ Bryan
how do you feel about using a single runner across two anchor points with a magic x?
I personally prefer the redundancy of two different runners, Dan. Thanks for the question! ~ Bryan
ITS Tactical / Imminent Threat Solutions thanks
What watch are you wearing in this video?
Resco Manus ~ Bryan
so if i tie 4 figure eight knots on a rope then it will snap as soon as i put weight on it?
No, the weakening effect of a knot in a rope does not multiply the weakness of the rope. If one knot weakens a rope 25% and another weakens it 50% the whole rope is only as strong as the weakest link, 50%.
thanks
Can you provide the source of the numbers you presented please?
His imagination, as the numbers are wrong
Static rope should never be used for climbing .. just saying. Climber and rescue technician to base my comment on ... The dynamic stretch to reduce force on your anchors is not there in static (low stretch ropes).
I'm assuming you mean that Static rope should never be used for leading.
Static cord has been used for toprope anchors by AMGA certified guides every day for years. It doesn't stretch so it doesn't rub and grind on the rock causing wear and tear which would happen on a dynamic rope.
Static cord is used for hauling on bigwall climbs. Much more efficient and burly than dynamic cord.
So in the real world only the carabiners have a chance to have the strength as specified on them.
Triple pass is 354K pounds? No sir. 96 Kn * 224 = 21k pounds. 354k pounds is the size of a large wooden house.
good post....want to work at REI?
its simple, if you fall climbing on static anything= dead, if you fall on something dinamic=better be bomb proof or redundant, thats all wear helmet
"rule of thumb with trees" should be changed to "rule of THIGH".
WHY NO KNOT OF THE WEEK UPLOAD
he did knot have time
Water/Beer Knot can work itself loose.
info on shirt?
I honestly can't remember, I bought it from a booth at the San Diego Comic-Con a few years ago. ~ Bryan
my show
Oh dear, another of your videos with incorrect or dangerous information in it. You say you triple wrap a sling by wrapping it twice. Wrong. You then say you have a 96KN rating. Your math is wrong and also doesn't take into account (or mention) the carabiner rating.
Worst of all is you talk about the american death triangle while completely missing the whole point. It's not just the angle between the anchors, it's using a single sling to go through them and form a triangle vs a V shape.
You really need to learn your stuff. Every single video I watch of yours has a MASSIVE error in it that promotes really dangerous technique or missing out a VITAL piece of safety information.
I feel like a lot of the math is off in this?
That shirt though.
Did your sister loan you her beard?
Pretty useless knowledge. If you reach forces that would Break a knotted webbing, something went horribly horribly wrong(people did Tests, on a top Rope Fall you produce about 2.5kn). and nevertheless, if you climb on a non redundant anchor, its your own fault if you Fall to your death
when is it not your own fault?
The force generated by a fall isn't just determined by the height of the fall, it is also determined by the amount of time it takes for the system to absorb all the force. The shorter the amount of time the larger the force. Google "fall factor".
Thanks man👍🏻