The Math of Rock Climbing
Вставка
- Опубліковано 25 сер 2024
- Follow us on Facebook: / emoryuniversity
Follow us on Twitter: / emoryuniversity
Follow us on Google+: www.Gplus.to/Emory
What's it like to fall 40 feet down a sheer cliff face, while dangling from a rope hundreds of feet from the ground? Emory mathematician Skip Garibaldi describes his rock climbing experiences on El Capitan in Yosemite National Park. He also explains some basic climbing math, such as the fall factor, used to reduce the risk of injury during a rope climb.
For more interesting science related stories go to:
esciencecommons...
The fall factor is nice to figure out how "bad" a fall is, but does little to explain or illustrate the actual force absorbed by equipment (and our bodies) in the event of a fall. If we want to know what the Peak Dynamic Force (PDF) of a fall is, we want to look at the physics. A handy solution is based on Hook's Spring Theory and goes something like this: PDF = 2/[MAH/S], where M = Mass, A = Acceleration, H = the drop (distance fallen) + the stop (the amount of rope below the last piece of protection, adjusted with the efficiency of bends in the rope over the protection) For instance, a rope bending around a carabiner at 180 degrees has an efficiency of about .6, a 90 degree bend has an efficiency of about .9. For pulleys, a 180 degree bend through a pulley has an efficiency of about .9. This is a very basic formula, but is great for guestimating the amount of force generated in a fall while taking into consideration the bends caused by pieces of protection, the belay device, and the elasticity of the rope we're falling on. Enjoy!
+Rudaorocks Lol...............YE I TOOK a 450N FALL ... DAUM BRAH I KNOW EXACTLY THE AMOUNT YOUR TALKING ABOUT x] no practicality in real life. but I do believe in the math for training just not for falls...
0:38 harambe is that you
My Ape index is also about 4.5 inches.
But I tell my girlfriend its more like nine inches.
Well.. Size DOES matter :D
Solving a problem under stressful conditions where there is risk associated with an incorrect choice greatly changes the calculative process.The ability to think clearly is reduced.
Golf is more like archery there is a calculation to be made but the parameters are restricted to the immediate task: hitting the ball right.Wind, distance, light, green condition.The task at hand can be concentrated on.In rock climbing there are factors external to the immediate task- rockfall, bolt/gear quality etc
Interesting, but less math than I expected. How about a video on anchoring? (specifically, the American Death Triangle)
Also, whilst talking about himself and the climbs he's done, skip forgot to mention that Friction in gear or against rock limits propagation of force generated by falls along the rope. Only the length of rope between the penultimate and the ultimate runner will be fully loaded, with each length between previous runners successively less loaded: energy absorbing capacity of the rope is not deployed fully all along its length: actual fall factor is much greater than the theoretical fall factor.
The bolt broke?!
I state again - the difficulty of the 2 sports was not the point, but the difference in mental approach required.
I learned that math is involved in lots of things even when you wouldn't expect it, such as rock climbing, where it is used to prevent deadly falls.
me personally i would expect math to be involved in physics
Agreed, climbing up to 5.12 is not that technical, we share a common ancestry with apes after all. But beyond that, and beyond V7, it begins to get technical in a way that golf never will. There is so much more to consider than in golf, where you are essentially refining the same basic movement. Golf is, as I said, like archery or shooting - a very closed set of movements made precise - whereas climbing has that too but the set of movements is far greater, as are the other external parameters.
@AndyRoddick969 Some bolts are glued. However traditionally something called an expansion bolt is used. A hole is drilled in the rock and the bolt placed in. Part of the bolt is designed to expand when you tighten the nut on it. The bolt then expands into the sides of the hole and will come tight. At this point it has a 4000lbs pull out strength and 5000lbs sheer which is where most of the force of a climbing fall is generated.
This video taught me the emphasis of math and rock climbing. also, theres a formula for falling off.
@benadril Not on fall factor per se, since its definition doesn't include rope drag. However, fall factor is only a "quick and dirty" measurement of how hard a fall is, not the be all end all of how to measure a fall. Friction in the draws will have an effect on the load placed on you and your pro and your belayer.
Usually they get battery drills there and climb to the spot and pull the drill up and they go fairly deep about any where from 6 to 24 inches in
100 feet so that's about 30 meter fall, which means your last clip was 15 meters below you when you fall. Do you do that often? I mean, one clipping point is so far to the next?
I think you need to throw away that rope after the fall.
The indoor climbing gym I go, is only 15 meters tall. One clipping point the next is usually 2-3 meters (6-10feet) at most.
But I understand that climbing style is very personal preference.
Nice vid on fall factor. Must see for the inexperienced trad climbers.
Look, I agree with you fully, but that still doesn't change the fact that golf is highly mental and involves lots of problem solving. I just felt the professor could have used a better example.
not really - if you make a mistake in golf you're not risking injury or death... it adds a certain something to any calculation made.
Cool video, although I highly disagree with saying that golf doesn't involve problem solving. Playing golf at a high level is a highly calculated activity. To keep a good round of golf going is an extreme mental task. You have to know when to take advantage of what the golf course is giving you (tee placements, pin placements, hazards), and also know when to be conservative. In fact, the more I think about it, golf is incredibly similar to climbing in terms of mental commitment and strategy.
@benadril It can do. Its also why you get rope drag, where it is hard to pull the rope up to the next draw.
so when he says permanently drilled into the rock. how the hell do you do that and how sure are you its drill in tightly?
at 1:41 the cap falls off
Climbing is after all all about falling or if you prefer not falling. Aerodynamic experiments while free climbing are scarier than falls taken while aid climbing.
(My Opinion)
The peeling experience when you bungle a sequence seems to take forever. But very often when aid climbing there is no preparatory moment where you are working to locate a way out of getting in the wind...its just POP...your falling..although a long zipper is scary and seems to take forever.
No it does not. In a situation where the belayer stands on the ground a fall factor greater than one ( actually far less with a dynamic rope) will result in the climber hitting the ground.
A fall factor greater than two cannot be achieved using a fixed belay point. I.E it never happens in rock climbing.
Great video but the math is backwards. If you fall 8 feet on 16 feet of rope, that is a factor .5 fall. A factor 2 fall is only generated when you are falling from a point above a fixed anchor. For example, if you stand 4 feet above the anchor ( like we all do when topping out !) and fall, you will fall 8 total feet on that 4 foot length.
That can break your back, anchor, piece, biner whatever in a hurry. Don´t do that.
Nice video! Love the stories too :)
dopest maths teacher/lecturer ever, you don't usually find mathematicians who are rock climbers
he's not a mathmetecian. he just knows the formula for fall factor. not exactly rocket science
the danger or injuries caused by falling are from hitting the wall or ground not from the force of the rope catching your fall. The ropes are stretchy (dynamic) we all know this.
Golf is only well paid because the majority of its adherents are well paid, & as such willing to spend. This has little to do with the actual difficulty of golf.
The points you make suffer from a disconnect between cause and effect (well paid) or between premise and conclusion (you find it hard, therefore it must be the hardest).
BTW I never said golf, or climbing, was either easy or hard, just that the problem solving (only one aspect of a sport) required for them was different.
ya fair enough. I think whoever brought that about was rather just talking about "the zone" you can get in when doing sports/menial labour/certain activities.
Good exposure... very cool.
Yeah, I'm British aswell. But I was referring to a youtuber who did a Livestream a few days before I say this comment.
You forgot one important piece of equipment--an awesome shirt. Click on my name to go to our channel and check out our rappelling/rock climbing shirts--and the Vietnamese model we enlisted to show them off!
Ape Index doesn't really give much of an advantage. Pretty much all the studies found it was either not predictor or a very slight predictor to ability. The issue being that the longer the arms the more strength needed to get leverage. Slightly positive ape indexes do seem "best" but it's quite negligible from what I've read/seen.
Thanks!
Nice overview!
@ 1:20 he's obviously not a golfer.
This is a climbing video, not a math video, but you're right, I like the math too. But I didn't get the ratio, I still see, the height, kind of, of the rope, to your last checkpoint.
Good video, just wish people commenting would understand the mathematical learning purpose behind it not just to know whether he's mormon or not.
I've only taken 1 big fall (~25ft), headfirst, and I can only remember thinking the same exact thing you said in your opening statement, "Why am I still falling? Shouldn't the rope have caught me already?"
Ropestretch.. 10%..
i like how your "f"s are written like integral signs
Were you in the Minesota burs PTFO live stream yesterday? I think I recognize your user name.
we have the same climbing shoes!
how good is this guy?
hello
very cool video, and very cool professor!
How is the example a fall factor of 2? Isn't it 1? There is 16 feet of rope between belayer and climber, not 8. 16 divided by 16.
The climber climbs 8 feet above the belayer and falls 8 feet below the belayer. There is only 8 feet of rope paid out.
I learned that there is a formula for each drop during rock climbing.
fall factor? oh shit god forbid I fall 2 feet with 4 feet of rope, OH EM GEE!!! FALL FACTOR OF 2!! I'M FUCKED!!!
Cool vid, but shouldnt you take into account that the ropes on a lead climb are dynamic? if you are 8ft off the ground and have gone up 7ft and fall, you will hit the ground as they are designed to stretch a little to absorb the energy.
maybe im just looking into it too much, still a nice vid with a interesting story.
So there should be lots of anchors when you are near the ground?
very cool video
Desert Gold at 3:36? Baddd ass...
Adam Ondra has a negative ape index... so its really good to have a big ape index?
adam ondra has a giraffe neck
People don't have wings.
So, if I'm getting this right, the entire math content of the video was "here's a ratio" with no mention of the physics/math behind why higher FF=>worse fall? Disappointing.
The "math" of rock climbing? I find this to be an extremely misleading title.
The guy couldn't even put a figure on the load rating of a bolt! FYI, they're rated to 25kN, NOT a truck! A "truck" is not a unit of measure!
The only math was calculating fall factors and even then there was no mention of rope stretch never mind the forces generated by the falls or how they are absorbed.
This video is all about him and what he's climbed. Not at all about the mathematics.
Golf may be the most difficult sport YOU ever played, but that means squat, given it is unlikely you have played all sports - the only criteria by which your statement would be anything but a personal statement.
at 1:41 the cap falls of the marker :D
PUFF @ 0:21. ;)
Just because climbing involves the possibility of death, that doesn't take away from the problem solving aspect of golf. I don't see your point.
彼らにはぜひ日本へ行って岩ぐずぐずの一ノ倉とか滝谷の登攀に挑戦してもらいたい。ヘッピリ腰になりそうな気が。。。
m = r/R
He used "golf" and "skill" in the same sentence. Good "lol", good "lol".
I had a brass nut 1/10th that size save my life. (there great).
*they're
@@TJGermany they are* let's be formal here
@@donovanholm Okay!
Is that Olive Oil at 1:20?
I didn't come here to learn math
Brass nuts are awesome!!
climbing is nothing like mma.
4:21 thiiiiiiiiiiiiiiiiiicckkk
Remind me not to study math at Emory University.
yes only one math, i was expecting some maths too :S
I hope you spend your time at school doing better things that this "equation".
I was going to say, "this guy is really annoying" but then I saw he's left handed so I can kind of tolerate his annoyance
Maybe you are telling the truth and if you are I should apoligise, but I'm not going to because frankly, I still don't believe everything you say. It just sounds exaggerated to me.
give the guy a break ya bunch of winers
no def not a must see for the inexperienced trad climbers
stick to mikebarter or supertopo
He looks like James Franco
@cbinsyd "I found something to be negative about! Woohoo!
Stop lying. Maybe a 30-footer, but a 100-footer? And maybe you've done FA, but your scariest fall during an FA, coincidence I think not. And no way is it a good thing when two ropes tangle during a fall. Ropes cut through each other like butter... So I'm sorry mate, but I don't believe you.
He's left handed. Thats annoying. It measn the writing takes too long. Good video, though.
Yeah I got my mistake after re-watching it, don't need to be all trololololol about it. And I do climb on a weekly basis... So I guess I'm not all that Fucked
bugga i forgot wat i was watching
Pfft - you obviously don't climb. Golf is like archery - very easy to get very good, and freaking hard to get any better.
I don't think this guy understands math. Of course a fall factor of 2 is bad. 2.001 means you hit the ground
The fall IS going to hurt more if you fall farther. Your distance between anchor points determines severity of fall unless you top rope. In LC you are always climbing to a fall factor of 2 until you clip in again
Nope, you can only get a fall factor 2 if you haven't clipped in at all on the whole route, so fall below the belayer by the same height you had climbed up
you don't know what you're talking about, so please spare us. The rope has elasticity to it - it STRETCHES. I've taken plenty of lead falls, the longer ones being 30', and two 60' falls. I had minor scrapes on my knuckles on the 30 footer and first 60 footer. Broke my hand and ankle in the 2nd 60 footer only because of the swing involved in the fall. I've taken factor 2 falls at beginnings of routes, and without a doubt they are much more jarring.and to make the point - it's not the FALL that hurts, it's that sudden stop at the end!
Borring
13 seconds in and I think I hate this guy.
Useless
Ignorant comment
mathS with an S
NO (depuis 1960)
knob x
pardon me for stating the obvious, mathematical formulae and having climbed The Nose do not make one a professional climbing instructor. a preceding caution at the beginning of the video to all that climbing is inherently dangerous and to seek qualified instruction and that no responsibility is taken in case of mishap might be prudent.
they, and I, know much more than you about climbing. Fortunately, the climbing world hasn't been completely absorbed by the "sue people if anything offends them, or if I break a nail" attitude. Particularly traditional climbers, take responsibility for their actions. You, obviously, have been watching too many videos or looking at too many books that have that traditional "climbing is dangerous . . ." We don't need it repeated every time the word "climb" is uttered. we know
SD - sorry, but you aren't pardoned. It is obvious, and you've wasted our time by stating it.