How do you calculate how many kN are generated in a fall?

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Messages 1 - 73 of total 73 in this topic
Oliv3r

Trad climber
SF
Topic Author's Original Post - May 8, 2012 - 07:11pm PT
Does anyone know how many kNs are generated when you take a vertical fall with your gear at your feet? Or even how to account for factors would affect that? Like the dynamic nature of a rope, the quality of your belay partner, or the integrity of a gear placement?

How big of a fall would be required to blow a well placed micro stopper that was rated at 4kN?
TGT

Social climber
So Cal
May 8, 2012 - 07:14pm PT
How fat are you?

































1/2 MVsq

That's the biggest variable.

Yer gonna die.
Ghost

climber
A long way from where I started
May 8, 2012 - 07:17pm PT
I think it depends on whether or not you have a blue Camalot on your rack.
Studly

Trad climber
WA
May 8, 2012 - 07:18pm PT
The answer is in the question.
Elcapinyoazz

Social climber
Joshua Tree
May 8, 2012 - 07:19pm PT
f=ma.
Oliv3r

Trad climber
SF
Topic Author's Reply - May 8, 2012 - 07:37pm PT
I'm 190lbs(ish)

Feel safe falling on a well placed blue camalot, but question how much of a fall a micro stopper is good for.
Norwegian

Trad climber
Placerville, California
May 8, 2012 - 07:38pm PT
dont kill o' newton, dude.
he's boss.
adatesman

climber
philadelphia, pa
May 8, 2012 - 08:11pm PT
Dunno about the one linked above, but the one by JT512@RC.com probably has the best mathematical model of what's going on during a fall. IIRC he improved upon the "Standard Model" put forth by RGold (I think that was his work) and put it online 'round about when Petzl pulled their online calculator.

http://jt512.dyndns.org/impactcalc.html
snowhazed

Trad climber
Oaksterdam, CA
May 8, 2012 - 08:12pm PT
F=sqrt(2mgA f)

Where f is the fall factor.


To calculate the force produced by a fall you need the springiness (or spring constant per unit length A). This can be calculated from the stretch percentage of the rope (%x) under a weight. This is quoted for a weight of 80 kg on most ropes.

A=mg/%x

For a Mammut Gym Rope ((world wide web).mammut.ch/mammut/katalog.asp?view=detail&did=9&dart=4&tid=54298) this is 9%.

A = 80 * 9.81 / 0.09 = 8720

In our example our 76.2 kg climber could produce a maximum force when the fall factor is 2.

Fmax=sqrt(2 * 76.2 * 9.81 * 8720 * 2) = 5.1 kN

This is the maximum force on the climber. The maximum force on the protection holding him would be more than this as it has to hold the force of the climber + the force that is transmitted down to the belayer. If no force was lost then the protection would get twice the force on the climber, but only 66% of this force gets transmitted to the belayer the rest gets lost as heat due to friction on the carabiner - no wonder it gets hot!

So the force on the belayer (Fbelay) equals 66% of the force on the climber (Fclimb).

Fbelay=0.66 * Fclimb

And the force on the protection (Fprotect) equals these added together.

Fprotect = Fbelay + Fclimb = 1.66 * Fclimb

So the maximum force our climber could produce on his protection during a fall would be

Fprotect = 5.1 kN * 1.66 = 8.5 kN

Enough force to break nuts # 1-5!

If our example climber were to place protection a 3 meters then take a 2 meter fall he would produce a force of

Fprotect=( sqrt(2 * 76.2 * 9.81 * 8720 * 2/4) * 1.66) = 4.2 kN

But if he were to place protection as high as 7 meters before taking a 2 meter fall

Fprotect=( sqrt(2 * 76.2 * 9.81 * 8720 * 2/8) * 1.66) = 3.0 kN

Now if his friend who is twice as heavy (24 stone or 152.4 kg) was to try the same climb and take the same fall onto the 7 meter protection he would produce a force of

Fprotect=( sqrt(2 * 152.4 * 9.81 * 8720 * 2/8) * 1.66) = 4.2 kN
Klimmer

Mountain climber
San Diego
May 8, 2012 - 08:18pm PT
Momentum = Impulse

mv = Ft

Solve for F:



F = mv/t

F = N (1000N = 1kN)
m = kg
v = gt
t = seconds (to solve t see below)
g = 9.8m/s^2




d = 1/2gt^2

Solve for t:

t = square root (2d/g)
pell

Trad climber
Sunnyvale
May 8, 2012 - 08:33pm PT
I just place my pro as good as I can and try hardly not to fall.

There're too many factors should be involved in calculations. It's nearly impossible to predict a pull force even in lab environment without thorough equipment testing. E.g., when DMM engineers tested slings they get a noticeable different results for the same setups in different tries, ref. http://dmmclimbing.com/knowledge/how-to-break-nylon-dyneema-slings/ (e.g., line 2, 16mm Nylon, min 10.5kN, max 11.4kN, assuming an average 10.95kN we get more than 4% deviation.
Spider Savage

Mountain climber
The shaggy fringe of Los Angeles
May 8, 2012 - 08:44pm PT
Fun thread.


Old School: The leader must not fall.



I saw a chart once that said a 150 lb weight falling 10 ft will generate 2000 lbs at impact.

That is how much I weighed and how far I fell onto my left ankle one time. There was damage.



Realistically, there are so many variables to the forces, if you have a specific placement on a specific route you could go to a lot of trouble to work it all out. Or you could do what it takes to climb it and not overload the piece.

I have used micro stoppers and the little tiny brass things. The small aluminum stoppers hold pretty well in short falls. I did a big tension traverse off a #1 stopper once. There was a point when It would have been a long bouncing fall but the going was only 5.5 or so.

Experience will take you there. Unless you die on the way.
michaeld

Sport climber
Sacramento
May 8, 2012 - 09:21pm PT
190lbs? Holy f*ck you're gonna die.
Chickenhead Climbing Gear

Social climber
Philadelphia, PA
May 8, 2012 - 10:04pm PT
Fwiw, JT credits both Attaway and Goldstone. In any event, from reading the paper that accompanies his calculator I suspect it is better than most, and many out there are worse than horrible.
rgold

Trad climber
Poughkeepsie, NY
May 8, 2012 - 10:40pm PT
A few comments.

(1) Jay Tanzman's fall calculator, http://jt512.dyndns.org/impactcalc, is now the best thing available on the web that I know of. It uses Jay's improved version of the "standard model." Chances are that standard model type calculations overestimate peak loads, but they are still quite useful as worst-case scenario estimates.

(2) The account I wrote of the "standard model," mentioned by Adatesman, http://www.rockclimbing.com/cgi-bin/forum/gforum.cgi?do=post_attachment;postatt_id=2957; has been been presented over and over again by different authors, including Attaway, often, unfortunately, without a hint of attribution to the real originators. The credit belongs to Richard Leonard and Arnold Wexlar, who first published an account (plus quite a bit more) in the Sierra Club Bulletin in 1946. In this matter, those guys were way ahead of their times.

(3) The equation given by snowhazed is incorrect. For example, it says that if you just hang on the rope (fall factor=0), the maximum tension in the rope will be 0 kN (good news for manky rap anchors…). See Equation~(9) of the above-linked account, or Equation (13) for a version more adapted to calculation. But if you just want some numbers, use Jay's calculator.

(4) Klimmer's account begins with the incorrect statement that momentum=impulse. The correct version is that impulse is equal to the change in momentum. The next error is the formula suggesting that impulse = Ft, which is only true if the force involved is constant over the time interval in question, which is certainly not true of the tension in a climbing rope. The product Ft needs to be replaced by the integral of F(t) dt.

(5) I'm not sure I agree with Jim's claim, quoted by Del Cross, that a useful mathematical model is impossible because of the number of variables. You can't include all variables in a model, otherwise it wouldn't be a model, it would be the real thing, so the challenge is to include the "right" number of variables. Counterbalancing the problems with a mathematical model omitting variables is the fact that variables in real-world tests sometimes confound each other and lead to so much variation that one cannot use the test to decide between different approaches. This situation is particularly relevant to falls caught by human belayers, whose performance varies enormously from trial to trail.
Ghost

climber
A long way from where I started
May 8, 2012 - 11:31pm PT
Ha! I knew R Gold would show up and blow all of the bullshit away. But even with a perfect understanding of the physics available on the internet, 99.9999% of us neanderthals will simply wiggle in the best pro we can, stroke our blue Camalot a few times, and go for it.
Captain...or Skully

climber
May 8, 2012 - 11:34pm PT
Given the options available, that's just what I'd do.
Except the Blue camalot part. Those things are junk.
Oliv3r

Trad climber
SF
Topic Author's Reply - May 9, 2012 - 12:31am PT
Thanks for the great replies.

I guess what it comes down to is trying to figure out if there is a rating in kNs that denotes that a piece of protection is aid gear as opposed to something that is appropriate for a trad rack.

Sounds like those really small brass microstoppers have very limited applications in moderate trad climbing (<5.10), and that I should stick with a set of regular BD stoppers or DMM walnuts or something similar?
tornado

climber
lawrence kansas
May 9, 2012 - 12:57am PT
Some of the micro stoppers have higher kn ratings than some smaller cams. For instance in the Black Diamond set only the two smallest sizes are for direct aid. The largest size 6 is rated 8kn http://www.blackdiamondequipment.com/en-us/shop/climb/protection/micro-stoppers
while the smaller master cams are rated below thathttp://www.metoliusclimbing.com/master_cam.html
Micro stoppers are great because they fit in places cams do not go (DMM brass offsets) and they do not add much weight to your rack. Sometimes something is better than nothing.
rgold

Trad climber
Poughkeepsie, NY
May 9, 2012 - 01:09am PT
The physics stuff is sometimes an interesting exercise after the fact, to try to estimate what kinds of forces might have been involved. It also can help to debunk outlandish claims, such as one made on another site that top-rope anchors need to be able to withstand 20 kN loads, when even the overestimating standard model indicates you'll never manage to get near 10 Kn, even with almost inconceivable worst-case scenarios.

As for micro gear, I think most of us it for free climbing. Success depends on many things. For example, the falls have to be short, which means after a few feet you ought to consider the piece worthless, the placements have to be made with great care and attention to the the local geometry, and the rock has to be excellent so that the trinkets don't break out of their placements.

Sometimes, with enough endurance and discipline, you can get in a string of pieces not far apart that will probably work because potential falls are kept very short, and other times you can place two or three pieces in one spot that may hold a longer fall.

Double-rope technique is especially useful in combination with small gear. You can try for a series of overhead placements, with new ones made before the previous placement is below knee level. With a bit of luck, your falls will be upper-belayed. The reason for double ropes is that if an overhead placement blows with a single rope, the large loop of slack created contributes to a long fall and so a big impact on the next piece down. With double ropes (properly managed by the belayer), there is no penalty for a blown overhead piece, because the other rope through the lower piece does not acquire slack when the overhead piece pulls.

For example, here's a shot of Dave Birkett using micro gear on The Walk of Life, perhaps most famous for being initially graded E12 7a, the hardest grade ever given to a route in the UK.

Klimmer

Mountain climber
San Diego
May 9, 2012 - 01:11am PT
(4) Klimmer's account begins with the incorrect statement that momentum=impulse. The correct version is that impulse is equal to the change in momentum. The next error is the formula suggesting that impulse = Ft, which is only true if the force involved is constant over the time interval in question, which is certainly not true of the tension in a climbing rope. The product Ft needs to be replaced by the integral of F(t) dt.



rgold,

The basic algebraic formula of mv = Ft is correct, without doing calculas, and taking the derivative of time.

It's a little hard to throw in the delta symbol in ST.

The change in Momentum = The change in Impulse, is correct, in this case.

(If the example was a golf ball at rest first, being teed-off then you could say The change in Impulse = The change in Momentum, Ft = mv )

In this case the falling climber has Momentum = mv, first.

The climbing rope is applying an Impulse = Ft, second, to stop the falling climber, which is equal to the momentum of the climber. The longer the impulse time the less the impulse force.

The t of the impulse would have to be accurately timed. Time for impulse would begin the moment the dynamic climbing rope started to take any load of the falling climber, until the moment the climber came to a complete and full stop. So F in this case would be the sum of all forces, during the entire impulse time.

That is why we have dynamic climbing ropes to extend impulse time. If we climbed on steel cables, then the impulse time would be unbelievably short and the impulse Force would be unbelievably high. So high in fact our bodies would be dismembered, and this is a very good reason we don't climb on static ropes.
Karl Baba

Trad climber
Yosemite, Ca
May 9, 2012 - 01:14am PT
Use Yates screamers if you think you're going to fall on a piece that may or may not break

Or even how to account for factors would affect that?


the Devil is in the details. I doubt the result of most people's calculations actually matches the actual force on the gear because of so many factors like friction, the give in the body and whatnot. Has anybody tested how theory matches up with reality?

Theoretically a fall on your daisy chain should mess you up and/or rip your gear but many people have got away with them.


Peace

Karl
Ed Hartouni

Trad climber
Livermore, CA
May 9, 2012 - 01:24am PT
klimmer, if you need a Δ look for it here:
http://www.supertopo.com/climbing/thread.php?topic_id=351467&msg=352411#msg352411

you calculation isn't a productive approach to calculating the force...


the better way of looking at the problem is through the work done...
rgold

Trad climber
Poughkeepsie, NY
May 9, 2012 - 01:44am PT
Karl, at this point, there are quite a few papers comparing theory to reality, and a number of approaches, more complex than the standard equation mentioned here, that have very good correlation with measurements made with real climbers and real belayers. Unfortunately, much of these accounts are in Italian and German and are not well-known in this country.

For an idea of some of this work, look at

http://user.xmission.com/~tmoyer/testing/Simulation_of_Climbing_and_Rescue_Belays.pdf

(scroll past initial frames on rescue configurations).
Klimmer

Mountain climber
San Diego
May 9, 2012 - 02:26am PT
klimmer, if you need a Δ look for it here:
http://www.supertopo.com/climbing/thread.php?topic_id=351467&msg=352411#msg352411

you calculation isn't a productive approach to calculating the force...


the better way of looking at the problem is through the work done...


Ed,

Yes, I agree it could be done that way too. I suppose distance would be easier to measure accurately than time. d = the point at which a load is on the rope to the full dynamic stretch length of the rope.


ΔKE = ΔWork.

ΔKE = ΔW


1/2mv^2 = Fd


Solve for F:


F = 0.5mv^2/d


v = gt




Thanks for the character tip!
JimT

climber
Munich
May 9, 2012 - 02:32am PT
It certainly is the case that jt´s calculator will give you the best value you are will get at the moment.

The debate at that time was to some extent at cross purposes as I was discussing a true model and others a standard model.
My objections were of a more technical nature in that the calculator (and the standard models) fail to reflect the complexities which occur in a real-life fall, belaying etc. This is not something which would really concern a normal climber but not very helpful for the work I was doing at that time where an accurate (and horribly complex) model would have allowed the identification of the forces at all points in the system at any point in time.
The subtlety is that I wrote "To produce a theoretical force calculator at this time is impossible...." not "a useful force calculator...)" since at the moment we still have to put measured values (rope characteristic and karabiner friction) into any calculator and some of these measured values are very variable. Currently for research we still have to do drop tests since the standard model is not detailed enough.


Not falling off is the key to survival, model or not!
Ed Hartouni

Trad climber
Livermore, CA
May 9, 2012 - 02:34am PT
klimmer,

you want the total energy to be mgh where h is the total length of the fall
Klimmer

Mountain climber
San Diego
May 9, 2012 - 02:47am PT
OK, got it.

ΔKE = ΔGPE


ΔKE = ΔW


So therefore, . . .

ΔGPE = ΔW

mgh = Fd

Solve for F:

F = mgh/d


h= length of fall in meters (m)

d = dynamic stretch of the climbing rope in meters (m)




Ok, easier still.
rgold

Trad climber
Poughkeepsie, NY
May 9, 2012 - 03:19am PT
Klimmer (and everyone else), I promise this is my last word on the subject of these calculations.

Both your original approach and the latest version have the same mistake, which is that you are treating the maximum tension in the rope as if it was constant during the entire time the rope stretches to arrest the fall.

In the original treatment, you had mv=Ft, but what is needed is



and of course with this you can't divide both sides by t any more.

In the latest version, you have mgh=Fd. Here you treat F as if it was constant throughout the entire stretching process, but in fact F is a function of the stretch x, and so rather than Fd you need



and so you can't divide both sides by d.

There is another error in the second approach, which is that mgh isn't correct, at least if, as I imagine Ed intended, h denotes the distance the climber falls. The reason mgh isn't the correct change in potential energy is that the climber goes an additional distance, I think symbolized by d according to you, due to the stretch in the rope, making the net change in potential energy mg(h+d).

The link I provided has a derivation based on the conservation of energy approach you attempted; I believe this is the way Leonard and Wexlar originally derived the "standard model" formula



where F is the maximum rope tension, w is the weight of the climber, K is the rope modulus (which has to be calculated from the UIAA impact rating of the rope), and R=h/l is the fall factor.

If you just want an answer for the UIAA standard 80 kg climber, the following expression can be obtained from the formula above:



where as before R is the fall factor, U is the rope's UIAA impact rating, and F the maximum rope tension in kilonewtons
Ed Hartouni

Trad climber
Livermore, CA
May 9, 2012 - 11:47am PT
actually I intended h to be the total distance... which included stretching the rope...

but I gave up with the derivation since you had done such a good job on your rockclimbing.com link deriving the expression in two ways...

Ksolem

Trad climber
Monrovia, California
May 9, 2012 - 12:32pm PT
I’m no mathematician, but I’ve got enough common sense to understand that every fall will generate a unique amount of force. Even the same fall taken twice will be unique (your knott will be tighter or looser, your belayer will be situated differently, the rope will be less dynamic from the previous fall...)

I’m with RGold on the use of double ropes. If the deal is really serious I like two belayers as well.

And for a climb which involves thin delicate pro I like having belayers who have the skill and presence of mind to perform a good soft catch.
Hawkeye

climber
State of Mine
May 9, 2012 - 07:46pm PT
If the deal is really serious I like two belayers as well.


if the deal is really serious the best outcome is dont fall. the next best outcome is recognize that if falling is possible and you are not willing to take that risk, then you had best be a good downclimber.

the most important part of all of this when serious injury is a possibility? keeping your wits about you. placing very small pieces just might give you the extra mental confidence that you need to pull it out. all situations are different and only experience will get you out.

frankly, your ability to keep your wits about you is far more useful than calculating how much force you will exert on a questionable piece. by wits i mean the ability to exercise the judgement that will tell you how much danger you are in and whether you have the ability to climb through it, or bail before you get into a drastically dangerous situation.

by the way, this is not taught in gyms.
Seamstress

Trad climber
Yacolt, WA
May 9, 2012 - 08:00pm PT
I generate roughly half the force that my husband does. Nonetheless, I have been known to place two blue camelots, cry to reduce my weight, and invoke the name of "christ" as in Chapin's tune about naming the only person who can save me now.

I find it very helpful to attempt to understand the math. It is a good realituy check on just what the consequences might be. Love to do some of the match and compare answets from the competing sources....
pell

Trad climber
Sunnyvale
May 9, 2012 - 09:19pm PT
Will the microstopper hold or pop?

It depends on many-many factors- rock quality, and surface of "brass-rock" contact, and an angle between direction of pull and a microstopper's wire, and a history of microstopper's usage (metal fatigue is accumulated every time it is loaded) - and a whole lotta other I don't know and can't imagine.

The only way to know - fall and see what'll happen.

It's like a car driving - the only way to know whether you will survive on your way to home or will be killed in a road accident is to jump in your car, start it and drive home.

We all gonna die.
donini

Trad climber
Ouray, Colorado
May 9, 2012 - 09:46pm PT
Climbing safety is an experiential thing, testing in the lab is of little consequence.
donini

Trad climber
Ouray, Colorado
May 9, 2012 - 10:04pm PT
The testing goes on in the development stage of climbing related products, how you use them is the most critical factor.
mission

Social climber
boulder,co
May 9, 2012 - 11:49pm PT
If you use a safety bend, the force generated in a fall will never exceed twice your body weight. The rope goes up from your harness to the carabiner, bends around the lower part of the biner, and goes down your belayer.

As Hugh Banner once said, "If it's below the waist, it's not a runner."


Ksolem

Trad climber
Monrovia, California
May 10, 2012 - 12:15am PT
If you use a safety bend, the force generated in a fall will never exceed twice your body weight. The rope goes up from your harness to the carabiner, bends around the lower part of the biner, and goes down your belayer.

Maybe I'm just thick, but that post is harder to understand than all the equations...
WBraun

climber
May 10, 2012 - 12:19am PT
Ksolem

That's just yokel speak for ....

"Don't worry everything will be all right"
Dr.Sprock

Boulder climber
I'm James Brown, Bi-atch!
May 10, 2012 - 12:29am PT
just put the rope in a bucket of water right after you fall and measure the temp change of the water, deduct .098 for each 1000 feet of elevation,

it takes longer to cook muffins in denver than SF, right?


WBraun

climber
May 10, 2012 - 12:33am PT
lol ^^^^
mucci

Trad climber
The pitch of Bagalaar above you
May 10, 2012 - 12:34am PT
Sprock



WTF






OVER?
pell

Trad climber
Sunnyvale
May 10, 2012 - 03:07am PT
Lab results can and do provide very important information.

Lab results can provide a lot of information on "how to use gear to get the most it can provide". Those kNs and other numerical stuff are intermediate outcome. It's more for comparison and development the best strategies than for direct in-field usage.

Anyway belay is just a belay. It's not a lifesaver. No guaranties. It's the last frontier - if belay actuate you definitely did several mistakes one-by-one and allowed the situation gets out of control when your (and your buddy!) health and life depends on kN, wires, materials elasticity/braking strength and other technical stuff not on your skills. It's a defeat.

It doesn't mean we should not make a belay in mountains - it's a chance and we can develop our skills and modern gear is good enough (e.g., ref. http://www.supertopo.com/climbing/thread.php?topic_id=1808515 thread) so the chance would really count.

Nowdays we have excellent gyms where we can fall on a perfect belay many times each day to learn and push our limits. But in mountains belay is just a belay - the last frontier without any guaranties.
crock

Trad climber
The Windiest Mountain, Wyoming
May 10, 2012 - 04:12am PT
It's actually very easy to measure the force if you use a car as the top anchor. Simply attach the rope to the car by wrapping it several dozen times around the driveshaft (this is easy to do if you jack up the wheels and run the engine a bit).

Now, place the vehicle in neutral and start climbing. When you fall, you'll hear the car 'peel out'. Measure the length and thickness of the strip of black rubber and you'll very easily be able to determine the force vs time.

pell

Trad climber
Sunnyvale
May 10, 2012 - 04:34am PT
Now, place the vehicle in neutral and start climbing. When you fall, you'll hear the car 'peel out'. Measure the length and thickness of the strip of black rubber and you'll very easily be able to determine the force vs time.

And don't forget to put on your Da Brim - skin cancer is able to wait.
Klimmer

Mountain climber
San Diego
May 10, 2012 - 08:26am PT
rgold,


Thanks for your last post.
Phil_B

Social climber
Hercules, CA
May 10, 2012 - 10:10am PT
All models are wrong!


Some are useful.
rgold

Trad climber
Poughkeepsie, NY
May 10, 2012 - 10:58am PT
But with an actual belayer instead of a tied off tree stump it'll be different. These models don't address that difference.

The statement is at least sometimes true but the implied conclusion may not be. I say "sometimes" because friction in the system often contributes enough so that no rope slips through the belay, which is the primary mechanism for load reduction at the top anchor.

As for implied conclusions, when experiments are done with real belayers and climbers (as has been done extensively by the Italian Alpine Club), the performance of the system shows so much variation that almost no useful conclusions can be made about the effects of individual elements in the belay chain. The way in which various choices affect the loads is overwhelmed by the extreme variability in belayer performance, even when everything else is kept exactly the same. (We don't like to think our belaying is subject to wide variation but, apparently, it is.)

This is one of many applied situations in which a good mathematical model is almost a necessity if one wants to study the effects of various elements. (For an example of such a study, more than about 20 cm of lift for the belayer contributes nothing further to peak load reduction on the top anchor.)

The standard equation mentioned is the first stage of a modeling process which has to be extended considerably to get something that gives consistent good agreement with real-life performance; as I said above the standard equation tends to overestimate the loads. There are several far more sophisticated models (involving more computation but almost nothing new in terms of the basic ideas), including one by the CAI, that correlate far better with results obtained with real belayers and leaders.

All models are wrong!

Some are useful.

Absolutely! One of the things that seems to confuse people is that being "wrong" is part of what makes a model a model. If you don't ignore some of the details of the system you are modeling, then you don't have a model, you have an exact replica of the system. Of course, the devil is in the details you chose to ignore...
jstan

climber
May 10, 2012 - 11:21am PT
No one has mentioned in this complexityfest whether the rope has just previously held an earlier fall. And whether it is fresh out of the bag and further did not spend years on the shelf. Years ago when I needed to know the peak force that would be exerted on these nut things, I went out and measured it,

(Oh yes, some tests I did in the nuclear reactor at the National Bureau of Standards revealed that the catalyst used in the manufacture of nylon remains in the nylon. I am not surprised that nylon has a shelf life.)

The numbers were surprising.

First I tied a loop in 8mm perlon but put a drilled out cylinder of plastic on one leg of the rope, fixed to the sling on one end by pushing a finishing nail through the perlon. There was another nail pushed through the perlon such that when the perlon stretched it would push a brass slider along the plastic cylinder. By measuring its position after the fall you could estimate the peak force to which the perlon had been exposed. I calibrated the rig using using static loads applied by a tensile machine. (We had a tensile machine at work so we could test to see whether our work on shooting down missiles with high powered lasers was getting anywhere. Apparently we weren't.)

I need to set the scene. The McCarthy wall is a good place so I went there, Just to the right of Something Interesting. There is a prominent overhang( surprise surprise) about 70 -80 feet up. I put in a piece of protection so that if I hauled 165 pounds of shale in an army duffle bag up to the ceiling and dropped it, it would free fall around forty feet. It was tied in with a waist loop and came to rest ten or fifteen feet up, i would guess. Almost a ground fall.

As an aside I also did an experiment with a really poor nut and stayed right at the placement during the test. The bag went winging past me but the nut followed so swiftly I never saw the manner in which it failed. I had backed the whole system up to an old piton. The old piton also followed directly leaving a cloud of rust in the air. As I was well up the wall I was spared having my friends detecting my embarrassment. They were more interested in all of the excitement, I suspect.

Now the surprise. When I just anchored the belay rope to a big tree trunk we got a peak force of 1000 pounds. When I belayed the fall with me anchored to the same tree I was whipped up into the air. In that case the peak force was about 500 pounds. This is why I keep railing against belays directly off anchors. Doing so makes one imperturbable, but you are not doing good things for the leader.

Using the generated forces to accelerate a second massive object is a really good idea. Go to accounts of poorly protected leads on gritstone to see how shrewdly the Brits use the idea of a second massive object. A natural shock absorber.

My main concern was not in modelling to allow a calculation to approximate the measurements. When I held the belay I successfully showed myself the fall was a doosey. We know ropes and carabiners are very hot after a big fall and there was a lot of lateral whipping in the system that would extend the peak force application over time. The dynamics of the system have to play a role.

I had what I sought. When my hydraulic system put 3000 pounds on a nut during later experiments

I knew I was in the ball park.





Someone above mentioned wishing they could predict when a nut will fail (and how). I published an approach to that back in 1971 based on shear modulus. I have repeated it endlessly since

to no apparent result.

Suffice it to say I have had only one nut fail on me and that was a small brass RP

in Eldorado. I concluded falling in Eldorado is probably

not a good idea.




Sandstone. Well metamorphosized

but still.........

sandstone.

It will groove.
rgold

Trad climber
Poughkeepsie, NY
May 10, 2012 - 11:23am PT
Climbing safety is an experiential thing, testing in the lab is of little consequence.

Well, yes and no. For example, how you place your favorite single blue Camelot belay anchor of course influences how effective it will be, but the fact that you have such a device at all and the fact that it responds in ways that are capable of correlating with "experience" is because of the sophisticated engineering thinking (logarithmic spiral cam outline) and testing (appropriate cam angle) that went into it. The fact that all this work is hidden as your experienced eyes seek out and find the ideal placement and you slide that cam in should not be mistaken as the primacy of experience over "testing."

And frankly, climbing experience is a wonderful thing, but still has very substantial deficits as a way of understanding what practices are best.

The fact of the matter is that our decisions are never subjected to robust testing and sometimes are not subjected to any testing whatsoever (consider the tiny fraction of climbing anchors that have been subjected to a factor-2 fall, and compare that to the number of climbers who are certain they have built a "bombproof" anchor, in spite of the fact that not one of their anchors has ever been subjected to a worst-case scenario test).

In this regard I'm reminded of some tests conducted, I think, by the DAV that found, unsurprisingly, that very experienced climbers had no ability to judge the worth of fixed protection. The same is surely true of bolting, where only a substantial testing program can ever tell us what best practice should be.
rgold

Trad climber
Poughkeepsie, NY
May 10, 2012 - 03:43pm PT
I would like to add that, even if many people were unaware of it, that John's tests played a hugely significant role in climbers accepting the use of small nuts and so in the transition away from pitons.

At the time, it was commonly assumed that smallish wired nuts were aid pieces. John went out and did his tests and realized they could be used for protection. More than that, he developed an excellent sense of how far one could climb above such things. Then he put his money where his mouth was and did scores of ground-breaking ascents with those small nuts, ascents which don't see a whole lot of traffic from today's climbers.

I really believe that John's knowledge, obtained from testing and then refined by experience, spread from him to the rest of country. His partners learned to use and trust small gear from him, and as they traveled, they spread John's knowledge. (Of course, there were people in other areas who placed small gear, but unlike John, they generally did not have a good idea of what kinds of loads the gear would or would not take. John knew.)

Years after John's tutelage, I still found myself climbing with climbers, some quite prominent, who didn't trust small gear and didn't even want to bring it on our climbs, and so were still carrying pitons. I once did a long climb in which my partner placed a piton on every pitch he lead and I never had to place a single one, because John had taught me about the use of small gear.

What happened here is that John's tests turned into what others, who may not even have known about those tests, viewed as experience.

jstan

climber
May 10, 2012 - 04:28pm PT
It was a very exciting time.

Everyone was learning.

It is a very sad thing when people try not to learn.
Jay Wood

Trad climber
Land of God-less fools
May 10, 2012 - 05:03pm PT
If the question behind the question is whether micro nuts are worth carrying on a trad rack,

I would say yes. As Tornado said- light, and fit where nothing else will. I have used them even for anchors when nothing else worked. It's not only about maximum strength. Sometimes I bring a few small cams and some micros when using someone else's rack, for back up.


rgold

Trad climber
Poughkeepsie, NY
May 10, 2012 - 05:50pm PT
Del, the CAI found tremendous variation in results when human belayers were involved. That point had nothing to do with belaying off tree stumps, and I did not mean to suggest that human belayers were equivalent to static belays.

On the other hand, if I recall another paper I read, belayers who jump backwards, as they sometimes do to try to prevent a leader decking, or belayers who mis-time a jump dynamic belay, can achieve anchor loads in the same range as a tied-off anchor. In other words, within the range of human behavior are, albeit very occasionally, loads of the sort you might get from a gri-gri on a tree stump.

As for preferences, I take the human harness belay any day when climbing. But if I want to understand the effect of lifting the belayer, then a sophisticated mathematical model will probably be much better.
rgold

Trad climber
Poughkeepsie, NY
May 10, 2012 - 06:20pm PT
Yeah...brevity is not a virtue I have ever acquired.

(Just for fun I tried it here.)
jstan

climber
May 10, 2012 - 09:17pm PT
The following youtube seems almost comedic till you think about what it is showing.

http://www.youtube.com/watch?v=0RZo4AM0QRU

The kinetic energy of the falling climber is transformed directly into raising the belayer. This extends the time interval during which the force is applied to the top anchor. We are working in integrals here. If you integrate over a very short time the peak forces have to become much increased.

OK a real example. When I freed To Have and To Have not (just some aid climb - nothing to lose your blob over) there was only one nut in the system. A number three stopper. I had no idea what problems lay ahead meaning I had to plan on a forty footer on that one nut. So I had my 110 pound wife belay me unanchored, I judged she still felt I was a halfway useful guy and would hold onto the rope. I had her stand out from the base of the cliff. That way as she was dragged into the cliff the initial transient in the force would be limited and would increase substantially only as she would be shot up into the air. I think it is really important to avoid very sudden shocks to protection. Doing an integration when you have a singular argument causes all kinds of difficulty. Go ahead - ask Hartouni. Those residues are something awful. It was a steep descent but I was not into the Steepest Descent Method(Copson).

And oh yes. There was a subsequent divorce.


jstan

climber
May 10, 2012 - 09:25pm PT
Tell me about it!

I would have asked Bragg to belay me, even at his larger weight and higher peak force, but he was off somewhere putting in Gravity's Rainbow. Kids! They never stick around.
Ed Hartouni

Trad climber
Livermore, CA
May 11, 2012 - 12:32am PT
Doing an integration when you have a singular argument causes all kinds of difficulty. Go ahead - ask Hartouni. Those residues are something awful.

If the integrand you desired
Near an analytic function required
To find the closed path in the complex plane
Corresponding to your real interval's a pain
Ask Richard Goldstone for some advice
His teaching experience will suffice
rgold

Trad climber
Poughkeepsie, NY
May 11, 2012 - 01:47am PT
A physicist name of jstan
had a bold and unusual plan.
But from the crux pitching
he heard his wife bitching,
"I need to be tied to a van!"

A climber named Stannard one day
had to make sure a nut would just stay.
So he roped up his wife
and caused marital strife
when she flew up the cliff on belay.

A climber who might have seemed callous
had a need to stay out of the talus.
So his wife he employed
as a counterweight droid
which she took as a sign of some malice.

It turned out to be Stannard's lot
to free the climb Have or Have Not,
To keep a nut tight
his belayer was light
and up in the air she was shot.

D Fred

Trad climber
san francisco, ca
May 19, 2012 - 02:15pm PT
i'll be damned, you're right...

BD #6 stopper rated at 10kN is the same size as BD C3 00 cam which is rated to only 6kN

go nuts!
Steve Grossman

Trad climber
Seattle, WA
May 19, 2012 - 02:52pm PT
Nice Limericks Rich!
bit'er ol' guy

climber
the past
May 19, 2012 - 04:11pm PT
jump
Mike Bolte

Trad climber
Planet Earth
May 19, 2012 - 04:20pm PT
Those are excellent Rich! Very clever.
Chrisw1096

Gym climber
Jan 7, 2013 - 09:12am PT
Well 4 kilonewtons is about 899.23 pounds or 407.8 kg.

So if you weighed about 80kg (average) and fell about 5-6m with a static rope then maybe you could break it
philo

Trad climber
Is that light the end of the tunnel or a train?
Jan 7, 2013 - 09:34am PT
Great post Rgold.
This was turning into rocket science.

The answer is in the question.
I loved this Studly response.
Wish I would have had that reply in my parenting quiver when my kids were little.
kc

Trad climber
the cats
Jan 7, 2013 - 10:44am PT
Well, rated appropriately or not, my feeling is that it's better to place something than nothing at all. After all, you can't be caught by a piece if you don't put one in.
Steve Grossman

Trad climber
Seattle, WA
Jan 7, 2013 - 10:58am PT
Reach for the Aid Screamers for load-limiting peace of mind and torture that little wired nut to the tune of hundreds not thousands of pounds of impact force. Put a couple on your Hula Harness...LOL
Ed Hartouni

Trad climber
Livermore, CA
Jan 7, 2013 - 12:27pm PT
there is an interesting subthread here: the roll of a fundamental understanding of the physical system in explaining our experiences.

From the point-of-view of most people reading this thread, the explanation of even the simplest system is so complicated and arcane that they assume nothing from that explanation can be used to understand a "real" situation.

That's an unfortunate consequence of using a short hand means of explanation, the mathematical description of the system instead of translating it into a simple explanation, which would be quite lengthy.

So the onus is on us to provide the description and the limits of the model used to do the calculation, and how those limits affect the conclusions. However, they have already provided a huge insight.

That insight is simply that very few anchors have ever been tested at the forces generated in a factor 2 fall. There have also been few tests of such situations using modern gear.

We achieve this insight by noting that the calculations we perform for even simple systems give us an idea of what is going on in the dynamics of a fall (where I use the word "dynamics" in its physics sense) including the distribution of forces on the anchor system.

The lack of experience in holding these types of falls is a good thing, people are climbing cautiously enough to avoid such "tests" but if our assumption that our anchor methodologies are able to hold such falls is not based on sound principles, which are also verified by tests, then we have been lucky rather than good.

We should be both. And our calculations tell us we don't actually know. For this particular aspect of climbing, we should know.
Jim Brennan

Trad climber
Vancouver Canada
Jan 7, 2013 - 01:02pm PT
What are the calculations to resolve this problem ?

Michelle

Trad climber
Toshi's Station, picking up power converters.
Jan 7, 2013 - 01:21pm PT
You know, I was seriously considering returning to school for my math degree. I think I'll pass on it. Too much work! But this is an awesome topic.
Ed Hartouni

Trad climber
Livermore, CA
Jan 7, 2013 - 11:48pm PT
part II

the calculation that Richard has repeatedly worked through is simple enough to understand if you have some calculus background. But we can put it into words too.

The climber is out some distance which we take to be the length of rope, and is climbing above the last piece of protection, we can call that the length of runout.

When the climber falls we'll make our first approximation, that the fall is into free space. Obviously there are many other scenarios, but the largest forces are going to be for falls where the energy of the fall is not transferred to, say breaking bones or sliding friction or spinning.

The work done by gravity is just the gravitational force multiplied by the distance the climber falls. This becomes kinetic energy, that is, the climber speeds up in the fall as the length of the fall increases.

We make another approximation by neglecting the aerodynamic drag of the climber falling in air. This drag might be significant in some very long falls, but for the scenarios we're talking about, this is usually a good assumption. Also, the force of the fall without taking into account aerodynamic drag is greater than when it is taken into account.

The climber falls twice the runout length before the rope is a factor. Once this happens, the rope starts to stretch and the force on the climber is the sum of gravity pulling down, and the rope pulling up. The force the rope exerts is proportional to the fraction of its increased length multiplied by a constant which we call the "spring constant" or the "Young's Modulus" of the rope, but the rope model we consider here is that of a spring which is yet another approximation.

You can see that as the climber continues to fall, the fractional length of the rope increases and the therefore the force pulling up increases. The energy of the fall is going into stretching the rope. It does this incrementally, until all of the energy of the fall is used to stretch the rope to the length that "stores" the energy in the stretch.

This is where the calculation stops. We can show what the force is on the rope as a function of time using this method, so the peak load is known.

If the runout length is not equal to the length of rope out to the climber, we assume that whatever the rope runs through does not impede the ability of the rope to stretch under load, we assume a frictionless system.

Certainly this is not an issue for a factor 2 fall, that is, where the runout length is equal to the length of the rope out to the climber. In such a fall, the maximum force is calculated in this manner.

The more length of rope out to the climber, and the less runout the climber is, the smaller the force, the force factor is just the ratio of twice the runout length divided by the length of rope out.

You can see why a low fall factor fall has less force, the fractional stretch of the rope is much less when more rope is out, if the fall is short the energy required to stop it is less. You might have experienced this simul-climbing when your second falls and weights the rope, not much more additional force than the weight of your partner coming onto the rope. This happens when you belay the second, holding a fall with a lot of rope out entails much less force than when the second is at the top of the pitch.

More elaborate models are possible, putting anchors in with realistic friction is possible, and including into the rope model a way of dissipating energy gets rid of the oscillatory behavior we neglected by terminating our calculation with energy conservation. If you read Italian, German or French there are many good articles written by those alpine club safety sections. As far as I know, the American Alpine Club avoids such things entirely, seems somewhat irresponsible.

Knowing what the maximum forces are on the anchors provides an input to the setups you might design to test anchors. It isn't trivial, as jstan related above, to provide a test that is safe to the testers without some initial calculations that give you an idea of what needs to be provided.

Models of the cordelette and the sliding-x are also possible to make that incorporate realistic features and reproduce test results. In fact, I claim that a relatively simple analysis of equalizing systems shows that every such system reduces to combinations of those two... so there isn't much to discover in proposing new ways of torturing webbing, they all reduce to combinations of those two. That's from analysis...

...Where the AAC could come in is how to interpret this for John Q. Climber so that all the "theory" didn't need to be hashed over and good, practical solutions to some of these problems might be created and transmitted for the good of the sport.
JimT

climber
Munich
Jan 8, 2013 - 02:38am PT
One should be clear that the standard model used is ONLY a rope model and not a system model.
One could add to the standard model to give more accurate predictions and Jay and myself have discussed this previously BUT all the additional factors you have to input are variables (in fact even the standard model uses an input value which is variable since the rope factor is not constant over the life of a rope or even from day to day). This would make the model unusable in practice since to account for these we would need to know what the variability is and for most realistic climbing situations we can only make a wild guess. It also makes the maths vastly more complicated since even such an apparently simple thing as friction over a karabiner has six or so variables and then getting to grips with belay systems is another level of difficulty altogether.
For those involved in equipment design or perhaps evolving and teaching techniques a better model could be useful to show directions to go in to reduce the forces but for normal climbers the biggest variable of all can never be included which is gear placement.
Its worth remembering that the standards for equipment are based on experimentation and historic experience, theoretical modelling doesn´t come into the picture.
Understanding strategies to reduce fall forces is useful for the average climber but understanding the importance of good gear placement and general good practice is vastly more important. Badly tied knots and abseiling off the end or the rope are the sort of thing killing people, not failing to accurately estimate fall forces.
Steve Grossman

Trad climber
Seattle, WA
Jan 8, 2013 - 10:37am PT
Between Ed, Rich and Jim T you have all the physics resources you could want for answering climbing related questions.

Thanks guys!
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