UKC

I'm trying to calculate the impact force of a fall and everything I have found so far has been unsatisfactory. I'll make it clear that I'm not looking for the fall factor equation but ideally a specific force measured in kN. I appreciate there are many variables but I doubt that means no one has ever written an equation with reasonable accuracy.

If data is desired then the following stats are the ones I'm trying to calculate:

Weight of Climber: 80kg
Rope: 10.5mm Dynamic
Length of rope: 8m
Height of fall: 8m

I appreciate that this is a fall factor 1 and the hypothetical climber has decked out but the intention is to demonstrate the maximum theoretical force an "average" climber could achieve lead climbing on a 8m climbing wall.

Two sources I've looked at are as follows:

http://en.wikipedia.org/wiki/Fall_factor
http://www.myoan.net/climbart/climbforcecal.html

The first there is a lot of conjecture over if you read the notes and the second calculates fall factors in a weird/ wrong way so I don't trust it (that and the equations aren't clear).

Any help/pointing in the right direction would be much appreciated.

In reply to Ranger Ray:

There is this one here.
junkfunnel.com/fallforce

Not sure if it is accurate. I think it assumes a runner above the stance. Friction values for the krab are a guess but probably a bit lower if a large size and diameter krab is used as typical at climbing walls.

Petzl used to do one but think it has now been taken off the site.

Off thread slightly, but I am looking for one which calculates the rope stretch as well.

Wont you also need to know how much the rope will stretch so that the force absorption rate can be found?

A lower stretch rope will have higher peak forces for the same data set compared to a high stretch rope.

IE climber falls 8m.
Rope starts to slow climber down & applies force.
Force increases as rate of speed reduction increases.
At some point rate reduces & forces reduce.

In reply to Rick Graham:

Thank you! The sums are around what I was expecting.

In reply to Ranger Ray:

Start by reading this:-
http://www.rockclimbing.com/cgi-bin/forum/gforum.cgi?do=post_attachment;pos...

The junkfunnel calculator is rubbish same as myoan, the only good ones were from Beal and jt512 both of which are now unavailable.
All of the models are rope models nort system models and so don´t reflect what happens with a belayer in the picture which is usually the biggest single factor in the impact force when rock climbing. Many have tried to model the whole system and a few have got reasonably close but in reality it is better to measure it a lot of times and just get a general overview, it just isn´t easy to calculate because of the number of variables.

In reply to jimtitt:



If that link doesn't work (it doesn't for me) try http://4sport.ua/_upl/2/1404/StandardEqn.pdf

In reply to Ranger Ray:

If what you are trying to do is learn/teach about the role of the different variables rather than work out the forces if you fall off a particular move on a particular route, then I have an excel model on www.multipitchclimbing.com

The link is on the contents page under Chapter 3. As it is excel you can see the equations

In reply to rgold:

How valid is Hooke's law to climbing ropes and climbing magnitude forces?

In reply to needvert:

Well, models based only on Hooke's law, like the one I wrote up in the link originally posted by Jim, are no more than very rough estimates, because there is so much else going on besides elastic deformation. More sophisticated approaches add damping to Hooke's law and account for friction over carabiners and rock. Other approaches model a rope as a combination of damped oscillators in series and in parallel. None of the models account for the very broad range of belayer responses (even when it is the same belayer in multiple trials). It is possible to construct models by beginning with an assumption that, say, the tension in a rope is a quadratic, rather than a linear function of elongation, and then determine the parameters in the quadratic equation by fitting the the equation to experimental data. I would say that such models do not use Hooke's law at all.

So what we have is a collection of models of increasing complexity in which Hooke's law is still a component of the total package, and at least a few models that have abandoned Hooke's law form some experimentally-parameterized alternative. In the view of this, it is hard to frame and appropriate definition of "validity" for Hooke's Law, much less decide on an answer.

In reply to needvert:

The next problem once you have a rope model is that this will give you a force on the climber. All the calculators (and the crude model) assume you can divide these in some way to get the force on the belayer and the top piece. In reality we see that the peak forces are all seperated by time and that the peak force on the top piece for example is not the total of the peak force on the climber and the peak force on the belayer. Such are the difficulties in life and why a theoretical approach has realistically been abandoned, the approach some of the CAI guys have taken is the better one which is to find a model which fits the observed data.

In reply to jimtitt:


May I split some hairs? (Sorry, an occupational proclivity.) All the approaches to modeling are fundamentally theoretical. The equations are not the rope, they are a mathematical construction. Moreover, every model from the simplest, the poor much-maligned standard model, through an increasing range of less inaccurate ones (I'm choosing double negatives intentionally), require some input from observed data. The CAI guys have strung together a bunch of modules, one for each element of the belay chain, each one of which is the good old "theoretical" standard model with an equally "theoretical" viscous damping term added on. These things are classical theoretical damped harmonic oscillator terms. Then they've added terms to describe friction losses between each point in the belay chain, and yes, having created a host of independent parameters, now require a large amount of experimental data in order to determine those parameter values. And yes, now that their model is a big system of differential equations, they cannot provide an analytic solution, instead requiring a computer to implement standard numerical analysis techniques in order to get answers, which apparently agree very well with real-world results.

Did they "realistically abandon" a "theoretical approach" to do this, or rather, did they implement a considerably more complex theoretical approach capable of taking into account more features of the real-world situation? I'd vote for the latter view.

This is, of course, a matter of philosophy rather than any kind of practical distinction. The CAI guys got a better fit, and they needed a big load of data to get it---but they got a better fit. But I can't detect any "theory" abandoned by the roadside.

I mention this, if there is anyone still listening and still interested, because it can happen that a data-fitting approach gives us predictions but no understanding, where by "understanding" I mean the sense that the phenomena we observe can somehow be seen to be consequences of some set of fundamental truths. This is Newton's paradise, and although we may have neither the time nor the ability to dwell there, some of us anyway long for a path back, whereas others want useful answers now that they can employ in the design of better stuff.

Ok, back to your regularly schedule programming...

In reply to Ranger Ray:

What do you mean by 'impact force' ? the name implies a very sharp peak in force whereas in reality the force - time profile is anything but (the rope is specifically there to smooth out the curve). In determinig whether something can cause any damage or stress you have to have a lot more information than one parameter which is not clearly defined in any case (unless you mean peak force ?)

In reply to GrahamD:

It´s called the impact force because it is the force produced by a free-falling body impacting onto the end of a climbing rope. It´s the normal term used.

In reply to jimtitt:

Yup, the normal term used. If Graham wants to call it the peak force that's fine too. It is the maximum tension in the rope for the fall arrest in question.

In reply to jimtitt:

I think "impact force" is one of those terms which is easily misinterpreted and misused. The name has an implication of an impulsive force which simply does not exist. I guess to people who do loads of work in the area like yourself, its meaning is clear. To others, I think its a misleading term both in its implication and in its apparent simplicity.

In reply to GrahamD:

Well it´s defined as a high force over a short time period so it fits the description perfectly which is probably why it is the "official" term used by the UIAA, CENORM and al the rope companies. Can´t see as its confusing anyone particularly and there´s no reason to change a term used for centuries due to the limitations of a few.

In reply to Ranger Ray:

The impact force for any given rope is stated by the manufacturer and is the result from a UIAA drop test on a new rope (fall factor approaching 2 and 80kg mass). This should give you an idea.

In reply to GrahamD:


As Jim suggests, get over it.
The UIAA test has done us all a great service being basically unaltered for over 50 years, though I may be corrected in this recollection.

Also be aware that numerous forces occur in a fall such as that on the various sections of the rope, belayer, runner and climber.

Apart from the junkfunnel calculator, the www.multipitchclimbing.com one also estimates rope stretch.
These calculators both acknowledge their simplistic nature and have been described as rubbish or better than nothing.
It is interesting to input actual UIAA test data into the spreadsheets ( but they may have been formulated around giving the correct answer).
How accurate they can be for the fall factors bet 0 +2 will be compromised by all the factors ignored in the formulae.
Its fascinatingly complicated

In reply to jimtitt:


No reason to change it, but limitations of the few ? the number of threads started on this and related topics demonstrate a pretty widespread misunderstanding or misinterpretation of these terms. I suspect you as an expert are actually the minority.

In reply to GrahamD:

Careful, he might take that as a compliment

"Impact force" is the peak force on the climber.
Infinitely preferable to impact on the ground.

In reply to Ranger Ray:

Nowadays I'd have thought that it would be easier to measure the deceleration of a known mass by taping a mobile phone to an 80kg weight and attaching that to your rope and dropping it 2m. You just need the right app on the phone.

In reply to GrahamD:

It would still be misunderstood or misinterpreted even if we called it something different, at least the group that matters all use the same language
And it´s the correct term as we´d have to invent another one for impact attenuators as well (that´s the rope in techie speak).

In reply to Ranger Ray:

An article that may be of interest

A constitutive equation for the behaviour of a mountaineering rope under stretching during a climber's fall

http://www.theuiaa.org/upload_area/files/1/sdarticle.pdf

In reply to Rick Graham:



There is a need I think to understand why people might have produced and made available such calculators. Certainly the www.multipitchclimbing.com one is there as a teaching tool only. In fact, I'm not sure why a climber (rather than a product developer) would want a more accurate model of the forces in a fall. It would all be so dependent on the route, how the climber falls and the belayer, that it would either be so generic or so focused on a single situation I can't see how it would inform anyone's climbing.

In reply to David Coley:


"These calculators both acknowledge their simplistic nature and have been described as rubbish or better than nothing."
I was attempting here to pre empt any negative backlash comment on the calculators limitations.
Yours is clearly labelled as a teaching tool. As such it is quite illustrative (maybe ?) of why belaying and safety techniques etc best advice has been formulated by the UIAA et al. Thanks for including it in your e books.
It would be interesting to include ( if practical) how much slippage or belayer movement is needed to reduce the loading on the runner.

On the DMM website, Ben Bransby explains how he endeavoured to minimise the loading on the old bolts protecting Baron Greenback at Wimberry.
This is an extreme example at the cutting edge, but understanding more, as opposed to just doing as told, is in my mind, a better way to learn best practice.

So, thanks again for referring me to the calculator. Now if anybody knows of a more detailed one.......