Calling all friction engineers

Many belay devices these days have "teeth" (some non-smooth area near the brake end of the strand). Do these "teeth" really enhance the braking power or is it just a cosmetic sales gimmick? As far as I remember, frictional forces are independent of surface area, so I can't see how these wavy "teeth" would do anything. Is there maybe some other effect than pure friction involved?

Let's take a look at the BD ATC Guide and see.

 
Notice the "V" groove.  If I could find a top view, you will see another "V" groove there it is fatter in the back than in the front.  The "teeth" give the device the added ability to "bite" onto the rope.  A normal ATC with no grooving what so ever has less area of the rope touching the device allowing the rope to pass easier.  Does that make any sense to you?

Edited for spelling *hangs head in shame*

John Wilder wrote: It's not the teeth so much as the 'V' and yes, it helps quite a bit with today's skinny lines. I wouldn't want to try and catch a high factor fall on a 9mm line with a regular atc.

I agree that the "V" gives an easier catch, but once the rope has stopped running through the belay device, the rope will expand into the grooves to give a stringer bite.  I have not tried it with any rope less than 9.2 mm. doubles and it caught just fine.

You might be confusing cooeffecient of friction (which wouldn’t change with friction area), with total friction force, which is dependent on surface area. 

Jon Rhoderick wrote: You might be confusing cooeffecient of friction (which wouldn’t change with friction area), with total friction force, which is dependent on surface area. 

Well OP is basing his theory on the ideas of basic Coulomb friction, where Friction Force=coefficient of friction x Normal Force. In which case he's right, friction is independent of surface area.

But squeezing a soft rope into a grooved metal slot really doesn't fit any of the assumptions of that model.

Here is some reading material:
http://www.paci.com.au/downloads_public/PPE/19_Belay_Device_Theory.pdf

Its a little old.  Jim Titt the author of the above paper posts on MP often. So wait until he chimes in, or contact him directly.  There are probably not many people who are more knowledgeable on belay device friction than he is.

Well the v grooves make a difference of about 20%   to the whole effectiveness but really it is because the initial bend in the rope is split into two seperated parts. The intermediate grooves do  more or less nothing.
I'm climbing right now so posting is difficult

^^^ well stop that climbing right now & focus on what's really important, which is ... er, what was that again ... ?

Unlke Jim, I'm rehabbing some ankle tendonitis and so am out of the climbing game at the moment.

Coulomb's law is a very rough first approximation which all "friction engineers" recognize as seriously flawed.  It comes closest to being accurate when the resisting mechanism comes from forces at the molecular level, which means between two highly polished surfaces.  As soon as the surfaces have physical features, even on microscopic scales, that can interact, Coulomb's law is no longer accurate.  This does not deter engineers from designing things, such as the shape of climbing cams, as if Coulomb's law is in effect.

Friction (whatever that really means) is poorly understood in general, and you can write an engineering PhD thesis on the subject.  We think of an ATC as a "friction device," but what is going on is considerably more complicated.  Jim, in the referenced write-up, refers to bending forces, which contribute to the device's holding power.  The grooves introduce a pinching effect on the rope, and this is a different mechanism from friction.

I have no idea what the ridges in the grooves are for or whether they do anything.  It is conceivable that there could be some interaction between the ridges and the rope core, although it is a bit hard to imagine that could have a measurable effect.  It is also conceivable that the ridges have nothing to do with device friction and are there to promote cooling when the device heats up.

On small race boats there is a common cleat called the clam cleat that is a similar design to the ATC exit except with far more aggressive teeth. It works quite well for holding small diameter lines. I think it's safe to assume that the "V" and teeth combo adds a significant amount of holding power considering the clam cleat holds completely (aka would lock off with zero force on the brake strand).

https://www.clamcleat.com/

Maybe, and it is plausible that the ATC engineers copied the teeth from clam cleat design.  But clam cleats are designed as progress-capture devices that hold ropes statically.  They taper in the direction of anticipated load and/or have much more radical v-slots.  The effect is to compress the rope and force it into the teeth.  You couldn't possibly belay with a clam cleat design, because you wouldn't be able to pay out rope at all.  Once you've modifed the design to allow the rope to slip through under load (eg rappelling), the question of whether the "vestigial" teeth still do anything remains.

You could definitely belay with a clam cleat, the rope runs freely when the tag end is 90 degrees to the cleat.

What you could not easily do is rappel....though I believe current devices could be optimized to have more variable friction by a modification of the "cleat" ridges on an ATC.

But this might make the device too bulky and potentially damage the rope in a fall etc.

If you  saw me climbing you would think l suffered multiple injuries last week!
The intermediate ridges have no effect we could measure when we removed them but might do something so why not, they look like they might.
Angling the entry vee and making it more agressive just makes rhe device grabbier and hard to use, that horrible 9 or whatever its called does this and it is virtually unusable.

rgold wrote:Coulomb's law is a very rough first approximation which all "friction engineers" recognize as seriously flawed.  It comes closest to being accurate when the resisting mechanism comes from forces at the molecular level, which means between two highly polished surfaces.  As soon as the surfaces have physical features, even on microscopic scales, that can interact, Coulomb's law is no longer accurate.  This does not deter engineers from designing things, such as the shape of climbing cams, as if Coulomb's law is in effect.

Seriously flawed is a strong claim.  If we start heading away from friction between surfaces being proportional to their normal force then we would head into some seriously wacky behaviour and the world around us would behave very bizarrely.

Engineers continue to design things as if Coulomb's law is in effect because in a vast number of circumstances it is a very good model of the behaviour.  In the same way engineers keep designing things as though "Newtonian physics is in effect".  Well it is for most purposes of mechanics and civil engineering.  Though in other aspects less common aspects of life quantum and relativistic behaviours need to be considered.

(I have little doubt that you are well informed here.  But using the claim 'seriously flawed' to describe a model that is relied upon in many parts of engineering and science is a little strong.)

It is an interesting day when you get called out on MP for a statement that is "a little strong!"  In support of your comment, we have

 "...the formula is a good empirical rule for judging
approximately the amount of force that will be needed in certain
practical or engineering circumstances. If the normal force or the speed
of motion gets too big, the law fails because of the excessive heat
generated. It is important to realize that each of these empirical laws
has its limitations, beyond which it does not really work."

But also,

"It is quite difficult to do accurate quantitative experiments in
friction, and the laws of friction are still not analyzed very well,
in spite of the enormous engineering value of an accurate
analysis. Although the law F=μN is fairly accurate once the
surfaces are standardized, the reason for this form of the law is not
really understood...

...At any rate, this friction law is another of
those semiempirical laws that are not thoroughly understood, and in
view of all the work that has been done it is surprising that more
understanding of this phenomenon has not come about. At the present
time, in fact, it is impossible even to estimate the coefficient of
friction between two substances."

This is the renowned physicist Richard Feynman speaking in The Feynman Lectures.  Note that you can find tables of this impossible-to-estimate thing all over the internet, and that the design of climbing cams is based on an estimate of the coefficient of friction between aluminum and granite. Ha! Probably polished aluminum and polished granite; Feynman says the estimates are only meaningul for "standardized sufaces."  Meanwhile, we have a certain amount of engineering doublethink going on, in which the cam is designed according to the assumptions of Coulomb's law and then, for example, for soft rock, Metolius increases the cam surface area (their Fatcams), even though Coulomb's law says this doesn't matter, and DMM develops a complicated surface treatment that is supposed to "increase friction."

Perhaps I should have said that attempts to apply Coulomb's law to a particular situation can be seriously flawed?

Never used Coulombs law in 40 years as an engineer, all my tribology books tell me to determine the coefficient of friction experimentally for the conditions that will be encountered.

I would guess that these "teeth" reduce the pressure on the rope itself because the forces are distributed over a larger area (multiple teeth as opposed to one). Maybe they don't add any additional braking friction, but don't we want some slippage during a really hard fall?

David Bruneau wrote: I would guess that these "teeth" reduce the pressure on the rope itself because the forces are distributed over a larger area (multiple teeth as opposed to one). Maybe they don't add any additional braking friction, but don't we want some slippage during a really hard fall?

The only way to avoid all rope slippage would lead to cut ropes in severe falls, as I understand it.

On the other hand, most belays are completely clueless that slippage does occur in bad falls with disastrous results.

Harumpfster Boondoggle wrote:

The only way to avoid all rope slippage would lead to cut ropes in severe falls.

On the other hand, most belays are completely clueless that slippage does occur in bad falls with disastrous results.

Have you got some accident reports on this? I'd like to see what happened. I guess if slippage starts and the climber has enough momentum, they just keep going....

The reports are out there.

If the fall gets stopped the belayer gets burned hands. If it doesn't the leader craters.

rgold wrote: Meanwhile, we have a certain amount of engineering doublethink going on, in which the cam is designed according to the assumptions of Coulomb's law and then, for example, for soft rock, Metolius increases the cam surface area (their Fatcams), even though Coulomb's law says this doesn't matter, and DMM develops a complicated surface treatment that is supposed to "increase friction."

It isn't double think if you are dealing with soft surfaces.  If you one surface crushing and changing characteristics because of the normal force then that is a different story.

Jim Titt wrote:
Never used Coulombs law in 40 years as an engineer, all my tribology books tell me to determine the coefficient of friction experimentally for the conditions that will be encountered.

Yep.  There are plenty of areas where it may not be particularly helpful.  There are also a bunch of areas where it is.  It is used in many areas of civil construction.   If you could come up with a more accurate model then great.  But meanwhile Mohr-Column will continue to be used guide engineering in safe construction.

Oh, and what exactly did you mean by "coefficient of friction".  Is this a coefficient of the normal force or something else?  If it is a coefficient of the normal force then that is exactly what I've said.  Also are you talking about kinetic friction?  If so I'm not sure the relevance....  You are right tribology is a whole lot different.  But that really isn't what we are talking about here, we are talking about static friction.

Yep, a rope in a belay device is normally not static.  That is why I was very willing to defer to your expertise. :-)