Cam Math

Hi, does anyone know of a good description on the web of the math of the forces on the rock and the cam, when the cam is in a vertical crack?

Thanks in advance.

http://www.indiana.edu/~iubphys/undergraduate/theses/Thesis_Phillip_Anuta.pdf
web.mit.edu/custer/www/rock…

David,

Here's one more source:

www.vainokodas.com/climbing/cams/html

"A Brief Discussion of the engineering principles used in the design of camming devices for rock climbing"

Marty

Marty C wrote:David, Here's one more source: vainokodas.com/climbing/cam… "A Brief Discussion of the engineering principles used in the design of camming devices for rock climbing" Marty

Sorry Marty, that URL just gave me a 404 error.

Merlin wrote:http://www.indiana.edu/~iubphys/undergraduate/theses/Thesis_Phillip_Anuta.pdf web.mit.edu/custer/www/rock…

Thanks Merlin, but I think the math in those models is for a horizontal roof crack. For a vertical crack the stem will be pointing out at an angle. I'm trying to think about the force needed to keep the cam from rotating.

David,

Don't know why link isn't working.

I typed in the article title in Bing search engine, and it did pop up; so try that.

also, there is an old website called "theclimbinglab.com" that had some cam articles on it - you should try that as well.

Good luck.
Marty

Typically there is no force keeping the cam from rotating in a vertical crack. It's just the spring preload which is negligiable.

Agreed; there is no force counteracting cam rotation beyond spring resistance.

The Vaino Kodas link (it's "...cams.html," not "...cams/html"):

vainokodas.com/climbing/cam…

I think the best account is in the material on Totem cams, which begins with a discussion of ordinary cams before moving on to the Totem configuration.

totemcams.com/files/galeria…

Cool link, thanks. I think that's going on my physics 1 with calculus test next semester.

Thanks everyone.

This is an awesome thread.

I'm sure this has been discussed previously, but today was my first look at the Totem Cams website. I get the whole direct loading thing, and the ability to load just one set of lobes (though Totem says not to do this for fall protection, just for aid climbing; not too surprising). But the following text from the site makes me wonder if they are actually inferior to conventional SLCDs in downward flares.

From the website:
Another limitation is that, unlike in another regular cams, the holding power of the Totem Cam decreases with the increase of flaring angle. In consequence, poor friction rocks are not suited for this use. However, Totem Cam has a theoretical downward maximum flaring angle of 40.7 degrees moderately greater than regular cams. (emphasis added)

It is true that the outward force on the walls remains the same with a conventional cam. However, these cams literally fall out of flares at double their camming angle, so the usual approx. 14 degree cam is toast in a 28 degree flare, whereas the Totem manages up to 40 degrees.

The other fact of note is that in a conventional cam, as the flare approaches double the camming angle, the compressive forces on the axle increase without bound. In other words, while you are enjoying the fact that the outward force on the walls isn't changing, the cam is destroying itself because of the internal forces involved.

All told, I'd much rather have a Totem for a flared placement (and for every other placement too for that matter).

rgold wrote:All told, I'd much rather have a Totem for a flared placement (and for every other placement too for that matter).

They're like magic. I wish I had more than one.

DannyUncanny wrote:Typically there is no force keeping the cam from rotating in a vertical crack. It's just the spring preload which is negligiable.

I know I'm about to sound very stupid, but why is it only the spring preload? Why isn't it the spring preload plus the outward force of the cams on the rock from the weight of the climber?

I'm sure I have placed cams that I could rotate when unweighted by moving the stem with my finger, but that point out of the crack at 45deg when loaded with my bodyweight.

Are Totem cams the same lobe design as CCH? Just wondering if this data is applicable to older CCH cams.

Thanks

J. Serpico wrote:Are Totem cams the same lobe design as CCH? Just wondering if this data is applicable to older CCH cams. Thanks

They aren't even the same basic principle. Unless you're taking about the Totem Basic, which is similar to an Alien.

I believe I was.

The behavior of the Basic is just like any other cam in a downward flare. Force increases to infinity as the angle widens, and it pulls at double the camming angle.

The unique ability of the standard Totems to hold in up to 40-degree downward flares relies on a different mechanism, well described in their website.

David Coley wrote: I know I'm about to sound very stupid, but why is it only the spring preload? Why isn't it the spring preload plus the outward force of the cams on the rock from the weight of the climber? I'm sure I have placed cams that I could rotate when unweighted by moving the stem with my finger, but that point out of the crack at 45deg when loaded with my bodyweight.

Not even remotely stupid; I think cam dynamics are complicated and I don't know whether anyone understands them. The most obvious reason for a cam to stop rotating is that the crack tapers inward and the cams that are moving (the lower pair) reach maximum compression. Another possibilitiy is that the fallen climber is bracing against the wall with his feet, the load is not vertical and the cam is aligned with it.

That said, there does have to be some rotational resistance and so we should not expect the cam to necessarily rotate all the way to the vertical position. The cam pivots around the contact points of the upper cams; this creates an inward moment on the lower cams that actually compresses them. Those upper pivot points are maintained by the pressure of the cams against the crack and will surely offer some rotational resistance. This resistance indeed an artifact of the outward force of the cams on the rock from the weight of the climber, but is not equal to that force and isn't strictly speaking a force but is rather a torque.

The mechanism for the cam rotating some distance but not all the way vertical would be that as it rotates down, the torque supplied by the falling climber decreases (since only the component normal to the cam stem counts). At some point, this torque will decrease to the point that it is balanced by the frictional resistance torque, at which point cam rotation will stop. Whether the effect is noticeable or not in general I don't know, but the chances of the cam stopping significantly above vertical would be enhanced by having some very high-friction rock.

Another related question: Does texture or a tooth pattern have any effect on the way a cam pivots?

The way Aliens wear down from toothy to smooth suggests that a little texture is sheared off or mashed each time the cam gets loaded. Does that imply that the cam slips a little as it bites? Or does it imply that the malleable metal is deformed and 'bitten' by the rock? Highly textured cam lobes have less surface area in contact with the rock and might rotate slightly easier until weighted enough to really set.

Do two-lobed Splitter cams pivot more easily under a moderate load? (I know they don't walk into the crack.)