Coefficient of Friction

Does anyone know the Coefficient of Friction of 7000 series aluminum against granite, or any other type of rock for that matter.

Smooth granite (like a countertop)? or naturally occurring granite (like on a rock face)?

The extremely simplified treatment of friction encountered in an introductory physics class won't really tell you anything about the latter case, which is what I assume you're interested in...unless it's a very large piece of aluminum with a whole lot of surface area in contact with the rock.

It would be very relevant to the discussion if you, eli poss, could add more background to the discussion. The nature of the inquiry will dictate the response.

As an added note, friction is something that is very easy to measure, but very difficult to calculate.

1. Read this thread mountainproject.com/v/textb…

2. If you don't have time, here's a quote from rgold

rgold wrote: According to David Custer in web.mit.edu/custer/www/rock…, the coefficient of friction of aluminum against granite has been measured at 0.38. These students got 0.41 hypertextbook.com/facts/200…, and The Valley Giant folks say 0.5 valleygiant.com/cam_math.html. If Mapeze is around, as a designer he probably has some values, especially for Euro limestone, where cams are known to be less reliable. Obviously, the particular combination of aluminum against granite is not of great interest to researchers, so it isn’t easy to find values. But beyond that, the simple coefficient of friction concepts found in Amonton’s law are in fact the roughest of empirical estimates and are not any kind of natural law—people write PhD dissertations on friction; it is in fact an extremely complex and far from well-understood concept. The concept is most applicable to contact between highly polished surfaces, in which the friction forces are primarily influenced by molecular interactions. Once the surfaces are physically irregular, all hell breaks loose because of the variety of ways the bumps and recesses can interact to produce resistance. I think that the almost universal practice of notching cam lobes is intended to leverage potential roughness interactions. I think the message from research on the subject is that until you get up to loads of geological magnitude, the roughness of the surfaces matters far more than the materials, and so speaking as if there is a coefficient of friction between, say, granite and aluminum is far from illuminating. When surface roughness and deformability matters, so does contact area, in which case one of the fundamental precepts of Amonton’s law is out the window. (Everyone knows more shoe rubber on the rock produces more adhesion, even though Amonton’s law would say not.) Another important issue is the well-known disparity between static and sliding friction. Since cams often move when a fall happens, the applicable coefficient of friction may well be the lower sliding value rather than even a locally-measured static value. Then there is the fact, totally unrelated to friction, that a well-placed cam fails not because frictional forces are insufficient to hold it in, but because of shear yield stresses on the aluminum lobe material. In such cases there will be evident gouging of the cam and it may be possible to find aluminum deposited on the crack walls. (I've seen the aluminum left behind in testing jigs but not in real rock.) Given that Amonton’s law may be a poor description of what happens between a cam lobe and crack wall, I think it is something of a miracle that cams designed in accordance with that law work anywhere near as well as they do.

basically i want to try to calculate how much upward force a cam with x spring tension will resist depending on different materials and different rock types. ie will a cam with brass lobes resist more upward force than with aluminum? or how much spring tension will resist x amount of upward force in yosemite granite? i'm trying to educate myself on the physics involved in cams walking. and before you guys start lecturing me, yes i know that a long sling and/or a flexible stem is going to do much more and all of this is likely irreverent

Some of your question should be addressed with material science. Most things in engineering are the result of trade-offs. Aluminum is a good choice for cam lobes because it is light weight, is cheap, and has excellent ductility even though it is not as strong as brass. The deformation of the cam lobe in-situ is actually beneficial to the strength.

In this case ductile refers to the amount of strain energy a material can absorb before yield failure. It is a complicated subject as noted by Nathanael above and people get degrees in the subject.

Cam lobes fail when enough stress occurs in the metallic bonds and shear failure happens. Look up stress-strain diagrams and notice that aluminum has a fairly flat stress-strain curve. Thus it can undergo a relatively high amount of strain before inducing stress in its metallic bonds.

Brass; brass is more dense and weighs more than aluminum (and costs much more). Brass also has a much steeper stress strain curve. The stress increases much more rapidly with applied strain. However because the curve is much higher brass fails at a much higher stress, in other words it is stronger in the sense that it can withstand higher loads. But instead of deforming in the rock from a big whipper it might be strong enough to cleanly slide out of its placement instead of holding.

The other part of your question can be answered with more questions. Cam walking is related to the force of the spring internally based on the fact that friction is based on the normal force. The spring strength however was a designers choice and the magnitude of the spring constant was the result of engineering trade-offs as well. To prevent cam walking should we use stronger springs?

Probably not. Primarily because we don't want to have a terrible case of shake leg, have our forearms super pumped, and then NOT be able to place a cam because we can't activate the lobes. The trade-off is that we choose X strength because it is strong enough to activate the lobes but we can still use the cam when pumped. The problem of walking is more simply solved with solutions such as a longer sling and/or flexible stem.

I recommend your future research focus on cam weaknesses and solutions to those. From an overall perspective, we typically don't see cam lobe shearing to be the failure of cams. Other components in the cam are weaker. For example stems will usually break before a cam lobe will shear. The axles of the cam also break before the cam lobe will shear as well.