The Science Of Friction... Rubber is not metal

The false frame of reference

As mentioned in my previous post, the physics classical mechanics approach to friction is based on scientific studies carried out on smooth metal surfaces, further more of hard metals of similar hardness (no deformation occurs). This approach has many prerequisites that does not work all that well when it comes to the soft, sticky rubber on our climbing shoes.

Please note that this is not a scientific paper, it is only my personal interpretation of scientific analysis on rubber friction and how I think this applies to rock climbing.

The actual science of friction... of rubber on rock!

The formula for Static Friction Force of rubber on rock (FT), known as the unified theory of rubber friction is:

FT = FA + FHS + FHb + FC

where:

FT = The total frictional slip resistance
FA = Friction from adhesion
FHS = Friction from surface deformation (microhysteresis)
FHb = Friction from surface bulk deformation (macrohysteresis)
FC = Friction from rubber wear

I will not dig into each of these in detail, but I will try to explain what they are about and what the factors that influence them are.

F_A - Adhesion

Adhesion is the force between two surfaces that exists on the molecular level, between molecules and atoms of the two surfaces. Atoms on the surface are not bound to other atoms, like the atoms deep in the material. This leaves the ability to form bindings with the surrounding atoms. This force originates from temporary bonding between the surfaces. This force is proportional to the Normal Force up to a threshold level. One issue with this part of the friction is that the atoms on the surface are free to form any type of bond, with most any available atom. Oxidation starts immediately with any surface exposed to air and this substantially affects the ability to bond with further atoms. Rubbing your climbing boots with your hands to get a fresh layer of rubber before getting on the rock will actually give better friction as you wear off a bit of the oxidized rubber, leaving fresher rubber exposed. This gain is however very short lived as oxygen in the air will start bonding immediately with the fresh rubber.

F_HS - Microhysteresis

Microscopic asperities in the surface of the rubber sole interlocks with microscopic asperities in the rock surface (or climbing hold surface). This interlocking takes force to break apart, thus contributes to not slipping, that is contributes to the total friction force (F_T) between the shoe and the rock.

This force though, is independent of the Normal Force.

F_Hb - Macrohysteresis

Think of this as stepping on a surface with a crystal, small ledge or similar. The rubber will flex somewhat around the protuberance causing a larger contact area between the two surfaces. The added adhesion this creates is a significant part of this friction contribution. In fact the nature of the macrohysteresis friction component pretty much mirrors the nature of the adhesion friction component. They are both proportional to the Normal Force up to a threshold level. Above the threshold the force decreases with a small exponential factor. Climbing shoe rubber designers will probably aim to have this threshold beyond what gravity and human weight and muscle force are able to produce.

F_C - Wear

The rubber of your shoes gets worn, tearing off microscopic pieces of rubber from the sole of your shoe takes force. This force contributes to the total friction force experienced. This is of course a factor when you slip off and leave a skid mark of black rubber on the wall, not so much when you do not slip. If you never slip, your shoes will still wear down... but it may take a lifetime and this type of wear is negligible in static friction (not slipping).

Conclusions

The loading of the climbing shoe on the wall may actually have an effect on the friction experienced, decreasing the friction gain as the load gets higher. I would think that shoe designers will do anything to minimise this effect, or move this threshold outside of the range of the forces in play in rock climbing. I will have to do actual scientific testing to find out how well they actually achieve this. This might merit a post on this topic in the future.

The load increase will result in a decreased friction gain. This translates into pressure per square inch. This in turn means that just as increased force plays a role in the friction, so does the size of the surface area. So, we are back to the fact that smearing a large area of your shoe's rubber on the wall actually has a positive effect over loading only an edge of the rubber on your shoe. Most likely though, this is an insignificant effect compared to the factor of the Normal Force. As with the previous conclusion, actual testing will have to be done to discover how significant this is.

Regardless of how all the components of the friction force act, the overall major component of the friction comes from the Normal Force and this is most definitely the factor you can control the most.

Stay tuned for a full summary of all factors for rubber friction on rock and a detailed break down of the Normal Force...

May The Normal Force Be With You!

References

Robert Horigan Smith, Analyzing Friction in the Design of Rubber Products and Their Paired Surfaces, CRC Press 2008, ISBN: 0-8493-8136-3