The Science Of Friction... Factors for rubber

How to make every possible effort to push the limits!

The factor that influences the friction of your climbing shoes on rock the most, is by far the Normal Force. You should spend time analyzing it and always having this in mind as you place and load your feet. In my next post I will focus on breaking down the Normal Force into something comprehendible, but now I will dig deep into the minute details of the other factors.

If you are climbing at the very limits of what is physically possible, every sliver of contribution will actually be important. Knowing what these factor are will be essential, and knowing what can be done about them is what separates you from the rest.

The factors that influence friction

Besides the main contribution from the Normal Force, there are the factors that influence the coefficient of static friction.

Humidity

It should come as no surprise that humidity is a factor. This is a factor that all climbers have battled. Rain just shatters all your (outdoor) climbing plans, it does not even have to be raining on the day of your climb to ruin it. Moisture takes time to dry. Even rain elsewhere, or no rain at all... just humidity in the air or lack of air circulation to transport away moisture could be enough to prevent the friction from being optimal. The actual (negative) contribution of humidity on friction is dependant on several factors, like the surface of the rock in question. Some rock seems to be just as good to climb regardless of air humidity, while others are useless with even slightly humid air.

The Bleausards of Fontainebleau have fine tuned this aspect to a level where they routinely whack the holds with a cloth to remove as much moisture as possible before getting on the rock. I am not talking about wet holds, they whack the seemingly dry rock when humidity in the air causes issues with friction.

How significant is this factor?
I have found no scientific studies on rubber friction on rock with regards to the effect of humidity, nor any similar studies that I could extrapolate from. I might pursue this later, please advise me (comment) if you stumble across any relevant studies.

I will however suggest that the impact of humidity on the friction of your shoes on the rock is far less than the impact it has on the friction between your fingers and the rock.

Temperature

Just as with humidity, heat is a known enemy of friction. Professional climbers migrate the globe in structured patterns, chasing the winter for cold, crisp conditions. The effect of temperature on friction is significant, but can be ignored if you are only looking for an enjoyable climb. If you aim to tick your list or break new ground, you need to keep an eye on the thermometer and the forecasts.

How significant is this factor?
Studies have proven a link between temperature and rubber friction and it effects adhesion, microhysteresis and macrohysteresis (see my previous post on these contributors to the total friction). The only data I found were from aircraft tire testing and extrapolated from that data the effect is about 0.24% per degree Celsius. This is not good enough to be used for anything scientific, but it is good enough to give an indication of temperatures effect on friction for your rubber shoes on the rock.

I will again, however suggest that the impact of temperature on the friction of your shoes on the rock is far less than the impact it has on the friction between your fingers and the rock.

Pressure / Area

Pressure and area are two sides of the same thing. The pressure per square inch on the rubber sole is dependant of the actual force applied and the surface area of the contact surface. Applying more force will not result in an equally increase in friction. As you apply more and more force, the friction gain will decrease.

Note that applying more pressure is always good for the friction as long as the majority of the extra force is a contribution to the Normal Force.

The practical value of this is that smearing is better for friction than edging and that distributing your weight on both feet gives better friction than standing on one foot.

How significant is this factor?

There are studies that expose this factor, but they are performed with "hard rubber" and "soft rubber" etc. These indicate that this factor can be as large as 10 to 30%, or even higher. These however may not apply that well as they do not cover the entire range of force that a human body will produce by its weight and it is not targeted at the custom designed, sticky climbing shoe rubber. To get a better indication further studies has to be carried out. I might venture into this in later posts.

We should also assume that climbing shoe brands put a lot of effort into tuning the rubber blend to achieve characteristics that perform well within the range of force produced by the human body.

Oxidation

As described in the previous post about rubber friction, the adhesion part of the friction is highly dependant on the availability of atoms and molecules to bind with atoms and molecules on the contact surface. Oxygen in the air will bind with any surface and reduce this availability to a minimum. 

Does this imply that friction is better at high altitude where the air is thinner? Not likely, as oxygen is plentiful, it might effect the time it takes for a surface to be "saturated", fully oxidized, but I would suggest that this is insignificant.

How significant is this factor?

You would definitely experience a totally different friction if you were climbing in an oxygen free environment, but that is not really an option. Within the practical aspect of climbing, rubbing your shoes down to get fresh rubber exposed before stepping on the rock will give you some effect of this, but only slightly.

I have found no studies on rubber for this to give an indication on the significance, but it is enough to have climbers identify this by themselves without scientific studies. So if the very limit is your playground, you should definitely start to rub your shoes with your palm before attempts when you chase your projects.

Contact Time

As with oxidation this factor is about adhesion, the bonding of atoms and molecules between the contact surfaces. This bonding is dependant on the availability of atoms and molecules to bond with, but this bonding actually improves with time. As time passes, the atoms and molecules adapts to the intermolecular forces and more and more bonds are formed. If you push the limits of what will not slip, climbing slower, allowing those feet to settle in and the rubber to stay in place a little longer will actually help.

How significant is this factor?

Scientific studies have detected and quantified this effect in the testing of tribometers. I have not found any actual data from these studies, but it is of significant size when it comes to determining the coefficient of friction with these instruments. I guess most climbers will not need to adopt a conscious habit of considering this factor, but again, if you are pushing the boundaries you should consider every possible aspect.

The Normal Force

The Normal Force is not the focus of this post, but it is the single most important factor of friction. You should pay attention to all factors, but if you miss out on the Normal Force all the other efforts are in vain. My next post will take friction back to the basics and focus entirely on 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

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

The Science of Friction

The known fact about friction

The common understanding is that getting as much rubber as possible on the rock is good and will work against you slipping. This is pure intuition, everybody knows this! I have seen this fact argued by professional climbers and I too have argued this point.

Now... what are the actual facts of friction?

The actual science of friction

Static friction, the friction before starting to slip, is what we care the most about in climbing. The friction force works against the force that pushes towards making you slip... until it no longer can equal that force, and you do slip.

The formula for Static Friction Force (Fs) is:

Fs = μs * N

Where μs is the coefficient of static friction and N is the Normal Force.

To dig a bit further

• the coefficient of static friction is all about how one material responds to the other. Generally, rough and sticky surfaces yields a high coefficient and polished smooth surfaces yields a low coefficient. Note that a material does not have a coefficient, the coefficient is between two surfaces.
• the Normal Force is the force acting perpendicular to the surface plane (between the two surfaces).

Do you see the drawing on the wall?

Before we dig further down the rabbit hole... did you see the area of the surfaces anywhere in the formula? Are you sure?

Yes, it's a fact... the surface area has nothing to do with the friction force!
It truly does NOT matter if you smear that rock with all your toes straight in a big shoe or if you touch the rock with a sliver of an edge of a tight shoe (given that the rubber and the rock is the same).*

It might be worth having a look at this lecture on friction by Dr. Walter Lewin at MIT, you should really stick with it for the first 12 minutes to have your reality adjusted.

The mechanics of you slipping is either down to the surfaces or the force you apply, there are no two ways about it! So... you need to be particular about cleaning your shoes and the rock before getting on. Dirt, sand, chalk, moisture... most anything will lessen the coefficient of static friction, including temperature. Other than that, you can pick your shoes with care and switch shoes according to rock and conditions to get the optimal rubber blend / rock type combo. The big picture is that this factor is pretty much out of your control.

Now all that's left is the Normal Force, and that is the subject of most of my analysis and conclusions on advanced climbing technique. How do you control the Normal Force?

Please stay tuned for more posts on rubber friction analysis.

May The Normal Force Be With You!

*This is taught at most universities etc with little respect for the finer details of friction and how this formula came about. If you have Phd in rubber friction analysis you will know that this formula is not entirely accurate and is deducted from friction between smooth metals, but for practical application in climbing I will stipulate that for now... it is close enough :-) Please stay tuned for more scientific posts on rubber friction analysis.

After rock... there was plastic!

Documenting Moves - Take Three!

Setting out to produce the first video to document climbing moves, I searched the woods in Fontainebleau looking for problems that would give nice footage for demonstrating matching. I found a few holds and shot some footage. Shot some more, changing angles, making the move obvious... demonstrating transitions etc.

I soon found that even this simple move required quite a few different types of holds. Finding all these holds in relevant angles to be able to demonstrate and document the move well proved difficult. Being in a gym with a good choice of holds in various colors and with the ability to rearrange them to fit the demonstration is far more simple and will provide far better documentation.

The quality of the footage could also be better. The problem was not the lighting or angles, the problem was that the holds themselves did not visually stand out very well from the wall on natural rock. The hold and the rock are the same color and the usage of a hold looks insignificant, especially when it comes to foot placement. In Fontainebleau, smearing is essential on mostly everything and this makes for lousy demonstration of foot on hold positioning and movement.

Demonstrating foot placement on holds that are almost invisible on video and at the same time using a technique that makes the hold seem insignificant and tiny does not lend well to this demonstration.

Going indoors

So the next attempt will be going indoors, setting up holds to demonstrate specifically and exactly what I want to document.


May The Normal Force Be With You!