B) The Physics of Slipperiness...

The physics of slipping is fascinating. If you want to ask more specific questions or if something is not covered below then please contact us or the UK Slip Resistance Group.

B1) Why do people slip?

B2) Do all people require the same amount of friction?

B3) What is the definition of the coefficient of friction (µ)?

B4) How is friction developed?

B5) Do materials have a unique value of coefficient of friction?

B6) Does µ depend on contact pressure?

B7) How does the presence of a wet contaminant affect µ?

B8) How do dry contaminants affect µ?

B9) Is slip resistance the same as coefficient of friction?

B10) Which is more critical, the shoe sole or the heel?

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B1) Why do people slip?

When you walk, you need friction between your shoes and the ground to give you the ability to move forwards. Without friction you would not be able to remain standing for very long, let alone walk. If at some stage the amount of friction that the ground-shoe contact can provide is less than you need, then you will slip over. It is thus important to know how much friction a particular surface will provide.

B2) Do all people require the same amount of friction?

Work at the Building Research Establishment in the late 1950s discovered that in straight walking the average dynamic coefficient of friction required by the population as a whole was around 0.19. However, it did vary substantially from person to person, and they calculated that 1 person in 1 million would require a coefficient as high as 0.36.

If you include turning when walking, this 1 in 1 million requirement goes up to around 0.39. For this reason the value of 0.4 is usually regarded as the criterion for safety.

B3) What is the definition of the coefficient of friction?

If a body of mass W rests on a plane horizontal surface and needs a force F to move it horizontally across the surface in a sliding mode then the coefficient of friction is numerically equal to F/W. It is usually given the symbol µ.

However, there are two coefficients:

i) The limiting coefficient of static friction. This is based on the force required to start the body moving.

ii) The dynamic coefficient of friction. This is based on the force required to keep the body moving at constant velocity across the surface.

With many combinations of materials, µ static > µ dynamic, but for rubber and plastics in particular, µ dynamic may increase with velocity and become greater than µ static.

B4) How is friction developed?

There are essentially two components of friction that create the horizontal/lateral forces that occur in sliding.

The first is an interaction between the peaks and troughs inherent in the micro roughness and indeed macro roughness of the two sliding surfaces. These peaks are sometimes referred to as asperities. It is a form of interlocking of the surfaces which requires a particular level of force to overcome it.

The second component of friction is a molecular adhesion between the two surfaces. Whilst not a major component in very rough surfaces, it becomes the major component when the surfaces are smooth, and in particular when one surface is rubber or plastic. With a smooth surface such as glass and a very slightly damp, soft rubber (the slight dampness appears to enhance the adhesion) one can achieve far higher values of µ than can be obtained with even the roughest surfaces.

B5) Do materials have a unique value of coefficient of friction?

The coefficient of friction is dependent on both the material of the surface and that of the body which is sliding over it. One might argue that if both these were the same material then one would get a unique value for that material. Unfortunately, this is not generally true since it can depend on the degree of roughness of each of the surfaces.

B6) Does µ depend on contact pressure?

With many hard, non-resilient materials, such as metals, ceramics and timber, µ is independent of the contact pressure over a relatively wide range. This unfortunately does not extend to any system where one or both surfaces are rubber or plastic. Depending on the hardness of the rubber/plastic one can get some degree of independence of contact pressure, but it is over a much restricted range of pressures.

B7) How does the presence of a contaminant such as water affect µ?

Not only does the presence of a contaminant such as water or oil affect the value of µ, but also the manner in which it affects µ is very dependent upon factors such as the contact pressure, the size and shape of the contact area, the velocity of movement and the viscosity of the liquid. This makes the measurement of µ in wet conditions much more complex. The failure to understand this complexity has resulted in different models of slip test machine giving totally different test results for the same surface (see next section).

B8) How do dry contaminants affect µ?

Dry contaminants such as dust, powders, etc., can well affect µ by various different mechanisms. These contaminants can act like tiny spheres and have a ball-bearing effect. They can effectively destroy the adhesion factor in the creation of friction forces (see B4). They can fill in the troughs of the roughness, thus changing the nature of the surface. It all depends on the dry contaminant itself and the nature of the two sliding surfaces.

B9) Is slip resistance the same as the coefficient of friction?

Slip resistance is the dynamic coefficient of friction of a walking surface as determined in relation to a given contaminant and a given shoe heel material, as would be experienced by a slipping pedestrian. It should always be quoted in relation to the contaminant, e.g. water wet or dry/clean. If no heel material is quoted, it is generally assumed in the UK to be in relation to a standardised rubber known as Four S.

B10) Which is more critical, the shoe sole or the heel?

Slips generally take place either when the heel of the ‘front’ foot lands or as the sole of the ‘rear’ foot pushes off. The latter rarely leads to a fall, it is merely an annoyance to the pedestrian. It frequently happens when pushing a heavily loaded trolley in a supermarket.

The most dangerous slip occurs as the heel lands on the floor. At this precise moment, the foot/leg needs restraint to stop it moving forwards as it lands and if it does not find it, the foot/leg slips forwards uncontrollably. Indeed, unless the pedestrian is able to somehow stop the slip by stumbling, or by some other means, once the foot has moved about 100mm or even less, the geometry of the body (the angle of the legs) becomes such that more and more restraint is required. The slipping system thus becomes very rapidly out of control.

The ‘classic’ slip is for the leading leg to shoot forward, the rear leg buckles at the knee and that foot also shoots forward due to the increase in lateral loading on the foot caused by the forward bending of the knee. The body then falls vertically to the ground with the person usually landing on their bottom or the base of their spine. Usually they land almost exactly over the spot where their foot originally slipped.

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