Tyres
F1 tyre manufacturers think very carefully about the composition of the tyres, usually made up of soft synthetic rubber compounds mixing varying levels of carbon (for strength) and oil. Generally, the more oil, the softer the tyre, which means more grip and therefore quicker times, but also a quicker rate of deterioration [9]. It is all about finding the balance between the two.
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The Friction circle is a mathematical representation of the frictional forces whilst cornering. If we consider a right hand corner, the force on the car pushes towards the outside edge of the corner (to the left). It is the equal but opposite resultant frictional force from the tyre opposing this motion which allows the vehicle to corner without slipping. The circumference marks the boundary between static and dynamic friction, and the arrows are vectors showing the frictional forces [10].
Whilst the vehicle is not slipping, mu is the coefficient of static friction, however, once the vehicle begins to slip, the coefficient will be that of dynamic friction, which is generally much lower. This relation can be seen via the mu-slip relation. The mu-slip relation describes the lateral friction experienced whilst cornering. As the slip angle increases, so does the coefficient of static friction (the initial, linear, part of the mu-slip curve) up to maximum. Beyond this maximum, the car is said to be slipping and from there the coefficient of friction becomes dynamic. In theory, this change is instantaneous but due to real life factors this occurs over a range of slip angles. The peak range is where drivers attempt to keep the slip angle as this maximises the frictional coefficient and allows the corner to be taken at its fastest. At the zero degrees, the tyre is rolling freely, and at 90 degrees it is essentially fully locked up [11].
As rubber is a viscoelastic material, it deforms under loads, in the case of cornering, the lateral forces resultant from cornering. The contact patch, the area in contact with the road, is deformed with respect to the direction the tyre is rolling and its direction is tangential to the arc that the patch is travelling along. The difference between contact patch direction and tyre direction in the slip angle [12].
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Temperature and tyres
There is no simple relationship between temperature and coefficient of friction, although generally, the higher the temperature, the higher the coefficient of friction. The reason why drivers and engineers will heat the tyres prior to racing is because the tyres are designed to operate at a previously calculated operating temperature; essentially the temperature that the tyres will reach during racing.
However, the reason why the tyres have a higher coefficient of friction at higher temperatures is because rubber, a polymeric material [14], undergoes intermolecular rearrangement under heating. The molecules which make up the rubber are more able to move around.
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Implying that as temperature increases, so does the velocity of the molecules. It is this movement which increases the ‘stickiness’ of the tyres leading to better grip, as the molecules are more likely to interact with another surface, thus generating an increased frictional force. However, increase this temperature much beyond their optimal working temperatures, and the tyre will become too soft and begin disintegrating…which wouldn’t be very good.
The bits of rubber at the side of the track are as a result of such deterioration and are colloquially known as "the marbles" due to their slippery nature.
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The simulation illustrates the importance of the grip of the tyres in producing the fastest possible lap time. We see that with increasing coefficient of friction we decrease the 0-60 time due to a greater frictional force which also increase the cornering speed, all resulting in quicker lap times.