**The rolling resistance of tires**

Every time the wheel turns, the tire becomes deformed to adapt to the road and absorb the irregularities of the ground. It is in the contact area created that all the effort is transmitted enabling the vehicle to accelerate brake or take bends. The deformation of the tire and its adherence therefore constitute the basis for the way it functions.

Tires are made of textile and metal reinforcement and viscoelastic mixings called “rubber”. The viscoelasticity of the rubber is at the origin of the grip mechanisms but also results in a loss of energy in the form of heat due to tire deformation.

**How can we reduce the loss of energy by a tire without deteriorating its performance?**

Limit deformation, choose rubber with the lowest possible energy loss during deformation and minimize the quantity of material deformed are the three major channels of action to reduce tire rolling resistance.

**Limit deformation**

A tire becomes deformed due to the many forms of stress to which it is subjected. The first of these is obviously the application of the weight of the vehicle. The resulting generation of the contact patch leads to deformation in each part of the tire on the opposite side to the surface contact. A balance is achieved when the product of the surface on the ground by the inflation pressure is equal to the load.

We can therefore think of limiting deformation by making the structure more rigid by simply increasing the inflation pressure - but what would then happen to the quality of contact with the ground which plays on all the facets of tire performance? In reality, deformation can only be limited by completely redesigning the structure. Thus, by introducing steel cord into truck tires in 1936 and the radial structure for passenger vehicle tires in 1946, Michelin enabled tire rolling resistance to be **halved** in both these categories.

Constant progress in profile expertise enables rolling resistance to continue to develop towards increasingly lower levels. The rolling resistance of tires has thus been **divided by five** since the outset. It can be noted that current truck tires are gradually tending towards railroad style - at the same time retaining considerable grip supremacy.

**Using low-loss viscoelastic mixings**

The other avenue consists of formulating low-loss rubber and, at the same time, preserving specific properties: for example, grip and wear resistance for the tread in contact with the ground, adhesion and mechanical characteristics required in contact with reinforcement cords, flexibility and resistance to mechanical, physical and chemical aggression for the sidewall mixings, etc.

The tread band in contact with the ground is a point where there is a very high level of compromise between the various facets of tire performance such as grip, wear resistance, rolling resistance, comfort, noise and handling. In particular, we have long been aware of the close relationship existing between grip and loss of rubber. Did we have to use rubber with a high level of loss in order to obtain good grip? A fine analysis enabled a distinction to be made between the low frequency zone where losses only produce heat and the high-frequency zone where losses play a relevant part in grip mechanisms.

This still meant a mixing had to be formulated showing low losses in low frequencies and a satisfactory level of loss in the area of high frequencies. This revolution is at the origin of the so-called "green" tires where part of the carbon black has been replaced with silica.

**Minimizing the volume of rubber deformed** also constitutes a significant channel of progress but it is essential that this optimization takes place without altering any of the functions which often demands more than a simple reduction in thickness.

*Image captions:*

Evolution of rolling resistance since 1890: a few notable values

Rolling resistance coefficient (C_{RR}), in kg/t

Solid tire

First tires

First tires with cords

First metallic tires

First radial tires

Green X

Energy 3

XDA2 Energy

Source: ® Michelin 2003

**Tire force and rolling resistance coefficient**

The rolling resistance force exerted on a vehicle in motion depends on the tires fitted to the vehicle and its weight (or Z load).

The rolling resistance of a tire is characterized by a rolling resistance coefficient C_{RR} equal to the rolling resistance force in relation to the Z load:

C_{RR} = F_{RR} / Z

This coefficient evidencing the relation of two forces is therefore without dimension but it is often expressed in old units of force as "kilos per tonne - kg/t", the abbreviation of kilogram-force by tonne-force.

For example, a tire with a rolling resistance force of 120 N with a load of 10000 N has a C_{RR} = 0.012 or 12 kg/t.

**Approximate figures in 2012**

Tires for passenger cars: 7 to 12 kg/t

Special tires for electric vehicles (mainly urban): 6 kg/t

Tires for trucks: 4.5 to 10 kg/t

Tires for on-road bicycles: 2.5 to 5 kg/t

The rolling resistance force exerted on a 1,200 kg vehicle equipped with tires with a C_{RR} of 10 kg/t is equal to: 10 x 1.2 x 9.81 = 118 N. The corresponding power lost at 90 km/h (25 m/s) is therefore: 118 x 25 = 2.95 kW.

3 kWh are therefore lost due to heat every 100 km. For a combustion engine with an output of around 30 % in top conditions, a minimum of 9 kWh are absorbed, i.e. around 1 liter of fuel per 100 km.

This value is far from negligible which is why for the past 20 years Michelin has chosen to act on rolling resistance.

**Contribution by rolling resistance to the forces slowing down a vehicle**

It can vary between 20 and 30 % depending on the type of journey, as shown by the following graph:

Contribution by rolling resistance to forces slowing a vehicle

(for four standard journeys)

Contribution as %

Urban

Extra-urban

Open road

Freeway

Rolling resistance forces

Internal friction forces

Aerodynamic forces

Inertia forces

Source: ® Michelin 2003

**Parameters affecting tire rolling resistance**

The inflation pressure has a very strong effect on rolling resistance: here we find the effect of material deformation.

For example: a passenger vehicle tire under-inflated by 1 bar (with a constant load) sees a 30 % increase in its C_{RR}. It is unnecessary to point out that this situation must be corrected quickly for safety reasons.

*Image captions:*

Inflation pressure

The RR increases when the inflation pressure decreases due to the increase in deflection

- Rolling resistance increases appreciably with the load. For a 100 base at 80 % of the maximum load of a tire, the F
_{RR}amounts to 80 to 60 % of this load and 120 with a maximum load.

- The rolling resistance force (RRF) decreases in line with the ambient temperature: between 10 and 40°C a 1°C increase in temperature corresponds to a 0.6 % decrease in rolling resistance. (Yes, this is actually correct!)

- Speed has little influence up to 120 km/h then increases sharply (effect of solicitation frequency and movement in the air).

*Image captions:*

Speed

The RR varies little with speed up to 120 km/h and then increases sharply.

At low speed, the RR decreases due to the increase in the operating T° and inflation pressure.

At high speed, the RR increases due to the increase in solicitation frequency and the appearance of standing waves.

Evolution RR 205/55R16 NRJS VLET (308)

Speed effect on various loads/pressures at 25°C and on 7J16 rim

CRR [kg/t]

Speed (km/h)

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