Tyre Rolling Resistance

Tyre rolling resistance can have a noticeable impact on maximum speed. At the higher speeds of 300 km/h it can absorb as much as 400-500 N.

Several books cover this topic, such as Chapter 6 of Enrico Benzing - Dall'aerodinamica alla potenza in Formula 1 and Genta - Motor Vehicle Dynamics.

Genta or Benzing model:

Crr = f0*tanh(1000*v) + f1*v + f2*v^2

tyre drag force = Crr*vehicle_mass*9.81*tanh(1000*v)

with velocity in m/s (SI)

This quadratic formula historically has been validated by Jante, Marres, Saal, Wolf.

Starting values:

f0 = 0.008 (smooth) to 0.037 (rough)

f1 = 0

f2 = 3.8*10^-6

Pirelli model:

Crr = f0 +f1*v + f2*v4

with velocity in m/s (S)

This 4th order formula has been validated by the tyre manufacturer.

Starting values:

f0 = 0.0134

f1 = -8.64E-5 (note: this coefficient is negative)

f2 = 3.0905E-10

Values for front Pirelli 255/40R18

f0 = 0.0127

f1 = -8.31E-06

f2 = 8.163E-11

Values for rear Pirelli 295/35R18

f0 = 0.01136

f1 = -1.0044E-05

f2 = 9.49E-11

Reza Jazar - Vehicle Dynamics Theory and Application (page 119):

ur = u0 + u1*v^2

where u0 = 0.015 & u1 = 7*10-6 s^2/m^2

Alternatively, a Fourth degree equation

Fr = C0 + C1*v + C2*v^4 (Page 119)

where C0 = 9.91*10-3, C1 = 1.95*10-5, C2 = 1.76*10-9

Mathworks model:

Tyre Rolling Resistance - Mathworks

Tire pressure

Inflation pressure of the tire. The parameter must be greater than zero. The default value is 250e+3 Pa.

Alpha

Exponent of the tire pressure in the model equation. See Pressure and Velocity Dependent Model. The default value is -0.003.

Beta

Exponent of the normal force model equation. The default value is 0.97.

Coefficient A

Velocity independent force component in the model equation. The parameter must be greater than zero. The default value is 84e-4.

Coefficient B

Velocity dependent force component in the model equation. The parameter must be greater than zero. The default value is 6.2e-4 s/m.

Coefficient C

Force component that depends on the square of the velocity term in the model equation. The parameter must be greater than zero. The default value is 1.6e-4 s^2/m^2.

Velocity Threshold

Velocity at which the full rolling resistance force is transmitted to the rolling hub. The parameter ensures the force remains continuous during velocity direction changes, which increases the numerical stability of the simulation. The parameter must be greater than zero. The default value is 1e-3 m/s.