PROFESSIONAL MOTORSPORT

SIMULATION SOFTWARE

LapSim uses a strongly simplified Pacejka style model

Tires are one of the most influential parts of the simulation. Often there is not much tire data available and if it is available, it is presented in a different form than used in LapSim.

Example of tire characteristic, lateral force versus vertical load

Tires are not constant

One should always keep in mind that in real life, tires do not behave exactly to a constant characteristic. Their behaviour is influenced by tire pressure, track surface, tire temperature, wear, humidity, to name just a few.

So any characteristic used in the simulation only describes a certain situation of the tires dependent on the combination of external factors. Keeping this in mind, it diminishes the reason for complicated characteristics. It would only add complexity without improving the accuracy.

Example of tire characteristic, longitudinal force versus vertical load

Lateral and longitudinal

The used tire 'model' in LapSim is a strongly simplified Pacejka style model, which can be divided in 5 parts: overall parameters, grip, form, camber dependence and combined slip. Some of these parameters distinguish between longitudinal and lateral behaviour.

The tire 'compound' parameter

Example of tire characteristic, lateral force versus vertical load

There is an overall grip factor for a tire as a base. The grip factor is the same in lateral and longitudinal direction.

The overall grip factor can be seen as heavily compound related, regardless of the construction of the tire.

The construction of the tires has subsequently a strong influence on the influence of vertical load on the lateral and longitudinal tire force generation.

Resistance to vertical load

The higher the vertical load the more the relative grip of a tire decreases. This mainly due to deformation of the contact patch. In LapSim it is assumed that this relation is linear and negative.

Example of tire characteristic, lateral force versus vertical load

Due to this negative relationship, the handling of a vehicle can be influenced by shifting the weight transfer from on axle to the other. More weight transfer on an axle means decreasing the overall performance of that axle.

Should you experience that the model react less fierce to a change of roll bars than your real car, you should increase this parameter. Subsequently you will need to adjust the overall grip factor to achieve a similar performance.

Generally the influence of vertical load is less sensitive for longitudinal than lateral.

Example of the combined slip friction circle

Combined slip

Tires have a tendency to generate more combined forces under traction than they do under braking. This is mainly tire (construction) dependent.

Therefor LapSim has a parameter to decrease the braking performance of the tires compared to acceleration.

The results can be seen in the plotted grip circle. It is calculated with about 40% of the vehicle mass acting on the tire, thereby supplying a realistic estimate of the potential accelerations.

'Optimal' camber in lateral direction

Example of the inlfuence curve of lateral tire grip versus camber angle

The influence of camber on the tire characteristic is separately specified. In lateral direction, the “optimal” camber angle needs to be specified as well as the corresponding increase in lateral grip. At zero camber the influence of camber is assumed to be zero. Out of these two parameters a second order relationship is determined.

Grip decrease in longitudinal direction

Example of the influence curve of longitudinal tire grip versus camber angle

A similar approach is valid for the longitudinal direction, albeit that in longitudinal direction, camber only creates a loss of grip. One specifies how much longitudinal grip is lost at 3 and 6 degrees of camber. The software subsequently determines a second order relationship.

The construction related parameter

Example of tire characteristic, longitudinal force versus slip percentage for several vertical loads

The shape of the tire characteristics are defined by the cornering stiffness parameter as well as the slip where the maximum tyre force occurs.

The cornering stiffness parameter determines the angle with which the tire force starts from zero slip. Basically the first derivate value @ zero slip.

In longitudinal this parameter direction has a big influence in combination with a LSD differential. In lateral direction, the cornering stiffness of the tires determines the angle of the lateral tire force and thereby the longitudinal (resistance) component of the tire force.

Spring stiffness, rolling resistance and roll radius increase

Part of the LapSim GUI where the overall tire parameters are specified

Last parts to specify are the overall parameters for the tires: vertical spring rate, rolling resistance and the increase of the tire diameter over speed.

The vertical spring stiffness influences the behaviour of the body due to accelerations, roll and pitch movements, etc.

The rolling resistance generates a resistance force equal to the specified percentage multiplied with the vertical load acting on the tire. Typical values are between 0.5 - 1.5 [%}

Finally the increased tire diameter due to speed, changes the overall transmission ratio. The relationship to speed is quadratic. Typical values are between 1.5 - 3 [%} @ 300 [km/h]