# Polynomial tire model

Nonlinear relation between tire lateral force and slip angle expressed by a third order polinomial equation. This model is used by several authors [1] [2] [3].

The code of this class can be found in TirePolynomial. It inherits methods from abstract class Tire. The complete list of class codes is in API.

## Sintax

Fy = TireModel.Characteristic(alpha)

TireModel.PlotTire()

## Arguments

The following table describes the input arguments:

## Outputs

 Fy Tire lateral force [N]

## Description

Model equation:

$F_y = k_1 \alpha - k_2\alpha^3$

where $$F_y$$ is the lateral force and $$\alpha$$ is the tire slip angle. $$k_1$$ and $$k_2$$ are the model coefficients.

Hypothesis

• Nonlinear tire model
• Valid up to the maximal lateral force (Tire saturation).

## References

[1] JOHNSON, D.; HUSTON, J. Nonlinear lateral stability analysis of road vehicles using Liapunov's second method. SAE Technical Paper, SAE International, 1984.

[2] SADRI, S.; WU, C. Stability analysis of a nonlinear vehicle model in plane motion using the concept of lyapunov exponents. Vehicle System Dynamics, Taylor & Francis, v. 51, n. 6, p.906-924, 2013.

[3] SAMSUNDAR, J.; HUSTON, J. C. Estimating lateral stability region of a nonlinear 2 degree-of-freedom vehicle. SAE Technical Paper, 1998.