# 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.

## Contents

## Sintax

`Fy = TireModel.Characteristic(alpha)`

*TireModel*.PlotTire()

## Arguments

The following table describes the input arguments:

alpha | Tire slip angle [rad] |

## 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.