- #1

Payam30

- 46

- 1

I was thinking of the slip that is defined as following:

$$

s = \frac{R\omega}{v_x} -1

$$

The definition of the effective radius according to Chand and Sandu [1]

$$

\begin{equation}

R_e = \left\{

\begin{array}{l l}

R - R \left(1- \frac{1 -\frac{\delta}{R_g}}{\cos\theta} \right) & \text{if } \theta_r < \theta \leq \theta_f \\

& \\

R - R \left(1- \frac{1 -\frac{\delta}{R_g}}{\cos\theta_f} \right) e^{-\beta z (\theta -\theta_f}) & \text{if } \theta_f < \theta \leq \pi \\

&\\

R - R \left(1- \frac{1 -\frac{\delta}{R_g}}{\cos(2\pi + \theta_r)}\right) e^{\beta z'(\theta -(2\pi + \theta_r))} & \text{if } \pi < \theta \leq 2\pi + \theta_r \\

\end{array} \right.

\end{equation}$$

The effective radius is depending of the variabel $$\theta$$ which is the angel defined on the contact patch. Reza N.Jazar [2] propose the unloaded radius and not the effective radius when calculating the slip. while some people go with effective radius. what are the arguments for using and not using the effective radius in calculating the slip?

[1] J. Y. Wong.

*Theory Of Ground Vehicles*. John Wiley & Sons New York, 3rd edition, 2001

[2] Reza N.Jazar.

*Vehicle Dynamics Theory and Application 2th Edition*. Springer New York

Heidelberg Dordrecht London.2014