## 4 Model Verification
### Constant Radius Cornering Tests
#### 4.1.2 Yaw Rate Gain  
As a vehicle corners, or undergoes certain lateral tilting motions, a yaw effect is induced in which the vehicle performs rotary angular movement around the vertical axis. For general vehicles, the yaw rate (i.e., the angular velocity of yaw) varies linearly with the steering wheel angle during cornering at low speeds. However, to ensure driving comfort and safety, the yaw rate should be suppressed as the cornering speed increases. Together with the roll gradient, the steady-state yaw rate gain (defined as the ratio of the yaw rate to the front wheel angle) is one of the most important measures for evaluating the cornering performance of a vehicle. Figure 7 shows the simulation results obtained for the yaw rate gain of the present vehicle at speeds in the range of 10-80 km/h. At low speeds, the yaw rate gain increases linearly with an increasing vehicle speed. However, as the speed increases beyond 70 km/h, the yaw rate gain decreases, indicating the occurrence of understeer. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Experimental Data**} \\ \hline Speed (km/h) & Tire steering angle (degree) & Lateral acceleration (G) & \(K_{us}\) (rad/g) \\
10 & 12.9 & 0.048 & 4.68 \\ \hline \multicolumn{4}{c}{**CAE model Data**} \\ \hline Speed (km/h) & Tire steering angle (degree) & Lateral acceleration (G) & \(K_{us}\) (rad/g) \\
10 & 9.47 & 0.032 & 5.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental and simulation results for \(K_{us}\) in constant radius cornering tests. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Velocity (km/h)** & **Lateral Acceleration (G)** & **Roll Angle (\({}^{\circ}\))** & **Roll Gradient (\({}^{\circ}\)/g)** \\ \hline
10 & 0.018 & 0.046 & 2.56 \\
20 & 0.064 & 0.17 & 2.65 \\
30 & 0.165 & 0.45 & 2.72 \\
40 & 0.252 & 0.7 & 2.78 \\
50 & 0.393 & 1.13 & 2.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation results for roll gradient at different speeds. Table 3 shows the full-vehicle parameters obtained from the experimental measurement tests for the target vehicle. Based on the parameters presented in Table 3, the effects of tire stiffness, aligning torque, lateral force compliance steer, roll steer, and roll camber on the understeer coefficient, \(K_{us}\), can be evaluated as follows. 1. Tire Cornering Stiffness \[ \begin{array}{c}K\text{\emph{tires}}=\frac{W_{d}}{C_{af}}-\frac{W_{r}}{C_{ar}} \\ K\text{\emph{tires}}=\frac{8829}{78,855.7}-\frac{5886}{71,687}=1.71^{\circ}\end{array} \] (2)
2. Aligning Torque  
The vehicle tire generates an aligning torque to resist the cornering. However, the aligning torque produces a lateral force which acts on the pneumatic trail at the contact point behind the tire center and produces an understeer effect. In general, the understeer term is given by:  
\[ \begin{array}{c}Kat=W\frac{p}{L}-\frac{C_{af}+C_{ar}}{C_{af}C_{ar}}\end{array}  \tag{3}\]  
When \(C_{af}\) has a positive value, the aligning torque effect of the tire is positive (i.e., understeer). For the target vehicle, the understeer effect is computed as:  
\[ \begin{array}{c}Kat=15,696\times\frac{0.018754}{2.8}\times\frac{(78,855.7+71,687)}{78,855.7\times 71,687}=0.16^{\circ}\end{array} \]
3. Lateral Force Compliance Steer