## 5 Discussions
### Cornering Stiffness
#### 5.2.2 Impulse Steering Test: Four-Parameter Radar Plots (Transient-State Response)  
Table 12 and Figure 16 show the simulation results obtained for the phase lag, natural frequency, steady-state yaw rate gain, and damping ratio of the vehicle in impulse steering tests performed using the three different values of the initial toe-in angle. It can be seen that the toe-in angle had only a minor effect on the natural frequency and damping ratio. However, the phase lag and steady-state yaw rate gain exhibited a more significant change as the toe-in angle increased.  
The phase lag (\(\phi\)) for the Type 4 toe-in angle is better (i.e., lower) than that for the other two angles since the vehicle understeer is enhanced when the initial toe-in angle is negative, indicating that a larger steering wheel angle is required. However, in the impulse steering tests, the vehicle body was required to reach a 0.4 G lateral acceleration within 0.4 s. In other words, the steering wheel angle for the Type 4 toe-in angle increased more rapidly, and the phase lag was smaller. For the Type 6 and Type 5 toe-in angles, the vehicle body should reach the required 0.4 G lateral acceleration at the same steering wheel angle and in the same period of time. The lateral acceleration (0.395 G) for the Type 6 toe-in angle was slightly higher than that for the Type 5 toe-in angle (0.389 G). Consequently, the phase lag for the Type 5 toe-in angle was better (i.e., lower) than that for the Type 5 toe-in angle. Regarding the steady-state yaw rate gain (a\({}_{1}\)), Figure 16 shows that the Type 6 toe-in angle resulted in a better steady-state yaw rate gain than the Type 4 or Type 5. This finding is consistent with the results presented previously in Figure 14 and can be attributed to the same reasons as those described in relation to Figures 15 and 16. An inspection of Figure 16 reveals the following observations:  
1. The enclosed diamond area for the Type 4 toe-in angle moved towards the top-right corner and, therefore, indicates the occurrence of understeer. By contrast, that for the Type 6 toe-in angle moved towards the bottom-left corner, and therefore indicates the occurrence of oversteer. It is noted that these tendencies are consistent with the results presented in Figure 14 for the yaw rate gain in the constant radius cornering tests.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Item** & **Phase Lag (\(\phi\)) (\({}^{\circ}\))** & \
\begin{tabular}{c} **Natural Frequency** \\ **(fn) (Hz)** \\ \end{tabular} &
\begin{tabular}{c} **Steady-State Gain** \\ **(a1) (l/s)** \\ \end{tabular} & **Damping Ratio (\(Q\))** \\ \hline Type 4 & \(-24.88\) & \(1.9432\) & \(0.15898\) & \(0.9656\) \\ Type 5 & \(-26\) & \(1.8825\) & \(0.18099\) & \(0.94961\) \\ Type 6 & \(-25.5408\) & \(1.8106\) & \(0.1871\) & \(0.96911\) \\ \hline \hline \end{tabular}
\end{table}
Table 12: Simulation results for impulse steering tests performed using different toe-in angles.  
Figure 16: Simulated four-parameter radar charts for impulse steering tests performed using different toe-in angle values.  
Although the Type 6 toe-in angle appears to result in oversteer, it is not in fact true oversteer but simply oversteer in comparison with the original toe-in angle design (Type 5). Based on an inspection of the radar chart area, the Type 6 toe-in angle actually resulted in a better overall handling performance than the Type 5 design.