# Study on the Driver/Steering Wheel Interaction in Emergency Situations
## 5 Steering Power Evaluation  
While analysing the differences between the two types of manoeuvres (one or two hands on the steering wheel), we studied the differences in the steering power used by the drivers while counter steering. The steering power is defined as  
\[P_{sw}=T_{SW}\dot{\delta} \tag{4}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(\Delta\)t1 (s) & \(\Delta\)t2 (s) & \(\Delta\)t3 (s) \\ \hline  & Avg \(\pm\) St. Dev. & Avg \(\pm\) St. Dev. & Avg \(\pm\) St. Dev. \\ \hline Driver 1 & 0.150 \(\pm\) 0.035 & 0.270 \(\pm\) 0.026 & 0.420 \(\pm\) 0.026 \\ Driver 2 & 0.160 \(\pm\) 0.042 & 0.090 \(\pm\) 0.057 & 0.250 \(\pm\) 0.057 \\ Driver 3 & 0.187 \(\pm\) 0.090 & 0.160 \(\pm\) 0.069 & 0.347 \(\pm\) 0.069 \\ Driver 4 & 0.177 \(\pm\) 0.015 & 0.193 \(\pm\) 0.146 & 0.433 \(\pm\) 0.146 \\ Driver 5 & 0.137 \(\pm\) 0.055 & 0.093 \(\pm\) 0.045 & 0.260 \(\pm\) 0.045 \\ Driver 6 & 0.133 \(\pm\) 0.071 & 0.213 \(\pm\) 0.055 & 0.347 \(\pm\) 0.055 \\ Driver 7 & 0.173 \(\pm\) 0.089 & 0.210 \(\pm\) 0.060 & 0.383 \(\pm\) 0.060 \\ Driver 8 & 0.073 \(\pm\) 0.035 & 0.300 \(\pm\) 0.035 & 0.373 \(\pm\) 0.035 \\ Average & 0.148 \(\pm\) 0.051 & 0.208 \(\pm\) 0.082 & 0.356 \(\pm\) 0.080 \\ \hline \hline \end{tabular} \(\Delta\)t1: delay between the lateral disturbance and the peak of torque unconsciously applied, \(\Delta\)t2: delay between the peak of torque and the effective rotation of the steering wheel, and \(\Delta\)t3: delay between the lateral disturbance and the effective rotation of the steering wheel.  
\end{table} 
Table 2: Drivers with one hand on the steering wheel. Figure 6: Moments on the steering wheel. The kick plate manoeuvre. The driver used one hand. where \(T_{SW}\) is the torque applied at the steering wheel, calculated by means of the instrumented steering wheel, and \(\dot{\delta}\) is the speed of variation of the steering angle \(\delta\). As the input of the kick plate is in random directions, the drivers reacted in two different possible ways. Some of them were able to immediately understand which steering wheel rotation direction was required to recover the desired trajectory. In other cases, they started the steering rotation in the wrong direction and then corrected the steering action. We named the first way as the correct approach, the second as the non-correct approach. In Figure 7, two examples of correct and incorrect actions are shown, together with the values of steering torque (multiplied by 10) and the steering wheel angle. When using the correct approach, the direction of the steering torque and the steering angle were immediately correct, while in the case of the incorrect approach, they were both in the wrong direction. As expected, when the incorrect action was applied, the required steering power, as defined in (4), was higher to correct the error. Given the large difference between the drivers and the large difference between the single manoeuvres, we decided to analyse the peak of steering power in the first instants in which the steering wheel started to rotate after the lateral excitation. Figure 8 shows the values of the steering power peak, averaged for each driver, together with its standard deviation. In the event that the driver did not perform any manoeuvres that match the description, the average value was set to zero, as well as the standard deviation value if the driver had performed only one test. Referring to Figure 8, drivers 4 and 5 performed the one-handed manoeuvres only with the incorrect approach, while drivers 6 and 8 applied only the correct approach. At the same time, driver one performed the one-hand manoeuvres one time with the correct approach and two times with the incorrect one. In these situations, the standard deviation cannot be defined. The analysis was differentiated for the case of correct and incorrect approaches since, in this second case, the applied steering power was higher.