## 4 Simulation
### Human Sensation Model  
Humans feel translational motion by detecting specific forces in their otolith and rotational motion by detecting rotational angular acceleration in vestibular [3; 4; 5; 17]. The specific force detected in an otolith is obtained by subtracting acceleration of gravity from translational acceleration, such as  
\[\overset{\rightarrow}{sF}=\overset{\rightarrow}{a}-\overset{\rightarrow}{g} \tag{14}\]  
where \(\overset{\rightarrow}{a}\) is translational acceleration, and \(\overset{\rightarrow}{g}\) is the acceleration of gravity.  
Human sensory organ is modeled with a spring-mass-damper system. The transfer function of the otolith system [3; 4; 5; 17] is written in  
\[G(S)_{ otolith}=\frac{k(\tau_{A}s+1)}{(\tau_{L}s+1)(\tau_{S}s+1)} \tag{15}\]  
where \(\tau_{L},\tau_{S},\tau_{A}\) are, respectively, a long-time constant, short-time constant of the otolith and the time constant related to phase caused by the communication process in the nervous system. The characteristic of frequency response has good perception in the band of 0.01-0.5 Hz. Table 2 shows the parameters of the otolith model [3; 4; 5; 17].  
The transfer function of the vestibular system [3; 4; 5; 18] is expressed as follows.  
\[G(S)_{vestibular}=\frac{T_{L}T_{A}s^{2}}{(T_{L}s+1)(T_{S}s+1)(T_{A}s+1)} \tag{16}\]  
where \(T_{L},T_{S}\) and \(T_{A}\) are, respectively, a long-time constant, a short-time constant of the vestibular and the time constant related to the phase caused by the communication process in a nervous system. The characteristic of frequency response has good perception in the band of 0.01-0.5 Hz. The parameters of the vestibular model [3; 4; 5; 17] are shown in Table 3.  
The motion sensation, which is recognized from otolith and vestibular perception model without any signal processing, such as in the washout algorithm, can be assumed it is the same as the motion sensation of the actual vehicle. The specific force, in Equation (14), can be transformed into the following equation in the coordinate system at the center of the seat.  
\[\overset{\rightarrow}{F}_{P}^{S}=\overset{\rightarrow}{a}_{P}-\overset{ \rightarrow}{G}R(\alpha,\beta,\gamma)\overset{\rightarrow}{g}=\begin{bmatrix} a_{Px}+gsin\beta\\ a_{Py}-gsin\beta\\ a_{Pz}+gcosacos\beta\end{bmatrix} \tag{17}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Motion** & **Surge** & **Sway** & **Heave** \\ \hline \(\tau_{L}\) & 5.33 & 5.33 & 5.33 \\ \hline \(\tau_{S}\) & 0.66 & 0.66 & 0.66 \\ \hline \(\tau_{A}\) & 13.2 & 13.2 & 13.2 \\ \hline \(k\) & 0.17 & 0.17 & 13.2 \\ \hline \end{tabular}
\end{table}
Table 2: Parameters of the otolith model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Motion** & **Roll** & **Pitch** & **Yaw** \\ \hline \(T_{L}\) & 6.1 & 5.3 & 10.2 \\ \hline \(T_{S}\) & 0.1 & 0.1 & 0.1 \\ \hline \(T_{A}\) & 30 & 30 & 30 \\ \hline \end{tabular}
\end{table}
Table 3: Parameters of the vestibular model.  
where \(\overset{\rightarrow}{a}_{P}\) is translational acceleration in a driver's seat coordinate system, and \(-\overset{p}{G}R(\alpha,\beta,\gamma)\overset{\rightarrow}{g}\) is the acceleration of gravity in a driver's seat coordinate system.  
The specific force in a driver's seat coordinate system [3; 4; 5; 6] is defined as  
\[\overset{\rightarrow}{F}_{P}^{s}=\overset{\rightarrow}{F}_{Pt}^{s}+\overset{ \rightarrow}{F}_{Pr}^{s} \tag{18}\]