## Appendix A Appendix A.1. Parameter of Magic Formula for a Lateral and Longitudinal Slip  
\[\sigma_{xA}=\frac{\lambda_{A}}{1+\lambda_{A}},\ \sigma_{yA}=\frac{tan_{A}}{1 +\lambda_{A}},\ \sigma_{tA}=\sqrt{\sigma_{xA}^{2}+\sigma_{yA}^{2}}\] \[F_{xA}(\alpha_{A},\mu_{A},F_{zA})=D^{*}\sin[C_{x}^{*}\text{arctan} (B_{x}^{*}(1-E)\lambda_{i}+E_{x}\text{arctan}(B_{x}^{*}\lambda_{A})]\] \[F_{yA}(\alpha_{A},\mu_{A},F_{zA})=D^{*}\sin[C_{y}^{*}\text{arctan} \Big{(}B_{y}^{*}(1-E)(\alpha_{A}+\Delta S_{hA})+E_{y}\text{arctan}\Big{(}B_{y} ^{*}\alpha_{A}\Big{)}\Big{]}+\Delta S_{pA}\] \[B_{x}^{*}=B_{x}(2-\mu_{A}),\ C_{x}=1.65,\ E_{x}=\frac{E}{B_{x}}\] \[B_{y}^{*}=B_{y}(2-\mu_{A}),\ C_{y}=1.65,\ E_{y}=\frac{E}{B_{y}}\] \[D^{*}=\mu_{A}\big{(}a_{1}F_{zA}^{2}\big{)}+a_{2}F_{zA},\ B_{x}= \big{(}\frac{a_{3}F_{zA}^{2}+a_{4}F_{zA}}{C_{x}D^{*}e^{8}F_{zA}}\big{)},\ B_{y}=(1-a_{ 12}|\xi|)\big{(}\frac{a_{2}\sin(a_{4}\text{arctan}(a_{5}F_{zA}))}{C_{y}D^{*}} \big{)}\] \[E=a_{6}F_{zA}^{2}+a_{7}F_{zA}+a_{8}\] \[\Delta S_{hA}=\big{(}a_{10}F_{zA}^{2}+a_{10}F_{zA}\big{)}\xi\] \[\Delta S_{vA}=a_{9}\xi\]  
Here, \(B^{*},C^{*},D^{*}\), and \(E\) denote the tire stiffness, shape, peak, and curvature factors, respectively, whereas \(\xi\) represents the wheel camber angle. In addition, \(\Delta S_{h}\) and \(\Delta S_{v}\) indicate the horizontal and vertical shifts, and \(\mu\) signifies the road coefficient of friction. Equations are determined for front left tire and for others can calculated similar way.  
Using [PERSON]'s law, the mathematical equations was derived for the vertical motions of suspension system as indicated below:  
\[m_{s}\ddot{s}_{z,i}=\Delta N_{f,i}-b_{s,i}\big{(}\dot{s}_{z,i}- \dot{u}_{z,i}\big{)}-k_{s,i}(s_{z,i}-u_{z,i})\] \[m_{u}\ddot{u}_{z,i}=b_{s,i}\big{(}\dot{s}_{z,i}-\dot{u}_{z,i}\big{)} +k_{s,i}(s_{z,i}-u_{z,i})-k_{t,i}(u_{z,i}-r_{s,i})\]  
where \(m_{s}\) and \(m_{u}\) denote the quarter of the sprung and unsprung masses of the vehicle, respectively; \(s_{z,i}\), \(u_{z,i}\) and \(r_{s,i}\) show the vertical displacements of sprung mass, unsprung mass and road disturbance for each tire, respectively. \(k_{s,i}\), \(b_{s,i}\) and \(k_{t,i}\) represent the stiffness of spring, damping coefficient and tire stiffness, respectively. Dynamic forces for each tire, \(\Delta N_{f,i}\), which occurs during acceleration and deceleration situations is presented as follow:  
\[\Delta N_{f,i}=m_{s}g\mp\frac{m_{t}\dot{V}_{x}h_{g}}{4l}\mp\frac{m_{t}\dot{V} _{y}h_{g}}{4w}\]  
where \(\dot{V}_{x}\) and \(\dot{V}_{y}\) represent the longitudinal and lateral accelerations, and \(h_{g},l\) and \(w\) indicate the height of center of gravity, half length and half width of the vehicle, respectively. Sign \(i\) is indicated the related tire; \(A\) is left front, \(B\) is right front, \(C\) is left rear and \(D\) is right rear tire.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Hydrogen Pressure** & \(\mathbf{P_{H_{2}}}\) & **1.5 [bar]** & **Oxygen Pressure** & \(\mathbf{P_{O_{2}}}\) & **1.5 [bar]** \\ \hline Front tire lateral stiffness & C\({}_{f}\) & 41,000 [N/rad] & Rear tire lateral stiffness & C\({}_{r}\) & 40,000 [N/rad] \\ \hline Damping coefficient & \(b_{s}\) & 3500 [Ns/m] & Stiffness of tire & \(k_{t}\) & 193,000 [N/m] \\ \hline Stiffness of spring & \(k_{s}\) & 35,000 [N/m] & Fixed power loss & \(P_{0}\) & 0.9 [\(kW\)] \\ \hline \end{tabular}
\end{table}
Table 1: The values of the vehicle parameters.