## 2 Materials and Methods  
### Center of Gravity Measurement  
The procedure for the measurements of the center of gravity (COG) position corresponds to typical procedures for motor vehicles. By measuring all wheel loads in the horizontal position, the longitudinal (\(l_{f}\)) and lateral (\(\Delta y\)) center of gravity position was determined. The front axle of the vehicle was then lifted. The resulting wheel-load shift was used to determine the vehicle's center of gravity height. The experimental setup for determining the center of gravity position is shown in Figure 2.  
Figure 2: Test arrangement for determining the position of the center of gravity based on the wheel loads \(\mathbb{F}_{z,i}\), wheel base \(l\), track width \(t\), and inclination angle \(\alpha\).  
The determination of the COG position of the vehicle was based on the equilibrium of forces and moments shown in Figure 3. The COG position parameters \(l_{f}\), \(l_{r}\), \(\Delta y\) and \(h_{z}\) can thus be determined using Equations (1)-(4).  
\[l_{f}=\frac{F_{z,r}\cdot l}{F_{G}}=\frac{m_{r}\cdot l}{m} \tag{1}\]  
\[l_{r}=\frac{F_{z,f}\cdot l}{F_{G}}=\frac{m_{f}\cdot l}{m} \tag{2}\]  
\[h_{z}=\Delta h_{z}+r_{r}=\frac{l_{r}}{\tan\alpha}-\left(\frac{l}{\tan\alpha}+ \Delta r\right)\frac{F_{z,f}}{F_{G}}+r_{r} \tag{3}\]  
\[\Delta y=\frac{F_{z,f,l}-F_{z,f,r}}{F_{G}}\cdot\frac{t}{2}=\frac{m_{f,l}-m_{f, r}}{m}\cdot\frac{t}{2} \tag{4}\]  
with:  
\(l_{f},l_{r}\)--Distance of the COG to front/rear axle,  
\(F_{z,f},\ F_{z,r},\ m_{f},m_{r}\)--Vertical force or wheel load at the front/rear axle,  
\(F_{z,f,l},\ F_{z,f,r},\ m_{f,l},m_{f,r}\)--Vertical force or wheel load at the front left/right wheel,  
\(l\)--Wheelbase,  
\(t\)--Track width,  
\(m\)--Total mass,  
\(F_{G}\)--Total weight force,  
\(h_{z}\)--COG height above ground,  
\(\Delta h_{z}\)--COG height above rear wheel center,  
\(\Delta y\)--Lateral deviation of the COG from the vehicle's center plane,  
\(\alpha\)--Inclination angle,  
\(\Delta r\)--Difference in wheel radius rear to front,  
\(r\)--Rear wheel radius.  
Figure 3: (**a**) Horizontal equilibrium for determination of the COG longitudinal position \(l_{r}\), \(l_{r}\); (**b**) Tilted vehicle for the determination of COG height \(h_{z}\); (**c**) Horizontal equilibrium for the determination of the COG lateral position \(\Delta y\).  
The wheel loads were measured with industrial scales (resolution 2 g, linearity 6 g). For each measurement, the weight values were averaged in a time interval of 5 s with an internal sampling rate of 10 Hz. The display value of the scales is the average value over the measurement interval. There was no access to the time-dependent values with the measuring system used. The driver did not move during this time. For all experiments, a sitting position as shown in Figure 4 was used. The right leg was stretched out and the left leg was bent. Possible changes of the COG position due to movements of the driver during the ride, as they were investigated for wheelchairs in [17], were not considered as the measurement system only supported static measurements. Investigations regarding the influences of driver movement might be an interesting consideration for further studies.