# Concept Design and Development of an Electric Go-Kart
## 2 Materials and Methods
### Vehicle Dynamics Modeling  
In this section, we present the vehicle dynamics modeling. For the loads on the chassis, the major parameter is the static distribution of loads from the weight of the vehicle and driver. Additionally, dynamical loads arriving from road imperfections, such as a bulge or a dent, and accelerations on curved trajectories were taken into account for the approximation of a maximum load on each wheel. Dynamical loads are shown in Figure 2. For the approximation of maximum acceleration at braking and on a curve, the friction coefficient, in case of a dry tarmac, is presumed to be 0.8, according to references [35; 36]. With an approximated average of the driver's anthropometric parameters, the maximum force on each tire is derived based on a concept sketch presented in Figure 3. The driver is presumed to have a maximal mass of 80 kg, and the vehicle 50 kg. The combined center of gravity position was approximated by the available equations for the mass of body segments found in [45; 46] for the expected sitting position in driving. The body segments were drawn symbolically as lines with the center of gravity and respective mass omitted here for the sake of brevity. Then, the driver's COG components \(x_{\text{CG,d}}\), \(y_{\text{CG,d}}\) in the coordinate system \(Oxy\), shown in Figure 2 with origins in the contact point of the rear wheel, were calculated according to  
\[x_{\text{CG,d}}=\frac{\sum\limits_{i=1}^{14}m_{i}x_{\text{CG}}^{i}}{\sum \limits_{i=1}^{14}m_{i}},\;y_{\text{CG,d}}=\frac{\sum\limits_{i=1}^{14}m_{i}y_ {\text{CG}}^{i}}{\sum\limits_{i=1}^{14}m_{i}}. \tag{1}\]  
Figure 3: Inertial force of the go-kart, top view, while driving on a curved trajectory. Figure 2: The inertial force of go-kart with the driver, side view. The human body can be described by 14 segments in the calculation of its kinetics, according to [[PERSON]]. Each segment's center of gravity coordinates, \(x_{\text{CG}}^{i}\), \(y_{\text{CG}}^{i}\), were derived from geometry based on the drawing of the driver sitting in the go-kart seat. Further on, the vehicle's COG was calculated in SolidWorks and introduced as information into the calculation of the combined COG. The driver's COG alone was approximated for an adult person, as well as the average height, according to [45; 46]. Specific parameters for the chosen go-kart and driver are: \(x_{\text{CG,d}}=0.434\) m, \(y_{\text{CG,d}}=0.418\) m, \(x_{\text{CG,v}}=0.56\) m, \(y_{\text{CG,v}}=0.165\) m. The same way the driver's COG was calculated by Equation (1), the combined COG was calculated by  
\[h_{\text{CG}}=\frac{y_{\text{CG,d}}m_{\text{d}}+y_{\text{CG,v}}m_{\text{v}}}{m _{\text{d}}+m_{\text{v}}},\ L_{\text{CG}}=L-\frac{x_{\text{CG,d}}m_{\text{d}}+ x_{\text{CG,v}}m_{\text{v}}}{m_{\text{d}}+m_{\text{v}}}. \tag{2}\]  
In Equation (2), \(L\) is the wheel base, \(m_{\text{d}}\) is the driver's mass, and \(m_{\text{v}}\) is the vehicle mass. The final COG position according to Figure 2 is \(L=1.103\) m, \(h_{\text{CG}}=0.32\) m, \(L_{\text{CG}}=0.62\) m. Figures 2 and 3 depict the inertial forces at acceleration, causing redistribution of ground reactions on a vehicle concept design. In Figure 2, the driver's center of gravity is shown with a green circle, the vehicle's center of gravity with orange, and the combined center of gravity (COG) with a red circle, with its height relative to the ground level marked by \(h_{\text{CG}}\), and the distance from the front wheels marked by \(L_{\text{CG}}\). The inertial force at braking in a straight trajectory is shown with the red arrow, and the combined weight with the blue arrow. In Figure 3, the inertial force components at braking in a curved trajectory are shown, with tangential in red and normal (centrifugal) in light purple. Kinematics of this case were determined by combined COG moving on a curve with radius \(r_{\text{CG}}\).