## 2 Materials and Methods
### Forces Acting upon the Transportation Model  
The weight of the load itself, as well as that of each if the trailer's component, must be considered. Thus, the total weight of the load is the sum of the weights of all individual components:  
\[W=M\cdot g=\left(m_{load}+\sum\limits_{i=1}^{n}m_{i}\right)\cdot g \tag{5}\]  
with the total mass of the trailer and load in kilogram as \(M\), the load's mass as \(m_{load}\), the mass of the trailer's component \(i\) as \(m_{ij}\), the acceleration of gravity as \(g\) and the weight as \(W\). This force is exerted on the CoG. The latter is located at a point that corresponds to the weighted average of the CoGs of all items or parts that are being transported:  
\[ \begin{array}{l}x_{CoG}=\frac{1}{M}\cdot\left(m_{load}\cdot x_{load}+\sum \limits_{i=1}^{n}m_{i}\cdot x_{i}\right)\\ y_{CoG}=\frac{1}{M}\cdot\left(m_{load}\cdot y_{load}+\sum\limits_{i=1}^{n}m_{i} \cdot y_{i}\right)\\ z_{CoG}=\frac{1}{M}\cdot\left(m_{load}\cdot z_{load}+\sum\limits_{i=1}^{n}m_{i} \cdot z_{i}\right)\end{array}  \tag{6}\]  
Figure 3: 3-point suspension and stability area. with (\(x_{CoG}\), \(y_{CoG}\), _and_\(z_{CoG}\)) as coordinates of the final CoG and (\(x_{i}\), \(y_{i}\), _and_\(z_{i}\)) as the coordinates of the component i's CoG. Breaking (acceleration or deceleration) creates an inertial force in the driving direction (axis X). This force is calculated by the following Equation (7):  
\[F_{A}=M\cdot a \tag{7}\]  
with \(F_{A}\) for the acceleration force, \(M\) for the total weight, and \(a\) for the acceleration. \(F_{A}\) is applied at the CoG. A turn can be described as a movement by the trailer along a circular path or along a circumference, both of which generate centripetal acceleration. This, together with the weight of the load, creates an inertial force in a direction that is perpendicular to the driving direction (axis Y). This force is calculated by Equation (8):  
\[F_{T}=M\cdot\frac{v^{2}}{R} \tag{8}\]  
where \(F_{T}\) is the centrifugal force, \(M\) is the total weight, \(R\) is the turn's radius, and \(v\) is the trailer's velocity. \(F_{T}\) is applied to the center of gravity. Depending on the turning direction, it can be positive or negative. The radius in Equation (8) is positive when it appears on the left. It is negative if it appears on the right (See Figure 4). The relative movement between the air and the trailer creates an aerodynamic force against the trailer. This study considers only the forces of drag on the cargo, as they are much greater than those on truck and trailer. The equation to calculate the drag is the same one that is employed to calculate the longitudinal (\(F_{Dx}\)) and transversal (\(F_{Dy}\)) drag forces that movement through a fluid creates:  
\[F_{Dx}=\frac{1}{2}\cdot\rho\cdot(v+v_{w~{}x})^{2}\cdot A_{x}\cdot C_{dx}= \frac{1}{2}\cdot\rho\cdot(v+cos(\alpha_{w})\cdot v_{w})^{2}\cdot A_{x}\cdot C _{dx} \tag{9}\]  
\[F_{Dy}=\frac{1}{2}\cdot\rho\cdot v_{w\cdot y}^{2}\cdot A_{y}\cdot C_{dy}= \frac{1}{2}\cdot\rho\cdot(sin(\alpha_{w})\cdot v_{w})^{2}\cdot A_{y}\cdot C _{dy} \tag{10}\]  
with \(F_{Dy}\) for the longitudinal and transverse drag forces, \(\rho\) for the fluid's density, \(v_{w}\) for the velocity of the air, \(\alpha_{w}\) for the angle between the air velocity and the trailer's longitudinal axle, and \(A_{x}\) and \(A_{y}\) denote the reference areas. Finally, \(C_{dy}\) and \(C_{dx}\) are drag coefficients, and are dimensionless (they depend on the geometry, surface, and relative position). One should remember that three aerodynamic forces generally act on the trailer. They are a longitudinal force (axis X), a transversal force (axis Y), and a lifting force (axis Z). However, the equations for these forces are valid for certain objects. The drag force on the truck, trailer, and load together cannot be determined easily. Obtaining realistic values for the forces that are acting on the three axles requires CFD and/or wind tunnel experiments.