## 2 Ground Sinkage and Motion Resistance of Off-Road Tracked Vehicles  
The track system, namely, the mobility system of off-road tracked vehicles, transfers driving torque and vehicle weight (\(W\)) to the ground (Figure 1). The driving torque shears the ground and the vehicle's weight exerts a vertical force. From the view point of terramechanics, driving torque and vehicle weight can be expressed by longitudinal and vertical force on the soil-track interface, respectively [2]. The tractive performance of off-road tracked vehicles is reduced by the shearing action and sinkage caused by these forces. In the soil-track interaction theory of [PERSON] [4], ground shear displacement caused by the track system is represented by slip displacement (\(j\)). Slip ratio (\(i\)) is defined as the relative extent of \(j\) that occurs when the track system moves longitudinally by a certain distance (\(x\)). \(i\) is calculated as shown in Equation (1). \[i=j/x \tag{1}\]  
\(i\) is determined by the ground's shear characteristics. Assuming the ground is homogeneous, \(i\) of the entire soil-track interface is constant. In this case, as shown in Equation (1), \(j\) varies with \(x\) (i.e., the position of the soil-track interface in proportion to the longitudinal distance by which the track system moves). When off-road tracked vehicles drive at non-zero slip, ground sinkage (\(z_{t}\)) can be expressed as the sum of static sinkage (\(z_{0}\)), which occurs due to vehicle weight, and slip sinkage (\(z_{j}\)), which occurs due to ground shearing (i.e., when j occurs), as shown in Equation (2) [16]. \[z_{t}=z_{0}+z_{j} \tag{2}\]  
Ground sinkage causes motion resistances such as compaction resistance (\(R_{c}\)) and bulldozing resistance (\(R_{b}\)) on soil-track interfaces, thereby limiting the tractive performance of off-road tracked vehicles (Figure 1). \(R_{c}\) occurs because part of the force transmitted to the ground through the track system contributes to ground sinkage. The work consumed in compacting the ground equal to the area of the soil-track interface is equal to the work used in \(R_{c}\) when towing the track system longitudinally by the soil-track contact length. This work can be assessed as shown in Equation (3) [3]. \[R_{c}l=wl\int_{0}^{z_{t}}(W/wl)dz \tag{3}\]  
Here, \(w\) and \(l\) represent the track system width and soil-track contact length, respectively. \(R_{b}\) is the resistance caused by ground deposited at the front of the track system when driving the off-road tracked vehicle. Only static sinkage occurs in the front portion of the off-road tracked vehicle; here, slip displacement and slip sinkage do not occur (\(j=z_{j}=0\)). Thus, \(R_{b}\) is the force required to push the ground corresponding to \(z_{0}\) of the front of the track system (i.e., the force required to overcome passive earth pressure) using a plate of the same width as that of the track system. \(R_{b}\) can be expressed using Equation (4), which uses the Rankine passive earth pressure theory. \[R_{b}=2w\int_{0}^{z_{0}}\left(\gamma K_{p}z+2c\sqrt{K_{p}}\right)dz \tag{4}\]  
Here, \(\gamma\) is the unit weight of the soil, \(c\) is the cohesion of the soil, and \(K_{p}\) is the Rankine passive earth pressure coefficient determined by the internal friction angle (\(\phi\)) of the soil. The total motion resistance that occurs in off-road tracked vehicle driving can be assessed as the sum of \(R_{c}\) and \(R_{b}\), which are calculated independently using Equations (3) and (4). To sum up, the motion resistance of the off-road tracked vehicle occurs due to ground sinkage. In particular, the compaction resistance is affected by static sinkage and slip sinkage. However, due to  
Figure 1: Schematic diagram of the ground deformation (settlement and slip displacement) and motion resistances. the current lack of theoretical background research on assessing slip sinkage, most studies considered only static sinkage when calculating motion resistance.