# Comparison of Multi-Tracked Running Gears in Terms of Obstacle Negotiation Capabilities
## 4 Simulation Results  
### Roadside Ditch Negotiation  
The first test on this obstacle showed an advantage of the double-jointed solutions (D and E). They overcame the obstacle with the lowest ground shearing resistant angle \(\O\). The minimal ground shear strength characteristics enabling negotiation of the ditch in all solutions are shown in Figure 10. The tangent value was 64% smaller than for the single module solution (A).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Soil cohesion C & 3 kPa \\ Ground shearing resistant angle \(\O\) [\({}^{\circ}\)] & 28\({}^{\circ}\) \\ Ratio of residual stress \(K_{r}\) & 0.5 \\ Shear displacement where the maximum shear stress occurs \(K_{\omega}\) & 35 mm \\ Ground stiffness k & 50 N/mm \\ Ground damping c & 100 N\(\cdot\)s/mm \\ Contact force exponent e & 2 \\ Contact penetration depth \(d\) & 10 mm \\ \hline \hline \end{tabular}
\end{table}
Table 2: Ground parameters assumed in simulation.  
Figure 9: (**a**) Obtained drawbar pull characteristics; (**b**) correlation analysis of model and experimental data.  
The three multi-tracked solutions provide better obstacle-negotiation performance, because they allow sharing the generated traction force between modules. Figure 11 shows solution E's module driving forces. It can be seen that the entire system is initially driven by the downhill driving front module. Then, the rear module, using the gravity component when going down a slope, pushes the front module uphill. Finally, the front module pulls the rear module in. Negative values of forces indicate the \"braking\" by the ground forces of one of the modules. This is the result of the kinematic discrepancy--since the modules were driven at the same speed. The higher the ground strength applied, the greater the differences in drive forces between the modules. This unfavorable phenomenon requires separate research on the control of the track drive in order to minimize the power circulation in this system.  
The second test results--the simulation with the same ground conditions \(\text{tg}\emptyset\) = 0.75 C = 3 kPa --are presented in Table 3. Figure 12 shows each solution's tracked system positions at the critical moment (of the highest load). It can be seen that solution B achieves only a few segments in contact with the ground. The small distance between the modules does not allow better track-shape adjustment to the ground. As a result, it achieves the highest slip value--almost three times higher than solution E. The single module (A) solution overcomes the obstacle in the shortest time. This is caused by the loss of traction and sliding down the slope of the ditch, which saves about 0.5 s. Solutions E's single frame reduces the angle of inclination of the system by 34% and also reduces the maximum angular velocity of pitching by almost four times, compared to solution A.  
Figure 10: Ground shear strength characteristics enabling overcoming the ditch for each solution.  
Figure 11: Courses of solution E’s front and rear tracked module driving force during ditch negotiation.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Solution**} & **Obstacle Overcoming** & **Track Slip at a** & **Maximum Pitching Angle of the** & **Maximum Pitching Angle Speed of** \\  & **Time [s]** & **Critical Moment** & **Platform Frame [Degrees]** & **the Platform Frame [Degrees/s]** \\ \hline A & 6.29 & 0.40 & 38 & 189 \\ B & 6.63 & 0.52 & 38 & 185 \\ C & 6.75 & 0.35 & 39 & 172 \\ D & 6.54 & 0.29 & 34 & 132 \\ E & 6.74 & 0.18 & 25 & 49 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results of second test for ditch negotiation.  
Figure 12: Comparison of the tracked modules’ position for solutions A to E (**a–e**) at the moment of reaching the highest driving force load.