## 2 Materials and Methods
### Field Tests  
To perform the aforesaid full factorial experiment, tests were carried out in spring (March) in an agricultural field, which had been plowed with a chisel to 25 cm depth the previous autumn (September). Place of the field experiments: Ukraine, Melitopol (46\({}^{\circ}\)50\({}^{\circ}\)56\({}^{\prime\prime}\) north latitude, 35\({}^{\circ}\)21\({}^{\prime}\)55\({}^{\prime\prime}\) east longitude, altitude: 37 m). A BELARUS model MTZ-1221.2 wheel tractor was used, whose main technical characteristics were: (i) rate power, 95.6 kW; (ii) total weight, 54.6 kN; (iii) front wheels, 420/70R24; (iv) rear wheels, 18.4R38; (v) weight on front wheels, 16.2 kN. In the chosen agricultural field 4 plots of 10 \(\times\) 30 m each were considered. In each plot the MTZ-1221.2 tractor formed the PTL tracks of depth \(h\), moving in the forward and reverse directions with the same gear to ensure the double repetition of the experiments (Figure 1). The average speed of the tractor during the experimental studies was constant and equal to 2.1 m s\({}^{-1}\). The minimum and maximum values of the parameters \(H\) and \(\rho\) of Table 2 were assessed as follows. The values of the soil density (\(\rho\)) and soil cone index (\(H\)) of all plots \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & \multicolumn{2}{c}{**Measurement**} \\ \hline  & **Min** & **Max** \\ \hline \(P_{w}\) (MPa) & 0.10 & 0.16 \\ \(\rho\) (kg m\({}^{-3}\)) & 1020 & 1260 \\ \(H\) (MPa) & 0.48 & 0.90 \\ \(N_{w}\) (N) & 8100 & 10,100 \\ \hline \multicolumn{3}{c}{Variation level} \\ \cline{2-4} p-terms & \(-1\) & 0 & +1 \\ \hline \(\pi_{1}\) & 3 & 6 & 9 & 3 \\ \(\pi_{2}\) & 0.0002 & 0.00085 & 0.0015 & 0.00065 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Levels and interval variation of parameters and p-terms. were measured in the spring (March) before the experiment tests and were considered the maximum values for these parameters. Both the soil density and the soil cone index were measured in 50 points within each plot. The values of all these measurements performed in all the plots were used to assess the average values of soil density (\(\rho\)) and soil cone index (\(H\)), respectively, reported in Table 2.  
Furthermore, the soil on 2 plots of the field (plot 2 and plot 4) was then tilled with a disc narrow to a depth of 15 cm. After the tillage, through the same method described above the average values of the soil density (\(\rho\)) and soil cone index (\(H\)) of these two plots were measured and considered as the minimum values for these parameters (Table 2). The test plan reported in Table 3 was then implemented. The PTL trace depth was measured on each site as follows. The left track depth made by the MTZ-1221.2 tractor was measured in duplicate with a ruler-depth meter with an error of \(\pm\)0.005 m. Measurements were carried out at the center of the wheel track, as shown by the white points along the red line in Figure 2. The measurement points were 100, with a measurement step of 0.1 m [35]. The soil cone index \(H\) was assessed using a Model Lan-M penetrometer ([PERSON], Kyiv, Ukraine) with the following main technical characteristics: 0 to 7.8 MPa soil cone index measure range and 0.05 MPa accuracy. The soil bulk density \(\rho\) was evaluated as follows [49,50]. The soil sample was taken with a 28.35 cm\({}^{3}\) cylinder (height--1.7 cm; diameter--4.6 cm) and weighed on the scales, which were configured to measure in ounces. As 1 oz. = 28.35 g, the scales showed the soil mass value that was equal to its density in g cm\({}^{-3}\). In addition to soil cone index \(H\) and soil bulk density \(\rho\), soil moisture \(M_{s}\) was measured during field studies. Measurements of these parameters were carried out in the same zone where the depth of the wheels was determined after the passage of the tractor (see Figure 2). The depth of the soil layer for measuring soil moisture and soil density was 0-15 cm.