## 3 Results and Discussion  
Experimental studies were carried out on the soil, which was dark chestnut chernozem with a humus content of up to 4.5%. Before the experiment, the soil moisture content \(M_{s}\) was 20.9%, the soil cone index \(H\) was 0.90 MPa and density \(\rho\) was 1260 kg m\({}^{-3}\). After the tillage with a disc narrow, the soil cone index in the range from 0 to 5 cm layer decreased to 0.48 MPa and density to 1020 kg m\({}^{-3}\). Processing of the experimental data shows that the functional dependence (15) can be approximated by a linear polynomial:  
\[\frac{hp\beta}{P_{w}}=0.01-0.001\pi_{1}+3.7\pi_{2}. \tag{16}\]  
Figure 3: Research algorithm. If we substitute Equations (12) and (13), Equation (16) takes the following final form:  
\[h=0.01\frac{P_{w}}{\rho g}-0.001\frac{H}{\rho g}+3.7\frac{N_{w}\rho g}{P_{w}^{2}} \tag{17}\]  
Analysis of Equation (17) shows that as the tractor front tires inflation pressures \(P_{w}\) increases, and the track depth increases (Figure 4). In principle, this occurs according to a nonlinear law. As the vertical load \(N_{w}\) on the wheel increases, the parameter \(h\) changes in direct proportion, and therefore according to the straight-line law (Figure 5). According to scientific logic, the regularities shown in Figures 4-6 are quite natural and understandable. In qualitative terms, the influence of the parameters \(P_{w}\), \(N_{w}\), \(\rho\) and \(H\) on the value of \(h\) are known to researchers [52; 53]. Of interest is their quantitative influence. At the same time, their quantitative and qualitative influence are not separate, but joint, i.e., complex. As follows from Table 2, the parameters \(P_{w}\), \(N_{w}\), \(\rho\) and \(H\) had different limits of variation. The inflation pressure in the wheel tire \(P_{w}\) was considered from 0.10 to 0.16 MPa, i.e., increased by 60%. The soil cone index \(H\) increased even more: from 0.48 to 0.90 MPa, i.e., by 88%. As for the values of the soil density \(\rho\) and vertical load \(N_{w}\) on the tractor wheel, their changes were almost the same and approximately equal to 25%. With increasing soil density \(\rho\), the depth \(h\) of the PTL trace naturally decreases (Figure 6). The same occurs with increasing soil cone index (Figure 7). Figure 4: Dependence of the track depth PTL (\(h\)) on the tractor tire inflation pressure (\(P_{w}\)). Figure 5: Dependence of the PTL track depth (\(h\)) on the vertical load on the tractor wheel (\(N_{w}\)). On this basis, it has been estimated the degree of change in the PTL track depth if the parameters \(P_{w}\), \(N_{w}\), \(\rho\) and \(H\) are increased by the same amount: 25%. It makes no sense to take a larger value because \(N_{w}\) and \(H\) increased by no more than 25% during the study of the mathematical model (17). The analysis of the experimental data obtained considering such restrictions showed that the greatest contribution to the change in the parameter \(h\) is made by the soil cone index \(H\) (Figure 8). In this case, this contribution has been 24.0%. The contribution of the tractor front tires inflation pressures \(P_{w}\) to the change in the PTL track depth \(h\) has been less and is 15%. Soil density \(\rho\) and vertical wheel load \(N_{w}\) had approximately the same effect on the change in the parameter \(h\), namely 9 and 7%, respectively. It follows from this analysis that to obtain PTL tracks of acceptable (specified) depth \(h\), the initial soil background should have a low cone index. The lesser degree of influence of the \(\rho\) parameter on the PTL depth (\(h\)) can be explained by the following. Although there is a direct correlation between soil density \(\rho\) and soil cone index \(H\), it is not directly proportional. According to our studies of about 300 soil samples with 12-20% moisture content, a decrease in soil cone index \(H\) by 0.5 MPa led to a decrease in soil density \(\rho\) by only 50-80 g m\({}^{-3}\). Approximately the same data with a difference of no more than 5% were obtained by other authors [54].