## 3 Results and Discussion  
### Results of the Statistical Analysis  
Based on the analysis of variance and the matrix of correlation coefficient values, the statistical analysis results provided important information about the influence of individual independent variables and their interaction with the draught forces, \(F_{x}\), and vertical forces, \(F_{y}\). The study showed that the key variables influencing the forces acting on duckfoots were time stiffness, \(k\), tool depth-to-width ratio, \(d/w\), tool movement speed, \(v\), and soil moisture, \(MC\). Each of these variables had a statistically significant effect on the forces \(F_{x}\) and \(F_{y}\), which was confirmed by the values of the Fisher-Snedecor coefficients and the significance level \(p\) < 0.0001 for most of the analysed principal factors and their interactions (Table 2). The ratio of the depth to the width of the tool, \(d/w\), showed the most significant impact on the differentiation of draught and vertical force values. This variable had the relatively highest values of the Pearson's correlation coefficients, amounting to 0.326 for draught \(F_{x}\) and 0.547 for force \(F_{y}\) (Table 3). Higher values of correlation coefficients for a variable \(d/w\) indicated a direct relationship between a change in the depth-to-width ratio  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Force** & & \multicolumn{4}{c}{\(F_{x}\)} & \multicolumn{4}{c}{\(F_{y}\)} \\
**Effect  
and an increase in the forces acting on the tools. The importance of this variable has also been confirmed in the literature, where many studies have shown that a more excellent value of the ratio \(d/w\) increased the resistance of the cut soil, which, in response, translated into increased draught and vertical forces, which affected the efficiency of cultivation and energy consumption by the tool [30]. The second important variable was the movement speed of the tool, \(v\), which positively affected the values of draught and vertical forces. The correlation coefficients for speed were 0.257 for \(F_{x}\) and 0.168 for \(F_{y}\). These results supported the findings of previous studies that indicated that an increase in the speed of working implement movement led to increased draught forces, which was associated with dynamic effects of acceleration and soil deformation [39]. The high movement speed of the working implements contributed to higher soil resistance, increasing the tool's energy consumption, but it could also promote more efficient soil loosening under certain conditions. Tool stiffness, \(k\), was another critical variable that affected the values of draught and vertical forces. The correlation coefficient for this variable was 0.165 for \(F_{x}\) and 0.031 for \(F_{y}\), which suggested that the stiffness of the spring used to make the duckfoots mounting tines had a more significant impact on \(F_{x}\) than \(F_{y}\). The literature emphasises the importance of the stiffness of the working elements of tillage tools in the context of the forces acting on the tools. Studies show that tools with higher rigidity are more effective on hard soil, while flexible tools can generate less pulling resistance, which confirms the results obtained [40]. Soil moisture, \(MC\), showed a minimally negative effect on the values of both forces. This result was in line with those of previous studies that showed that sandy soil with a low proportion of clay particles with higher moisture content has lower pulling resistance due to lower soil cohesion and better tool slippage in moist soil layers [41]. Lower soil-tool adhesion force in conditions of increased moisture reduces the pulling resistance, which can also lead to more effective tool operation. However, it should be emphasised that other soil species may show different properties with increasing moisture. The analysis of interactions between variables allows us to conclude that most of the analysed interactions had a significant impact on the values of forces \(F_{x}\) and \(F_{y}\).