Modification and Application of Söhne, McKyes, and Perumpral Models for Predicting Draught Forces in a Duckfoot Tool

The study aimed to modify the models of Söhne, McKyes, and Perumpral to predict the draught force acting on duckfoot tools. Classic models, developed for narrow tools, do not consider the specific geometry of the wide duckfoot wings or the dynamic soil-tool interactions. In laboratory studies, duckfoots with widths of 105, 133, and 200 mm were used in the soil bin, operating at depths of 0.03–0.07 m at speeds of 0.84–2.31 m·s⁻¹ in soils with 10% and 14% moisture content. The results showed that the modified models predicted a draught force with a global error δg of 23–25% for the whole data, while the classical solutions achieved higher values (25–62%). The best fit was obtained for the Perumpral model (RMSE = 58 N), while the Söhne and McKyes models had a higher error value (RMSE = 64 N). The developed modifications increase the reliability of predictions and can support the design of tools for work in compacted soils. The falsification of hypotheses showed that while modifications improve accuracy, they do not eliminate limitations under varying operating conditions. It is necessary to improve the models by considering the three-dimensional effects of soil deformation, the variability of its properties over time, and random terms describing field factors.