A semi-empirical traction prediction model for an agricultural tyre, based on the super ellipse shape of the contact surface

•A traction model for the agricultural tyres–soil interaction.•Super ellipse shape of the contact surface.•Comparison between theoretical and experimental data.•Validation of the model.

This study presents a semi-empirical model for predicting the traction force and traction efficiency for a 2WD agricultural tractor, assuming that the shape of the tyre–ground contact area is a super ellipse. The model assumes that, under the vertical load, the wheel sinks into the soil and that the load induces tyre deflection; as a result, the virtual radius of the deformed tyre increases, as it flattens in the tyre–ground contact area. A computer programme was developed in order to solve the equations of the model, using an iterative process. In order to evaluate the maximum traction force it was assumed that it is limited only by the soil shear strength and the Mohr–Coulomb equation was used to calculate the soil maximum shear stress.Because the available literature presents a large range of values for the super ellipse exponent, field tests were performed in order to validate the model; the experimental data were collected during ploughing tests. In order to evaluate the precision of the model the predicted data were compared with the test data by the means of a goodness-of-fit analysis.The results predicted by the model show that the length of the tyre–ground contact surface is not affected by the shape of the contact surface (value of the super ellipse exponent), while increasing the value of the super ellipse exponent results in an increased of the area of the contact surface.The best fit between model data and experimental data was achieved when the value of the super ellipse exponent was set to k = 3.5.