The existing models for predicting forces on narrow soil cutting tines are based on different assumptions and give different results of calculated values. A new mathematical model for predicting forces on narrow soil cutting tines has been developed including a more realistic geometry of soil wedge, compared to previous mechanical models. The new model takes into account variability of the inclination angles of bottom failure surface in the side segments. Also included is the calculation of inertial forces for differential side segments based on the spatial position of the velocity triangle, which gives different absolute velocity for particular segments. The forward rupture distance depends on critical depth and the side rupture distance is given by a regression equation. Draft prediction is based on the complex set of forces, including the critical depth and two-dimensional failure zone together with inertial forces in the three-dimensional zone. The unknown values of the critical depth together with the rupture angle have been calculated by the minimisation of the total force acting on the tool. In order to check the extended model, experiments were performed in a soil bin and the results were compared with those calculated from the new model as well as from existing models. Absolute values of difference between calculated and observed values, related to measured values, taken as an error of different theoretical models, amounted to 11.7% for our model, and 17.1-34.9% for existing models. Statistical analysis of measured and calculated forces showed that for 58 degrees of freedom and a confidence level alpha=0.05, the t-test value amounted to 0.795 and the significance level was 0.430. It means that the H0 hypothesis cannot be rejected and the developed model predicts the forces satisfactorily. The main result of our model is the possibility of more exact prediction of the resistance of narrow tines, by introducing a variability of the inclination angles of bottom failure surface in side segments of different deflections from the direction of a tine motion, which was not taken into consideration in the existing models. (C) 1998 Elsevier Science B.V. All rights reserved.
