Tine forces established by a two-level model and the draught requirement of rigid and flexible tines

To investigate the force requirement of flexible and rigid tines a field experiment was conducted on a clay loam soil at two different sites. One site comprised no-tilled soil, and the other site newly ploughed loose soil compacted with a roller. The tines used were rigid straight tines, flexible straight tines and flexible S-tines. The draught force and the tine deflection were measured with a frequency of 32 Hz. The driving speeds were around 1 m s−1 and 2 m s−1.Analysis showed that the tines mostly experienced peak force or trough force levels. Based on the peak and trough forces a two-level model was therefore introduced. Such a model assumes that the tines are either subjected to a peak force or a trough force. Testing of the model confirmed its validity. In order to compare the draught requirement of the different tines, the peak and trough forces had to be related to a term containing both tilling depth and tine speed. A combined depth-velocity term provided by Godwin and O’Dogherty [Godwin, R.J., O’Dogherty, M.J., 2003. Integrated soil-tillage force predictions model. In: Ninth European Conference of the International Society of Terrain Vehicle Systems, Harpur Adams University College, Newport, England.] met this requirement. Relating the peak and trough forces to this term clarified the effect of tine flexibility. Compared to rigid straight tines, the two flexible straight tines gave a draught reduction in no-tilled soil according to tine flexibility, while flexible S-tines gave a draught reduction only due to a lower rake angle. At both driving speeds the greatest draught reduction due to tine flexibility occurred at the highest magnitude of the depth-velocity term, i.e., the greatest tilling depth. The magnitude of this draught reduction was approximately 10% at the low driving speed and approximately 20% at the high driving speed (*P < 0.05). In tilled soil only the softest flexible straight tine gave a draught reduction. The other flexible straight tine and the flexible S-tines did not give any draught reduction compared to rigid straight tines.In addition, the peak and trough forces and the corresponding tine speeds were found to deviate by just one standard deviation from the mean draught force and mean tine speed. This greatly simplifies the application of the model.