A simulation of the influence of spinning on the ballistic flight of spherical fertiliser grains

• A model for motion of spinning fertiliser grains on a concave spinning disc with radial straight vanes was developed.
• A three dimensional ballistic model that takes into account spin of fertiliser grains was developed.
• Simulations indicate a major effect of fertilizer particle spin on their landing position.

A three dimensional ballistic model was developed to investigate the effect of spin on the trajectory of fertiliser grains in the air and their subsequent landing position. In addition to the gravitational- and drag force, also the Magnus force and drag torque were included in the model. Because of the considerable uncertainty regarding the spinning velocity of the grains, initial conditions for the ballistic model were simulated using a newly derived analytical model that describes motion on a concave disc. In both models, grains were presumed to be perfectly spherical. Simulations indicated a major effect on the landing positions of individual grains although the magnitude was dependent on fertiliser- and spreader characteristics. Deviations up to 33% of the total travelled distance in the direction of the initial horizontal velocity vector were found. Furthermore, the Magnus force clearly causes a deflection of the trajectory in the horizontal plane.