Mathematical modeling of the dynamics of air jet crossing the canopy of tree crops during pesticide application

A mathematical model was developed to get an equation of the decrease of air velocity crossing the canopy of tree crops during pesticide application using air carrier orchard sprayers. The utility of such a model rises from the need for an aid to understand the experimental results of several authors, who agree with the opinion that air jet velocity greatly affects environmental pollution from pesticides. Further, probably in the future it will arise the demand to implement the equation of air velocity decay in self-adjustment systems of the fan installed on orchard sprayers to limit spray drift. Based on momentum theorem applied under three assumptions, a differential equation was found and its integration lead to a closed solution that can easily be implemented in a PLC for the self-adjustment system to develop. The integral equation thus obtained, together with the assumptions made, was submitted to on-field verification on three crops (peach, vine and apple). The results show a good correspondence between measured and estimated air speed as predicted by the mathematical model, with a relative mean error 3.3% and a maximum value of 6.2%.