Mathematical modelling and optimization of the uniformity of distribution in fixed rate fertilizer application

Disc broadcasters are the most widely used machines in fertilizer distribution applications. There are various parameters, which affects the distribution uniformity of these machines. The objective of this study was to obtain the mathematical models and optimize the distribution uniformity in twin-disc granular broadcast spreader. The ultimate goal expected from this study was to optimize the variables considered in the study in order to minimise the coefficient of variation (CV) for three different fertilizer used. In addition, the study was expected to help making the amount of fertilizer in both sides in longitudinal direction within allowed limits. A domestic twin-disc granular broadcast spreader was used along with three different granular fertilizers namely urea, compound fertilizer of 15-15-15, and compound fertilizer of 20-20-0. The variables considered in the study were the height of vanes (H), vane angle (α), fertilizer flow rate (Q) and disc peripheral speed (V), as they were related to construction and operating conditions in this fertilizer distribution phenomenon. Not only the main effects on the distribution uniformity of each of these variables, but also interactions of these variables are matter of this study. Therefore, the models formed in polynomial form, including the interactions of variables, were expressed the performance of distribution uniformity in mathematical form. In order to achieve the objectives set in this study, Response Surface Methodology (RSM) was used. Totally 93 experiments - 31 experiments for each fertilizer - conducted according to ASAE S341.4 standard. RSM has helped to develop mathematical functions in the form of polynomial models, the optimum level of the variables could be found from these models and the optimums were verified. According to the results of the verification tests, the twin-disc granular broadcast spreader provided "good" range of distribution uniformity which were 6,775 % for urea fertilizer 8,135 % for compound fertilizer of 15-15-15 and 8,110 % for compound fertilizer of 20-20-0.