Method of calculating the throwing angle of fertilizers and seeds by a centrifugal apparatus with blades displaced from the radius as a function of random coordinates of the feed point

Uniform distribution of seeds or fertilizers over the surface of the field ensures the quality of the technological process and ultimately increases the yield of the cultivated crop. A jet of fertilizers or seeds fed to a centrifugal apparatus, under the impact of the blades, receives a spread along the angle and radius of the feed. The characteristics of the angle of throwing the blade of a centrifugal spreader are revealed, which make it possible to improve the uniformity of the distribution of seeds and fertilizers. In this article, the characteristics of the throwing angle are calculated using the Mathcad software package. The package consists of four programs. The first program calculates the probability densities of the feed point coordinates under the assumption of a two-dimensional normal distribution of the system including the feed radius and the angular coordinate of the feed point. The infeed radius and the angular coordinate of the infeed point are specified in the program as vectors. The result of the count is displayed in the form of a matrix. The second program calculates the throwing angles for all combinations of the feed radius and the angular coordinate of the feed point specified in the first program. To calculate the angle of throwing, solutions of the equations of motion of a particle along the blade of the apparatus are used with the initial data: the radius of the disk, the angular velocity of the disk, the coefficient of friction of fertilizers on the blade, the angle of inclination of the blade to the radius. The third program selects from the matrix of the first program the elements corresponding to the receipt of the throwing angle less than the required number. The fourth program summarizes the elements of the matrix of the third program. By multiplying the resulting sum by the intervals of the feed radius vectors and the angular coordinate of the feed point, the values of the distribution function of the throwing angle are obtained. The calculated throw angle distribution function is approximated by a standard normal distribution function.