631.333

solid mineral fertilizers, divisor, resulting speed, coordinate, curved surface.

The main mass of granular mineral fertilizers is applied by spreading them over the surface of the field, both during the main fertilization of the soil and when feeding agricultural crops. Existing machines of domestic production do not meet agronomic requirements in terms of indicators of uneven application of mineral fertilizers. At the current stage, there are no theoretical dependencies that would adequately describe: the process of feeding fertilizers through the lower link of the feeder-conveyor; the movement of fertilizers from the feeder to the fat diverter and their movement along the latter; the movement of fertilizers from the working body to the surface of the field under wind conditions. Known models of applying mineral fertilizers to the surface of the field do not agree with the real process and contradict the standard method of determining the unevenness of their application on the working width of the machines. The purpose of the work: to develop an analytical model that functionally describes the process of movement of mineral fertilizers in the guide cone of the divider of the distribution device depending on the parameters of the working body. The article provides a theoretical analysis of the movement of a particle of mineral fertilizers along the curved surface of the divider, taking into account the direction of the wind and the resistance of the air environment. According to the research results, an analytical and graphical model was developed that characterizes the change in the speed of movement of mineral fertilizers depending on the initial coordinates of their placement in the guide cone of the divider. It was established that with changes in coordinates within 0.1...0.4 m and the diameter of fertilizers from 4 to 6 mm, the resulting speed of movement of fertilizers is in the range of 1.0...2.9 m/s.

1. Adamchuk V., Petrychenko E. Study of the movement of the combined sowing unit with simultaneous application of mineral fertilizers. Herald of Agrarian Science, 2015, volume 93, no. 3, pp. 47–51. [In Ukrainian]
2. Berezhenko E., Pankiv М., Jobbagy Jan, Berezhenko B. Experimental research of the module for gathering plant of chicory roots. Scientific Journal of TNTU, 2021, no. 1 (101), pp. 56–67.
3. Adamchuk V., Yaremenko V., Boris N. Mathematical model of spreading mineral fertilizers by centrifugal method. Agricultural Engineering, 2013, vol. 45, issue 1, pp. 6–8.
4. Bondarenko A. M., Savkin V. I., Shelkovnikov S. A., Kachanova L. S. Approaches to the economic evaluation of elements of organic agricultural production of innovative type. Astra Salvensis, 2019, T. 7, No. S1.
5. Boyko V., Baranovsky V., Pankiv V., Onyshchenko V., Marinenko S. The results of the study of the cutter of the remains of root crops haulm. Scientific Journal of the Ternopil National Technical University, 2023, vol. 99, no. 1, pp. 99–109.
6. Wang Y., Sierakowski A., Prosperetti A. Rotational dynamics of a particle in a turbulent stream. Physical Review Fluids, 2019, no, 4 (6).
7. Adamchuk V. V. Justification of the method of determining the parameters of the centrifugal scattering body. Herald of Agrarian Science, 2005, no. 2, pp. 45–48. [In Ukrainian]
8. Inns E. M., Reece A. R. The Theory of the disk centrifugal distributor. Motion on the disk off centre feed. Agricultural engineering research, vol. 7, no. 4, pp. 45–353.
9. Fukada T., Takeuchi S., Kajishima T. Effects of curvature and vorticity in rotating flows on hydrodynamic forces acting on a sphere. International Journal of Multiphase Flow, 2014, no. 58, pp. 292–300.
10. Koller К. Wurf-oder Pneumatikstreueroz. Landwirtschaftiche Zeitschrift, 1987, no. 10, pp. 628–630.
11. Voytiuk D. G., Baranovskyi V. M., Bulgakov V. M. and others/ Agricultural machines. Basics of theory and calculation: Textbook / under the editorship of D. G. Voytyuka K.: Higher education, 2005. 464 p. [In Ukrainian]
12. Loveykin V. S., Chovnyuk Y. V., Dityuk A. I. Mathematical modeling of the movement of a particle of mineral fertilizers after descending from the disc of a centrifugal spreader in the presence of variable aerodynamic resistance of the medium (air). http://www.nbuv.gov.ua/portal/Chem_Biol/Vzhnau/ 2010_2/21.pdf. [In Ukrainian].
13. Luo J. et al. Application of bio-organic fertilizer significantly affected fungal diversity of soils. Soil Science Society of America Journal 74. 2010. P. 2039.
14. Pantaleo A., Villarini M., Colantoni A., Carlini M., Santoro F., Rajabi Hamedani S.Techno-Economic Modeling of Biomass Pellet Routes: Feasibility in Italy. Energies, 2020, vol. 13, pp. 1636.
15. Misselbrook T., Bittman S., Cordovil C., Rees B., Sylvester-Bradley R., Olesen J., Vallejo A. Field application of organic and inorganic fertilizers and manure. Discussion at the workshop on integrated sustainable nitrogen management, Brussels 30 September – 1 October 2019. URL: https://ec.europa.eu/ info/sites/default/files/field_application_of_organic_and_inorganic_fertilizers_23sep19.
16. Pare M. C., Allaire S. E., Khiari L., Parent L. E. Improving physical properties of organo-mineral fertilizers. Applied Engineering in Agriculture, vol. 26 (3), pp. 447–454
17. Simpson R. J. et al. Strategies and agronomic interventions to improve the phosphorus-use efficiency of farming systems. Plant and Soil 349, 2011, pp. 89–120.

1. Adamchuk V., Petrychenko E. Study of the movement of the combined sowing unit with simultaneous application of mineral fertilizers. Herald of Agrarian Science, 2015, volume 93, no. 3, pp. 47–51. [In Ukrainian]
2. Berezhenko E., Pankiv М., Jobbagy Jan, Berezhenko B. Experimental research of the module for gathering plant of chicory roots. Scientific Journal of TNTU, 2021, no. 1 (101), pp. 56–67.
3. Adamchuk V., Yaremenko V., Boris N. Mathematical model of spreading mineral fertilizers by centrifugal method. Agricultural Engineering, 2013, vol. 45, issue 1, pp. 6–8.
4. Bondarenko A. M., Savkin V. I., Shelkovnikov S. A., Kachanova L. S. Approaches to the economic evaluation of elements of organic agricultural production of innovative type. Astra Salvensis, 2019, T. 7, No. S1.
5. Boyko V., Baranovsky V., Pankiv V., Onyshchenko V., Marinenko S. The results of the study of the cutter of the remains of root crops haulm. Scientific Journal of the Ternopil National Technical University, 2023, vol. 99, no. 1, pp. 99–109.
6. Wang Y., Sierakowski A., Prosperetti A. Rotational dynamics of a particle in a turbulent stream. Physical Review Fluids, 2019, no, 4 (6).
7. Adamchuk V. V. Justification of the method of determining the parameters of the centrifugal scattering body. Herald of Agrarian Science, 2005, no. 2, pp. 45–48. [In Ukrainian]
8. Inns E. M., Reece A. R. The Theory of the disk centrifugal distributor. Motion on the disk off centre feed. Agricultural engineering research, vol. 7, no. 4, pp. 45–353.
9. Fukada T., Takeuchi S., Kajishima T. Effects of curvature and vorticity in rotating flows on hydrodynamic forces acting on a sphere. International Journal of Multiphase Flow, 2014, no. 58, pp. 292–300.
10. Koller К. Wurf-oder Pneumatikstreueroz. Landwirtschaftiche Zeitschrift, 1987, no. 10, pp. 628–630.
11. Voytiuk D. G., Baranovskyi V. M., Bulgakov V. M. and others/ Agricultural machines. Basics of theory and calculation: Textbook / under the editorship of D. G. Voytyuka K.: Higher education, 2005. 464 p. [In Ukrainian]
12. Loveykin V. S., Chovnyuk Y. V., Dityuk A. I. Mathematical modeling of the movement of a particle of mineral fertilizers after descending from the disc of a centrifugal spreader in the presence of variable aerodynamic resistance of the medium (air). http://www.nbuv.gov.ua/portal/Chem_Biol/Vzhnau/ 2010_2/21.pdf. [In Ukrainian].
13. Luo J. et al. Application of bio-organic fertilizer significantly affected fungal diversity of soils. Soil Science Society of America Journal 74. 2010. P. 2039.
14. Pantaleo A., Villarini M., Colantoni A., Carlini M., Santoro F., Rajabi Hamedani S.Techno-Economic Modeling of Biomass Pellet Routes: Feasibility in Italy. Energies, 2020, vol. 13, pp. 1636.
15. Misselbrook T., Bittman S., Cordovil C., Rees B., Sylvester-Bradley R., Olesen J., Vallejo A. Field application of organic and inorganic fertilizers and manure. Discussion at the workshop on integrated sustainable nitrogen management, Brussels 30 September – 1 October 2019. URL: https://ec.europa.eu/ info/sites/default/files/field_application_of_organic_and_inorganic_fertilizers_23sep19.
16. Pare M. C., Allaire S. E., Khiari L., Parent L. E. Improving physical properties of organo-mineral fertilizers. Applied Engineering in Agriculture, vol. 26 (3), pp. 447–454
17. Simpson R. J. et al. Strategies and agronomic interventions to improve the phosphorus-use efficiency of farming systems. Plant and Soil 349, 2011, pp. 89–120.