MATHEMATICAL MODELING OF LOGISTIC GROWTH OF THE WOOL-DOWN COVER OF SHEEP AND GOATS
The purpose of the research was to develop mathematical models of technical and technological solutions in the process of mechanical treatment of animals’ skin as well as to solve the problem of labor productivity enhancement at the final stage of production, i.e. obtaining wool from sheep and downy fiber from goats. In the course of studies there were used methods of mathematical modeling, time series estimation (observations) and mathematical processing of statistical data. The material for studies was obtained on the farms of the Orenburg region, engaged in breeding of downy goats and sheep. By combining the time series data on the animals’ wool-downy cover, the interdependence between the dry mass of the product substance obtained and the growth period of the wool-down cover within the single mathematical expression of W=f(t), with f being a certain functional link has been established. A significant factor, determining growth intensity of the wool-downy cover, is the quantity and quality of feeds consumed by the animals, which was taken into account in the mathematical model being developed. The practical significance of the suggested mathematical model of logistic growth has been realized in the design of the combing device, which allows combing of 90 to 95% of down in the first phase of its maturation, shortening the time of wool and down hackling and obtaining the product of higher quality. Using the model developed it is possible to determine the readiness of the sheep's wool cover to shearing. The use of the proposed mathematical model makes it possible to evaluate impartially the operation quality of the devices for sheep and goats shearing.