Abstract
The so-called V.P. Goryachkin’s rational equation is commonly used to calculate plow drag value and estimate the pulling force required during tilling in the field. Its first component represents drag value of the plow mass multiplied by the friction ratio (rolling friction, sliding friction) of the plow elements against the furrow bottom and walls. The second component describes the parameters of soil layer tilled and the ratios describing the type and condition of the soil. The third element describes the soil layer parameters, plow speed squared and energy ratio, which reflects the soil characteristics, type and condition of the plow surfaces rubbing against the soil and the soil lifting force. The rational equation has been tested in numerous experiments and proved satisfactory in most cases, with different plows and different soil types; the margin of error varies, however. Moreover, the formula proved to be universal and found use in other cases to calculate the drag of a certain object in liquid or gaseous environments. In this work the authors derive a general system of differential equations which can be solved to derive V.P. Goryachkin’s rational equation and its numerous variants and specific applications.
Highlights
Where f is the friction ratio between outer surfaces of the plow and the furrow walls and bottom; G - is the plow mass; K - is the soil resistance to deformation ratio; ɚ - is the tilling depth; ɜ - is the width of the soil layer; İ - is the energy change ratio of soil particles when thrown aside by the plow breast; V - is the speed of the plow in the direction of travel
There is nothing theoretical about this component, as it represents the ordinary and well known physical law of pressure drag exhibited by any object that has to be moved from an idle position: the force resulting from the mass of the body has to be multiplied by the friction ratio against the bearing surface
Three parameters are taken as source data: G – the plow mass, F = a · ɜ – cross-section area of the soil layer tilled and V – the plow speed
Summary
V.P. Goryachkin’s equation is based not on strict mathematical calculations but on the general principles of rationality and practicability, as any complex process can always be represented as a sum total of its simple elements. The classical equation to calculate plow pulling force, or the so-called V.P. Goryachkin’s rational equation, looks as follows [1]: P = fG+ Ʉɚɜ + İ a ɜ V V.P. Goryachkin represented the complex process of plow drag during tilling as a sum total of three components, which fully correspond to the physical process of plow operation.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
