V.P. Goryachkin’s rational equation in differential form

Federal Research Agro-Engineering Center VIM, 1st Institutskiy proezd, 5, Moscow, 109428, Russia

^* Corresponding author: zhalnin@yandex.ru

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.