## 2 Materials and Methods  
The theoretical studies were carried out using the methods of mathematical modeling and theoretical mechanics, as well as methods for compiling computer programs and analyzing the results of calculations on a PC and graphical dependencies. We have developed a new haulm harvester, equipped with a loading mechanism for loading the haulm after its copyless cut with a cutting apparatus to be loaded into a vehicle in addition to the haulm harvester. The main structural element of this loading mechanism is a blade thrower, with the possibility of using blades of various geometric shapes [24]. The design and technological scheme of the haulm harvester with an improved loading mechanism are shown in Figure 1.  
As shown in the equivalent scheme, the haulm harvester performs a copyless cut of the sugar beet tops without extracting the root crop from the soil, using a rotary haulm harvesting apparatus 3. After that, the haulm, cut across the entire working width, is transported to the end part of the haulm harvester and fed to the loading mechanism, namely, to the blade thrower 4. The blades of the thrower 4 disperse portions of the haulm, located on them, and direct them to the unloading pipe 5, through which the haulm is fed into the body of the vehicle, moving beside the haulm harvester. An important element of the technological process of haulm loading is that the blades during rotation create air pressure, which also contributes to the more efficient movement of the haulm into the vehicle. In other words, the thrower additionally works as a fan. In order to substantiate the rational parameters of the haulm loading mechanism, it is necessary to build a mathematical model of this process from the moment it hits the thrower blade and the process of particle acceleration by the blades, then its movement along the cylindrical and rectilinear parts of the casing (the unloading pipe), and, finally, the process of haulm flight into the body of the transport funds after departure from the unloading pipe [25]. Let us first construct a calculated mathematical model for the movement of a haulm particle along the thrower blade from the moment it hits the blade until the moment it leaves the blade. It should be immediately noted that such a model has already been built without taking into account the airflow force created by the blades during the rotation of the thrower and significantly affecting the relative speed of haulm particle movement along the throwing blade [26]. Therefore, in this article, we will build a refined mathematical model of haulm particle movement along the throwing blade, namely, taking into account the influence of the airflow on the process of haulm particle movement along the throwing blade. To do this, we first construct an equivalent scheme (Figure 2). First, consider the cross section of the mechanism for loading beet tops, which in the thrower installation area has a cylindrical casing of radius \(R\) in which a blade thrower is installed on the drive shaft of radius \(r_{0}\). This thrower has four blades that are rigidly fixed on the drive shaft, and they are located at some angle to the radial direction. When the thrower rotates, each of the blades in turn approaches the loading window area and captures a certain haulm portion that has entered this area. Being on the blade, a portion of the haulm begins forward movement along the blade, simultaneously performing transfer rotation along with the blade. When the blade reaches the area of the unloading window, the dispersed haulm portion is thrown upwards in the direction of the loading nozzle. Further, the movement of the haulm portion, captured by the blade, is carried out in a closed space, which is limited by two adjacent throwing blades and the casing of the thrower. Since the process of the haulm movement along all four blades occurs in the same way, to simplify the equivalent scheme, we will show only this one blade on it.