Analysis of the width of the headland, the length of turns and time of their carrying out by trailed symmetrical agricultural units

Abstract

Optimization of work of agricultural aggregates is related to reduction of time for making non-working moves, main part of which are turns made by units in headlands. There are different algorithms that can minimize the time for making turns as the main difficulty is the choice of way of movement and the type of turn in the fields of irregular shape. Usually these algorithms considered two types of curves - pear-shaped (Ω-turn) and mushroom-shaped (fish-tail). This article discusses three other types of turns that can be used in fields with irregular shape - oblong pear-shaped, shortened pear-shaped and eight-shaped. The dependencies for determining the length of turns and the width of headland needed to perform them are listed. Length of turn is the distance traveled by the unit from turning off the machine when it reaches the boundary of the headland until it is turned on for the next working move again at the boundary of the headland. In the dependencies for calculating the length of the turn (lT), the first addend is the length of the curvilinear section of the turn (lc), and the remaining addends form the length of the straight-line section of the curve (ls). The aim of the present work is to analyze width of the headland, length of the turns and time of their execution by agricultural units with trailed symmetrical farm machinery in shuttle movement in the field. The calculations are made for angle α between the direction of movement of the unit and the boundary of the headland in a variation interval of 20˚ to 90˚ only at a positive value on the angle. Angle α is considered positive when it is on the right side of the unit when it enters the in the headland. All calculations are made for a specific aggregate with working width B = 3.6 m, kinematic length la = 3 m and turning radius R = 3.7 m. In a negative angle, the results are the same, but the direction of the turn is changed. The time for turning is calculated by assuming that in the curvilinear part of the turn the unit moves at a speed of 3 km*h-1 and on the straight-line part with speed 7 km*h-1. From the analysis we found that shortened pear-shaped turns have the smallest length and the least time to perform. In them the length of the curvilinear part of the turn is constant and the length of the straight-line part decreases with increasing α. In case of small values of α, a shortened or oblong pear-shaped left turn should be used, because besides small length they also provide a smaller width of the headland. For larger a values of α, a shortened pear-shaped left turn should be used, and for the largest values of α, shortened pear-shaped left and right turns can be used because they have the same lengths and headlands. Eight-shaped turns are not recommended because of their greater length and the relatively larger share of the curvilinear part, which increases the time for carrying out them.