Study on the Plowing Capacity of the 4 Wheel Tractor (IV)

On the Factors Affecting to the Distance of Futile Run

Abstract

Both the distance of futile run and the speed of tractor are important factors for the plowing capacity.
In the factors that are used to the calculation of the futile run, the width of plowing (b) controls directly the distance of running, and controls the number of turning indirectly.
The turning radious (r) changes by the wheelbase of tractor as shown in Tab. 1, and the former is proportional to the latter.
The distance of head land (L) is affected by the plowing and turning methods, and the maximum value arises in the Octopus type of S-turn, and the minimum value arises in the Popet and the Medusa type.
In these formula of calculation, we can understand that the number of turning is closely related to the distance of futile run.
(1) In the case of the S-turn, the distance of futile run and the number of turning has a relationship as shown in Fig. 2.
(2) In the case of the U-turn, if we devide the short side (B) into m parts, we get next formula: B/m-2r=bu,
In this formula, we understand if we want to decrease the number of turning (u) we must decrease m or b.
(3) In the case of E-turn, the formula is as follows:
4(πr+b)e=B/b⋅2πr+2B,
Therefore, to increase the plowing width (b) we must decrease the number of turning
In addition to this, there are next factors, that are excluding in the formula revealed the distance of futile run.
(4) The size of the field.
In the homologous rectangular field, the variation of the futile distance that is correspond to the area is shown in Fig. 3. Therefore, we see that the larger the field area, the better the plowing capacity.
(5) The slenderness rate of the field.
If the area is constant and the value of A/B is vatiable, we get the curve as shown in Fig. 4.
Therefore, we know that the larger the value of A/B, the better the efficiency.
(6) The shape of the field.
i) A parrallelogram
The number of turning is equivalent to the rectangle that has the same area and has same large side ‘A’. But in the case of U-turn, the number is increase as B=H/sinα⋅And the distance of head land is increase as 2rsin (90°-α)
ii) A triangle
In the case of continuous plowing method, the value of cycle number will be found by deviding the radius of circle that is inscribed to the triangle by width of plowing. But the distance of futile run is 4πr, which is constant value. Therefore the total of the distance of futile run is dependent on the cycle number.
Fig. 7. is the relation between the ratio of the radius of the inscribed circle (R) to the base (a) and the vertical angle of the triangle (Q). From this figure, we see that the value of an isoseles triangle is always maximum, but when a vertical angle changes in the range of 0°-180°, the value of R/a changes gently in the range of 1/2-0. And the smaller the vertical angle, the larger the value of R/a, and we can see the tendency that the decreasing rate is increasing.
iii) A sector
In using the continnous plowing method, the variation of the distance of futile run by a central angle is such that the futile run is maximum when the central angle is a little larger than 90°. But if the angle changes from the point, the value is reduced quadratically, and in the case of larger than 180°, the rate of decrease is gently, and is straight line.
iv) A segment of a circle
In using the continuous plowing method, the height of the shape is shown by next formula.
d=a/2⋅tanγ/2
We see that the smaller the ‘d’, the better the efficiency, as shown in Fig. 10.
v) A square
In using the continuous plowing method, we can calculate the number of cycles by the triangle that is circumscribed to the circle that is inscribed to the 3 sides of the square.