Hitching affects both vertical and horizontal force relations between tractor and implement. Vertical effects on the tractor are of special interest because of their effect on the tractive performance of the tractor. The force imposed on the tractor by the implement (Figure 7.5) could be transmitted through a drawbar or through a semimounted or fully mounted hitch. The following equations can be obtained by taking moments about points C2 and C1, respectively:
where
Rr = total vertical soil reaction on rear wheels, kN
Rf = total vertical soil reaction on front wheels, kN
mt = tractor mass, Mg
g = acceleration of gravity = 9.801 m/s2
Fhz = z-component of hitch force, kN
Fhx = x-component of hitch force, kN
x1 = wheelbase of tractor, mm
x2 = distance from rear axle center to tractor center of gravity, mm
z = distance from ground to intersection of Rr with line of pull, mm
Figure 7.5 – Force and moment relations for a tractor when pulling an implement at a uniform velocity on level ground.
Points C1 and C2 are directly under the axle centers when a tractor is sitting on level ground with Fhx = 0, but move forward somewhat due to rolling resistance when the tractor is moving. The vertical wheel forces calculated from Equations 7.1a and 7.2a when Fhx = Fhz = 0 are called the static wheel reactions. The quantity, (Fhx z/x1), is called weight transfer because it is removed from the front wheel reaction and added to the rear wheel reaction due to the moment of the pull transmitted through the hitch. If the line of pull is inclined as shown in Figure 7.5, an additional term, Fhz, is also added to the rear wheel reaction. Some weight transfer is helpful on 2WD (two-wheel drive, typically rear-wheel drive) tractors because the tractive ability of the drive wheels is limited by the vertical soil reaction. However, too much weight transfer will bring Rf to zero, upon which the front wheels will raise off the ground. For 4WD (four-wheel drive) tractors, weight transfer is not helpful because tractive effort gained at the rear wheels is lost at the front wheels.
While Equations 7.1a and 7.2a give exact values for wheel reactions, they are difficult to use in practice. The distances x2 and z are not easily measured and are constantly changing during agricultural operations. Thus, an approximate method has been developed for computing wheel reactions. The approximate equations are:
Experimental studies have shown that the approximate values for Cdw are 0.20, 0.45, and 0.65 for towed, semimounted, and fully mounted hitching, respectively. The Cdw values were chosen to incorporate the effect of force Fhz on the rear wheels; thus Equation 7.2b somewhat overestimates the weight transfer from the front wheels.
