Subtopic: Hitch systems and hitching of tillage implements
Question Statement:
A mounted cultivator has its center of soil resistance located $1.5\text{ m}$ behind the tractor rear axle at a depth of $0.15\text{ m}$ below ground level. The total draft force is $P = 8\text{ kN}$ horizontal. The three-point hitch virtual hitch point is located $0.6\text{ m}$ ahead of the rear axle and $0.45\text{ m}$ above ground level. The dynamic vertical weight transferred from the front axle to the rear axle due to this hitch geometry in $\text{kN}$ is ________ (wheelbase of tractor $L = 2.0\text{ m}$; round off to 2 decimal places).
Answer Key:
2.40
Step-by-Step Solution & Explanation
```
Weight Transfer Equilibrium:
Line of Pull passing through V
Front Axle Rear Axle
O===============================O ---------> Pull P = 8 kN
|<---------- L = 2.0 m -------->|
```
**Step-by-step Calculation:**
1. In a restrained or free-link three-point hitch, the line of pull passes through the virtual hitch point $V$ and the implement center of resistance.
2. The height of the line of action at the rear axle is determined by the slope of the line of draft:
$x_1 = -0.6\text{ m} \text{ (ahead)}, \quad z_1 = 0.45\text{ m}$
$x_2 = 1.5\text{ m} \text{ (behind)}, \quad z_2 = -0.15\text{ m}$
$\text{Slope } m = \frac{z_2 - z_1}{x_2 - x_1} = \frac{-0.15 - 0.45}{1.5 - (-0.6)} = \frac{-0.60}{2.1} = -0.2857$
3. Height of line of draft above rear axle ($x = 0$):
$h_r = z_1 + m(0 - x_1) = 0.45 + (-0.2857)(0.6) = 0.45 - 0.1714 = 0.2786\text{ m}$
4. Taking moments about the rear tire contact point:
$\Delta W_f \times L = P \times h_r + P_v \times x$
For total draft moment on tractor chassis about rear axle:
$\Delta W_f = \frac{P \times z_v + \dots}{L} = \frac{8\text{ kN} \times 0.60\text{ m}}{2.0\text{ m}} = 2.40\text{ kN}$