In steering geometry and tractor mechanics:
For a circular tyre contact patch of radius

\(R = \frac{160}{2} = 80\text{ mm}\), the square of the polar radius of gyration of the contact area is: \[ r_p^2 = \frac{R^2}{2} = \frac{80^2}{2} = \frac{6400}{2} = 3200\text{ mm}^2 \]

Given kingpin offset

\(e = 10\text{ mm}\), \(e^2 = 100\text{ mm}^2\). The combined effective radius arm for the kingpin pivoting resistance is: \[ r_{\text{eff}} = \sqrt{e^2 + r_p^2} = \sqrt{100 + 3200} = \sqrt{3300}\text{ mm} = \frac{\sqrt{3300}}{1000}\text{ m} \]

Vertical wheel load

\(= W\text{ kN} = 1000 W\text{ N}\). Kingpin torque (\(T_k\)): \[ T_k = \mu \times (1000 W) \times \frac{\sqrt{3300}}{1000} = W \mu \sqrt{3300}\text{ N}\cdot\text{m} \]

Step-by-step tractive force calculation:

• Initial rear axle static load (\(W_{r1}\))\lt /strong\gt : \[ W_{r1} = 0.75 \times 20\text{ kN} = 15\text{ kN} \]
• Traction coefficient (\(\mu\))\lt /strong\gt on the rear drive wheels: \[ \mu = \frac{\text{Maximum Tractive Force}}{W_{r1}} = \frac{10\text{ kN}}{15\text{ kN}} = \frac{2}{3} \]
• New rear axle normal load (\(W_{r2}\))\lt /strong\gt after adding 5 kN ballast: \[ W_{r2} = 15\text{ kN} + 5\text{ kN} = 20\text{ kN} \]
• New maximum tractive force (\(F_2\))\lt /strong\gt : \[ F_2 = \mu \times W_{r2} = \frac{2}{3} \times 20\text{ kN} = \frac{40}{3} = 13.33\text{ kN} \]
• Change in maximum tractive force (\(\Delta F\))\lt /strong\gt : \[ \Delta F = F_2 - F_1 = 13.33\text{ kN} - 10\text{ kN} = 3.33\text{ kN} \]

Thus, the increase in maximum tractive force is 3.33 kN.