Question Bank • QB_FP_080 NAT • 2 Marks

Section 3: Farm Power

Tractors and Power Tillers

Subtopic: Steering and hydraulic control systems used in tractors

Question Statement:

An agricultural tractor has a wheelbase of $l = 2.10\text{ m}$ and a front wheel track width of $w = 1.30\text{ m}$. When making a tight headland turn, the inner front steering wheel turns through an angle of $\theta_i = 35^\circ$. According to the ideal Ackermann steering condition ($\cot\theta_o - \cot\theta_i = \frac{w}{l}$), the ideal steering angle of the outer front wheel $\theta_o$ in degrees is ________ (round off to 1 decimal place).

Answer Key:

26.0

Step-by-Step Solution & Explanation

1. Ackermann steering equation: $\cot\theta_o - \cot\theta_i = \frac{w}{l}$ 2. Calculate terms: $\cot(35^\circ) = \frac{1}{\tan(35^\circ)} = \frac{1}{0.700208} \approx 1.42815$ $\frac{w}{l} = \frac{1.30}{2.10} \approx 0.61905$ $\cot\theta_o = 1.42815 + 0.61905 = 2.04720$ $\tan\theta_o = \frac{1}{2.04720} \approx 0.48847$ $\theta_o = \arctan(0.48847) \approx 26.03^\circ \approx 26.0^\circ$
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