Subtopic: Steering and hydraulic control systems used in tractors
Question Statement:
A farm tractor has a wheelbase of $L = 2.10\text{ m}$ and a kingpin center-to-center lateral spacing of $c = 1.20\text{ m}$. While executing a turn according to correct Ackerman steering geometry, the inner steerable wheel is turned to an angle of $\theta_i = 35^\circ$. The required steering angle of the outer front wheel ($\theta_o$) in degrees is ________ (round off to 2 decimal places).
Answer Key:
26.57
Step-by-Step Solution & Explanation
```
Ackerman Steering Kinematics:
cot(theta_o) - cot(theta_i) = c / L
Wheelbase L = 2.10 m
Kingpin distance c = 1.20 m
Inner angle theta_i = 35 deg
```
**Step-by-step Calculation:**
1. Fundamental Ackerman equation:
$\cot\theta_o - \cot\theta_i = \frac{c}{L}$
2. Calculating $\cot 35^\circ$:
$\tan 35^\circ = 0.70021 \implies \cot 35^\circ = \frac{1}{0.70021} = 1.42815$
3. Ratio $\frac{c}{L}$:
$\frac{c}{L} = \frac{1.20}{2.10} = 0.57143$
4. Solving for $\cot\theta_o$:
$\cot\theta_o = \cot 35^\circ + \frac{c}{L} = 1.42815 + 0.57143 = 1.99958$
5. Solving for outer angle $\theta_o$:
$\tan\theta_o = \frac{1}{1.99958} = 0.500105$
$\theta_o = \tan^{-1}(0.500105) = 26.569^\circ \approx 26.57^\circ$