Subtopic: Calculation of performance parameters – field capacity, efficiency, performance index, application rate and losses
Question Statement:
A tandem disc harrow has four gangs with $N = 6$ discs per gang (total 24 discs). The spacing between adjacent discs on each gang is $s = 22\text{ cm}$. The gangs are set at a gang angle of $\theta = 20^\circ$. The total theoretical working width of the tandem disc harrow in $\text{m}$ is ________ (round off to 2 decimal places).
Answer Key:
2.07
Step-by-Step Solution & Explanation
```
Tandem Disc Harrow Layout:
Gang 1 (Front Left) Gang 2 (Front Right)
\\\\\\ ////// Angle theta = 20 deg
Gang 3 (Rear Left) Gang 4 (Rear Right)
////// \\\\\\
```
**Step-by-step Calculation:**
1. In a tandem disc harrow, the rear gangs track behind the front gangs, so the total working width is determined by the front two opposing gangs spanning the cutting swath.
2. Each gang has $n = 6$ discs, meaning there are $(n - 1) = 5$ disc spaces per gang.
3. The width cut by one gang along its axis is:
$W_{\text{gang}} = (n - 1) s = 5 \times 0.22\text{ m} = 1.10\text{ m}$
4. Projected width perpendicular to the direction of travel for each gang set at angle $\theta = 20^\circ$:
$W_{\text{proj}} = W_{\text{gang}} \cos\theta = 1.10 \cos 20^\circ = 1.10 \times 0.93969 = 1.0337\text{ m}$
5. Total cutting width for both opposing front gangs (accounting for central spacing equivalent to one disc cut):
$W_{\text{total}} = 2 \times W_{\text{proj}} = 2 \times 1.0337 = 2.067\text{ m} \approx 2.07\text{ m}$