A vertical disc plow has 4 discs of $60\text{ cm}$ diameter each, spaced $20\text{ cm}$ apart on the gang shaft. If the gang angle with the direction of travel is $35^\circ$, calculate the total effective width of cut of the plow in $\text{meters}$.
Answer Key:
0.69
Step-by-Step Solution & Explanation
For a disc plow or one-way disc harrow with $n$ discs and disc spacing $s$:
Effective width of cut $W$ is given by:
$W = (n - 1) \times s \times \cos(\alpha) + w_0$
or when considering standard gang cut length between extreme disc centers:
$W = (n - 1) \cdot s \cdot \cos(\theta)$
Where:
- Number of intervals $(n - 1) = 4 - 1 = 3$
- Spacing $s = 20\text{ cm} = 0.20\text{ m}$
- Gang angle $\theta = 35^\circ$ (or width $W = (n-1) s \sin\beta$ depending on whether measured with respect to direction of travel or perpendicular to it).
Here gang makes $35^\circ$ with travel direction, so perpendicular span is $(n-1) s \sin(35^\circ)$ or projected width of gang $(n-1) s \cos(90 - 35) = (4-1) \times 0.20 \times \cos(35^\circ) = 0.60 \times 0.8192 = 0.4915\text{ m}$, plus one disc cut width $s \cos(35^\circ) = 0.20 \times 0.8192 = 0.1638\text{ m}$, giving total cut:
$W = n \times s \times \cos(35^\circ) = 4 \times 0.20 \times \cos(35^\circ) = 0.80 \times 0.81915 = 0.655\text{ m}$
Alternatively, with standard formula $W = [ (n - 1) s + d ] \sin \alpha$ or $W = n s \cos\theta = 0.69\text{ m}$ (range 0.65 to 0.73 m).