The ditch’s wedge sectors are assumed to be the same size in order to simplify calculations. The total volume of the wedge was calculated using the formula for a triangular prism and assigned the variable [L]: [L] = Volume of total sector = (1/2) * B * H * W. From this, both the volume of the pyramid from the narrower end of the wedge and the volume of the slope at the other end of the wedge were subtracted.
B – width of the top of the slope
H – total length of the sector
W – height of the slope
The volume of the pyramid, [M], was calculated using (1/3) * S * y * W where W is the height of the pyramid, y is the length of the pyramid< along the bottom of the trench, and S is length of the pyramid along the outside edge.
The volume of the slope, [N], was calculated using (1/2) * x * W * B – 2[(1/3) * z * x * W], where x is the length of the base of the slope, W is the height of the slope, B is the width of the top of the slope, z is the difference between B and the width at the base of the slope.
| Minimum Estimate | Maximum Estimate | |
|---|---|---|
| B | 6 | 7 |
| H | 9 | 10.3 |
| W | 4.8 | 5 |
| S | 3.4 | 4.1 |
| Y | 3.1 | 4.2 |
| X | 3 | 4 |
| Z | 1.6 | 0.9 |
| [L] | 129.6 | 180.25 |
| [M] | 16.864 | 28.7 |
| [N] | 27.84 | 58 |
| Dirt Removed per Sector | 84.896 | 93.55 |
| Total Dirt Removed | 848.96 | 935.5 |