THE SLOPE GRADIENT FACTOR
Fig. 1. Burned slopes above Pala Mesa Resort in Fallbrook, CA in 2007. The area to be treated was estimated using a combination of aerial photographs and topographic maps.
For determining square footage of an area to be treated with hydraulic mulch, slope length and width can be determined using a measuring tape or wheel… if the slopes aren’t too steep. However, for job estimation for large areas or slopes that are difficult to traverse – such as post-fire areas represented in Figure 1 – area estimations are typically calculated from aerial photographs, topographic maps or a combination of both.
In order to get an accurate measurement of the area of a slope it is important to include a slope gradient factor.
In the diagram below, the top of a slope is represented by A and the bottom, or “toe” of the slope is represented as C. The slope length (for area calculations) is the distance between A and C. The vertical height of the slope is represented by the distance between A and B.
For example, the extent of the area to be treated is determined by the aerial photograph with the perimeter of the burn transferred to a topographic map. From the topographic map:
1. The horizontal, plan view or “run” length (B-C) is determined;
Figure 2. Slope Measurement Table and Calculations
2. The height or “rise” of the slope is determined (A-B) by measuring the contour intervals;
3. The slope inclination is determined by comparing the horizontal measure (B-C) to the vertical measure (A-B) to; and finally,
4. The area is estimated by multiplying the run length (B-C) by the rise height (A-B) then by the multiplying factor in Figure 2.
To calculate area in acres for hydraulic or other mulch applications:
1) Multiply square feet by the slope factor above and divide by 43,560; or,
2) Multiply square yards by the slope factor above and divide by 4,840
From Figure 2 one can see that as slope gradient decreases, so does the multiplying factor: for example a 1:1 slope has a multiplying factor of 1.4142 when compared to a 5:1 slope (1.0198 multiplying factor). The figures below also illustrate graphically that as slope inclinations decrease the length of slope (A-C) more closely approximates the horizontal run (B-C). What does this mean in terms of practical job estimation?
1) If a multiplying factor is not used when estimating areas comprised of steep slopes, then the amount of area to be treated will be consistently underestimated and time, material and labor will most likely exceed the engineer’s projections; and/or,
2) The contractor will under-apply the specified amount of mulch material in order to “stretch” the application to cover 100% of the designated area, albeit at a lower application rate.
Finally, there are a couple of other factors that should be considered when estimating jobs; the surface roughness of a site and alternative forms of payment. These subjects are covered in the white papers entitled “Topographic Index”
and “Payment by Slurry Unit”.