Once again, I have another blog post that starts off with, “I’ve seen this crop up a lot lately…” This seems to be a recurring trend for this blog and, honestly, one I’m not intending to stop.
So, you are wanting to calculate the volume of a pond. You’re using Civil 3D and loving it and you start up the Stage Storage tool and then, it hits you. Which method do you use? The Average End Area Method or the Conic Approximation Method? Well, if there are two options in Civil 3D, most likely the answer is, “It depends”.
In my experience, the majority of people calculating storage volumes for a pond use the Average End Area Method because, well, isn’t that what we’ve always used for calculating volumes? And, in most cases, this is a great method for calculating volumes. So, how does the average end area work? Take the area at one section, add it to the area of the next section, divide that by 2, and then multiply by the distance between them. [(A1+A2)/2]*D
What’s the problem with this method? Well, it’s a one dimensional equation. In other words, it works great when the areas change by getting wider OR by getting longer, but not both! A perfect example where this particular equation works great is calculating material volumes for roadway cross sections. The pavement between two cross sections may vary in width but, rarely does it vary in depth.
If you don’t believe me, try it yourself. In AutoCAD (you do have AutoCAD, don’t you?) draw a wedge. This is a perfect example of something that varies in one dimension between the two cross sections. The area of a wedge is [0.5 x base x width x height]. In other words, the average end area, one area being base x width and the other area being 0. For this example, I’ll use a base of 3′, a width of 4′, and a height of 5′; we get a volume of 30 cu. ft. (0.5x3x4x5=30).
If we take and modify this wedge slightly, invert it and give it a tapering along one axis (i.e. a pond with vertical sides north and south and sloped sides east and west), the same equation holds true.
A1=4×1, A2=4X3; [(A1+A2)/2]*D;[(4+12)/2]*5=40.
Now, if we take these exact same lengths but change the wedge into a pyramid, the volumes are no longer valid. The volume of a pyramid is 1/3 x base x width x height and this is where we as engineers begin to over estimate the volume of ponds. What shape more closely represents the shape of your pond? Well, in most cases (definitely not all cases), it’s a pyramid, or at least a part of a pyramid.
In geometric terms, a pyramid or cone with the top portion cut off is called a frustum. The volume of a frustum is h/3 x [b1 +b2 +sqrt(b1 x b2)] where h is the height between the two areas, and b1 and b2 are the areas of the two cross sections. This is what Civil 3D uses for the Conic Approximation method.
Hopefully this will help you determine which method to use the next time you have to go about calculating volumes based of sections.
p.s. I probably got something wrong in this discussion. If you see any errors, please let me know.