Engineering 101: The Rational Method for Runoff Calculations

We’ve all been working hard here at Engineered Efficiency to bring you useful content related to Civil 3D, including the recent launch of our new service offerings, EE CivilAccess and EE GuidedAccess which both include unlimited instructor-led, hands-on training and the EE ProPack add-on. However, someone who’s been in the industry a very long time and whom I greatly respect suggested I tackle a different bunch of postings: civil engineering basics. I thought it was a great idea and decided to turn this into a regular series of Engineering 101 postings. If you didn’t study civil engineering in school, or if you did, maybe your emphasis was in another engineering discipline (Ceramic Engineering, anyone?), or maybe you just want to brush up on some engineering principals that underlie the use of Civil 3D, this series of posts is for you.

This first in the series covers the basics of calculating runoff using one of the most popular methods, the Rational Method. Maybe you know it better as Q = ciA. Read more after the jump.

Knowing the amount of water runoff volume rate is one of the most important tasks in designing a site, as it is used for the design of many other site features, including the size of detention basins, the size and slope of pipes, the width and depth of swales, the diameter of a outlet restrictor, and so on. There are many different methods for determining the runoff from a given site (or small section of the site), and perhaps the most popular (and easy to use) is the Rational Method.

The equation itself is rather simple and requires math no more complicated than basic algebra:

Q = ciA

Where

Q = runoff rate (cubic feet per second, or cfs)

A = area of the site (acres)

c = surface runoff coefficient (dimensionless)

i = rainfall intensity (inches/hour)

Note: if you’re really paying attention to details, you’ll notice that the units for c, i, and A, when multiplied together, don’t come out to cfs. In reality, there is a unit conversion factor of 1 acre-inch / hour = 1.008 cfs.

So the little effort in determining runoff is spent in determining the values for c, i, and A.

Area, A:

Finding the area, A, is easy. Just draw a polyline around the area in question a list its area. Or better yet, use the new Catchment Area in Civil 3D 2009 to find the drainage area tributary to a point on a surface.

This tool works reasonably well, but you’ll certainly want to verify the results.

Runoff Coefficient, c:

Finding the runoff coefficient , c, is also pretty straightforward. The values are indications of the permeability of the surface and therefore how much water runs off the area (as opposed to soaking in to the ground or evaporating). So, for example, concrete is nearly impervious, and has a c = 0.9. Long grass, on the other hand, absorbs most of the rainwater that hits it, so it most pervious, with c = 0.25. Many sources are available listing this empirical value and your local municipality may even have its own tables. For example, in Chicago, the Metropolitan Water Reclamation District of Greater Chicagoland uses values published here.

When working with an area of mixed surface coverage (say, partial pavement and partial grass) c is calculated as a weighted average. Let’s look at a simple example.

Assume we have a 1 acre site that is 80% paved and 20% grass.

Further assume the following c values:

Pavement: 0.9

Grass: 0.25

The composite c value is calculated as follows:

[(0.80 acres x 0.9) + (0.20 acres x 0.25) ] / 1 acre = 0.77

There are many tables published that list c values based not on surface type (such as concrete or grass) but rather on land use (such as 1/4-acre residential). The values in these tables are based on historical data for land usage. An example of this type of table can be found here.

Rainfall Intensity, i:

With A and c, the last item needed is the rainfall intensity, i. Rainfall intensity is measured in inches/hour and varies by geographic location. There are three main factors used to determine i: Location, Time of Concentration (Tc), and the storm type (duration and frequency). Calculating intensity is a minor task in and of itself. Therefore, I think I’ll cover it in my next posting.

Once you know your runoff, you can do all sorts of great things, like size your detention basin and storm sewer pipes. These are also topics for later posts. If you are interested in seeing a particular topics discussed, please comment and let me know.

Enjoy!