The Theory
The resulting solution for an infinite line source is:
where:
x is the distance from the observer to the roadway
y is the height of the observer
u is the mean wind speed
α is the angle of tilt of the line source relative to the reference frame
c and d are the standard deviation of horizontal and vertical wind directions (measured in radians) respectively.
This equation was integrated into a closed form solution using the error function (erf), and variations in geometry can be performed to include the full infinite line, line segment, elevated line, or arc made from segments. In any case one can calculate three dimensional contours of resulting air pollutant concentrations and use the mathematical model to study alternative roadway designs, various assumptions of worst case meteorology or varying traffic conditions (for example, variations in truck mix, fleet emission controls, or vehicle speed).
The ESL research group also extended their model by introducing the area source concept of a vertical strip to simulate the mixing zone on the highway produced by vehicle turbulence. This model too was validated in 1971 and showed good correlation with field test data.
Read more about this topic: Roadway Air Dispersion Modeling
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