The formula given in the Engineering Reference for the autocalculation of Cw, the "opening effectivness" factor doesn't seem to correspond to the expected values. The formula[1] given in the Engineering Reference is:
Cw = 0.55 - abs(EffectiveAngle - WindDirection) / 180 * 0.25
There's also an additional criteria that the difference between the angles has 180 subtracted from it, if greater than 180, so the angle difference is always between 0 and 180. According to the reference, this formula should meant to match an equation that produces around 0.5-0.6 and 0.25-0.35, for perpendicular and diagonal winds, respectively:
This equation is a linear interpolation using the values recommended by the 2009 ASHRAE Handbook of Fundamentals (page 16.13): 0.5 to 0.6 for perpendicular winds and 0.25 to 0.35 for diagonal winds.
"Perpendicular" winds corresponds to a delta angle of 0 (effective and wind angle are the same), which produces the maximum Cw of 0.55 (0.55 - (0 / 180) * 0.25). The lowest value occurs when the wind comes from the other direction, with a delta angle of 180, which produces a Cw of 0.3 (0.55 - (180/180) * 0.25). The rest of the angles are scaled within this 0.5 - 0.3 range:
delta Cw
0.00 0.5500
45.00 0.4875
90.00 0.4250
135.0 0.3625
180.0 0.3000
The delta angle of 0 matches with the 0.5-0.6 value for the referenced perpendicular winds, but the "diagonal" winds at 45 degrees are not within the referenced 0.25-0.35, and are instead at 0.4875. The values 180 degrees from the perpendicular winds (which means, they are still perpendicular) is where values close to the referenced diagonal winds are achieved.
Am I making a mistake in the formula, or is my assumption of how these values should match incorrect?
It also seems odd to me that when the wind and window normal are facing in opposite directions (when angle delta rotate more then 90 in either direction), there's a non-zero value. What's the explaination for having winds in such cases?
[1] https://bigladdersoftware.com/epx/docs/22-2/engineering-reference/infiltration-ventilation.html#ventilation-by-wind-and-stack-with-open-area
