Directional transmittance of non-clear glass ti -- Algorithm 2.35

Petherbridge(1) developed a technique for calculating the directional solar transmittance of non-clear, heat-absorbing solar control glasses based upon the Fresnel monochromatic radiation equations. Sharples(2) modified this technique to allow the directional daylight transmittance of such glasses to be estimated.

Input

Specular monochromatic reflectance, rx
Angle of incidence, i
Normal incidence KL value for daylight, KL
Refractive index of the glass, n

Equation


The x subscript signifies that each component must be evaluated separately for radiation polarised with its planes of vibration parallel (rpl) and perpendicular (rpd) to the plane of the glass, where

The angle of refraction, , is found from Snell's law : sin i = n sin
For non-polarised radiation the value of ti is based on the average of the parallel and perpendicular reflectances.
The parameter g represents the fraction of the incident energy remaining after transmission through the glass, and is found from

If the normal incidence KL value for daylight is not known it can be derived from the normal incidence daylight transmittance to via the equation KL = loge X where

For completeness, the directional absorptance aix and the directional reflectance rix are given here:

Source

Sharples(2)
References

1. Petherbridge P Transmission characteristics of window glasses and sun controls Sunlight and buildings: CIE Conference Bouwcentrum, Rotterdam 1967.

2. Sharples S, Page J K and Souster C G Incorporating body-tinted glazing into daylight computer models Lighting Res & Tech 16 (3) 143-145 (1984) .

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