The Dependence of the Perspective Illuminance Distribution on the Roadway Surface on the Luminaire Cross Factor (CF)

In this work a mathematical equation has been derived to express the relative
illuminance at a point P on the road surface ε(P) as a function of luminaire mounting height (h), the indices of the luminaire lighting distribution (mt) across, (ml) along the road surface and the Cartesian coordinates of the point (x, y). For each value of the luminaire CF, the equation represents the geometrical locus of the point P having a certain value of ε(P) (isolux contours). To take advantage of such equations the calculation of ε(P) aimed to realize the two following technical points. Firstly, i) Drawing the isolux diagram corresponding to the case at which CF =10 and H= 10 m.
ii) Calculating ε(P) and the relative luminance L'(P) at the point P corresponding to different values of CF for the standard road surface R2. Secondly, i) -Obtaining the isolux diagram features corresponding to different values of CF. ii) The obtained values of the isolux diagram features allow us to readily comprehend the distribution of illuminance, and luminance over the road surfaces. According to the definition of both the absolute illuminance and luminance uniformities, the two quantities are equaled to the minimum values of ε(P) and L'(P) respectively. This enables determining the quality of the lighting systems.