Equipment: Road Surfaces - Road Lighting: Fundamentals, Technology and Application - page 167

Fig. 12.4 Four different road
surfaces. Left compared to
right : low as opposed to high
specularity (S1), i.e. a diffuse
and a shiny surface. Bottom
compared to top :lowas
opposed to high lightness
(Q0), i.e. a dark and a light
surface

Lightness

Q 0

Specularity S1

determine Q 0 or, more generally, the reflection properties of a road surface, by a
limited number of carefully-chosen luminance coefficients. Some of these propos-
als are based on the consideration that the average luminance coefficient is for an
important part determined by the diffuse part of the reflections viz. by the “sphere-
shaped” part of the reflection indicatrix. Burghout ( 1979 ) proposed the use of the
luminance coefficient for perpendicular light incidence, q( 0), instead of

Q 0 , which however was shown to lead to unacceptable large deviations in luminance
calculations for road lighting (Van Bommel 1980 ). Demirdes ( 2008 ) assumes in his
considerations the average luminance coefficient Q 0 to be the sum of a diffuse and, a
smaller, specular component. Based on 244 different R-tables, obtained from actual
road surface reflectance measurements (Erbay 1974 ), Demirdes concluded that Q 0
can be approximated with sufficient accuracy by:

ʲ = 0, ʳ =

10 . 304 ∗ { R ( ʲ = 90, tanʳ = 2) + 0 . 085 R ( ʲ = 0, tanʳ = 2) }

The first R value in this equation stands for the diffuse reflection contribution and
the second one for the specular reflection contribution to Q 0 .
It has to be noted that these considerations have been based on road surfaces
measured in the 1960s and 1970s. Actual measurements on road surfaces carried out
recently, show that the older, last-century road surfaces are no longer representative
enough for today's practice (Fotios et al. 2005 ; Chain et al. 2007 ; Dumont and
Paumier 2007 ; Iacomussi et al. 2011 ). Explorations have been started to find good
approximations for Q 0 and possible alternatives for S1, based on an extensive set of
more recent R-tables (Dumont and Paumier 2007 ; Chain et al. 2011 ). First results
have shown that Demirdes approach (as above described), using two R values to
approximate Q 0 , is not accurate enough. A third or fourth R value improves the
accuracy. For example, using R(

ʲ = 0, tan ʳ = 2), R( ʲ = 0, tan ʳ = 0) and R( ʲ = 5,

ʳ =

tan 5) in an approximation formula for Q 0 improves the accuracy considerably

(Chain et al. 2011 ). Korobko ( 2013 ) is trying to approximate the spatial distribution of
luminance coefficients (i.e. the reflection indicatrix) with the help of a mathematical
model considering the indicatrix as an ellipsoidal body. In this way it would perhaps