---

Ek is the angle of incidence of the light path at the point (°);

dikp is the distance between the luminaire, U and the point P at the centre of the rectangular basis of the semi-cylinder.

NOTE It is advised not to include lamp survival factor in the overall maintenance factor in road lighting if all failed light sources will be spot replaced..

«=1

where

E_v

к

Пій

Жг)

/м

£k

a_k

Key

1 luminaire к

2. vertical plane at right-angles to flat surface of semi-cylinder

3. calculation point

4. flat surface of semi-cylinder

Figure 12 — Angles used in the calculation of semicylindrical illuminance

7.2.5 Vertical illuminance at a point

Calculation points shall be located on a plane 1,5 m above the surface in the relevant area.

Vertical illuminance varies with the direction of interest. The vertical illumination plane in Figure 13 shall be oriented at right-angles to the main directions of pedestrian movement, which for a road are usually up and down the road.

The vertical illuminance at a point shall be calculated from the formula or a mathematically equivalent formula:

E /)4l Sin£_k -1 + COSff_k

is the maintained vertical illuminance at the point (lx);

is the index of current luminaire in the summation;

is the number of luminaires involved in the calculation;

is the luminous intensity in candela of the fc^th luminaire being C and у calculated as indicated in 6.4 (cd);

is the overall maintenance factor, the product of the light source lumen maintenance factor and the luminaire maintenance factor;

is the angle of incidence of the light path at the point (°);

is the angle in degree between the vertical plane containing the incident light path and the vertical plane at right-angles to the vertical plane of calculation, as shown in Figur

e13 (°);

rfikp is the distance between the luminaire, I* and the point at the centre of the basis of the rectangle in the vertical illumination plane (m).

This formula is valid only for e < 90° and a < 90°.

NOTE It is advised not to include lamp survival factor in the overall maintenance factor in road lighting if all failed light sources will be spot replaced.

Key

1. vertical plane at right-angles to vertical illumination plane

2. luminaire

3. calculation point

4. vertical illumination plane

Figure 13 — Angles used in the calculation of vertical illuminance

The field of calculation shall be the same as that indicated in Figure 10.

NOTE To economize on computer processing time, for staggered installations the calculation field can be taken between consecutive luminaires on opposite sides of the road without affecting the result.

The calculation points shall be evenly spaced in the field of calculation (see Figure 14] and their number shall be chosen as follows:

a] In the longitudinal direction

The spacing in the longitudinal direction shall be determined from the formula:

D = — (33)

N

where

D is the spacing between points in the longitudinal direction, in metres

S is the spacing between luminaires, in metres

N is the number of calculation points in the longitudinal direction with the following values:

for S< 30 m, N= 10;

for S > 30 m, the smallest integer giving D < 3 m.

The first row of calculation points is spaced at a distance D/2 (in metres) beyond the first luminaire.

Key

1. luminaire

2. width of relevant area W_r

3. field of calculation

x denotes lines of calculation points in the transverse and longitudinal directions

Figure 14 — Information for illuminance calculations; calculation points on relevant area

b) In the transverse direction

w

d = (34)

n

where

d is the spacing between points in the transverse direction, in metres;

W_r is the width of the carriageway or relevant area, in metres;

n is the number of points in the transverse direction with a value greater than or equal to 3 and is the smallest integer giving d < 1,5 m.

The spacing of points from the edges of the relevant area is D/2 in the longitudinal direction, and d/2 in the transverse direction, as indicated in Figure 14.

In the case where the field of illuminance calculation points covers the lanes of a carriageway, the definition of grid points shall respect the definition for luminance calculation given in 7.1.3 and Figure 9.

Luminaires that are situated within five times the mounting height from the calculation points shall be included in the calculation.

For these areas it might be necessary to choose a rectangular calculation field which encloses and is therefore larger than the relevant area. Grid points used for the calculation of the quality characteristics should be chosen from those points which lie within the boundary of the relevant area. When the spacing of the luminaires is not regular it might not be possible to link the spacing of the grid points to the spacing of the luminaires, but the spacing in either direction shall not exceed 1,5 m. The principal directions of traffic flow for the calculation of vertical illuminance and semi-cylindrical illuminance shall be decided after considering the use or likely use of the area.

8 Calculation of quality characteristics

Quality characteristics relating to luminance or illuminance shall be obtained from the calculated grids of luminance or illuminance without further interpolation. If the grid points do not coincide with the centre of the lanes, for the calculation of longitudinal uniformity of luminance it shall be necessary to calculate the luminance of points on the centre line of each lane and the hard shoulder, if present, in accordance with 8.4.

For initial average illuminance or initial average luminance,/м is 1,0 and initial values of the luminous flux shall be taken. For average luminance or average illuminance after a stated period, the/м for the luminaire after the stated period in the environmental conditions of the installation shall be taken together with the luminous flux after this stated period.

The average luminance shall be calculated as the arithmetic mean of the luminances at the grid points in the field of calculation.

The calculated value shall be printed or displayed on the form, with the number of digits that are defined in the tables of requirements of EN 13201-2 (summarized in Clause 4 of this Part 3), i.e. two decimal places.

The overall uniformity shall be calculated as the ratio of the lowest luminance, occurring at any grid point in the field of calculation, to the average luminance.

The calculated value shall be printed or displayed on the form, with the number of digits that are defined in the tables of requirements of EN 13201-2 (summarized in Clause 4 of this Part 3), i.e. two decimal places.

The longitudinal uniformity shall be calculated as the ratio of the lowest to the highest luminance on points in the longitudinal direction along each centre line of each lane of the grid used for the calculation of average luminance, (see Figure 9). The observer shall be positioned in the centre of each lane in turn. The operative value is the minimum longitudinal uniformity from all the lanes.

The calculated value shall be printed or displayed on the form, with the number of digits that are defined in the tables of requirements of EN 13201-2 (summarized in Clause 4 of this Part 3), i.e. two decimal places

.

T

(35)

he threshold increment is calculated from the formulae or mathematically equivalent formulae:

^/T,=65W'⁸

In Formula (35), valid for: 0,05 cd-nr² < < 5 cd-nr², L_v is calculated as follows.

(36)

Where the contribution of the pending luminaire, L_Vk is: either:

or:

6_vk-9,86- 1 +

( л Л⁴
У

66,4

ЇЇ

when: 1,5° <0k< 60°

(37)

10

^£vk = ^£k • +

и

N V
^лу

62,5

when: 0,1° < 6_k <1,5°

(38)

NOTE 1 Formula (38) is drawn from CIE collection on glare: CIE 146:2002 Formula (6) with a nil iris pigmentation factor but with a limited field of view in the range 0,1° to 1,5°. This formula is introduced just as a complement to conventional Formula (37) in order to deal with the rare cases where the luminaires stand very near to the line of sight of the observer, what was not envisaged in previous EN 13201-3:2003.

In these formulae:

£? is the average initial road luminance (cd-nr²);

L_v is the equivalent initial veiling luminance (cd-nr²);

к is the index of the pending luminaire in the summation;

niu is the number of luminaires involved in the calculation;

Ek is the initial illuminance (in lux) produced by the k^lh luminaire in its new state on a plane normal to the line of sight and at the height of the observer’s eye;

0k is the angle between the line of sight and the centre of the k^th luminaire, in degrees;

A_y is the age of the observer, in years.

Conventionally for road lighting installation design the following values are adopted:

• Л_у=23у;

• the line of sight is 1° below the horizontal and in a vertical plane in the longitudinal direction passing through the observer’s eye;

• the observer’s eye is positioned at a height 1,5 m above road level and in the centre line of each lane in turn, as indicated in Figure 10;

• the initial longitudinal distance of the observer ahead of the first luminaire Li in front of the field of calculation is given by Formula (39):

X_d = 2,75 • |Л -1,5| (39)

where

H is the mounting height of the luminaire, in m;

1,5 (m) is the default value for the height of the observer's eyes to the road surface.

NOTE 2 See Figure 15 for an example of lighting installation with one row of luminaires.

Consequently, in the evaluation of L_Vk in Formula (37) or Formula (38), only the luminaires under a screening plane which is inclined at 20° to the horizontal, and which passes through the observer's eye shall be included in calculation.

NOTE 3 In cases where screening above the horizontal does not apply, it is advised to take into account the contributions from all luminaires of the designed road installation in the observer’s field of view for angles between the observer’s line of sight and the direction of light incidence up to 60°.

The evaluation of 0k in Formula (37) or Formula (38) can be obtained by using the scalar product in Formula (40).

Thereby:

farces bu.->_Obs)^_{g +} (_ZLb-_Zobs)sin_a(40)

(^xLk -^xObs)²⁺(Уьк “.TObs)^{2 +}(^zLk ^-zObs)²

where

x,,, y,, and z,, are the coordinates of the k^th luminaire;

Lk ^J Lk Lk

,y„. andz„, are the coordinates of the observer’s eyes;

Obs Obs Obs ^J

a - -1° is the fixed angle of the line of sight of the observer under the horizontal

.

*

Key

1. edge of the carriageway

2. centre line of a lane

3. focal line of luminaires:

luminaire included in luminaire not included in calculation

calculation

4. field of calculation

5. line of sight of the observer

~ is a unitary vector at the eye of the observer oriented in the run of the road parallel to the carriageway axis and tilted one degree under the horizontal;

Obs is the point of observation, at the eye of the observer;

Li is the first luminaire of the row closer to the calculation field that shall be included in calculation.

Figure 15 — Number of luminaires in front of the field of calculation

The summation is performed from the first luminaire within the observer dihedron of sight at or under the screening plane of 20° (see Figure 15) and luminaires beyond, up to a distance of 500 m in each luminaire row or for the whole installation length if it is lower than 500 m. The distance shall be considered from the actual position of the observer.

The calculation is commenced with the observer in the initial position x_d evaluated from Formula (40), and repeated with the observer moved forward in increments that are the same in number and distance as those used for the longitudinal spacing of luminance points. The procedure is repeated with the observer positioned in the centre line of each lane using the initial average road luminance appropriate to the observer transverse position.

If the road lighting installation has more than one row of luminaires, this process shall be repeated for every initial position of the observer on each lane axis and the maximum value of/п retained.

In C and P classes the main performance requirement is the average horizontal illuminance and usually luminance is not calculated.

In the conventional hypotheses of road lighting installations, calculations are made assuming the use of identical luminaires using identical light sources with same flux, same adjustment (and therefore same light distribution) evenly spaced along a straight section of road. These criteria are not all fulfilled for C lighting classes. Furthermore for P lighting classes the road surface photometric properties are usually not defined and pedestrians’ observation conditions differ from those belonging to drivers of motorised vehicles.

Whilst the evaluation of/fi is not strictly realistic, if based just on the photometric characteristics of the luminaire, a clearly specified calculation method is considered preferable to the simple G* classification based on the luminous intensities of a single luminaire.

For C and P lighting classes, the evaluation of disability glare,/ті following the algorithm described in sections 8.5.1 and 8.5.2, requires the calculation of the average initial road luminance, / in addition to the average initial horizontal illuminance E/j .

For C lighting class the missing data to evaluate / is the r-table of the road surface. Considering that the main users are drivers, it is acceptable to use an r-table from those already available for M classes when the lighting design is based on luminance evaluation. Thus, considering a representative section of road with a mean spacing, the evaluation of fTI is possible applying Formulae (35) to (40).

For P lighting classes, it should be noted that the conditions of observation of pedestrians can notably differ from those of drivers of motorised vehicles.

When the lit surface is not seen at low angles (as in motorised traffic conditions where a = -1°) it is possible to use Lambert's law to evaluate the average luminance of the assumed diffusing surface whose reflection factor needs to be evaluated and declared as hypothesis of design calculation.

In this last case, the following formula shall be used:

= (41)

л

where

/7 is the initial average horizontal luminance of the lit surface;

£^7 is the initial average horizontal illuminance of the lit surface;

p is the average diffuse reflection factor of the lit surface. If measured data is not available, p = 0,2 is taken as default value.

The equivalent initial veiling luminance L_v shall be evaluated following the calculation process described in 8.5.2, i.e. considering all the luminaires of the installation in the observer's dihedron of sight up to 500 m, at most, or the actual number of luminaires for installations shorter than 500 m.

8.6 Edge Illuminance Ratio Rei

The edge illuminance ratio is the minimum from the evaluation on each side of the carriageway of the ratio of the average horizontal illuminance on the longitudinal strip adjacent to the edge of the carriageway, and lying off the carriageway, divided by the average horizontal illuminance on the corresponding longitudinal strip lying on the carriageway. The width of all four strips shall be the same, and equal to the lanes’ width of the carriageway or equal to the width of the unobstructed strip lying off the carriageway if lower. For dual carriageways, both carriageways together are treated as a single carriageway unless they are separated by more than 10 m.

The horizontal illuminance shall be calculated by the procedure specified in 7.2.2. The field of calculation shall be as indicated in 7.2.7. The number of luminaires considered shall be the same as indicated in 7.2.9. The position of the calculation points within each strip shall be as indicated in 7.1.3 and Figure 9.

Figure 16 gives examples of the location of the strips and their location for the calculation of the edge illuminance ratio. For this figure, the following formulae apply:

Rei 12 for strips 1 and 2:

_nEh, strip 1

"e!12 ““ (42)

E h, strip 2

Re 43 for strips 3 and 4:

_nEh, strip 4

'Гиз ~ = (43)

В h, strip 3

From which the operative Rei is defined:

7?ei = min(T?Ei 12; f?Ei 43) (44)

The calculated value shall be printed or displayed on the form, with the number of digits that are defined in the tables of requirements of EN 13201-2 (summarized in Clause 4 of this Part 3), i.e. two decimal places.

a) Case of a 2-lane carriageway

b) Case of 3-lane carriageway

Key

1. strip 1

2. strip 2

3. strip 3

4. strip 4

5. luminaire

6. edge of carriageway

IVs width of strips = width of one lane

Figure 16 — Location and width of strips for calculating edge illuminance ratio Леї

9 Ancillary data

When photometric performance data are prepared for an installation, the following ancillary data shall be declared:

1. identification of the luminaires;

2. identification of /-table;

3. identification of the r-table with a clear declaration of the value of Qo used; required for luminance calculations;

4. tilt during measurement of the luminaires;

5. tilt in application of the luminaires;

6. rotation of the luminaires, if different from zero;

7. orientation of the luminaires, if different from zero;

8. identification of the light sources;

9. luminous flux of the light sources on which the calculations are based;

10. maintenance factors applied;

11. definition of the field of calculation, of the origin of the reference system and coordinates of the grid points;

12. position of the luminaires in plan or a numerical description;

13. mounting height of the luminaires;

n) direction of interest for vertical illuminance and semi-cylindrical illuminance;

o] any deviations from the procedures given in this standard, including the calculation of threshold increment for an observer of other than 23 years old or when the mounting height of luminaires is less than or equal to 2 m. In this last case the use of an extended r-table is needed for luminance calculation (see Table B.l).Annex A
(informative)

Mathematical information technology conventions
and flow chart diagrams

A.l Mathematical and Information Technology conventions used in addition to Clause 4 to define the variables used in the following logical flow charts of the lighting calculation program

This annex suggests the use of "friendly" variable names in the source code of software in order to facilitate their maintenance and eventual releases. The linear "do loop" calculation chart is very common in lighting but nothing is said about the accuracy of the variables. For decimal numbers and numerical arrays the "double" accuracy is advised to ensure less difference between the results than those obtained nowadays from different software and corresponding calculation programs.

The algorithms of lighting calculation defined by flow charts in A.3 (Figures A.3 to A.7) is the way to avoid the dependence with a given programming language, even recent and more powerful than those used in the past (like were the FORTRAN [FORmulation TRANslator, an old IT scientific language] listings of the source code of the CIE standard calculation program, "STAN”, and that of the more general CIE "LUCI" calculation program both included in CIE 30.2 1982, reprint in 1990 but now obsolete).

The presentation of the results, which is very important for lighting designs, is not dealt with in this annex as it is the role of professional software providers to produce this presentation and the user­friendly, data input and savings in complex designs.