English version. Road lighting - Part 3: Calculation of performance

Transcription

1 EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISHE NORM EN 0- Noveber 00 IS English version Road lighting - Part : alculation of perforance Eclairage public - Partie : alcul des perforances Straßenbeleuchtung - Teil : Berechnung der Güteerkale This European Standard was approved by EN on Septeber 00. EN ebers are bound to coply with the EN/ENELE Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national standards ay be obtained on application to the Manageent entre or to any EN eber. This European Standard exists in three official versions English, French, Geran. A version in any other language ade by translation under the responsibility of a EN eber into its own language and notified to the Manageent entre has the sae status as the official versions. EN ebers are the national standards bodies of Austria, Belgiu, zech Republic, Denark, Finland, France, Gerany, Greece, Hungary, Iceland, Ireland, Italy, Luxebourg, Malta, Netherlands, Norway, Portugal, Slovakia, Spain, Sweden, Switzerland and United Kingdo. EUROPEAN OMMITTEE FOR STANDARDIZATION OMITÉ EUROPÉEN DE NORMALISATION EUROPÄISHES KOMITEE FÜR NORMUNG Manageent entre: rue de Stassart, 6 B-050 Brussels 00 EN All rights of exploitation in any for and by any eans reserved worldwide for EN national Mebers. Ref. No. EN 0-:00 E

2 EN 0-:00 E ontents page Foreword... 4 Introduction... 5 Scope... 5 Norative references... 5 Ters, definitions, sybols and abbreviations Ters and definitions List of sybols and abbreviations Matheatical conventions Photoetric data General The -table Interpolation in the -table General Linear interpolation Quadratic interpolation Quadratic interpolation in the region of = 0, or = 0 or The r-table Interpolation in the r-table alculation of, General Matheatical conventions for distances easured on the road Matheatical conventions for rotations alculation of and... 7 alculation of photoetric quantities Luinance Luinance at a point Total luinance at a point Field of calculation for luinance Position of calculation points llluinance General Horizontal illuinance at a point Heispherical illuinance at a point Seicylindrical illuinance at a point Vertical iluinance at a point Total illuinance at a point Field of calculation for illuinance Position of calculation points Luinaires included in calculation llluinance on areas of irregular shape alculation of quality characteristics General Average luinance Overall unifority Longitudinal unifority Threshold increent Surround ratio... 6

3 EN 0-:00 E 8.7 Measures of illuinance General Average illuinance Miniu illuinance Unifority of illuinance Ancillary data Bibliography... 4

4 EN 0-:00 E Foreword This docuent EN 0-:00 has been prepared by Technical oittee EN/T 69 Light and lighting, the secretariat of which is held by DIN. This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorseent, at the latest by May 004, and conflicting national standards shall be withdrawn at the latest by May 004. This European Standard was worked out by the Joint Working Group of EN/T 69 "Light and lighting" and EN/T 6 "Road Equipent", the secretariat of which is held by AFNOR. This docuent includes a Bibliography. This standard, EN 0 Road lighting, consists of three parts. This docuent is: Part : alculation of perforance The other parts of EN 0 are: Part : Perforance requireents Part 4: Methods of easuring lighting perforance According to the EN/ENELE Internal Regulations, the national standards organizations of the following countries are bound to ipleent this European Standard: Austria, Belgiu, zech Republic, Denark, Finland, France, Gerany, Greece, Hungary, Iceland, Ireland, Italy, Luxebourg, Malta, Netherlands, Norway, Portugal, Slovakia, Spain, Sweden, Switzerland and the United Kingdo. 4

5 EN 0-:00 E Introduction The calculation ethods described in this Part of this European Standard enable road lighting quality characteristics to be calculated by agreed procedures so that results obtained fro different sources will have a unifor basis. Scope This European Standard defines and describes the conventions and atheatical procedures to be adopted in calculating the photoetric perforance of road lighting installations designed in accordance with EN 0-. Norative references This European Standard incorporates by dated or undated reference, provisions fro other publications. These norative references are cited at the appropriate places in the text, and the publications are listed hereafter. For dated references, subsequent aendents to or revisions of any of these publications apply to this European Standard only when incorporated in it by aendent or revision. For undated references the latest edition of the publication referred to applies including aendents. pren 0-, Light and lighting Measureent and presentation of photoetric data of laps and luinaires Part : Measureent and file forat. EN 0-, Road lighting Part : Perforance requireents. Ters, definitions, sybols and abbreviations. Ters and definitions For the purposes of this European Standard, the following ters and definitions apply... vertical photoetric angle of a light path angle between the light path and the first photoetric axis of the luinaire NOTE Unit degrees. NOTE See Figure... aziuth of a light path angle between the vertical half-plane passing through the light path and the zero reference half-plane through the first photoetric axis of a luinaire, when the luinaire is at its tilt during easureent NOTE Unit degrees. NOTE See Figure. 5

6 EN 0-:00 E.. angie of incidence of a light path at a point on a surface angle between the light path and the noral to the surface NOTE Unit degrees. NOTE See Figure 4, Figure and Figure angle of deviation with respect to luinance coefficient suppleentary angle between the vertical plane through the luinaire and point of observation and the vertical plane through the observer and the point of observation NOTE Unit degrees. NOTE See Figure luinance coefficient at a surface eleent, in a given direction, under specified conditions of illuination q quotient of the luinance of the surface eleent in the given direction by the illuinance on the ediu NOTE Unit sr NOTE L q E where: q is the luinance coefficient, in reciprocal steradians L is the luinance, in candelas per square etre E is the illuinance, in lux..6 reduced luinance coefficient for a point on a surface r luinance coefficient ultiplied by the cube of the cosine of the angle of incidence of the light on the point NOTE Unit sr NOTE This can be expressed by the equation: r = q cos where: q is the luinance coefficient, in reciprocal steradians is the angle of incidence, in degrees NOTE The angle of observation, in Figure 4, affects the value of r. By convention this angle is fixed at for road lighting calculations. r is reasonably constant for values of between 0,5 and,5, the angles over which luinance calculations for the road surface are generally required...7 tilt during easureent of a luinaire angle between a defined datu axis on the luinaire and the horizontal when the luinaire is ounted for photoetric easureent NOTE Unit degrees. 6

7 EN 0-:00 E NOTE See Figure 8. NOTE The defined datu axis can be any feature of the luinaire, but generally for a side-ounted luinaire it lies in the outh of the luinaire canopy, in line with the spigot axis. Another coonly used feature is the spigot entry axis...8 tilt in application of a luinaire f angle between a defined datu axis on the luinaire and the horizontal when the luinaire is ounted for field use NOTE Unit degrees. NOTE See Figure and Figure 8. NOTE The defined datu axis can be any feature of the luinaire but generally for a side-ounted luinaire it lies in the outh of the luinaire canopy, in line with the spigot axis. Another coonly used feature is the spigot entry axis...9 orientation of a luinaire angle a chosen reference direction akes with the = 0, = 90 easureent direction of the luinaire when the first photoetric axis of the luinaire is vertical NOTE NOTE NOTE Unit degrees. When the road is straight the reference direction is longitudinal. See Figure 7, which illustrates the sign conventions...0 rotation of a luinaire angle the first photoetic axis of the luinaire akes with the nadir of the luinaire, when the tilt during easureent is zero NOTE NOTE Unit degrees. See Figure 7, which illustrates the sign conventions... first photoetric axis of a luinaire when easured in the, coordinate syste vertical axis through the photoetric centre of a luinaire when it is at its tilt during easureent NOTE The poles of the, coordinate syste lie in this axis. See Figure. NOTE This axis is tilted when the luinaire is tilted fro its tilt during easureent... longitudinal direction direction parallel to the axis of the road.. transverse direction direction at right angles to the axis of the road NOTE the road. On a curved road the transverse direction is that of the radius of curvature at the point of interest on 7

8 EN 0-:00 E..4 installation aziuth with respect to a given point on the road surface and a given luinaire at its tilt during easureent angle a chosen reference direction which is longitudinal for a straight road akes with the vertical plane through the given point and the first photoetric axis of the luinaire, when the luinaire is at its tilt during easureent NOTE Unit degrees. NOTE See Figure 4.. List of sybols and abbreviations The sybols and abbreviations used in this standard are listed in Table. 8

9 EN 0-:00 E Table Sybols and abbreviations Quantity Sybol Nae or description Unit Photoetric aziuth Figure degrees D Spacing between calculation points in the longitudinal direction d Spacing between calculation points in the transverse direction E Illuinance lx H Mounting height of a luinaire, Integers indicating the row or colun of a table - L Luinance cd/rn Luinous intensity per kiloluen cd/ki L p Total luinance at a point P cd/ MF Product of the lap flux aintenance factor and the luinaire aintenance factor - N Nuber of points in the longitudinal direction - n Nuber of luinaires considered in the calculation - q Luinance coefficient sr - Q 0 Average luinance coefficient sr - r Reduced luinance coefficient sr - S Spacing between luinaires TI Threshold increent % Equivalent veiling luinance cd/ W L Width of driving lane W r Width of relevant area W S Width of strip x Abscissa in x,y coordinate syste Figure 6 y Ordinate in x,y coordinate syste Figure 6 Luinous flux of lap or laps in a luinaire kl Angle between the incident light path and the noral to the flat surface of the seicylinder used for easuring seicylindrical illuinance Figure, or the designated vertical plane used for vertical illuinance Figure 4 degrees Angle of deviation Figure 4 degrees Vertical photoetric angle Figure degrees Tilt for calculation Figure 8 degrees Angle of incidence Figure 4 degrees Tilt in application Figure 8 degrees Tilt during easureent Figure 8 degrees Orientation of luinaire Figure 7 degrees Angle of observation Figure 4 degrees Installation aziuth Figure 4 degrees Rotation of a luinaire Figure degrees 9

10 EN 0-:00 E 4 Matheatical conventions The basic conventions ade in the atheatical procedures described in this standard are: the luinaire is regarded as a point source of light; light reflected fro the surrounds and interreflected light is disregarded; obstruction to the light fro luinaires by trees and other obects is disregarded; the atospheric absorption is zero; the road surface is flat and level and has unifor reflecting properties over the area considered. 5 Photoetric data 5. General Photoetric data for the light distribution of the luinaires used in the lighting installation are needed for calculating the lighting quality characteristics in this standard. These data are in the for of an intensity table -table which gives the distribution of luinous intensity eitted by the luinaire in all relevant directions. When luinance calculations are to be ade, photoetric data for the light reflecting properties of the road surface are required in the for of an r-table. Interpolation will be needed in using both these tables to enable values to be estiated for directions between the tabulated angles. 5. The -table For calculations ade to this standard, an intensity table -table prepared in accordance with pren 0- is required. The coordinate syste used for road lighting luinaires is the,, shown in Figure, although the B, coordinate syste ay be used for floodlights. In the figure, the luinaire is shown at its tilt during easureent. Luinous intensity shall be expressed in candelas per kiloluen cd/kl fro all the light sources in the luinaire. 0

11 EN 0-:00 E = 90 = 0 = 70 4 = 80 I, γ γ Key Luinaire at tilt during easureent Longitudinal direction First photoetric axis 4 Direction of luinous intensity Figure Orientation of, coordinate syste in relation to longitudinal direction of carriageway Maxiu angular intervals stipulated in this standard have been selected to give acceptable levels of interpolation accuracy when the recoended interpolation procedures are used. In the, syste of coordinates, luinous intensities shall be provided at the angular intervals stated below. For all luinaires the angular intervals in vertical planes shall at ost be,5 fro 0 to 80. In aziuth the intervals shall be varied according to the syetry of the light distribution fro the luinaire as follows: a luinaires with no syetry about the = 0 plane: the intervals shall at ost be 5, starting at 0, when the luinaire is at its tilt during easureent, and ending at 55 ; b luinaires with noinal syetry about the = plane: the intervals shall at ost be 5, starting at 70, when the luinaire is at its tilt during easureent, and ending at 90; c luinaires with noinal syetry about the = and = 0-80 planes: the intervals shall at ost be 5, starting at 0, when the luinaire is at its tilt during easureent, and ending at 90;

12 EN 0-:00 E d Iuinaires with noinally the sae light distribution in all -planes: only one representative set of easureents in a vertical -plane is needed. NOTE The angular spacings recoended in IE Publication 40 for -tables are wider than those recoended above, and ay not give results which are of a satisfactory accuracy for illuinance calculations. 5. Interpolation in the -table 5.. General Where the intensity is required in a direction which does not lie in one of the directions in which easureents are recorded, either linear or quadratic, interpolation will be necessary to estiate the intensity in the desired direction. Linear interpolation is the sipler procedure and ay be used where the angular intervals are in accordance with those stipulated in 5.. If the angular intervals are greater then it will be necessary to use quadratic interpolation. 5.. Linear interpolation To estiate the luinous intensity, in the direction,, it is necessary to interpolate between four values of luinous intensity lying closest to the direction, see Figure. + γ + γ Figure Angles required for linear interpolation of luinous intensity For this purpose, the following equations or atheatically equivalent equations shall be used: K K - - 4

13 EN 0-:00 E where: K and K are constants deterined fro the equations is the aziuth, easured about the first photoetric axis is the vertical angle easured fro the first photoetric axis, +,, + are integers indicating the nuber of the colun or row in the -table, =, K x [, - +, ] 5, + =, + - K x [, + +, + ] 6, =, K x [, -, + ] 7 where:, indicates the intensity in colun nuber and row nuber of the -table, and so on for the other siilar sybols. In these equations interpolation is first carried out in the cones, and then in the -planes. If desired this procedure can be reversed that is, the interpolation is first carried out in the -planes followed by the cones and the sae result obtained. 5.. Quadratic interpolation Quadratic interpolation requires three values in the -table for each interpolated value. Figure indicates the procedure. If a value of is required at,, interpolation is first carried out down three adacent coluns of the -table enclosing the point. This enables three values of to be found at. Interpolation is then carried out across the table to find the required value at,. If preferred, this procedure ay be reversed; that is, interpolation can be carried out across and then down the -table without affecting the result. To reduce interpolation inaccuracies as far as possible the following two rules should be followed in selecting the values for insertion in the interpolation equations: The two tabular angles adacent to the angle for interpolation are selected for insertion in the interpolation equations and the average calculated. If the angle for interpolation is saller than this average then the third tabular angle is the next lower tabular angle as shown for in Figure ; if the angle for interpolation is greater than this average then the third tabular angle is the next higher tabular angle as shown for in Figure.

14 EN 0-:00 E + + γ + γ + γ Figure Values required for quadratic interpolation When interpolation is carried out in the region of = 0, or y = 0 or 80, see The forula for quadratic interpolation is x x x x x x x x x x x x y x y y y 8 x x x x x x x x x x x x where it will be noticed that there is cyclic perutation of the suffices. This interpolation can be applied to either or. When it is first applied to, this paraeter is substituted for x in the above equation: x = x = x = + x = + where: is the angle at which is to be found by interpolation, +, + are integers indicating the nuber of the coluns in the -table, + and + are values of for the corresponding colun nubers Fro this substitution three constants can be defined, which can be conveniently evaluated by a subroutine progra: 4

15 EN 0-:00 E 5 K 9 K 0 K Fro these three equations it follows that K + K + K =. A set of three equations can then be written allowing evaluation in a calculation loop in a coputer progra with the variation of :,,,, K K K,,,, K K K,,,, I K I K K I 4 For interpolation of the angles further application of Equation gives three new constants: k 5 k 6 k 7 Fro these three equations it follows that k + k + k = and:,,,, k k k which gives the required value of luinous intensity. The order of the interpolation procedure, first for and then for, ay be reversed without altering the result Quadratic interpolation in the region of = 0, or = 0 or 80 For quadratic interpolation in these regions it ay be necessary to take the third value of luinous intensity fro the = 90 through to = 80 to 70 heisphere of the luinous intensity distribution, which ay be regarded as a irror iage of the = 70 through to = 0 to 90 heisphere of the luinous intensity distribution. 5.4 The r-table Road surface reflection data shall be expressed in ters of the reduced luinance coefficient ultiplied by 0 000, at the angular intervals and in the directions given in Table for the angles and indicated in Figure 4.

16 EN 0-:00 E Q H T ϕ ε S N β σ P Key H PN Q QT ST Mounting height of the luinaire N noral at P to the road surface Photoetric centre of the luinaire First photoetric axis of the luinaire Longitudinal direction Suppleentary angle Angle of incidence Angle of observation Installation aziuth Luinaire Light path Observer Figure 4 Angular relationships for luinaire at tilt during easureent, observer, and point of observation 6

17 EN 0-:00 E Table Angular intervals and directions to be used in collecting road surface reflection data tan in degrees X X X X X X X X X X X X X X X X X X X X 0,5 X X X X X X X X X X X X X X X X X X X X 0,5 X X X X X X X X X X X X X X X X X X X X 0,75 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X,5 X X X X X X X X X X X X X X X X X X X X,5 X X X X X X X X X X X X X X X X X X X X,75 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X,5 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X,5 X X X X X X X X X X X X X X X X X X X X 4 X X X X X X X X X X X X X X X X X X X X 4,5 X X X X X X X X X X X X X X X X X X X X 5 X X X X X X X X X X X X X X X X X X X X 5,5 X X X X X X X X X 6 X X X X X X X X X 6,5 X X X X X X X X 7 X X X X X X X X 7,5 X X X X X X X 8 X X X X X X X 8,5 X X X X X X X 9 X X X X X X 9,5 X X X X X X 0 X X X X X X 0,5 X X X X X X X X X X X X,5 X X X X X X X X X X 7

18 EN 0-:00 E 5.5 Interpolation in the r-table When a value of r is required for values of tan and lying between those given in the r-table it is necessary to use quadratic interpolation. This requires three values in the r-table for each interpolated value. Figure 5 indicates the procedure. If a value of r is required at tan, interpolation is first carried out down three adacent coluns of the r-table enclosing the point. This enables three values of r to be found at tan. Interpolation is then carried out across the table to find the required value at tan,. To reduce interpolation inaccuracies as far as possible the following rule shall be followed in selecting the values for insertion in the interpolation equations. The two tabular values adacent to the value for interpolation shall be selected. The third tabular value shall be the next greatest, shown in Figure 5. Linear interpolation shall be used at the boundaries of the table. The ensuing atheatical procedure is siilar to that described for the -table 5... β β β β + + tan ε + tan ε + tan ε tan ε Figure 5 Values required for interpolation procedure in the r-table 8

19 EN 0-:00 E 6 alculation of, 6. General To deterine the luinous intensity fro a luinaire to a point it is necessary to find the vertical photoetric angle and photoetric aziuth of the light path to the point. To do this, account has to be taken of the tilt in application in relation to the tilt during easureent, the orientation, and rotation of the luinaire. For this purpose it is necessary to establish atheatical sign conventions for easuring distances on the road and for rotations about axes. The syste used is a right-handed artesian coordinate syste. The corrections for turning oveents do not allow for any change in the luinous flux of the light source due to turning oveents. 6. Matheatical conventions for distances easured on the road A x,y rectangular coordinate syste is used Figure 6. The abscissa is aligned with the reference direction, which, for a straight road, lies in the longitudinal direction. Then: where: x = x p x l 8 y = y p y l 9 x p, y p are the coordinates of the calculation point x l, y l are the coordinates of the luinaire y x x i, y i x p, y p Key Edge of carriageway alculation point Luinaire Figure 6 x,y coordinate syste for locating luinaire in plan 9

20 EN 0-:00 E 6. Matheatical conventions for rotations Figure 7 shows the axes of rotation in relation to the x,y coordinate syste, and the sense of the rotations. Axis I is fixed in space, axis II and axis Ill can be turned about axis I. = 90 υ = 70 ψ 4 δ = 0 x = 80 y Key Axis Ill Longitudinal direction Axis II 4 First photoetric axis I Figure 7 Axes of rotation in relation to x,y coordinate syste Figure 8 shows the relation of tilt for calculation to tilt during easureent and tilt in application. Fro this it is evident that: f 0 where: f is the tilt in degrees for calculation is the tilt in degrees in application is the tilt in degrees during easureent 0

21 EN 0-:00 E θ f θ δ Key Tilt for calculation f Tilt in application Tilt during easureent Horizontal Figure 8 Tilt during easureent, tilt in application, tilt for calculation 6.4 alculation of and These can be deterined in four stages: Substitution of v,,, x and y in the equations: cos cos sin sin sin sin cosv sin cos sin cos sin sin cos cos cos sin sin sin cos cos sin sin sin cos sin cos cos sin where: x and y H are the longitudinal and transverse distances between the calculation point and the nadir of the luinaire in Figure 6 is the height of the luinaire above the calculation point

22 EN 0-:00 E x,y, H are the distances used for calculating and ; and ay be regarded siply as interediate variables v,,and are the orientation, tilt for calculation, and rotation Evaluation of installation aziuth. Evaluation of arctan X Y will give: Y 90 arctan 90 X 4 The angular quadrant in which this lies is deterined by: For x > 0, y > 0 y arctan x or For x < 0, y > 0 For x < 0, y < y arctan x y arctan x or or For x > 0, y < 0 y 60 arctan x or alculation of 9 where: is the installation aziuth in degrees is the orientation in degrees Figure 7, obtained fro the equations in 6.4, x and y being used in place of x and y respectively. 4 alculation of tan x H y 0 7 alculation of photoetric quantities 7. Luinance 7.. Luinance at a point The luinance at a point shall be deterined by applying the following forula or a atheatically equivalent forula:

23 EN 0-:00 E L r MF 0 H 4 where: L r is the aintained luinance, in candelas per square etre is the luinous intensity in the direction,, indicated in Figure and Figure 4, in candelas per kiloluen is the reduced luinance coefficient for a light path incident with angular coordinates,, in reciprocal steradians is the initial luinous flux of the sources in each luinaire, in kiloluens MF is the product of the lap flux aintenance factor and the luinaire aintenance factor H is the ounting height of the luinaires above the surface of the road, in etres is deterined fro the luinaire -table see 5. after: corrections have been ade for the orientation, tilt for calculation, and rotation of the luinaire as indicated in clause 6; and interpolation which follows the procedure in 5. has been applied; as well as any correction ade that ay be necessary because the light output of the lap is teperature dependent and the luinaire is not used at the teperature at which it was photoetrically easured. Likewise, r for the appropriate value of tan and is deterined after the use of quadratic interpolation, if necessary. 7.. Total luinance at a point The total luinance at a point, L P, is the su of the contributions, L, L, L.. L n, fro all the luinaires. n k k LP L L... Lk... L n L 7.. Field of calculation for luinance In the longitudinal direction of the relevant area, the field of calculation shall enclose two luinaires in the sae row Figure 9, the first luinaire being located 60 ahead of the observer. When there is ore than one row of luinaires and the spacing of the luinaires differs between rows, the field of calculation shall lie between two luinaires in the row with the larger or largest spacing. NOTE This procedure ay not give accurate luinances for the whole installation as luinances will differ in the different spans between adacent luinaires. It can be preferable to calculate luinances and uniforities over a longer longitudinal distance and consider a nuber of observer positions.

24 EN 0-:00 E Key Edge of relevant area Field of calculation Width of relevant area W r 4 Last luinaire in field of calculation 5 First luinaire in field of calculation 6 Observer 7 Observation direction Figure 9 Inforation for luinance calculations; field of luinance calculations for the relevant area 7..4 Position of calculation points The calculation points shall be evenly spaced in the field of calculation as shown in Figure 0. The first and last transverse rows of calculation points are spaced at one half the longitudinal spacing between points fro the boundaries of the calculation field Figure 0. NOTE This grid is siilar to the grid used for illuinance calculations as regards the positioning of the first and last row of calculation points in the transverse direction Figure 5. 4

25 EN 0-:00 E 7 60 S D = S/N 6 WL d=wl / 5 d/ 4 Key Edge of lane Last luinaire in calculation field Field of calculation 4 entre-line of lane 5 First luinaire in calculation field 6 Observation direction 7 Observer's longitudinal position X denotes lines of calculation points in the transverse and longitudinal directions. Figure 0 Inforation for luinance calculations; position of calculation points in a driving lane The spacing of the points in the longitudinal and transverse directions shall be deterined as follows: a In the longitudinal direction S D N where: D is the spacing between points in the longitudinal direction, in etres S is the spacing between luinaires in the sae row, in etres N is the nuber of calculation points in the longitudinal direction with the following values: for S 0, N = 0; 5

26 EN 0-:00 E for S > 0, the sallest integer giving D. The first transverse row of calculation points is spaced at a distance D/ beyond the first luinaire reote fro the observer. b In the transverse direction The spacing d in the transverse direction is deterined fro the equation: d W L 4 where: d W L is the spacing between points in the tranverse direction, in etres is the width of the lane, in etres The outerost calculation points are spaced d/ fro the edges of the lane. Where there is a hard shoulder and luinance inforation is required, the nuber and spacing of the calculation points shall be the sae as for a driving lane Position of observer For luinance calculations the observer s eye is,5 above the road level. In the transverse direction the observer shall be positioned in the centre of each lane in turn. Average luinance see 8., overall unifority of luinance see 8. and threshold increent see 8.5 shall be calculated for the entire carriageway for each position of the observer. Longitudinal unifority of luinance see 8.4 shall be calculated for each centre-line. The operative values of average luinance, overall unifority of luinance, and longitudinal unifority of luinance shall be the lowest in each case; the operative value of threshold increent shall be the highest value. Figure gives exaples of the observer position in relation to the field of calculation. 6

27 EN 0-:00 E Key Six lane road with central reservation Three lane road. Single side luinaire arrangeent Three lane road. Double side luinaire arrangeent 4 Three lane road. Staggered luinaire arrangeent 5 Two lane road. Single side luinaire arrangeent 6 Two lane road. Double side luinaire arrangeent 7 Two lane road. Staggered luinaire arrangeent 8 Observer position 9 alculation field Figure Exaples of positions of observation points in relation to the field of calculation 7

28 EN 0-:00 E 7..6 Luinaires included in calculation The boundary of the area for locating luinaires to be included in calculating the luinance at a point is deterined as follows Figure : a boundary on either side of the observer: at least five ties the ounting height H on either side of the calculation point; b boundary furthest fro the observer: at least H fro the calculation point in the direction reote fro the observer; c boundary nearest to the observer: at least 5H fro the calculation point in the direction towards the observer. NOTE The extent of these boundaries is governed by the area covered on the road by the r-table. 5H H 4 5H 5H Key alculation point Boundary of field of calculation Boundary of area for location of luinaires 4 Observation direction Figure Boundary of area in which luinaires are located for calculating the luinance at a point 8

29 EN 0-:00 E 7. llluinance 7.. General In this standard any of four easures of illuinance ay need to be calculated, depending on the design criteria chosen fro EN 0-. These ay be: horizontal illuinance; heispherical illuinance; seicylindrical illuinance; vertical illuinance. 7.. Horizontal illuinance at a point alculation points shall be located in a plane at ground level in the relevant area. The horizontal illuinance at a point shall be calculated fro the forula or a atheatically equivalent forula: 5 where: E H is the aintained horizontal illuinance at the point, in lux is the intensity in the direction of the point, in candelas per kiloluen is the angle of incidence of the light at the point, in degrees is the ounting height of the luinaire, in etres is the initial luinous flux of the lap or laps in the luinaire, in kiloluens MF is the product of the lap flux aintenance factor and the luinaire aintenance factor 7.. Heispherical illuinance at a point alculation points shall be located in a plane at ground level in the relevant area. The heispherical illuinance at a point shall be calculated fro the forula or a atheatically equivalent forula: E [cos cos 4 H ] MF 6 where: E is the aintained heispherical illuinance at the point, in lux 9

30 EN 0-:00 E H is the intensity in the direction of the point, in candelas per kiloluen is the angle of incidence of the light at the point is the ounting height of the luinaire, in etres is the initial luinous flux of the lap or laps in the luinaire, in kiloluens MF is the product of the lap flux aintenance factor and the luinaire aintenance factor 7..4 Seicylindrical illuinance at a point alculation points shall be located in a plane,5 above the surface in the relevant area. Seicylindrical illuinance varies with the direction of interest. The vertical plane in Figure, at right angles to the rear flat surface, shall be oriented parallel to the ain directions of pedestrian oveent, which for a road are usually longitudinal. The seicylindrical illuinance at a point shall be calculated fro the forula or a atheatically equivalent forula: E [ cos ] cos H -,5 sin MF 7 where: E is the aintained seicylindrical illuinance at the point, in lux is the intensity in the direction of the point, in candelas per kiloluen is the angle between the vertical plane containing the incident light path and the vertical plane at right-angles to the flat surface of the seicylinder, as shown in Figure H MF is the angle of incidence of the light to the noral to the horizontal plane, at the point is the ounting height of the luinaire, in etres is the initial luinous flux of the lap or laps in the luinaire, in kiloluens is the product of the lap flux aintenance factor and the luinaire aintenance factor 0

31 EN 0-:00 E ε 4 I α Key Luinaire Vertical plane at right-angles to flat surface of seicylinder alculation point 4 Flat surface of seicylinder Figure Angles used in the calculation of seicylindrical illuinance 7..5 Vertical iluinance at a point alculation points shall be located in a plane,5 above the surface in the relevant area. Vertical illuinance varies with the direction of interest. The vertical illuination plane in Figure 4 shall be oriented at right-angles to the ain directions of pedestrian oveent, which for a road are usually up and down the road. The vertical illuinance at a point shall be calculated fro the forula or a atheatically equivalent forula: E cos sin cos H -,5 x MF 8

32 EN 0-:00 E where: E is the aintained vertical illuinance at the point, in lux is the intensity in the direction of the point, in candelas per kiloluen is the angle in degrees 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 Figure 4 H MF is the angle of incidence of the light to the horizontal plane, at the point, in degrees is the ounting height of the luinaire, in etres is the initial luinous flux of the lap or laps in the luinaire, in kiloluens is the product of the lap flux aintenance factor and the luinaire aintenance factor This forula is valid only for 90 and ε I α Key Vertical plane at right-angles to vertical illuination plane Luinaire alculation point 4 Vertical illuination plane Figure 4 Angles used in the calculation of vertical illuinance 7..6 Total illuinance at a point The total illuinance at a point, E P, is the su of the contributions, E, E, E, E n, fro all the luinaires. n EP E E... Ek... En E 9 k k NOTE Only illuinance easures of the sae type can be sued. Moreover, these should have the sae directionality.

33 EN 0-:00 E 7..7 Field of calculation for illuinance The field of calculation shall be the sae as that indicated in Figure. NOTE To econoize on coputer processing tie, for staggered installations the calculation field can be taken between consecutive luinaires on opposite sides of the road without affecting the result Position of calculation points The calculation points shall be evenly spaced in the field of calculation Figure 5 and their nuber shall be chosen as follows: a In the longitudinal direction The spacing in the longitudinal direction shall be deterined fro the equation: S D N 40 where: D S N is the spacing between points in the longitudinal direction, in etres; is the spacing between luinaires, in etres; is the nuber of calculation points in the longitudinal direction with the following values: for S 0, N = 0; for S > 0, the sallest integer giving D. The first row of calculation points is spaced at a distance D/ in etres beyond the first luinaire.

34 EN 0-:00 E D / S D = S/N D / d/ d d/ Key Luinaire Width of relevant area W r Field of calculation x denotes lines of calculation points in the transverse and longitudinal directions Figure 5 Inforation for illuinance calculations; calculation points on relevant area b In the transverse direction Wr d 4 n where: d W r n is the spacing between points in the transverse direction, in etres; is the width of the carriageway or relevant area, in etres; is the nuber of points in the transverse direction with a value greater or equal to and is the sallest integer giving d The spacing of points fro the edges of the relevant area is D/ in the longitudinal direction, and d/ in the transverse direction, as indicated in Figure Luinaires included in calculation Luinaires that are situated within five ties the ounting height fro the calculation point shall be included in the calculation. 4

35 EN 0-:00 E 7..0 llluinance on areas of irregular shape For these areas it ay 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 fro those points which lie within the boundary of the relevant area. When the spacing of the luinaires is not regular it ay not be possible to link the spacing of the grid points to the spacing of the luinaires, but the spacing in either direction shall not exceed,5. The principal directions of traffic flow for the calculation of vertical illuinance and seicylindrical illuinance should be decided after considering the use or likely use of the area. 8 alculation of quality characteristics 8. General Quality characteristics relating to luinance or illuinance shall be obtained fro the calculated grids of luinance or illuinance without further interpolation. If the grid points do not coincide with the centre of lanes, for the calculation of longitudinal unifority of luinance it will be necessary to calculate the luinance of points on the centreline of each lane and the hard shoulder, if present, in accordance with 8.4. For initial average illuinance or initial average luinance, MF is,0 and initial values of the luinous flux of the lap or laps in the luinaires shall be taken. For average luinance or average illuinance after a stated period, the MF for the luinaire after the stated period in the environental conditions of the installation shall be taken together with the luinous flux in kiloluens of the light source or sources in the luinaire after the stated period. 8. Average luinance The average luinance shall be calculated as the arithetic ean of the luinances at the grid points in the field of calculation. 8. Overall unifority The overall unifority shall be calculated as the ratio of the lowest luinance, occurring at any grid point in the field of calculation, to the average luinance. 8.4 Longitudinal unifority The longitudinal unifority shall be calculated as the ratio of the lowest to the highest luinance in the longitudinal direction along the centre line of each lane, and the hard shoulder in the case of otorways Figure. The nuber of points in the longitudinal direction N and the spacing between the shall be the sae as those used for the calculation of average luinance. The observer s position shall be in line with the row of calculation points. 8.5 Threshold increent The threshold increent TI is calculated fro the equations or atheatically equivalent equations: T 65 average road luinance L 0,8 v % 4 5

36 EN 0-:00 E n E E E E E Lv k k k k k n n 4 where: the initial average road luinance in cd/ is the average road luinance calculated for luinaires in their new state and for laps eitting the initial lap flux, in luens; L v E k is the equivalent veiling luinance, in candelas per square etre; is the illuinance in lux, based on the initial lap flux, in luens produced by the kth luinaire in its new state on a plane noral to the line of sight and at the height of the observer s eye; The observer s eye, height,5 above road level, is positioned in the centre line of each lane in turn, as indicated in Figure, and longitudinally at a distance in etres of,75 H -,5, where H is the ounting height in etres, in front of the field of calculation. The line of sight is below the horizontal and in a vertical plane in the longitudinal direction passing through the observer s eye. k is the angle, in degrees, of arc between the line of sight and the line fro the observer to the centre of the kth luinaire. The suation is perfored for the first luinaire in the direction of observation and luinaires beyond, up to a distance of 500 in each luinaire row, and stopped when a luinaire in that row gives a contribution to the veiling luinance which is less than % of the total veiling luinance of the preceding luinaires in the row. Luinaires above a screening plane which is inclined at 0 to the horizontal, and which passes through the observer's eye, and which intersects the road in a transverse direction, shall be excluded fro the calculation. The calculation is coenced with the observer in the initial position stated above, and repeated with the observer oved forward in increents that are the sae in nuber and distance as are used for the longitudinal spacing of luinance points. The procedure is repeated with the observer positioned in the centre line of each lane using in each case the initial average road luinance appropriate to the observer position. The axiu value of TI found is the operative value. This equation is valid for 0,05 < average road luinance < 5 cd/ and,5 < k <60 degrees of arc. NOTE The constant 0 in equation 4 is valid for a year old observer. onstants for other ages can be calculated fro the forula: A 9,86 66,4 where A is the age of the observer, in years. 8.6 Surround ratio 4 The surround ratio is the average horizontal illuinance on the two longitudinal strips each adacent to the two edges of the carriageway, and lying off the carriageway, divided by the average horizontal illuinance on two longitudinal strips each adacent to the two edges of the carriageway, but lying on 6

37 EN 0-:00 E the carriageway. The width of all four strips shall be the sae, and equal to 5, or half the width of the carriageway, or the width of the unobstructed strip lying off the carriageway, whichever is the least. For dual carriageways, both carriageways together are treated as a single carriageway unless they are separated by ore than 0. The horizontal illuinance shall be calculated by the procedure specified in 7... The field of calculation shall be as indicated in The nuber of luinaires considered shall be the sae as indicated in The position of the calculation points within each strip shall be as indicated in Figure 6 gives exaples of the location of the strips and their location for the calculation of surround ratio. For this figure, the following equation applies: Surround ratio Average illuinance of strip Average illuinance of strip Average illuinance of strip 4 Average illuinance of strip 7

38 EN 0-:00 E a Width of strip equals s W W W W s s s b Width of strip less than 5 because of obstruction 8

39 EN 0-:00 E 6 6 s W W s W s W s c Width of strip less than 5 because width of carriageway is less than 0 Key Strip Strip Strip 4 Strip 4 5 Luinaire 6 Edge of carriageway 7 Obstruction W S Width of strip Figure 6 Location and width of strips for calculating surround ratio 8.7 Measures of illuinance 8.7. General Measures of illuinance include horizontal plane, vertical plane, heispherical, and seicylindrical illuinance Average illuinance The average illuinance shall be calculated as the arithetic ean of the illuinances at the grid points in the field of calculation. For conflict, pedestrian, and other irregularly shaped areas, the procedure in 7..0 shall be followed. 9

40 EN 0-:00 E 8.7. Miniu illuinance The iniu illuinance shall be taken as the lowest illuinance occurring at any grid point in the field of calculation of illuinance Unifority of illuinance The unifority of illuinance shall be calculated as the ratio of the lowest illuinance, occurring at any grid point in the field of calculation, to the average illuinance. 9 Ancillary data When photoetric perforance data are prepared for an installation, the following ancillary data shall be declared: a identification of the luinaires; b identification of -table; c identification of the r-table with a clear declaration of the value of Q 0 used; not required when the calculations are solely those of illuinance; d tilt during easureent of the luinaires; e tilt in application of the luinaires; f rotation of the luinaires, if different fro zero; g orientation of the luinaires, if different fro zero; h identification of the light sources; i luinous flux of the light sources on which the calculations are based; aintenance factors applied; k definition of the area of calculation; l position of the luinaires in plan or a nuerical description; ounting height of the luinaires; n direction of interest for vertical illuinance and seicylindrical illuinance; o any deviations fro the procedures given in this standard, including the calculation of threshold increent for an observer of other than years old. 40

41 EN 0-:00 E Bibliography pren/tr 0-, Road lighting Selection of lighting classes. EN 665, Light and lighting Basic ters and criteria for specifying lighting requireents. IE 40, Road lighting calculations. LiTG/LTAG Publikation Nr. 4:99, Methoden der Beleuchtungsstärke und Leuchtdichteberechnung für Straßenbeleuchtung. 4