The influence of the supply voltage of the entire road lighting installation should be evaluated separately. The presence of a luminous flux controller can significantly reduce its influence.
A.3 Mathematical model for tolerance evaluations
The proposed mathematical model considers all the key parameters as uncorrelated.
If the luminous intensity distribution of the selected luminaire/luminaires is expressed in units of candelas per 1 000 Im of lamp flux (relative measurement) the manufacturer should give tolerance data of the luminaire referred to the nominal value of the installed lamp/lamps and the tolerance of the luminous flux of the lamp/lamps may be considered as an uncorrelated parameter.
If the luminous intensity distribution of the selected luminaire/luminaires is expressed in candelas (absolute measurement) the manufacturers should give tolerance data considering the tolerances of the installed lamp/lamps. Using these data the tolerance of the luminous flux of the lamp is not included in the tolerance analysis as a key parameter.
Tolerance analysis requires a list of all the key parameters together with the associated tolerance and the methods of evaluating the final uncertainty. For the sake of clarity, these data are presented in Table A.2.
Table A.2 — Tolerance analysis with uncorrelated input quantities
Input quantities 

Quantity 
Nominal value 
Tolerance 
Probability distribution 
Sensitivity coefficient 
Tolerance contribution 

Xt 
Xi 
u(Xi) 

Cl 
Ui(T) = Ci u(Xi) 

x_{2} 
Xi 
u(x_{2}) 

C2 
u_{2}(V) = ^{c}2 u(X_{2}) 








Xi 
Xi 
u(Xi) 

Ci 
u,(Y) = c, u(X) 








X_{N} 
X_{N} 
u(x_{N}) 

Cn 
u_{n}(Y) =c_{n}u(X_{n}) 

Output quantity 

Quantity 
Nominal value 



Combined uncertainty 
Final uncertainty 
Y 
У 



Uc(y) 
1/(95 %) 
NOTE The symbols used in this table are described in A.4. 
A.4 Modelling the tolerance analysis
The calculated quantity Y depends on N key parameters through the functional relationship
Y = f(X_{1},X_{2},...,X_{i},...,X_{N}) (A.1)
where
Y is the calculated or output quantity (i.e. point luminance);
Xi is the іth influence or input quantity.
For the input quantities Xi (/' = ) the following values are known or are supposed:
the nominal value x, as a value of the input quantities Xi
its tolerance, i.e. the range of possible values of x_{i;}
the probability distribution of x,.
When a normal (Gaussian) probability distribution can be assumed for the quantity X, then the tolerance Ufa) is the square root of the variance of the distribution.
When a rectangular probability distribution with upper limit a,,_{u} and lower limit a_{y} can be assumed then the nominal value is:
1/
x, = 2^ ^{+0,}’l
and the tolerance is:
T
(A.2)
(A.3)
(A.4)
(A.5)
(A.6)
(A.7)
he output quantity is completely specified by two values: a) nominal value/;b) its combine uncertainty u_{c}(y);
The nominal value/ is:
y = /(x_{1},x_{2},...,x,,...,x_{N})
The combined uncertainty is: N i=i
Where the tolerance contribution u, are: ^{u}/W = ^{c}_{!}^{u}(x_{/}) and the sensitivity coefficients
' dXj dXj ^{X}l^{=X}l’^{X}2=^{x}2^{X}N=^{x}N
The sensitivity coefficients can be obtained numerically using algorithms of EN 132013 with small variation ofX,.
The result of a calculation is then expressed as:
Y = y±U (A.8)
y = /cu_{c}(/) (A.9)
where
U is the final tolerance;
к is called coverage factor.
Conventionally к = 2 is adopted in this standard
NOTE 1 Generally the combined tolerance is calculated numerically with:
Z_{l}=[/(x_{1},x_{2}^{x}i:+u(x_{l},x_{N})f(_x_{1},x_{2},...,x_{i}u(x_{i}),...,x_{N})] (A.10)
and
u,(y) = Z_{;} (All)
(A.12)
NOTE 2 A generally adopted value of the level of confidence is p = 95 %
NOTE 3 The value of coverage factor к is chosen in accordance with the desired level of confidence p. Statistically the value of к = 2 gives a confidence level p = 95 % in conditions that are fulfilled in the majority of cases encountered in road lighting design.Annex В
(informative)
Important particular parameters
General
For investigative purposes some normative photometric parameters may be evaluated on a longitudinal part of a lane instead of on the entire lane. Such information can be useful for understanding the reasons for reduced performance of a lighting system or the influence of screens (e.g. trees in a boulevard) or of light sources forming part of other public and private lighting systems.
Particular luminance and uniformity
Parameters of this type are evaluated on given points in a given longitudinal line j in specific measurement conditions p. They are:
the (particular) average luminance along a longitudinal line: L j,_{p};
the (particular) highest luminance along a longitudinal line Z,_{max},j,_{P};
the (particular) lowest luminance along a longitudinal line i_{m}m,j,_{P};
the (particular) overall linear uniformity of luminance along a longitudinal line t7_{0},j,_{P}(£);
the (particular) longitudinal uniformity of luminance along a longitudinal line f/i.j._{p}(£).
Similarly, the same particular parameters for illuminance can be used.
Use of extended uniformity
The normative definitions of uniformities, both overall and longitudinal, require knowledge of the minimum and the maximum values of luminance or illuminance at a set of grid points.
These values can be strongly influenced by nonhomogeneity of environment or of the road surface, such as oil spots, new pavement patches or shadows from objects, and uniformities evaluated in different zones of the same lane can differ significantly.
Uniformity obtained using average values on a given percentage of the total measured zone or line gives a more accurate description of the real situation than using the limit values at a single point.
To distinguish these particular uniformities and correlated parameters from the normative ones, the adjective "extended" is added to their name and the subscript "e(c)^{u} is added at the end of their symbol.
The parameter "c” specifies the percentage of the total measured area of the surface, or the total length of the line used to average the photometric parameter.
Suggested values for c can be 10 %, 5 %, 1 % and 0,5 %. The appropriate choice should be made from experience and related to the particular situation.
NOTE 1 In presence of nonuniformities of the road surface (oil spreads, road dips, pavement road patches), of parked vehicles, trees, leaves or of lighting sources different from those of the road lighting installation, values of c = 10 % or c = 5 % are adequate.
NOTE 2 On motorways or other highspeed roads low values of c (extended results are similar to the normative values) are generally correct, while on main roads or streets in towns high values of c are adopted because they have a greater "filtering"effect Generally, if c < 0,3 % the difference between extended and normative parameters is insignificant.
NOTE 3 The use of an 1LMD for luminance measurements permits the measurement of the entire road surface and therefore allows the use of any value of c.
Evaluation of extended uniformities
To evaluate an extended parameter of quantity Q (luminance or illuminance) the measured zone or line is divided into G surfaces or segments, respectively of area or length A_{g}(g = 1, G) and for every surface a value Q_{g},_{P}(g = 1, G) is measured. These values are then organized and renamed so that Qi < Q_{2}... < Q_{g}... < Qg.
To evaluate the extended overall uniformities U_{0},j,e(c)[Q}, the parameter В is chosen so that: в
c = 100 (%) (B.l)
Ta,
9=1
The extended overall uniformity U_{0},_{p},e(c)(Q) is obtained as the ratio between:
Q_{a} the weighted average value of Q in the first В surfaces or segments where Q has the lower values;
Qb the weighted average value of in the entire measured zone:
U«._{P},_{W}W) = ^ (B2J
where
в
^Qg,p^{A}g
Q_{a}=—_{B} (B3)
H^{A}g g=i
G
lLQg.p^{A}g
Qb=^ ^{(ВЛ)}
^^{A}g 9=1
When Q is illuminance or luminance and the measurement is carried out using the moving observer technique the area of the surfaces or the length of the segments can be considered equal to each other and the formulae become:
ВА_{а}в
c = £100 = —100 (%) (B.5)
and
The same formulae are true for the extended overall uniformities along a longitudinal line U_{0},i,_{p},_{e}^(Q).
To evaluate the extended longitudinal uniformities t/wp,e(c)(£2)> the parameters В and Л/are chosen so that:
в
c = ^ 100 (%)
g=i
• (B.8)
G
C = _{100}
G
5=1
The extended longitudinal uniformity У^рХсДС) is obtained as the ratio between:
Q_{a} the weighted average value of Q in the first В surfaces or segments where Q has the lower values;
Q_{c} the weighted average value of Q in the last (GM) surfaces or segments where the Q has the higher values:
»и.Р.Ф)(«=^ <^{B}^{9}’ where
G
X
(B.10)
5=M
NOTE Also the maximum, minimum and average illuminance or luminance can be defined as extended parameters. The above formula of the parameter Q can be used.Annex C
(normative)
Conventions for symbols of photometric quality parameters
The symbol of a parameter consists of one letter (e.g. L, E, E_{m}in, Emax) and eventually one or more subscripts separated by commas may be used. The first subscript x, if needed, specifies the meaning of the parameter:
r for requirement based on lighting classes (EN 132012);
d for values effectively required by the road authority (design expectations);
c for calculated values;
m for measured values.
The following subscript, if present, specifies the geometric conditions (e.g. along a line in a lane, etc.); and the last subscript specifies the measurement conditions (subscript p in 3.7) and, if necessary, the evaluation condition (see informative Annex B).
NOTE The normative parameters have no subscripts for measurement and evaluation conditions.
If the parameter evaluates measurements along a line and if needed to avoid confusion, the line is specified by adding a subscript to the parameter symbol, such as "11", "12", etc. Letters or numbers can be used for this subscript, but the convention used shall be made clear in the test report.
Generally the particular parameters need the measurement conditions to be clearly specified. The following convention shall be adopted for the subscript:
if the photometric quantity is integrated along a segment or in a condition that can be approximated in this way the subscript is letter "s" and the length of segment shall be specified with the photometric value;
if the photometric quantity is integrated over an area that cannot be considered differential the subscript is letter "a" and the area value shall be specified with the photometric value.
When static measurements are carried out the acceptance area of illuminance meter is considered to be a point.
When measurements are carried out using a dynamic measurement system one dimension of the integrated area can be very small with respect to the other dimensions. In these situations finite surfaces can be considered to be segments.
Knowledge of the effective dimensions of the segment or area measured is important when measurements are compared, or when corrections are made to obtain a normative parameter from a measured one. For this reason such information shall be given in the measurement report and, if necessary to avoid ambiguity, made clear in the symbol of the particular parameter.
EXAMPLE The symbol of the normative lowest luminance measured along the centre line is L_{mi}n,m,c and its value is obtained as the lowest value in the set of (normative) luminance values measured at N points on the longitudinal line along the centre of a given driving lane, as specified by EN 132013 and following the requirement of this standard. The symbol of the particular lowest luminance measured along the centre line is Lmin.m.c.p and its value is obtained as the lowest value in the set of particular luminance values L_{m},_{p} obtained at N' given points on the longitudinal line along the centre of a given driving lane.
The meaning of p (number of points, geometrical measurement conditions, etc.) shall be described in the context where the symbol is used.
Annex D
(normative)
Guidelines for measurement systems for adaptive road lighting
For measurement systems used in adaptive road lighting to control the lighting output of luminaires the following requirements should be considered in addition or as a modification of the general part.
Measurement requirements need meticulous choice of the measured parameters (luminance or illuminance) conditions and evaluation of measurement procedures and instrument characteristics to obtain the required accuracies. The use of particular parameters may simplify the measurement system and reduce its cost without compromising the measurement aims. The measurement uncertainty of the controlling system and of the set measurement should be considered in order to be sure to guarantee the maintained value of the photometric quality parameters as required in EN 132012.
Difficulties in adequately measures the illuminance near the road surfaces (position of the sensor, strong influence of stray light from light sources different from those of the road lighting installations, dusts on the detector surface, etc.) suggest to measure the road luminance, at a specified angle, also when the standard lighting requirement is given as average illuminance value
The controlling parameters should be measured within the time constraints specified in the design or pertinent standards requirements. ,
Other photometric or nonphotometric parameters may be measured for monitoring or to increase the accuracy and reliability of the controlling system.
No measured photometric quality parameters may be obtained from previous periodic measurements, from the final testing/commissioning measurement or from set measurement.
Strategies to avoid unwanted operating conditions of the road lighting installation when the measurement conditions can give wrong results should be adopted. These conditions include:
during the stabilization period the luminous flux control should be suppressed or applied following specific design requirements or pertinent standard. The stabilization period is determined considering guidance given in EN 130321;
climatic conditions that do not represent the conditions required by design and management of the road lighting installation;
the detector working conditions (temperature, humidity, condensation or moisture on light transmitting surfaces) are outside its operating range.
Extraneous and obtrusive lights may not be avoided during measurements. During the set measurement the influence of extraneous and obtrusive lights may be evaluated. Strategies for their management should be considered in the installation design or from pertinent standards.
If luminance is measured:
the luminance meter position may be different from the observer position required in EN 132013;
different measurement point/points of the grid described in EN 132013 may be adopted;
luminance meters with a narrower measurement cone can be used at a greater distance and at a proportionally greater height so that the angle of view of the meter should be at (89 ± 0,5)° to the normal to the road surface;
other angle of view may be adopted if during the set measurement a correlation factor between the measured luminance and the luminance in normative conditions is evaluated;
the constraints on field of view of the luminance meter may be relaxed, if only the road surface is framed and the correlation between the measured luminance and the luminance in normative conditions can be established.
If necessary during the set measurement a correction factor can be measured or calculated to estimate the normative luminance value.
The set measurement should be carried out after a period of aging not less than the period specified, for a given lamp type, in EN 130321.
If this is not possible, the set measurement and samples of the controlling signal should be acquired at the same moment.
Absolute calibration of the luminance and illuminance meter can be omitted if the control method guarantees the traceability of the controlled parameter for example using the set measurement, which gives a sort of calibration factor.
If to measure the quantity used to control the lighting output of luminaires, calibrated instruments in geometrical conditions similar to the normative ones are used, the set measurement can be omitted.
Consideration should be given to the long term ageing of the instrument and influence of environment conditions.
The presence of rain or snow may modify not only the instrument performances and therefore its reading but also the above mentioned calibration factor. Strategies to avoid unwanted operating conditions of the road lighting installation should consider also these aspects
.Annex E
(informative)
Measurements for investigation of discrepancies between photometric
measures and design expectation
Measurements carried out as and when required to investigate discrepancies between measured results and design expectations or to understand environment influence require additional requirements or considerations.
All the parameters necessary to understand discrepancies should be measured.
This may include geometrical parameters of the installation like height of the columns, tilt, orientation and rotation in application of the luminaires, type and model of luminaires and lamps, detailed electrical conditions (i.e. supply voltage at as many lighting columns as necessary) and the road surface photometric properties.