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Lumen Method

 

The quantity of light reaching a certain surface is usually the main consideration in designing a lighting system.

This quantity of light is specified by illuminance measured in lux, and as this level varies across the working plane, an average figure is used.

 

CIBSE Lighting Guides give values of illuminance that are suitable for various areas.

The section - Lighting Levels in these notes also gives illuminance values.

 

The lumen method is used to determine the number of lamps that should be installed for a given area or room.

 

Calculating for the Lumen Method

 

The method is a commonly used technique of lighting design, which is valid, if the light fittings (luminaires) are to be mounted overhead in a regular pattern.

 

The luminous flux output (lumens) of each lamp needs to be known as well as details of the luminaires and the room surfaces.

 

Usually the illuminance is already specified e.g. office 500 lux, kitchen 300 lux, the designer chooses suitable luminaires and then wishes to know how many are required.

 

The number of lamps is given by the formula:

 

            

 

where,

N  =          number of lamps required.

E   =          illuminance level required (lux)

A  =          area at working plane height (m2)

F   =          average luminous flux from each lamp (lm)

UF=          utilisation factor, an allowance for the light distribution of the luminaire

                 and the room surfaces.

MF=         maintenance factor, an allowance for reduced light output because of deterioration and dirt.

 

 

Example 1

 

A production area in a factory measures 60 metres x 24 metres.

Find the number of lamps required if each lamp has a Lighting Design Lumen (LDL) output of 18,000 lumens.

The illumination required for the factory area is 200 lux.

Utilisation factor = 0.4

Lamp Maintenance Factor = 0.75

 

         


N       =       (  200 lux  x   60m  x  24m  )     /   (  18,000 lumens  x   0.4   x   0.75  )

N       =       53.33

N       =       54 lamps.

 

 

Spacing

 

The aim of a good lighting design is to approach uniformity in illumination over the working plane.

Complete uniformity is impossible in practice, but an acceptable standard is for the minimum to be at least 70% of the maximum illumination level.

 

This means, for example, that for a room with an illumination level of 500 lux, if this is taken as the minimum level, then the maximum level in another part of the room will be no higher than 714 lux as shown below.

 

500 /  0.7     =       714 lux

 

Data in manufacturer's catalogues gives the maximum ratio between the spacing (centre to centre) of the fittings and their height ( to lamp centre) above the working plane (0.85 metres above f.f.l.)

 

 


Example 2

 


Using data in the previous example show the lighting design layout below.

The spacing to mounting height ratio is 3 : 2.

The mounting height (Hm) = 4 metres.

The spacing between lamps is calculated from from Spacing/Hm ratio of 3 : 2.

If the mounting height is 4 m then the maximum spacing is:

 

3 / 2   =       Spacing / 4

 

Spacing       =       1.5  x  4  =   6 metres

                               

The number of rows of lamps is calculated by dividing the width of the building (24 m) by the spacing:

 

                   24 / 6  =   4   rows of lamps

 

This can be shown below.  Half the spacing is used for the ends of rows.

 

The number of lamps in each row can be calculated by dividing the total number of lamps found in example 1 by the number of rows.

 

Total lamps 54  /  4         =   13.5   goes up to nearest whole number   =   14 lamps in each row.

 

The longitudinal spacing between lamps can be calculated by dividing the length of the building by the number of lamps per row.

          Length of building 60 m   /    14     =   4.28 metres.

 

There will be half the spacing at both ends    =   4.28 / 2

                                                                   =   2.14 metres     

 

                  

This can be shown below.


 The total array of fittings can be seen below.


For more even spacing the layout should be re-considered.

The spacing previously was 6 m between rows and 4.28 m between lamps.

 

If 5 rows of 11 lamps were used then the spacing would be:

 

Spacing between rows         =   24  /   5        =   4.8  metres

Spacing between lamps    =       60  /  11       =   5.45 metres

 

Installed Flux

 

Sometimes  it is useful to know the total amount of light or flux, which has to be put into a space.

Installed flux (lm) =  Number of fittings (N)  x Number of lamps per fitting  x  L.D.L. output of each lamp (F)

 

Example 3

 

A factory measuring 50m x 10m has a lighting scheme consisting of 4 rows of 25 lighting fittings each housing 2No. 65-Watt fluorescent lamps.

 

(a)      Find the installed flux in total.

(b)     What is the installed flux per m2 of floor area.

  


The output of the lamps in the above example may be found from catalogues. For a 65-Watt fluorescent lamp the Lighting Design Lumens (LDL) is 4400 lm.

 

(a)

Installed flux (lm)   =       N  x  no. lamps/fitting x F

                             =       4   x   25   x   2   x  4400

                             =       880,000 lumens

 

(b)

The floor area                 =       50  x  10   =   500  m2.

Installed flux per m2         =       880,000   /   500

                                       =       1760  lm/m2.

 

 

Example 4

 

A room measures 15m x 7m x 3.6m high and the design illumination is 200 lux on the working plane (0.85 metres above the floor).

The Utilisation factor is 0.5 and the Maintenance factor is 0.8.

If the LDL output of each fitting is 2720 lumens, calculate;

(a)      the number of fittings required.

(b)     the fittings layout.

(c)     If the spacing/mounting height ratio is 1 : 1 determine whether the current design is acceptable.

 

(a)  Number of fittings.

          N       =       ( 200  x   15   x   7 )  /  (  2720   x   0.5   x   0.8 )

          N       =       19.3

          N       =       20 lamps

 

 (b) Fittings layout

 

For shallow fittings, the mounting height (Hm) may be taken as the distance form the ceiling to the working plane.

 

Therefore              Hm     =       3.6   -   0.85

                             Hm     =       2.75   metres         

 

If  3  rows of  7  fittings are considered then the spacing is;

 

 

(c) Spacing/ mounting height.

 

Spacing / Hm ratio:

2.33  /  2.75 =       0.847           Therefore ratio is             0.85 : 1.0

2.14   /  2.75 =       0.778           Therefore ratio is             0.78  :  1.0

 

 

Example 5

 

A room, as shown below, has a design illumination is 500 lux on the working plane (0.85 metres above the floor).

The Utilisation factor is 0.5 and the Maintenance factor is 0.8.

If the LDL output of each fitting is 2720 lumens, calculate;

(a)      the number of fittings required.

(b)     the fittings layout.

(c)     If the spacing/mounting height ratio is 1 : 1 determine whether the current design is acceptable.

 

 

 

(a)

N       =       ( 500  x  10  x  12  )   /   ( 2720   x  0.5   x   0.8 ) 

N       =       55.15

N       =       56 lamps.

 

(b)

Spacing,       say  8 lamps   x   7   rows.

Spacing along 12 m wall  =       12 / 8 = 1.50 m

Spacing along 10 m wall  =       10 / 7 = 1.43 m

 

(c)

Mounting height     =       3.0  -   0.85  =       2.15 m

Desired Ratio        =       1:1

Actual ratio  =       1.5  /  2.15   =       0.69   Therefore ratio is             0.69 : 1.0

Actual ratio  =       1.43  /  2.15 =       0.67   Therefore ratio is             0.67 : 1.0

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