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 (m^{2})

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 (H_{m}) = 4
metres.

The spacing between lamps is calculated
from from Spacing/H_{m} 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 shown 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)**

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 m^{2} 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 m^{2}.

Installed flux per m^{2} =
880,000 /
500

= **1760 lm/m ^{2}.**

__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
(H_{m}) may be taken as the distance form the ceiling to the working
plane.

Therefore H_{m} = 3.6 -
0.85

H_{m} = 2.75 metres

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

(c) Spacing/ mounting height.

Spacing / H_{m} 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**