UNIT 4: ILLUMINANCE CALCULATIONS

4.1 Introduction4.2 Illuminance Calculations

4.2.1 Direct Illuminance (Spot) Calculations4.2.2 Inverse Square Law4.2.3 Flux from the Source4.2.4 Cosine Correction

4.3 Geometric Variations of the Basic Formula4.3.1 Calculation Procedure

4.4 Accuracy of Images & Volumetric Lighting4.5 Beam or Cone Diagrams

4.5.1 Use of Cone Diagram4.5.2 Design Technique4.5.3 Comparison and Large Offset4.5.4 The Size of the Illuminance Patch(Ellipse)

4.6 The Lumen Method4.6.1 Horizontal Illuminance

4.7 Distribution Factors and Light Output Ratios4.8 Room Characteristics

4.8.1 Cavity Index (CI)4.8.2 Room Surface Reflectance4.8.3 Room Index

4.9 Uniformity of Illuminance4.10 Maintenance Factors

4.10.1 Lamp Lumens Maintenance Factor4.10.2 Luminarie Maintenance Factor4.10.3 Room Surface Maintenance Factor4.10.4 Lamp Survival Factor

4.11 Design Technique4.11.1 Optimum Solution

4.12 Installed Power Density4.13 Uplighting Design4.14 Review Questions

Objectives:

You should be able to achieve the following objectives as you study this unit:

Use luminaire data to determine intensity Calculate illuminance using the inverse square law Determine the size of area illuminated by a spotlight using cone diagrams Note the effect of room shape and surface reflectance on design Calculate the effective reflectance of a cavity Design energy efficient lighting installations using Utilisation Factors Correctly space luminaires to achieve uniformity Apply ageing factors to determine an overall maintenance factor for an installation Calculate the illuminance provided by an uplighter

4.1 INTRODUCTION

This unit outlines a number of calculation techniques for lighting design; enabling one to work out how many and what type of luminaires are needed for a given simple lighting scheme and to ensure the effectiveness of such a scheme.

In current practice, a great deal of lighting analysis and calculation is done by computer, using software packages such as DIALux, RELUX or AGi32, for example, and these are extremely useful in developing schemes, especially more for complex spaces. However, it is very important to note that these programs are not lighting design packages – they are lighting analysis tools. In order to analyse a scheme on a computer, one needs to have some idea what scheme to put in place. In addition, one needs to be able to recognise when the results from the software analysis are reasonable and when there is something wrong.

This is why, although the software greatly assists the lighting design process and will be used for the majority of day-to-day tasks, it is still important for a designer to know the hand- calculation techniques outlined in this unit. They provide a starting point on which to base ones scheme, a method to check computer analysis results, and understanding the concepts behind the calculations assists in the understanding of the underlying theory behind lighting design and engineering.

4.2 ILLUMINANCE CALCULATIONS

4.2.1 Direct Illuminance (Spot) Calculations

In essence there are two techniques of illuminance calculation by hand:

Consider the total flux or quantity of light which enters a room and how this is distributed to the various room surfaces.

Consider the intensity of light projected by a light source, towards a specific point.

Both methods have their advantages and uses and will be studied as part of this unit, starting with the spot or illuminance at a specific point technique.

4.2.2 Inverse Square Law

Starting from a simple point source, the law can be quoted as follows (Fig. 4.2.1):

Fig. 4.2.1

The horizontal illumination at point A (EA(h)) is given by:

where: I is the intensity of light in the direction of the point (candela) d is the distance between the light and the point (metres)

θ is the angle between the light and the normal to the surface.

The reason that the illumination changes with the square of the distance can be demonstrated quite easily and forms the basis for the mathematics for the law.

As we can from Fig. 4.2.2, if we have a beam of light shining on an area of a surface, and we move that surface further away from the lamp, then the area of the spot of light increases, in relation to the square of the distance. Thus, as we move further away, the same amount of light falls on a larger area and hence the illumination (lumens/m²) reduces twice the distance gives 4 times the area and hence a quarter of the illumination. Three times the distance gives 9 times the area and a ninth of the illumination, etc.

Fig. 4.2.2

The inverse square law should only be used when the distance between the light source and the point is large, compared to the size of the source. Typically a distance five times the size of the source (or greater), is acceptable and should cause no problem where we use this technique for tungsten and tungsten halogen spot lamps or for many discharge lamps.

For fluorescent lamps, say 1.5m in length, this would require a distance of 7.5m – not really practical. However there are ways around the problem as we shall see.

As the size of light source increases, errors occur because of:-

(i) The cosine of the angle changes between the point and different parts of the source. (ii) The intensity towards the point changes, again from different parts of the source.

4.2.3 Flux from the Source

Imagine we have a uniform light source with an intensity of light (candelas) in all directions

(Fig. 4.2.3).

The total flux from the source will be given from:

Since for a sphere the total solid angle is 4π , the total flux emitted by the light is 4π x I (lumens).

Fig. 4.2.3

If we now imagine this light is positioned at the centre of an imaginary sphere of radius d, then the inside surface area of the sphere is given by 4π d2 and the illuminance of the sphere surface will be given by:

Hence:

4.2.4 Cosine Correction

Again, this is a question of area. As the surface is turned away from the light source, so the area over which the beam of light is spread increases.

The Area over which the light falls is proportional to cosθ , where θ is the angle between the beam of light and the normal to the surface.

Thus, in total the inverse square law is:

4.3 GEOMETRIC VARIATIONS OF THE BASIC FORMULA

Often, the position of a light source in relation to a surface does not change. For example consider the horizontal illumination at points A, B, C, and D below.

Rather than work out the distances dA2 , dB

2 , dC2 , etc, we can use trigonometry and show that:

If we now substitute this value for d in the inverse square law, we get:

And there are times, when using this formula will save some time. But – be careful – the angles shown as θ are only the same because of the geometry in this case. For example, if you had wanted to calculate the vertical illuminance at a point:

then the basic law is unchanged:

But the ‘quicker’ modified formula will be:

Similarly, if the surface to be lit is at an angle, then the modified formula becomes much more complex. Therefore, unless you are confident in your trigonometric skills, then stick to using the basic formula:

4.3.1 Calculation Procedure

To avoid confusion in using the inverse square law, especially where many of the angles may be similar, it is suggested that you proceed in the following order of calculation:

Step 1Determine the intensity of light (I, candelas), towards the point – and then forget any angles or geometry you have used to find the value of I .

Step 2Determine the distance (d, metres) between the light source and the point.

Step 3Determine the angle (θ, degrees), between the normal (right angle) to the surface and the incoming light:

Step 4Calculate the illuminance (lux) from:

These steps are illustrated in the following example.

Example 1

A spotlight with an intensity distribution as follows:

is used to light a painting as shown below:

Calculate the illumination on the vertical surface of the painting at points A, B, C & D from this spotlight.

Illuminance at Point A (aiming point)

Step 1Determination of intensity towards A

Since this is the aiming point for the spotlight, and therefore the angle is 0°, we can simply read off the beam-centre intensity as 450 cd.

Step 2Determination of distance from lamp to point

From the side elevation, the distance from the lamp to the point can be found using Pythagoras’s theorem:

Step 3Determination of angle of incidence to surface normal

Again, from the side elevation, we can determine the angle of incidence ( θ ) and its cosine.

Step 4Calculate the illuminance

Applying the Inverse Square Law:

Illuminance at Point B (top of painting)

Step 1

Determination of intensity towards B

Again from the cross-section, we can determine the angle of point B from the beam centre of the lamp.

Angle of Beam Centre (α) given by:

Angle of picture top ( β ) given by:

Thus angle of point B from beam centre = α – β = 56.3 – 26.6 = 29.7°

Hence, by interpolation from the table, the intensity towards point B, at 29.7° can be found from:

Angle from beam centre Intensity

25° 27530° 220

Difference -5°

therefore, a Difference of

55

and a difference of 0.3° = -11 x 0.3 = -3.3

So our required intensity at an angle of 29.7° = intensity at 30° – difference of 0.3°

= 220 + 3.3

= 223.3 cd

Step 2Determination of distance from lamp to point

From the side elevation, d can be found as:

Step 3Determination of angle of incidence to surface normal

Step 4Calculate the illuminance

Illuminance at Point C (bottom of painting)

Step 1Determination of intensity towards C

Again using the geometry we can find the angle from the beam centre:

Angle of Beam Centre ( α ) given by:

Angle of picture bottom ( γ ) given by:

Therefore, angle of point C from beam centre

By interpolation from the table, intensity is found as:

Angle from beam centre Intensity5° 445

10° 420

Difference -5° 25

Therefore a difference of

and a difference of 2.1° = -5 x 2.1 = -10.5

So our required intensity at an angle of 29.7° = intensity at 5° + difference of 2.1°

= 445 – 10.5

= 434.5 cd

Step 2Determination of distance from lamp to point

Step 3Determination of angle of incidence to surface normal

Step 4Calculate the illuminance

Illuminance at Point D (edge of painting)

This is perhaps the most difficult point to calculate because the point is not on the centre line axis of the spotlight. It therefore requires a 3-dimensional viewpoint that can be difficult to visualise.

Step 1Determination of intensity towards point D

To determine the angle from the beam centre, consider the following three-dimensional representation of the space.

From the cosine rule of a triangle:

Hence:

or, in our example:

therefore:

.

By interpolation from the table, intensity is found as:

Angle from beam centre Intensity20° 33025° 275

Difference -5°

therefore, a Difference of

55

Thus a difference of 2.4° = -11 x 2.4 = -26.4

So our required intensity at an angle of 22.4° = intensity at 20° + difference of 2.4°

= 330 – 26.4

= 303.6 cd

Step 2Determination of distance from lamp to point

The geometric construction to find the angle from the beam centre helped us to find the value of d,in this case m.

Step 3Determination of angle of incidence with normal to surface

Again, this is complicated by the three-dimensional geometry and the fact that the painting is not at right-angles to the incident ray.

Therefore .

Step 4

Calculate the illuminance

4.4 ACCURACY OF IMAGES & VOLUMETRIC LIGHTING

Light itself is invisible; it only becomes visible when it strikes an object. If the air through which the beam travels is dusty or smoky so that the tiny particles of dust reflect the light, it makes the ‘beam’ visible. To assist understanding of the size and direction of cones or beams of light, it is often useful to use this effect in illustrations. In the world of computer animation and 3-D virtual reality, the technique is called ‘volumetric lighting’ and the effect is to make the beams of light visible.

Summary of Illuminance Values

(Note that lux is a small unit and lighting calculations are subject to a variety of tolerances; it is usually not meaningful to give values of lux to decimal places, unless considering very low lux levels; this is why in the above calculations the lux values are given to the nearest whole number, unlike in this diagram.)

You may conclude the following:

1. Firstly, we can see that the illuminance range across the painting is virtually 4:1 (maximum : minimum) – this is not very even lighting, (there is more discussion of this in the Accent and Display Lighting section later).

2. Note how the cosine of the angle of incidence significantly affects the illuminance – compare the top and bottom of the painting. The intensity towards the bottom of the painting is virtuallydouble that towards the top, yet because of the extra distance and the cosine of the angle, the illuminance is a quarter.

3. Note how the calculations become very complex once the point of calculation moves away from the axis of the spotlight and/or if the plane of calculation is at an angle (ie not horizontal or perpendicular).

4.5 BEAM OR CONE DIAGRAMS

As we can appreciate, the calculation of point by point illuminance values can be a lengthy process and is often difficult to ‘visualise’, especially when the points of interest are off-centre. An effective design aid is therefore the Beam or Cone diagram provided by the lamp manufacturer.

4.5.1 Use of Cone Diagram

The cone diagrams indicate both the beam centre illuminance values together with the 50% intensity angles†5-3 and beam widths for a range of lamp operating distances.

Typically a symmetrical light source, the light from the lamp emerges as a cone of light and for a‘normal’ surface (i.e. one at right angles to the beam), illuminates a circular area with a soft edge. (Hard edges are usually only produced where the lamp is deeply recessed into the luminaire, so that the front edge of the luminaire obstructs and ‘cuts-off’ the beam). Where the surface being lit is not at right angles to the beam (as with our previous example), the beam produces a roughly elliptical patch of light.

4.5.2 Design Technique

A common technique of uniformly lighting a large area by spotlights (or floodlights, which are essentially wider-beam spotlights) is to align the elliptical patches of light so that they ‘just touch’.

Position, of course, is critical and will always be a compromise. The greater the OFFSET depth, the more the light will strike the vertical surfaces of an object closer to a right angle (i.e. ‘normal’ incidence). Thus will be larger and the illuminance will be higher. Against this however, is the disadvantage that, as we move the lamp away from the wall, the distance between the lamp and object increases. Thus not only does the illuminance fall (by 1/d2), but there is a risk that people standing to admire the object will cast their shadow across it.

To some extent shadows from people can be reduced by ‘crossing the light beams’, i.e. lamps on the left illuminate the right-hand side of the object and vice versa, but it can still be a problem.

In summary therefore:

4.5.3 Comparison of Close and Large Offset

Close offset:

(1) Values of d smaller and so potentially higher illuminance(2) Values of d from top to bottom of object vary widely(3) cos θ values are low so reducing illuminance.

Large offset:

(1) Values of d relatively high therefore illuminance levels lower, but cosθ values are higher therefore better use of flux;(2) Less variation of d values from top to bottom of object therefore better uniformity(3) Risk of shadows from people standing in the beam.

4.5.4 The Size of the Illuminated Patch (Ellipse)

Data required:

1. Beam Angle (θ, degrees)2. Beam Centre Intensity (I , candelas)3. Offset depth (Z , metres)4. Aiming point (YA , metres)

Calculation Theory:

(horizontal beam centre) (degrees)

(horizontal to top of ellipse) (degrees)

Distance YB(vertical distance to top of ellipse) (metres)

(horizontal to bottom of ellipse) (degrees)

Distance YC (vertical distance to bottom of ellipse) (meters)

Length of ellipse YC - YB (meters)

Distance OA

(meters)

Width of ellipse

= 2 OA tan (meters)

Distance OB

= meters)

Distance OC

= (meters)

Vertical Illuminance values:

Beam Centre (point A)

= EA(V) = (lux)

Top of ellipse (point B)

= EB(v) = (lux)

Bottom of ellipse (point C)

= EC(v) = (lux)

Distance HD

= (meters)

Distance OD

= (meters)

I lluminance at edg e of ellipse

= (lux)

Question 4.1

A painting 1.75m width x 1.25m height is mounted so that its top edge is 0.3 m below the spotlight, and is to be lit by low voltage tungsten halogen spotlights.

Using the lamp data table below, by calculation, determine the length and width of the “ellipse” ofillumination for each lamp type and for offset depths of 0.5m, 1.0m and 1.5m.

Hence, determine the number of lamps required to “vertically” illuminate the painting to anapproximately uniform level of 500 lux.

Lamp Power (W) Beam Angle (°) Centre Beam Intensity (cd)

50 10 15,000

50 24 5,000

50 38 2,300

4.6 THE LUMEN METHOD

The lumen method of lighting is commonly used to design the general lighting for rectangular rooms. It provides a method of calculating the average illuminance for a space, which it does by predicting the total amount of light which will reach the working area and then dividing this value by the size of the area.

In order to ensure a reasonably uniform illuminance across the working plane, the designer is required to position the luminaires in a regularly spaced array, using guide calculations on luminaire spacing to ensure a satisfactory design.

In essence, the lumen design formula is based upon:

= (lux)

where: φ is Lamp flux (lumen) n is the number of lamps per luminaire is the number of luminaires N is the Maintenance Factor for the installation MF is the Utilisation Factor for the installation is the area of the working plane (m²)

Luminaire manufacturers provide UF data values which vary with both the type of luminaire and the characteristics of the room.

The Utilisation Factor for a surface or UF is defined by:

thus the utilisation factor for the floor [UF(F)] is defined by:

Note the total light reaching the floor includes both direct and inter-reflected or indirect light.

4.6.1 Horizontal Illuminance

Typically, the Lumen Method technique is used to calculate the horizontal illuminance on the working plane and these notes and the examples that follow assume this. However, UF values are not restricted to the working plane and others, such as, UF(W) (for walls) and UF(C) (for the ceiling), may also be determined and used.

4.7 DISTRIBUTION FACTORS AND LIGHT OUTPUT RATIOS

The distribution factors indicate the distribution of direct flux to any of the room surfaces. For example:

The ratios are important because direct light is always more efficient in lighting a surface than indirect or reflected light. At each reflection, some light is always absorbed by the reflecting surface.

In addition, luminaire manufacturers usually quote the Light Output Ratio (LOR) of a luminaire, where the:

The LOR can also be further sub-divided into: Downward Light Output Ratio (DLOR) Upward Light Output Ratio (ULOR)

where:

From our previous definitions:

DF(F)+DF(W) = DLOR

where:DF(W) only considers direct flux to the wall area below the horizontal plane through the luminaire.

DF(C)+DF(S) = ULOR

where: DF(S) is the direct flux to the ‘frieze’ (ie direct flux to the wall area above the horizontal plane through the luminaire) as a proportion of the total lamp flux.

4.8 ROOM CHARACTERISTICS

Luminaire design data produced by manufacturers is based on a mounting height (height of luminaires above the working plane) noted by Hm and as shown above, i.e. the floor cavity is treated as though it were the floor and the ceiling cavity is treated as the ceiling. Nonetheless, it may still be necessary to determine the overall reflectance value for either cavity from the following method.

Note: In the Lumen Method, it is common to assume that the reflectance of the floor cavity is 0.2.

4.8.1 Cavity Index (CI)

eg, for the Ceiling Cavity CI(C) with a rectangular room:

and by using the tables overleaf, the effective reflectance (RE ) of the cavity can be found.

Alternatively you can use the slightly less accurate formula:

Where RAis the average area-weighted reflectance of all the ACTUAL surfaces within the cavity and is given by:

e.g. for CI(C):

Effective reflectance of cavity

4.8.2 Room Surface Reflectances

The total light reaching the working plane will include both direct and indirect (reflected) light and, whilst the indirect component is generally the smaller, it is nonetheless important. By definition, the indirect component involves reflection, so the reflective properties of the room surfaces naturally affect the final value of UF for an installation.

Room surfaces are usually referred to as: C (Ceiling), W (Walls) and F (Floor). Their respective reflectance values can be used directly where the luminaires are mounted and recessed into the (and therefore are flush with) the ceiling and the plane of interest is the floor. Often however, the luminaires are suspended below the ceiling and/or the working plane is at desk-top height (typically between 0.75m and 0.85m above the finished floor level) i.e. not at floor level. In such cases we need the reflectance value for the cavity.

Reflectance Values: Typical values of reflectance are quoted in the table below for guidance.

Surface Reflectance Material / Finish

Ceiling 0.8 White emulsion paint on plain plaster surface

0.7 White emulsion paint on acoustic tiles

0.6 White emulsion paint on concrete

0.5 White emulsion paint on wood-wool slab

Walls 0.8 White emulsion paint on plain plaster surface

0.7 Brick, white

0.65 Plaster, pink

0.4 White asbestos cement; Brick: Concrete, Light Grey

0.35 Stainless Steel

0..3 Brick: fletton

0.25 Portland Cement; Brick: London Stock; Timber (light)

0.2 Brick: Concrete, dark grey; Timber (medium/dark)

0.15 Brick: Blue Engineering

0.05 Chalkboard; painted black

Floors 0.45 Cement screed; PVC Tiles: cream; Carpet: (light)

0.35 Timber: (medium)0.25 Timber: (dark); PVC tiles: marbled; Carpet: (medium)

0.2 Timber: (dark); Tiles: cork

0.1 Quarry tiles: (dark); Carpet: (dark); PVC tiles: (dark)

4.8.3 Room Index

The shape of the room will also affect the UF for an installation. For example, with a wide room more light will go directly to the floor or working plane (remember direct light is more effective) and so the UF will be higher. Conversely, for a narrow room more light is initially directed onto the walls, rather than the working plane, so the UF will be lower.

The Room Index or RI is a measure of room shape and is given by:

RI =

where: L is room length is room W is the width Hm is the mounting height of luminaire above the working plane

Below is shown a typical lighting manufacturer’s UF table; note that UFs are defined by Room Index and room surface reflectances.

Question 4.2

Calculate the Room Index for a number of rooms where the mounting height (Hm) is fixed at 2m, but where the room dimensions increase in 2m increments.

For example,L = 2 m, W = 2m, 4m, 6mL = 4 m, W = 4m, 6m, 8mL = 6 m, W = 6m, 8m, 10mL = 8 m, W = 8m, 10mL = 10 m, W = 10 m

Use a simple spreadsheet, or otherwise, to calculate the Room Indexes in order to appreciate the size of a space with a Room Index of 5 compared to a space with a Room Index of 1.

4.9 UNIFORMITY OF ILLUMINATION

The Lumen Method only determines the average illuminance over the working plane and therefore requires the designer to correctly position the luminaires to achieve an acceptable uniformity. The aim is to achieve adequate uniformity of illumination so that the client is not restricted in using the space and can operate from anywhere within it.

The uniformity of illuminance is defined as the ratio of:

Reasonable uniformity in an area exists when this value equals 0.7 or better.

Spacing to Height Ratios

Uniformity tends to improve with reduced spacing between luminaires and most luminaire manufacturers quote a maximum spacing to mounting height ratio (SHR MAX) which will just achieve acceptable uniformity.

For example, on the UF table quoted previously, the twin lamp luminaire has a SHR MAX of 1.15 for a square array:

So that if the mounting height of the luminaire is say 2m above the working plane, then the maximum spacing between luminaires in a regular array is 1.15 x 2m = 2.3m between centres.

With linear luminaires, the intensity distributions in the axial and transverse planes can be quite different and this will affect the maximum SHRs in the axial and transverse directions – see the diagram below.

The manufacturer therefore calculates SHR MAX for a square array, but because the spread of light is usually greater in the transverse direction than the axial, it is possible to increase the transverse spacing provided we decrease the axial spacing to compensate. In comparison, increasing the spacing in the axial direction beyond the maximum SHR is not usually possible.

In the above diagram, each luminaire effectively lights an area of STR width and SAX length. Where the whole area lit by each luminaire is given by STR x SAX.

We can therefore increase (within reason) the transverse spacing (STR ) – for example, to accommodate ceiling tile layouts or avoid air conditioning grills etc. – provided we decrease the axial spacing in proportion, so that at all times:

STR

or, in terms of spacing to height ratios:

Maximum Transverse Spacing

Naturally this compensation cannot go on indefinitely and is usually limited where the axial spacings are reduced to the point where the luminaires form continuous rows.For this case the luminaire manufacturer provides a value of SHR MAX TR.

Nominal Spacing to Height Ratios

In order to simplify presentation and calculation of data, standard tables of UFs are based uponnominal spacing to mounting height ratios (SHR NOM).

UFs are quoted for the highest SHR NOM value in the series 0.75, 1.0, 1.25, 1.5, 1.75 (steps of 0.25) etc. For which the uniformity of illuminance is not less than 0.7.

4.10 MAINTENANCE FACTORS

During its life, the average illuminance on the working plane of an installation will decrease with time. Several factors affect this reduction which is due to:

(a) Ageing of the lamps and their subsequent reduction in light output (except the TungstenHalogen incandescent lamp for which this effect is negligible);

(b) The accumulation of dust and dirt on the luminaire over time and hence a reduction in light output ratio;

(c) The accumulation of dust and dirt on the room surfaces over time and hence a reduction in surface reflectances;

(d) The failure of individual lamps.

Thus to ensure a continuing satisfactory performance, the SLL Code for Lighting recommends that we design for a maintained illuminance, i.e. the lowest average illuminance on the working plane (or relevant room surface) at the time maintenance just before has to be carried out by replacing lamps and/or cleaning the equipment and room surfaces.

Hence there are a number factors affecting the reduction in illuminance, these are:

Lamp Lumen Maintenance Factor Luminaire Maintenance Factor Room Surface Maintenance Factor Lamp Survival Factor

All include a time element within their definition, based on the maintenance interval for an installation.

4.10.1 Lamp Lumen Maintenance Factor (LLMF)

4.10.2 Luminaire Maintenance Factor (LMF)

(usually estimated from table 4.6 of the SLL Code for Lighting, which should be used for reference, but which is reproduced below in graphical form and includes a guide to typical luminaire maintenance categories.)

4.10.3 Room Surface Maintenance Factor (RSMF)

(usually estimated from table 4.7 of the CIBSE Interior Lighting Code, which should be used for reference, but which is reproduced below in graphical form)

4.10.4 Lamp Survival Factor (LSF)

(see graph below)

Note: If in an installation, failed lamps are to be replaced as they fail, then LSF = 1.0.

The Overall Maintenance Factor (MF) is therefore given by:

4.11 DESIGN TECHNIQUE

In order to ensure a satisfactory uniformity of illumination, it is can be easier to design the installation by first considering the minimum number of luminaires to achieve uniformity.

This can be determined by dividing the maximum spacing into the two major room dimensions, since the total number of whole spaces between luminaires (including two half-spaces between the end luminaires and the walls) equals the number of luminaires.

Example

Room Dimensions: 10.5 x 9.00 x 3.00 m highWorking Plane Height: 0.85 mReflectances: 0.50 (Ceiling), 0.30 (Walls), 0.20 (Floor cavity) Luminaire: Surface mounted – use data shown belowInitial Lamp Lumens: 5200 lumens (1500mm, triphosphor, T8, 58W lamp)

or 3350 lumens (1200mm, triphosphor, T8, 36W lamp) Annual Operating Hours: 2500 (Bulk lamp replacement every 2 years, but with spot

replacement for individual lamp failures)Cleaning Interval: 2 years (Normal Environment) Maintenance Category: BLuminaire Mounting: Surface mounted to ceiling (assume no ceiling cavity), parallel

to longest wall.

Target Maintained Illuminance: 300 lux

Solution

Preliminary Calculations

Room IndexMounting Height Hm = 30.85 = 2.15m

Room Index:

RI =

Maximum SpacingSHR MAX – Single Lamp Luminaire = 1.15SHR MAX – Twin Lamp Luminaire = 1.15

Hence maximum spacing = 1.15 x 2.15 = 2.47 m (single or twin lamp luminaires).

Overall Maintenance Factor

LLMF = (0.91 + 0.87/2) = 0.89 (Interpolating from Typical (5000 hours) data curve)

LSF = 1.0 (Lamp replacement at every individual lamp failure)

LMF = 0.80 (Normal, Luminaire type B, 2 years)

RSMF = 0.96 (Normal, medium room, Direct [no upward light], 2 years)

Overall Maintenance Factor:

MF = LLMF LSF LMF RSMF = 0.891.00.800.96=0.68

Design Calculations

Minimum Number of Luminaires to Achieve Uniformity

(say 4 rows, for single or twin lamp luminaires)

(say 5 luminaires per row, for single or twin lamp luminaires).

It is usual, for aesthetic reasons, to align the fluorescent luminaires with the longest room dimension. In which case, the room width contains the number of rows and the room length the number of luminaires per row,

Utilisation Factors

Surface Reflectances: 50, 30, 20

Single Lamp Luminaire:for RI = 2, UF = 0.61; for RI = 2.50, UF = 0.64; therefore, interpolating for RI = 2.25:

(say 0.62)

Twin Lamp Luminaire:for RI = 2, UF = 0.58; for RI = 2.50, UF = 0.62; therefore, interpolating for RI = 2.25:

Illuminance Calculations

Trial Calculation 1:Single Lamp Luminaires (1200mm, 36W T8 lamp)

Maintained illuminance, EM :

Since 300 lux is the target, no further trail calculations are required.

4.11.1 Optimum Solutions

Quite by chance therefore, we have managed to produce the optimum solution at our first calculation. Very often however, the required illuminance is some way from our first trial. It is then the skill of the lighting designer to determine the optimum solution, using the following suggestions or combinations of them:

Test the design with an alternative lamp rating. Remember however that you do not want too many different lamp sizes/types for any installation because of the problems of keeping a stock of spare lamps for maintenance.

Test the design with twin or multiple lamp luminaires, again using different lamp sizes where necessary, but note that glare may be a limiting consideration.

Increase the number of rows or number of luminaires per row, bearing in mind the aesthetics of the space. Will the number of rows you need make the ceiling look ‘overcrowded’ with luminaires.

Usually, if these three suggestions do not meet your required illuminance, or, if you have to add too many ‘extra’ luminaires, then perhaps you should ask yourself the question “Is the luminaire I have chosen, suitable for the task”? In which case, a change to an alternative type luminaire might be necessary.

4.12 INSTALLED POWER DENSITY

Both the SLL Code for Lighting and Part L of the Building Regulations (Conservation of fuel and power) stress the need to use energy efficient light sources for buildings.

The SLL Code for Lighting for example, gives a range of targets for installed power density based on the type of space and the target maintained illuminance level. For example, for a commercial space with triphosphor fluorescent lamps and a target of 300 lux average maintained illuminance, the average installed power density recommended in the SLL Code for Lighting is 7 W/m². This power density includes the control gear losses for the lamp circuit, ie it should be the circuit or luminaire power, not just the lamp power that is considered.

This data is available from the luminaire manufacturer and for this luminaire the manufacturer quotes a circuit power of 45 watts for the 36 watt mains frequency control gear and a circuit power of 36 watts for the 36 watts high-frequency control gear. From which we obtain our installed power density figures of:

For mains frequency control gear:

For high-frequency control gear:

Since both of these exceed the recommendations in the Code, one should go on to review the type of luminaire used and seek a more efficient product (note that the luminaire used in this example is rather old, and would have met the requirements in past versions of the Code).

Question 4.3

A lighting scheme is required for a general office, 12m x 14m with a 3m ceiling height. The office is clean and the room reflectances are: 0.7 ceiling, 0.4 walls, and 0.2 floor.

Triphosphor fluorescent lamps will be used which will be bulk replaced every 14,000 hours (with spot replacement of any individual lamp failures between these intervals). The room surfaces and luminaires are to be cleaned annually.

Using the photometric data provided in Example 2 and assuming the luminaire to be an ‘open-top reflector’ type, determine a suitable lighting design to produce an average maintained illuminance of 500 lux.

4.13 UPLIGHTING DESIGN

The technique of uplighting involves using luminaires, which project their light onto the ceiling and which then acts as a large diffuse light source to illuminate the room. This produces lighting which is softer (the shadows are not so hard) and more diffuse than direct lighting and which may, for some installations, provide a better visual environment or help in the reduction of reflections from computer display screens. In addition, uplighting will often be chosen in order to highlight important architectural features of a building. For example, it may be used to reveal the texture and form of an ornately decorated ceiling within a church. However, if as in this example, the reflectance of the ceiling is low, additional direct lighting may also be required.

Uplighting can of course, be used to provide general uniform lighting. But it is equally effective when used for localised or task lighting.

Calculations

To ensure maximum efficiency, matt white ceilings and upper walls should be used (a neutral colour such as white also prevents colour being cast around the space) with a reflectance of at least 70%, or higher if possible.

Lumen Method

The lumen method of design can be employed where:

UF(F) = ULORTFC, F

where: TFC, F is the transfer factor from the ceiling to the floor (see table below)ULOR is the Upward Light Output Ratio of the luminaire

Standard conditions for published uplighter data

Point Calculations

A convenient method for manual calculations to determine point calculations for uplighting is to use the equivalent point source technique. (Developed from the paper Estimating uplighting; Bedocs L, Lynes J, and Hugill J; 1984 National Lighting Conference).

This separates the calculation into two components, namely - Ed a first reflection from the ceiling produced by an imaginary point source above the ceiling and - Ei from all subsequent inter- reflections.

Calculation of Ed

The uplighter manufacturer would normally provide an illuminance curve, typically as shown below, which would note the illuminance at various distances from the base of the uplighter.

The curves are provided for standard conditions of operation (as shown above), but may be modified by the application of the following correction factors.

Ceiling Height (m)

2.4 0.73 1.86

2.6 0.87 1.33

2.8 1.00 1.00

3.0 1.13 0.78

3.2 1.27 0.62

3.4 1.40 0.51

3.6 1.53 0.43

3.8 1.67 0.36

4.0 1.80 0.31

Variations of Ceiling Height and Ceiling Reflectance

These correction factors are applied to the axes of the illuminance curve for the luminaire, whereDk adjusts the ‘distance axis’ and Ek the ‘illuminance axis’.

So that the final illuminance is given by:

where: Rc is the actual ceiling reflectance. φ is the actual lamp flux (lumens)

Uplighter Height and Working Plane Height

For variations in uplighter height or working plane height, the correction factors are:

Which again are used to adjust the axes of the illuminance curve.

Calculation of Ei

The inter-reflected component ( Ei ) is assumed to be uniformly distributed over the whole area and is given by:

where: Ulf is the Utilance Value for the indirect component for the working plane. : Ulf is

given from the table below:

Utilance Table for ‘Indirect Light, (UIF ) for Floor Reflectance of 20%

Overall Illuminance

The total maintained illuminance is therefore given by:

Question 4.4

An office installation is to be lit by 250W, SON delux (SON comfort – elliptical lamp), uplighter luminaires.

Using the photometric data provided below, calculate the initial, direct illuminance at working plane height, both at 1m and 2m horizontal spacing from the uplighter.

You may assume the following information: Ceiling reflectance: 0.7Wall reflectance: 0.5Mounting height: 1.8mCeiling height: 3.0m

4.14 Review Questions

1. The inverse square law uses a cosine correction for the angle of light incidence. Why is the correction necessary and between what two lines is it measured?

2. List the suggested steps in applying the inverse square law.

3. Explain briefly, what is meant by a ‘Cone diagram’ and produce a simple sketch to explain the term ‘Beam angle’.

4. Write down the Lumen method formula.

5. Define the term Utilisation Factor (UF).

6. What are ‘Distribution Factors’, and why are they important?

7. Write down the equation for ‘Room Index’ and explain why the room index affects the value of UF.

8. What is mean by ‘Uniformity’ for a lighting installation?

9. Explain the term ‘SHR MAX’ and its application.

10. When can the transverse spacing increase beyond SHR MAX?

11. What is meant by the term ‘Maintained Illuminance’?

12. List the four factors that combine into the overall maintenance factor for an installation.

13. The CIBSE Code for Interior Lighting makes recommendations for ‘Installed PowerDensity’. What units are used and what does the ‘power’ value include?

14. The method of illuminance calculation presented for uplighter design, separates the light into two components. What are they?