# Glare from windows: current views of the problem

Pierrette Chauvel, J.B. Collins, Robert Dogniaux, J. Longmore

► To cite this version:

Pierrette Chauvel, J.B. Collins, Robert Dogniaux, J. Longmore. Glare from windows: current views of the problem. Lighting Research & Technology, 1982, 14 (1), pp.31-46. 10.1177/096032718201400103 . hal-04898515

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**Summary** This paper discusses daylight glare as a source of visual discomfort in terms of glare from the unobstructed sky and not glare related to direct or reflected sunlight. There is a difference between the glare experienced from a window and the glare experienced from a large source of artificial light of the same subtended area as the sky, due to the psychological differences in the visual content of the field of view. There is also a difference in the discomfort glare produced by one small source or a number of small sources and a source with the same glare index subtending a large solid angle, due to the effect of the larger source on the adaptation level of the visual mechanism. The paper reviews the laboratory studies using artificial light sources of large area which were carried out in England and the USA and also the studies using daylight seen through real windows which were carried out in France and in England independently. The link between the practical studies and the laboratory studies is indicated and the derivation of quantitative requirements is shown. The analysis of the theoretical results indicates the effect of the various parameters involved. The conclusion is that discomfort glare from a single window (except for a rather small one) is practically independent of size and distance from the observer but is critically dependent on the sky luminance. Practical guidance is given on the design of windows and their surroundings to reduce the problems of glare from the sky, which is otherwise certain to be uncomfortable for a very large part of the year. The requirements for the balance of interior and exterior luminances are discussed, and a method of calculation and its practical application is put forward.

# Glare from windows: current views of the problem

P. CHAUVEL, J. B. COLLINS, R. DOGNIAUX
and J. LONGMORE

## 1 Glare as a source of visual discomfort

The two most important functions of a window are to admit light into an interior and to provide a view out. This paper considers the glare discomfort arising from the direct view of the sky.

To fulfil the first of these functions most effectively throughout most of the working hours in a year, the usual design principle is to provide an opening to allow light from an adequate area of unobstructed sky to enter the interior. As a consequence of this, the window constitutes a light source which may subtend quite a large solid angle at the eye, depending on how close the observer is to the window. The luminance of the sky visible through the window may rise to 10,000 cd/m² even on overcast days and may be several times greater than this if bright sunlit clouds are seen, even though no direct sunlight may be entering the room.

Such a source is liable to be seen directly or at one side of the line of sight of a person in the interior,

and therefore more likely to give rise to disability or discomfort glare than artificial lighting sources which are usually mounted overhead. In all the great classical periods of architecture this problem has been appreciated and fenestration designs have been concerned with the amelioration of glare effects.

It has been possible for the past 50 years to quantify disability glare in terms of the reduction of contrast produced by the veiling glare due to a given illuminance at the eye from a glare source at a given displacement from the line of sight. Fischer¹ has studied this aspect in relation to the view towards windows experimentally, and van Ierland² has related these observations to the theoretical relationships of disability glare to derive provisional criteria, but only comparatively recently has it been possible to link laboratory studies of discomfort glare from large sources with the discomfort due to glare from windows.

The basic studies on discomfort glare by Luckiesh and Guth³, and by Petherbridge and Hopkinson⁴ examined the effects of source and background characteristics for relatively small sizes of sources and produced formulae which appeared to describe the relationships up to a size which subtended a solid angle on the eye in the region of 0.01 steradian. There appeared to be some evidence that as the source size increased above this value, the glare did not increase to the extent predicted. This seemed likely to be due to the effect of the glare source in occupying a large part of the visual field

<footnote>MMe. Chauvel is with the Centre Scientifique et Technique du Batiment, France; Mr. Collins recently retired from the Building Research Establishment of the DoE, Garston, Watford; M. Dogniaux is with the Institut Royal Meteorologique de Belgique, Belgium; and Mr. Longmore is with the Bartlett School of Architecture and Planning, University College, London.</footnote>

<footnote>The paper was prepared at the request of the CIE Technical Committee 42, and was first received on 15 April 1981 and in revised form on 31 March 1982.</footnote>
raising the adaptation level of the eye, thus reducing the visual response and the glare sensation and reducing the contrast effect.

The other consequence of the source occupying a large part of the visual field is that different parts of its area have different weightings by the 'position factor' which evaluates the effect of a small glare source seen off the direct line of sight. It would be clearly inaccurate to use such a position factor which merely related to the position of the centroid of the large area.

The laboratory experimental work to discover how to make appropriate allowance for the effect of large areas in a prediction formula, and the observations of sky through windows to interpret the laboratory data in terms of practical design are described in the following section.

## 2 Experimental results

### 2.1 Laboratory studies

Studies at the Building Research Station in England and at the Cornell University in the USA⁵ were carried out by observing a large illuminated diffusing screen set in a separately illuminated white surround extending to the limits of the observer's view. The source could be extended to occupy this whole field of view by an arrangement of plane mirrors, and in the other direction of magnitude could be reduced to subtend $10^{-3}$ steradians by appropriate masking of the luminous area. The source luminance could be varied between 3.5 and 15000 cd/m². Settings of source luminance for different source sizes with various background luminances were made using the multiple criterion method* following adaptation to the scene.

As a result of these experiments, it was proposed that the most practical way to take account of the problems of adaptation and of position in the field of view was to modify the original BRS glare formula so that the prediction of glare from large sources could be aligned with the prediction of glare from small sources. The modifications which were made empirically to give a best fit to the data produced a formula, subsequently known as the 'Cornell formula'. This gave G, the glare constant as

$$G = K \frac{L_s^{1.6} \Omega^{0.8}}{L_b + 0.07 \Omega^{0.5} L_s} \quad (1)$$

where K is a constant depending on the units and where $L_s$, $L_b$ and $\Omega$ are respectively the source luminance, the surround luminance and the solid angular subtense of the source at the eye in exactly the same form as is the BRS formula for small sources. $\Omega$ is the solid angular subtense of the source modified for the effect of the position of its elements in different parts of the field of view in

<figure><img src="image_2.png" /><figcaption>Fig. 1. Semi-sinusoidal (cylindrical) projection of field of view with allowance for influence of position of glare source on discomfort. Droop lines are shown defining horizontal edges in planes at right angles and parallel to the direction of view.</figcaption></figure>

the way put forward by Petherbridge and Longmore⁶. This is simply evaluated by referring to a diagram such as Fig. 1, from which $\Omega$ can be determined from the angles subtended in the horizontal and vertical directions by the source in relation to the direction of view.

The denominator of the expression indicates the effect of source luminance and size in adding to the surround luminance to increase the adaptation of the eye and reduce the glare effect of the source.

$$\text{Glare Index for small sources} = 10 \log \Sigma G \quad (1a)$$

### 2.2 Observations of glare from windows

#### 2.2.1 Studies in England

The use of the 'Cornell' glare formula was advocated for the prediction of glare from windows following an analysis of the laboratory data in 1960, but field studies to support these proposals were not reported until 1970⁷,⁸.

A series of windows in different buildings was assessed for glare under different sky conditions by teams of observers using the multiple criterion scale and also separate assessment of acceptability of the prevailing level of discomfort for the purpose of the interior. (It was expected for instance that a different degree of glare would be acceptable in a hospital ward from that in an office.)

At the time of the observation, physical measurements were made which enabled the predicted glare index to be calculated, and the correlation between the predictions and observations was determined. It was found that the correlation was not as good as that obtained in studies on glare from artificial lighting, which was expected from comments by observers during their assessments and by other workers⁹, ¹⁰, ¹¹ which indicated that many factors, particularly those

<footnote>* The multiple criterion method developed by Hopkinson⁴ involved the observer adjusting the surround luminance to achieve (in this case) the border line conditions between imperceptible and perceptible glare, acceptable and unacceptable glare, comfortable and uncomfortable glare, tolerable and intolerable glare.</footnote>
associated with the appearance of the window, the view outside, the degree of specular reflection from interior surfaces (eg shiny floors, table tops etc) and the surroundings to the window (eg curtains and the form of reveals) affected judgements of the discomfort produced in daytime. Nevertheless, the correlation was sufficient to enable two important conclusions to be drawn from this study. These were:

(1) the degree of discomfort glare due to the sky seen through a window can be predicted from a glare index based on the Cornell large source glare formula

(2) there appears to be a greater tolerance of mild degrees of glare from the sky seen through windows than from a comparable artificial lighting situation with the same value of glare index, but this tolerance does not extend to severe degrees of glare.

A numerical relationship for the second of these two conclusions was derived from regression curves of observations of criterion of discomfort against glare index plotted on the same scale as for the relationship found for artificial lighting. This gave the relationship set out in Table 1 below, which can be expressed by the equation:

$$ \text{DGI (Daylight Glare Index)} = \frac{2}{3} (\text{IES Glare Index} + 14) \quad (2) $$
for values up to 28.

<table><caption>Table 1 Comparison of IES Glare Index for artificial lighting with daylight glare index for similar criteria of discomfort.</caption><thead><tr><th>Glare criterion corresponding to mean relation</th><th>IES Glare Index (IES GI)</th><th>Daylight Glare Index (DGI)</th></tr></thead><tbody><tr><td rowspan="3">Just imperceptible</td><td>10</td><td>16</td></tr><tr><td>13</td><td>18</td></tr><tr><td>16</td><td>20</td></tr><tr><td rowspan="3">Just acceptable</td><td>19</td><td>22</td></tr><tr><td>22</td><td>24</td></tr><tr><td>25</td><td>26</td></tr><tr><td>Just uncomfortable</td><td>28</td><td>28</td></tr><tr><td>Just intolerable</td><td>28</td><td>28</td></tr></tbody></table>

The comparison of daylight glare indices, given above with the recommended IES glare indices and the values corresponding to the criteria of acceptability for the function of the interior recorded by the observers, led to the proposals of limiting daylight glare indices for a number of different interiors. A further set of observations in buildings was carried out to validate these recommendations, and the limiting values finally selected were published in the IES Code for 1973 and repeated in the IES Code for 1977.

With the intention of providing a tabular method for calculation of the daylight glare index in a similar form to the tables provided for the IES Glare Index for artificial lighting, a computer program was written to give Glare Index values for windows of different area seen at different distances in rooms with different average surface reflectances

when the part of the sky seen through the window had different luminance values.

The finding of the laboratory work that area subtended by a large source has little influence on the glare which it causes was confirmed by these calculations to be true over a wide range of conditions, which meant that window size and observer distance could be ignored for the purpose of giving general design guidance, provided that the window area was greater than one or two per cent of the floor area of the room which it lit.

The larger the window in a given room the higher will be the surround luminance and, for a given observer position, the higher will be the adapting effect on the eye. At a point further from the windows, the angular subtense of the window is less, but the surface luminances and hence the adapting effect of the source are also less. The reflectances of room surfaces have a significant influence on the glare experienced, but by far the greater influence is produced by sky luminance.

The consequences of these results on the provision of design guidance on fenestration to minimise sky glare are shown in Section 5.

### 2.2.2. Application of "Cornell" formula to prediction techniques

During the work on modification of daylight glare prediction techniques based on the small source (BRS) formula to accord with the 'Cornell' formula, it became apparent that the resultant Glare Index values were approximately constant, independent of window size for a given set of conditions of sky luminance, room dimensions and interior surface reflectances. The increased adaptation effects due to increasing window size tended to balance out the effect of window size.

Calculations were made for square windows of varying sizes from 0.3m × 0.3m to 5m × 5m viewed from a perpendicular distance of 6m from the bottom corner of the window in a room with dimensions 12m × 12m × 6m. The room dimensions were large in order to accommodate the range of window sizes. Two values of average reflectance of the interior surfaces, 0.4 and 0.6 were incorporated, together with five values of sky luminance, viz. 1713, 3426, 5139, 6852 and 8565 cd/m²*. A series of calculations was also made for a room with dimensions 6m × 6m × 3m for an average reflectance of 0.4 and average sky luminance of 1713 cd/m² over the range of window sizes from 0.3m × 0.3m to 2m × 2m viewed from 6m.

In these calculations, the terms in the 'Cornell' large source formula (see Equ. 1) were as follows:

$L_s$ (sky luminance visible through the window) based on:

<footnote>* These luminances have been converted from the original values in ft.L. In this paper the data has been adjusted to accord with rounded SI values, 1600, 3200, 4800, 6400, 8900 cd/m², and the glass transmission changed from 0.92 to 0.9.</footnote>
(1) the average luminance of the sky

(2) the C.I.E. overcast sky luminance distribution

$$L_{\theta} = \frac{L_{z}(1 + 2 \sin \theta)}{3}$$

where $L_z$ is the luminance at the zenith ($L_z = 1.29 \times$ average luminance) and $L_\theta$ is the luminance at an elevation of $\theta$° above the horizontal. $\theta$ was taken to be the angle of elevation of the centre point of the window to give the approximate average luminance of the patch of visible sky. (This assumes a linear relationship of sky luminance with angle of elevation over the range of angles used).

(3) the sky luminance was modified by a factor of 0.92 to allow for a glazing transmission loss corresponding to clean clear polished plate glass at normal incidence.

$\Omega$ (weighted solid angle). This allows for the position effect in the field of view and was derived directly from the Petherbridge solid angle diagram (Fig. 1).

$L_b$ (background luminance). This was calculated using the BRS nomograph¹² for the average internally reflected component of daylight factor. For each average sky luminance value, the background luminance was calculated for various window sizes and average reflectances of 40 per cent and 60 per cent, regarded as the lowest and highest values expected under normal conditions.

$\omega$ (solid angle subtended by patch of visible sky). This was derived directly from the semi-sinusoidal Waldram solid angle diagram (Fig. 2).

The results of the calculations are given in Figs. 3 and 4 for average reflectance of 0.4 and 0.6 respectively.

A study of these data indicates that:

(1) for any fixed set of room dimensions, interior surface reflectances and sky luminance, the

<figure><img src="image_3.png" /><figcaption>Fig. 2. Semi-sinusoidal (cylindrical) projection showing droop lines defining horizontal edges in planes at right angles to direction of view.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 3. The relationship between daylight glare index and window size for sky luminances between 1600 and 8900 cd/m². The window is viewed from a perpendicular distance of 6m in a room of dimensions 12m x 12m x 6m. Results for average reflectance of 0.4.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 4. Results (see Fig. 3) for average reflectance of 0.6.</figcaption></figure>

predicted level of glare discomfort is reasonably constant (± 0.5 Glare Index Units) for all source sizes greater than approximately 2 per cent of the floor area.

(2) this means that for all practical daylighting situations the space has a relatively fixed glare character.

(3) variation of the average reflectance of the room surfaces within a range normally encountered only
gives rise to approximately one Glare Index Unit variation.

(4) variation in sky luminance over a wide range of conditions (1600-8900 cd/m²) gives rise to a range of approximately four Glare Index Units.

The observations suggested that a reappraisal could be made of the current procedures and recommendations for designing to limiting daylight glare indices. It appeared that the usually accepted important parameters—source size, surface reflectance, distance of window from viewing position—produced only marginal variations in the predicted glare index.

The variable of consequence in glare discomfort appeared to be the luminance of the sky as seen through the windows, with the special significance that the sky luminance (and hence the daylight glare index) varies with time. Thus the principal means of meeting a specified limiting daylight glare index is by limiting the luminance, or visibility of the sky as seen through the window, by permanent means or by temporary means such as adjustable blinds or curtains.

### 2.2.3 A study in France (⁹, ¹⁰)

A study of discomfort induced by seeing the sky directly through the windows and of uncomfortable glare by daylight was carried out in one of the C. S. T. B. Laboratories. Observers, set in different situations assessed the discomfort in each case. Those various situations were selected in order to study the influence of:

(1) sky luminance

(2) window dimensions and shape

(3) luminance contrast between the sky and the inside of the window wall.

The room was facing north, which made it possible to present the observer with a real sky without introducing the sun. Three categories of skies were worked out:

(4) dark overcast skies

(1100 cd/m² < Lm < 2200 cd/m²)

(5) bright overcast skies

(2200 cd/m² < Lm < 5000 cd/m²)

(6) blue skies (1900 cd/m² < Lm < 3700 cd/m²)

The observer was sitting facing a window, two and a half metres away from it. Movable screens covered the lab window wall, therefore windows of different areas and shapes were presented during the same assessment session. Using electric lighting, it was also possible to light the inside of the window wall and thus to change the contrast between the sky and the surroundings of the windows. It was also possible to screen the windows with a thin curtain which reduced the sky luminance to about one half.

The study was carried out in two stages:

#### First Stage

The observer was successively presented with each window of Fig. 5. Through the window, he could see an unobstructed view. The average luminance of the

<figure><img src="image_6.png" /><figcaption>Fig. 5. Patterns of the windows. (A, B, C, D, E, F, and R<sub>A</sub> with electric lighting. G, H, I, and R<sub>S</sub> without electric lighting.)</figcaption></figure>

meadows and trees was roughly equal to one-tenth of the average luminance of the part of the sky seen through the windows.

For each window presented the observer had to assess the discomfort with the help of a scale with five points:

1 — not uncomfortable

2 — slightly uncomfortable

3 — rather uncomfortable

4 — very uncomfortable

5 — extremely uncomfortable

Twenty-five subjects took part in the experiment, each taking part in three assessment sessions (one for each category of sky). For an analysis of the results only 55 sessions could be used, the others were not to be taken into account because of the variability of the sky conditions.

So as to control the possible effect of the presentation order on the subjects' assessments, four series of presentations had to be undertaken (see Table 2). The results showed that the assessments are more severe after seeing the windows with electric lighting (series 1 and 3), ie when beginning with the less uncomfortable situations.

The most striking result is the difference between the three categories of skies. In Table 3 the distribution of the observers' answers can be seen; the differences are all statistically significant.

As regards the different windows the assessments do not always enable us to assert that the differences are significant.

For instance:

**Area effect:** Window A is less uncomfortable than window F, but there is no significant difference between windows F and C

**Shape effect:** There is no significant difference between windows D, F and E
<table><caption>Table 2. Order of presentation for the four series of assessments.</caption><thead><tr><th colspan="10">with electric lighting</th><th colspan="6">without electric lighting</th></tr><tr><th>Series 1</th><th>R<sub>A1</sub></th><th>A</th><th>B</th><th>C</th><th>D</th><th>E</th><th>F</th><th>R'<sub>A1</sub></th><th>R<sub>S1</sub></th><th>G</th><th>H</th><th>I</th><th>K</th><th>R'<sub>S1</sub></th></tr></thead><tbody><tr><th>Series 3</th><th>R<sub>A3</sub></th><th>E</th><th>F</th><th>C</th><th>A</th><th>D</th><th>B</th><th>R'<sub>A3</sub></th><th>R<sub>S3</sub></th><th>K</th><th>H</th><th>I</th><th>G</th><th>R'<sub>S3</sub></th></tr></tbody></table><table><thead><tr><th colspan="10">without electric lighting</th><th colspan="6">with electric lighting</th></tr><tr><th>Series 2</th><th>R<sub>S2</sub></th><th>C</th><th>H</th><th>I</th><th>K</th><th>R'<sub>S2</sub></th><th>R<sub>A2</sub></th><th>A</th><th>B</th><th>C</th><th>D</th><th>E</th><th>F</th><th>R'<sub>A2</sub></th></tr></thead><tbody><tr><th>Series 4</th><th>R<sub>S4</sub></th><th>K</th><th>H</th><th>I</th><th>G</th><th>R'<sub>S4</sub></th><th>R<sub>A4</sub></th><th>E</th><th>F</th><th>C</th><th>A</th><th>D</th><th>B</th><th>R'<sub>A4</sub></th></tr></tbody></table>

<table><caption>Table 3 Distribution (per cent) of the responses of subjects for the three types of skies, all windows compounded.</caption><thead><tr><th rowspan="2"></th><th colspan="3">Discomfort scale points</th></tr><tr><th>Points 4 and 5 per cent</th><th>Points 2 and 3 per cent</th><th>Point 1 per cent</th></tr></thead><tbody><tr><th>Bright overcast sky</th><td>16</td><td>65</td><td>19</td></tr><tr><th>blue sky</th><td>8</td><td>62</td><td>30</td></tr><tr><th>dark overcast sky</th><td>4</td><td>47</td><td>49</td></tr></tbody></table>

<table><caption>Table 4 Rank order of the windows (from the less to the more uncomfortable) according to C.S.T.B. study and to G<sub>N</sub> formula</caption><thead><tr><th>Rank Order</th><th>C.S.T.B. Study</th><th>G<sub>N</sub> Formula*</th><th></th></tr></thead><tbody><tr><td>1</td><td>A</td><td>A, G</td><td>DGI = 24</td></tr><tr><td>2</td><td>D, E, F, G</td><td>B, E</td><td>25</td></tr><tr><td>3</td><td>I, Ra</td><td>D, F, I</td><td>26</td></tr><tr><td>4</td><td>B, C, H</td><td>Ra, C, H</td><td>27</td></tr><tr><td>5</td><td>K, Rs</td><td>K, Rs</td><td>28</td></tr></tbody></table>

$$G_N = 0.48 \frac{L_s^{1.6} \Omega^{0.5}}{L_b + 0.07 \omega^{0.5} L_w} \quad (1) \text{ and}$$

$$DGI = 10 \log \sum G_N \quad (\text{See Appendix 1.3})$$

Contrast effect: Windows G and R<sub>a</sub> are less uncomfortable than windows H and R<sub>s</sub>, respectively.

Still the rank order in Table 4 can be proposed.
The main difference between the two rank orders occurs for window B. This window is in our opinion much more uncomfortable than indicated by the formula because of its special shape.

On the other hand, the values of DGI obtained are higher than those expected as regards the experimentation. Perhaps for real sky and real view, the subjects' assessments are less severe.

## Second Stage

The study was carried on taking into account the first results. The main purpose was to make a thorough analysis of the role played by the luminance contrast between the sky—seen through a curtain or not—and the interior side of the window wall; its luminance was increased by a variable amount of electric lighting (from 200 to 1500 lux, on a light grey wall, ρ = 0.7).

Only window K, one of the most uncomfortable windows of the first stage, was used. The observer, seated in the same position as during the first

<footnote>* values for Ls = 5078 cd/m²
ie for a CIE overcast sky of 28000 lux (average luminance 8900 cd/m²)</footnote>
stage, was presented with the window

(1) with or without curtain

(2) with or without electric lighting on the surroundings.

Another window of large dimension ($L = 9m^2$), which had not been used during the first stage, was added to this experiment. This window was shown without electric lighting, but with or without curtain.

In each situation, the observer had to answer six questions; the first five of them had to do with the assessment of the *luminosity* of the sky, of its surroundings, of the experimenter's features; the sixth question had to do with the assessment of the pleasantness of the situation.

...

6) On the whole does your situation facing the window seem

<figure><img src="image_7.png" /></figure>

very pleasant

very unpleasant

The skies considered here were divided into four categories, two for the blue skies (B), two for the grey skies (G).

Categories $B_1$ or $G_1$ $2000 cd/m^2 <$ mean luminance $< 4000 cd/m^2$

Categories $B_2$ or $G_2$ mean luminance $> 4000 cd/m^2$

An analysis of the results showed that there was no significant difference between the four categories of skies.

<table><caption>Table 5 Subjects' answer for question 6: mean score on the 'seven points' scale.</caption><thead><tr><th></th><th>window</th><th>mean score</th></tr></thead><tbody><tr><td>L</td><td>with curtain</td><td>2.5</td></tr><tr><td>K</td><td>with curtain<br>without electric lighting</td><td>3.5</td></tr><tr><td>K</td><td>with "1500 lux" electric lighting<br>without curtain</td><td></td></tr><tr><td>L</td><td>without curtain</td><td></td></tr><tr><td>K</td><td>with "1000 lux" electric lighting<br>without curtain</td><td>4.0</td></tr><tr><td>K</td><td>with "500 lux" electric lighting<br>without curtain</td><td></td></tr><tr><td>K</td><td>without electric lighting<br>without curtain</td><td>5.0</td></tr></tbody></table>

As regards the answers to the first five questions the larger number of significant results shows that the subjects' judgements concerning the photometry of the room are on the whole correct. Less significant results were obtained from question 6, nevertheless the Friedman tests enabled us to suggest the following rank order for the windows.

Taking into account that the curtain divided sky luminance by two, it seems correct that windows are more pleasant with curtain than without. But one must take notice that:

(1) Window L, the larger one, is more pleasant than window K (with or without curtain for both)

(2) Window K with electric lighting is more pleasant than without, but the difference between a small amount of electric lighting (100 cd/m²) and twice or three times more is not important when the difference between with and without electric lighting is larger.

To sum up both parts of the study, the most important parameters are:

(1) the luminance of the glaring source, but it is necessary to reach a very low level—2000 cd/m²—to improve the situation.

(2) the luminance contrast between the sky and surroundings, but a small amount of electric light, on a small area, seems enough.

## 3 Quantitative requirements for reducing discomfort glare from windows

As a consequence of the laboratory studies reported in Section 2, it appears to be expedient for reducing discomfort glare from windows to have recourse to a compromise between two following solutions:

(1) modification of the size and of the position of the windows in the facade for satisfying the recommended daylight glare index;

(2) reducing the glare due to the high luminances in the visible areas of the sky by an adequate balance of luminances in the visual field provided by permanent supplementary artificial lighting (PSALI).

The method of calculation for satisfying these quantitative requirements will be developed in the Appendix.

### 3.1 Glare index values

The calculation referred to above (in Section 2.2.2) indicated that for a given sky luminance and given average reflectance of room interior surfaces, a window would cause a given degree of glare related to a particular value of glare index¹³, whatever its size (as long as the area was greater than one or two per cent of the floor area of the room) and at whatever distance it was observed.

The glare discomfort experienced in a given room varies during the day and the year as the sky luminance varies, but frequency with which the glare from windows is likely to exceed certain
values can be estimated from the predictions of frequency of occurrence of corresponding values of illuminance out of doors from the sky (which can be related to average sky luminance).

The "standard" sky luminance for calculating daylight glare index in United Kingdom was chosen as the one which is only exceeded for 25 per cent of the working hours through a whole year in the South of England¹⁴. This is 8900 cd/m², which is the average sky luminance corresponding to an outdoor diffuse illuminance of 28 klux. Table 6 gives the daylight glare indices for windows in rooms with average surface reflectances of 0.4 and 0.6 for the occasions when the sky luminance reaches this value of 8900 cd/m². These glare indices will therefore not be expected to be exceeded for more than 25 per cent of the yearly working hours.

The average room surface reflectance values of 0.4 and 0.6 have been selected as representative of the highest and lowest values found in normal practice. It will be seen that the result of changing reflectance by this amount represents a change in glare index of 2, and it should be noted that, even with the lighter room surfaces, the limiting daylight glare indices recommended in the IES Code for most working areas will be exceeded. The only areas for which a limiting daylight glare index as high as 24 is recommended are circulation, assembly, reception and customs areas, auditoria and waiting rooms.

As the frequency of occurrence of other values of outdoor illuminance are known for various parts of the British Isles¹⁴, they can be referred to values of average sky luminance (although it is known in

practice that an overcast sky of uniform luminance is rare and for the luminance distribution standardised by the CIE for an overcast sky, the luminance near the horizon is only one half of the average value). Table 7 has therefore been constructed to show the percentage of annual working hours for which different values of daylight glare index will be exceeded in the South of England. For example, in the room with average surface reflectance 0.6, a daylight glare index of 24-1.5 or 22.5 will be exceeded for 54 per cent of the working hours in a year.

It should be noted that the sky luminance given is the outdoor luminance. Seen through clear glass, this will be reduced by 10-15 per cent. This will only make a small change in the glare index.

For spaces with large ceiling height (greater than 4m), conditions may arise in which the glare index is increased from the values quoted above by 1-2 units.

Note that the above evaluations apply to the 'worst condition' situation in a space, ie a single window directly ahead along the general line of sight: this type of 'worst condition' design criterion is that usually employed in discomfort glare work. Further, the work is not directly applicable to a window in a plane parallel to the line of sight: detailed data for this situation are not available at present, but for most people the discomfort glare will be less than that indicated for a window perpendicular to the line of sight⁷.

## 4 Practical design guidance for control of glare from windows¹³

### 4.1 Generalities

Predictions using the large source formula indicate that the discomfort glare index in interiors from windows is reasonably constant for all room sizes and windows greater than 1-2 per cent of the floor area. This means that a room or space has a relatively constant glare character for all practical daylighting situations.

The glare index values given in Table 6 will cover about 75 per cent of the normal working year based on a working day of 09.00 to 17.30. Under most circumstances, if these are greater than the recommended limiting glare indices for the location, some amelioration will be required, but the frequency of occurrence of some activities may allow a lower value to be considered (see Table 1).

### 4.2. Ameliorative designs excluding artificial lighting

The major controlling factor is the window luminance. There are several ways of dealing with this and at the same time retaining view out and the essential attributes of natural lighting. In some instances these can be treated as temporary measures for use only on the brightest days—such as curtains or blinds under the control of the users, whereas structural details impose permanent conditions. Examples of these ameliorative measures are:

<table><caption>Table 6 Daylight glare indices for average sky luminance of 8900 cd/m².</caption><thead><tr><td>Average reflectance of room surfaces</td><td>Daylight glare index</td></tr></thead><tbody><tr><td>0.4</td><td>26</td></tr><tr><td>0.6</td><td>24</td></tr></tbody></table>

<table><caption>Table 7 Daylight glare indices for various sky luminances</caption><thead><tr><td>Horizontal illuminance from whole sky (lux)</td><td>Average sky luminance cd/m²</td><td>Proportion of annual working hours exceeded per cent</td><td>Reduction in daylight glare index</td></tr></thead><tbody><tr><td>28 000</td><td>8 900</td><td>25*</td><td>0</td></tr><tr><td>20 000</td><td>6 400</td><td>38</td><td>0.5</td></tr><tr><td>15 000</td><td>4 800</td><td>54</td><td>1.5</td></tr><tr><td>10 000</td><td>3 200</td><td>68</td><td>2.5</td></tr><tr><td>5 000</td><td>1 600</td><td>87</td><td>4.0</td></tr></tbody></table>

<footnote>*This refers to the more recent data in ref. 14 and is greater than the value in ref. 13 derived from the 1933-1939 data.</footnote>
(1) A translucent curtain or blind (eg 'Open mesh plastics') may be fitted internally or externally to the window.

(2) Louvred or slatted blinds or fins, vertical or horizontal, may be fitted internally or externally. However, unless these are adjustable or removable they will restrict daylight penetration into the interior at all times. External screens can be effective in the control of solar gain. Retractable screens are particularly useful in that they need only be lowered on days of high sky luminance.

(3) Overhangs, canopies, awnings etc can reduce glare by cutting down sky view and reducing contrast, but daylight penetration into the interior is also reduced unless ceilings with high reflectances aided by reflections from light coloured external pavings are included in the design.

(4) If low transmission glass is used a decreased sky luminance is obtained but this, of course, permanently reduces the level of daylight admitted by the window.

When the luminance of the window is reduced by a known amount, eg by a factor proportional to the relative diffuse transmittance of the device being used, the resulting reduction in glare index can be obtained from Table 7.

A limited mediating effect is obtained by the use of high internal surface reflectances: as can be seen from Table 6, a reduction of two glare index units (to the nearest whole number) is obtained by a change from 0.4 to 0.6 in the average reflectance. Light coloured matt walls and ceilings produce an increase in field luminance which results in a reduction of contrast; conversely dark coloured walls, curtains, columns etc seen against the bright sky often cause discomfort through high contrast demarcations in the field of view.

There are other methods of ameliorating the discomfort due to sky glare which, although they cannot be defined on a quantitative basis, can be dealt with in a qualitative way. Many of these methods are concerned with the relationship of a window to the adjacent walls which affects the contrast between the bright sky and the near surrounding visual field. Placing the windows so that the immediate surrounding surfaces have a high luminance can give rise to a useful reduction in discomfort. Care should be taken, however, to ensure that these surfaces themselves are not too bright or shiny, or they themselves will form a secondary source of glare.

The use of windows in more than one wall can have substantial advantages. In addition to increasing the general surround adaptation luminance, there can be a contribution to the luminance of the window wall which, as discussed in the last paragraph, reduces the discomfort glare by decreasing the contrast with the sky.

The provision of light coloured matt finish window reveals and frames can reduce glare discomfort, and detailing which reduces sharp edge contrast effects also has a significant value in reducing glare

discomfort—sometimes up to two glare index units. Such light coloured splayed sills, heads and reveals can help by bridging the contrast between sky luminance and the comparatively low luminance of the window wall.

Glazing bars can also cause an annoying contrast effect when they are wide and or of low reflectance; but if they are white or light coloured and tapered there can be a reduction in glare discomfort.

A substantial transom when seen against bright sky can be irritating, particularly if it obscures the sky line from either a standing or particularly a sitting position.

The sill position is relevant in window design when the exterior view is of interest. A low sill can significantly increase the general illumination in an interior and consequently the adaptation level of the eye, thereby reducing the discomfort glare.

### 4.3. Ameliorative design combining daylighting and artificial lighting

Judicious use of artificial lighting during daylight hours can also help. Artificial lighting on surfaces surrounding the window, particularly at the head, can reduce the contrast between the brightness of the window and the window wall. As it is shown in Section 2.2.3 a small amount of electric lighting on the immediate surrounding (500 lux on a narrow belt of light coloured surface) may be enough to improve the situation of the user. Artificial lighting can also be used selectively to increase the general illumination of the interior or to increase the illuminance on tasks at the back of the room. Contrasts will be reduced and the glare discomfort from the window will be lessened.

Fig. 6 illustrates some of these ameliorative designs without or with electric lighting.

### 4.4. Glare prediction in interiors with combined daylighting and artificial lighting installations

The use of artificial lighting in an interior in which there is daylight produces a very complex visual environment and the assessment of discomfort glare conditions for the combined situation cannot be expressed simply in a predictive equation. In addition to there being less uniformity of the luminance of surfaces, and also variation with position in the interior, there is the complication brought about by the changing luminance of the sky relative to the luminance characteristics of the artificial lighting. There are some circumstances where one component of a combined lighting installation can raise the adaptation level and so mitigate a discomfort glare effect of the other component which by itself is beyond the limit of acceptability, but it is not possible to define these circumstances at the present time. However, studies have been made (discussed in an unpublished report to the Department of the Environment by Ralph Hopkinson and Newton Watson in 1973) which enables recommendations for design prediction to be given with adequate accuracy for practical use.
<figure><img src="image_8.png" /></figure>

A This unmodified window gives good light to the rear of the room but it will be glaring on bright days.

<figure><img src="image_9.png" /></figure>

B The splayed sill can help by buffering contrast between sky luminance and the comparatively low luminance of the window wall.

<figure><img src="image_10.png" /></figure>

C Overhangs reduce daylight penetration but if the ceiling is of a high reflectance and is aided by reflections, say from light coloured external paving, sky glare is reduced.

<figure><img src="image_11.png" /></figure>

D Splaying the head as well as the sill further reduces contrast with the window wall.

<figure><img src="image_12.png" /></figure>

E Screening with translucent blinds can reduce the zone of high sky luminance (2) while still allowing view out (1).

<figure><img src="image_13.png" /></figure>

F Artificial lighting can be used to illuminate the window surrounds and so reduce glare potential by reducing the contrast between the sky luminance and the luminance of the window wall.

<figure><img src="image_14.png" /></figure>

H Section showing vertical limitation of sky view. External screening can be used to reduce solar gain and to limit view of high sky (2) while retaining view out (1).

<figure><img src="image_15.png" /></figure>

G Splayed window detailing, i.e. jambs, head, sills, mullions and transoms, reduce hard edge contrast.

<figure><img src="image_16.png" /></figure>

J Plan showing horizontal limitations of sky view. Sky glare can also be reduced by horizontally limiting the area of sky visible from any position in the room. One way of doing this is to fit vertical fins to the windows. These can be separate elements or integral parts of the window framing or structure.

<caption>Fig. 6. Sketches showing some windows detailing designs which have advantages for the control of glare.</caption>
A method for calculating the permanent supplementary artificial lighting illuminance is given in the Appendix to this paper.

The design recommendations are as follows:

(1) The degree of discomfort glare for the two separate lighting situations, ie artificial lighting and daylighting, should be evaluated independently.

(2) If both are within their individual limits of acceptability, the probability is that the effects of the two installations will add up in such a way that the total will still be acceptable.

(3) If each installation causes glare at a level which would be judged to be uncomfortable or intolerable, when both operate together the total effect will be worse than that of either installation alone.

(4) However, if one installation is acceptable and the other is not acceptable, the addition may result in the two together being acceptable or unacceptable, depending on the actual levels of the two individually, and particularly on the relative luminances of the two sources.

Therefore, until a practical method of predicting a single glare index for combined installations is developed it is recommended that, to ensure that the degree of glare from the two installations operating together is acceptable, each installation should be designed to be independently within acceptable limits.

## 5 Conclusions

The discomfort glare resulting from the direct view through windows has been found to vary greatly from observer to observer and also to vary with factors associated with the appearance of the window, the view outside and the surroundings, etc. Nevertheless, the formula for large area glare sources derived from the results of experiments in the laboratory, was found to produce a glare index which had a reasonable correlation with the average experience.

The 'Cornell' large source glare formula predicted that the glare index for a person looking directly at a single window was, within reasonable limits, independent of the size of the window or the position of the observer, provided the area of the window was greater than about 2 per cent of the floor area of the room which it was lighting. The glare index for these conditions therefore depended mainly on the luminance of the sky seen through the window, and to a lesser extent, on the reflectances of the room surfaces, inasmuch as they affected the background luminance to the glare source.

From data on the frequency of occurrence of different levels of sky luminance, it could be predicted that a direct view of unobstructed sky through a window in a room with an average reflectance of interior surfaces of 0.4 would be uncomfortable on at least 60 per cent of the normal working hours during the year in the UK.

Although the application of the 'Cornell' formula indicates the need for very high levels of illuminance on the working plane from artificial lighting, an effective way of increasing the background illuminance (as well as providing a better quality of daylight) is by daylighting the room from more than one side. In CSTB experiments it was shown that a moderate level of luminance on the immediate surround to the window reduced the glare to an acceptable level.

Measures for the reduction of discomfort glare to the occupants of the room which would consume less energy for artificial lighting (and probably for cooling purposes in the summer) are:

(1) The siting of work places so that there is no direct view of the sky by the occupant.

(2) The reduction of the luminance of the window by curtains, blinds or tinted glazing.

(3) The reduction of sky view by appropriate louvred blinds, overhangs, canopies, etc.

(4) The provision of light coloured surfaces around the windows and the detailing of the sill, head, reveals, frames and window bars to produce a graded contrast, rather than a sharp one, with the sky seen through the window. Examples of some of these treatments are given in Fig. 6.

Apart from these above treatments, the way in which the room is used and the amount of interest in the view through the windows will have a major influence on the feelings of glare discomfort experienced by the occupants.

These are general conclusions based on limited experimental data. There is a need to make further investigations to derive a prediction method which correlates more closely with the differing experimental results.

# APPENDIX—Method of calculation of functional illuminance

## A.1. Mathematical derivation

### A.1.1. Functional illuminance for performing visual tasks

The minimum functional illuminances $E_{f min}$ necessary for performing a number of visual tasks are recommended in the standards or codes of practice which are generally in use in different countries.

Permanent supplementary artificial lighting is generally not required when the daylight level in the worst lit working place reaches the value recommended for performing the task under the minimum standardized conditions (dull CIE overcast sky and external illuminance on an unobstructed horizontal plane of 5000 lux).

When supplementary artificial lighting is required, the maximal illuminance $E_t$ to be provided is equal to the difference between the functional illuminance $E_{f min}$ required and the minimum available daylight
illuminance: E<sub>d min</sub> available in the room near the wall opposite to the window

$$E_1 = E_{f min} - E_{d min} \qquad (3)$$

### A.1.2. Balance of luminances

The luminance balance in an interior is generally considered to be satisfactory if the luminance of surfaces near the window (say at 1m away) does not exceed five times that of surfaces most distant from the window.

To satisfy this condition, supplementary lighting is required in the darkest part of the room with a minimum illuminance of E<sub>2</sub> [lux], where:

$$E_2 = \frac{E_H}{100} \left( \frac{J_{max}}{5} - J_{min} \right) \qquad (4)$$

where E<sub>2</sub> is the supplementary artificial lighting at the darkest part of the room. E<sub>H</sub> is the external illuminance at the level of a non-obstructed horizontal plane and J<sub>max</sub> and J<sub>min</sub> are respectively the maximum and minimum daylight factors within the room expressed in per cent; J<sub>max</sub> being calculated at 1m from the window and J<sub>min</sub> at 0.6m from the opposite wall for the rooms where there are windows in only one wall.

### A.1.3. Functional illuminance for compensating sky glare

The glare due to the direct view of the sky vault is considered to be acceptable when the Glare Index at any point in a room does not exceed the maximum value recommended, according to the type of work which is done in the room.

Since glare due to the direct view of sky through a window is generally more acceptable than the glare observed in comparable circumstances when artificial light is used, the numerical relationship between the daylight glare indices DGI and those for artificial light: IES G.I derived in section 2 can be adopted.

$$DGI = \frac{2}{3} (IES G.I + 14) \qquad (2)$$

If one refers to the limiting values of glare index which are recommended for artificial lighting (IES G.I)<sub>max</sub>, this relation makes it possible to obtain the maximum values of daylight glare index (DGI)<sub>max</sub> according to the type of task to be performed.

The daylight glare is calculated by means of the following relation:

$$DGI = 10 \log \Sigma G_n \qquad (5)$$

in which G<sub>n</sub> is the glare coefficient for each of the component parts of the view through the window (sky, obstruction, ground). It is obtained by means of the 'Cornell formula' modified to take account of the view through windows for large area sources (Section 2.1):

$$G_n = 0.48 \frac{L_s^{1.6} \Omega^{0.8}}{L_b + 0.07 \omega^{0.5} L_w} \qquad (1)$$

in which:

L<sub>s</sub> is the luminance in cd/m<sup>2</sup> of the patch of visible

sky, of the obstructions and of the ground seen through the window.

L<sub>b</sub> is the average luminance in cd/m<sup>2</sup> of the interior surfaces of the room which contribute to the visual field of an occupant of the room. If the task to be performed is limited to a working table, this average will take into account the luminances of the central part; of the immediate surroundings and of the general surroundings to the task. If the task to be performed requires clear vision of a moving object, this average will take into account the luminances of all the interior surfaces of the room. In the above formula, L<sub>b</sub> is usually calculated as the luminance which if averaged over the hemisphere of view would provide an illuminance E<sub>e</sub> lux on the vertical plane of the eye, so that:

$$L_b [cd/m^2] = \frac{E_e [lux]}{\pi} \qquad (6)$$

E<sub>e</sub> is thus the indirect component of illuminance from daylight and/or artificial lighting.

L<sub>w</sub> is the average luminance of the window weighted according to the relative areas of sky obstructions and ground.

ω is the total solid angle in steradians subtended by the window.

Ω is the corrected solid angle subtended by the window, with weighting factors for different areas depending on their direction with respect to the occupant's line of sight.

p is the position factor.

$$\Omega = \int \frac{d\omega}{p^2} \qquad (7)$$

In order to reduce the glare due to the window to such a value that visual discomfort will be avoided, L<sub>b</sub> must be controlled, in such a way that:

$$DGI < (DGI)_{\max} \qquad (8)$$

To that end, the factor L<sub>b</sub> must comply with the following condition:

$$L_b > 0.48 \frac{(L_s^{1.6} \Omega^{0.8})}{10^{0.1(DGI)_{\max}}} - 0.07 \omega^{0.5} L_w \qquad (9)$$

deduced from the relations (5) and (1), the denominator of formula (1) being independent of the summation of the G coefficients.

$$\begin{align*} \text{If we set: } & a = 0.48 \times 10^{-0.1(DGI)_{\max}} \\ & b = \Omega^{0.8} \\ & c = 0.07\omega^{0.5} \end{align*}$$

and if we assume that L<sub>s</sub> is constant for each individual patch of sky or ground seen through the window, this relation becomes:

$$L_b > a \Sigma(b \cdot L_s^{1.6}) - c L_w \qquad (10)$$

### A.1.4. Balance of luminances by PSALI

If relation (10) is not satisfied by daylight, we may
(subject to the caution in Section 4.4) provide an
illuminance $E_k$ of the task by permanent
supplementary artificial lighting providing a total
illuminance $T_t$ where:

$$E_g > \frac{\pi L_6}{\rho} \qquad (11)$$

$\rho$ being the average reflectance of the surfaces within the visual field, $L_6$ given by the expression:

$$L_6 = a \Sigma(bL_s^{1.6}) - cL_s \qquad (12)$$

The corresponding maximal permanent supplementary artificial lighting illuminance $E_3$ can be deduced from the relation:

$$E_3 = E_g - E_d \qquad (13)$$

$E_d$ being calculated by means of the method recommended in CIE Publication no. 16 (E-3.2) 1970¹⁵.

The value of $E_d$ and $L_s$ are calculated on the basis of an overcast CIE sky and an external illuminance ($E_H$) on an unobstructed horizontal plane of 28 000 lux. This figure may be changed according to the external illuminance frequency distributions of the sky in other countries.

For this overcast sky, the variation of luminances with the elevation angle of the zone of the sky is given by

$$L_o = \frac{3}{7\pi} E_H (1 + 2 \sin \theta) = 0.1364 E_H (1 + 2 \sin \theta) \qquad (14)$$

in which:

$\theta$ is the angle of elevation of the examined patch of the sky

$L_o$ is the sky luminance at this elevation.

The values of the luminances at the zenith ($L_z$) and at the horizon ($L_o$) are respectively:

$$L_z = \frac{9}{7\pi} E_H = 11\,459 \text{ cd/m}^2 \text{ and} \\ L_o = \frac{3}{7\pi} E_H = 3\,820 \text{ cd/m}^2. \qquad (15)$$

For $L_w$ the average value is adopted; the angles subtended by the parts of the window below the horizontal direction of view can be seen to be generally small.

The limiting values for $a = 0.48 \times 10^{-0.1(DGI)_{max}}$ are shown in terms of IES G.I.($i_a$)$_{max}$ on the curve of Fig. A.1. This curve has been drawn from relation (2). The values for $\omega$ and $\Omega$ are shown diagrammatically, according to $H/d$ and $L/d$ in Figs. A.2 and A.3, where:

$H$ is the height of the window above or below the horizontal plane through the eyes

$L_1$ and $L_2$ are the distances between the direction of view $Oy$ and the right and on the left outermost vertical edge of the window. The view is horizontal and perpendicular to the façade from a point opposite the centre of the window or windows,

<figure><img src="image_17.png" /><figcaption>Fig. A1. Limiting values for a.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Fig. A2. Values for $\omega$.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>Fig. A3. Values for $\Omega$.</figcaption></figure>
d is the perpendicular distance from the eye to the façade.

The values of the external luminances $L_s$ should be corrected values, ie the actual values reduced to take into account simultaneously the transmission factor of the glazing, curtains, dust layer on the glass and the obstructions represented by window frames.

### A.1.5. Practical performance

The various and often contradictory requirements of a PSALI system make its design an intricate problem. The high artificial lighting levels which may be required are such that its use may depend upon economic decisions.

The recommendations set out below are therefore a compromise between desirable aims and present economic conditions, as well as a pragmatic solution related to the sky conditions which occur most frequently in Northern Europe.

The calculation of PSALI is based on a dull overcast (CIE) sky providing an external illuminance $E_H$ of 5 000 to 28 000 lux on an unobstructed horizontal plane.

Below $E_H$ = 5 000 lux, it is assumed that daylight is inadequate and that a night lighting installation is required. The luminances are determined by assuming that the eye is located at 1.2m above floor level for rooms in which the occupants are normally seated, and 1.6m above floor level for other rooms.

The value of $E_1$ is calculated by assuming that $E_H$ = 5 000 lux. $E_2$ and $E_3$ are calculated by assuming that $E_H$ = 28 000 lux.

For a permanent supplementary artificial lighting ($E_{ps}$) the greatest value of $E_1$, $E_2$ or $E_3$ will be chosen.

Where it is planned to vary the PSALI illuminance proportionally to the external illuminance by means of an automatic variable control and a photocell, the PSALI illuminance $E_{ps}$ should be adjusted between external illumination values corresponding to $E_H$ = 5 000 lux and 28 000 lux.

## A.2. Example of application

Consider a room of parallelepiped form situated in an industrial zone, where laboratory work is carried out. The dimensions are as follows (see Fig. A.4); width 7.00m; depth 5.50m; height of ceiling 3.20m. This room is daylit by four vertical windows of 2.20m in height and 1.05m each in width occupying 60 per cent of the window wall. The windows are fitted with plain glass of which the average value of corrected transmission is 0.80. The windows face on to a site where there is no obstruction.

It is desired to know the supplementary artificial lighting illuminance to fulfil the following requirements:

(1) to ensure a permanent illuminance of 500 lux on every point of the working plane at 0.85m from the ground extended to within 0.60m from the walls;

(2) to ensure a balance of luminances in the interior such that for an occupant working in a seated position, facing the window at 2.50m from it, the glare index does not exceed the value recommended for the nature of the work (in the present case $I_{ESGI}$ = 16).

### Solution

#### (a) Natural lighting

By the application of methods of calculation described in publication CIE no 16 (E-3.2) 1970, the daylight factors can be determined at reference points in the room lying on the perpendicular

<figure><img src="image_20.png" /><figcaption>Fig. A4. Example room showing dimensions and layout. (Linear dimensions in metres.)</figcaption></figure>
through the centre of the windows at the level of
the working plane (see Fig. A.4).

It is found from this that:

$J_{min} = 1.6$ per cent at 0.6m from the wall opposite
the window

$J_{max} = 10.0$ per cent at about 1m from the window
giving in the case of a reference value of exterior
horizontal illuminance (overcast sky, unobstructed
site) of 5 000 lux, the following daylight illuminance
in the interior:

$E_{min} = 80$ lux at 0.6m from the wall opposite the
window

$E_{max} = 500$ lux at about 1m from the window.

(b) Requirements for minimum functional
illuminance

The supplementary artificial lighting illuminance $E_1$ necessary to perform the required visual task at every point on the working plane, even on overcast days, can be determined by application of the method described in Section A.1.1.

Functional illuminance required: 500 lux

Minimum daylight illuminance: 80 lux

Maximum supplementary artificial lighting:

$$E_1 = E_{f \min} - E_{d \min} = 500 - 80 = 420 \text{ lux.}$$

(c) Requirements for balance of luminances

By the application of Section A1.2, the value of the supplementary artificial lighting illuminance $E_2$ can be determined which satisfies the requirement:

$$E_2 > \frac{E_H}{100} \left( \frac{J_{\max}}{5} - J_{\min} \right)$$

$$E_2 > \frac{28\,000}{100} \left( \frac{10}{5} - 1.6 \right)$$

$$E_2 > 112 \ 1x$$

(d) Requirements for the reduction of discomfort
glare

The method of Section A.1.2 can be applied to
determine the value of supplementary artificial
lighting illuminance $E_3$ satisfying the requirement
for the reduction of glare in the following manner
(see Equations 13, 11 and 12):

$$E_3 = E_g - E_d$$

or

$$E_g > \frac{\pi}{\rho} L_b$$

and

$$L_b = a \Sigma b L_s^{1.6} - c L_s$$

Values of parameters involved in these expressions

Luminance of the ground seen through the window

$$L_{\text{ground}} = 0.80 \times 0.15 \times 3820 = 458 \text{ cd/m}^2$$

adopting for the luminance of the ground 15 per cent of that of the horizon sky.

Luminance of the sky seen through the window

$$L_{\text{sky}} = \tau \frac{3}{7\pi} E_H (1 + 2 \sin \bar{\theta}_c)$$

$$ \begin{align*} L_{\text{sky}} &= \tau \times 0.1364 E_H (1 + 2 \sin \bar{\theta}_c) \\ &= 0.8 \times 0.1364 \times 28\,000 (1 + 0.662) \\ &= 5\,078 \text{ cd/m}^2 \end{align*} $$

adopting for $\bar{\theta}_c$ the mean value of the angle of elevation at which the patch of sky is seen by an observer facing the window and seated at 2.5m from it, with the eye at 1.2m from the ground, the direction of view being horizontal at 0.20m above the height of the cill, or $\bar{\theta} = 38^\circ 40' = 2\theta_c$.

Weighted mean of luminous zones seen through the
window

$$L_w = \frac{5078 \times 2.00 + 458 \times 0.20}{2.20} = 4658 \text{ cd/m}^2$$

Value of c

$$\text{for } H/d = \frac{2.2}{2.5} = 0.88 \text{ and } L/d = \frac{2.1}{2.5} = 0.84$$

The value of c corresponding to the solid angle subtended by the half glazed area of the façade seen by the observer seated in a position perpendicular to the glazing and on the axis of the façade (see Fig. A.4) is found from the graph of Fig. A.2.

$$c = 0.07 \omega^{0.5} = 0.066$$

from which it can be deduced that:

$$cL_w = 0.066 \times 4658 = 307 \text{ cd/m}^2$$

Value of $\Sigma b L_s^{1.6}$

One can determine successively from the graph of Fig. A3 giving $\Omega$ the values of b corresponding to the solid angles corrected by position factors subtended by the zones of view of the window causing glare:

(a) Ground

$$\text{for } H/d = \frac{0.2}{2.5} = 0.08 \text{ and } L/d = \frac{2.1}{2.5} = 0.84$$

$$\Omega = 0.059 \times 2 = 0.118$$

$$b_g = 0.18$$

(b) Sky

$$\text{for } H/d = \frac{2.0}{2.5} = 0.80 \text{ and } L/d = \frac{2.1}{2.5} = 0.84$$

$$\Omega = 0.237 \times 2 = 0.474$$

$$b_{\text{sky}} = 0.55$$

$$ \begin{align*} \text{Hence } b L_s^{1.6} &= b_g L_g^{1.6} + b_{\text{sky}} L_{\text{sky}}^{1.6} \\ &= 0.18 \times (458)^{1.6} + 0.55 \times (5078)^{1.6} \\ &= 456\,831 \text{ cd/m}^2 \end{align*} $$

Value of a

For an IES index of 16 for artificial lighting corresponding to laboratory work, the value of a can be found from Fig. A.1 as $a = 0.0048$
$$ \text{Value of } a\Sigma bL_s^{1.6} $$

$$ a\Sigma bL_s^{1.6} = 0.0048 \times 456\,831 = 2\,193\,\text{cd/m}^2 $$

$$ \text{Value of } L_b' $$

$$ L_b = a\Sigma bL_s^{1.6} - cL_w = 2\,193 - 307 = 1\,886\,\text{cd/m}^2 $$

$$ \text{Value of } E_g $$

$$ E_g > \frac{\pi L_b'}{\rho} > \frac{3.1416 \times 1886}{0.5} = 11\,850\,\text{lux} $$

adopting $\rho = 0.5$ as a mean reflectance of surfaces in the visual field.

$$ \text{Value of } E_3 $$

Optimum daylight illuminance in the zone occupied by the worker. (2.5m from the window).

At 2.5m, the daylight factor is $J_{2.5} = 3.5$ per cent

$$ E_d = \frac{28\,000}{100} \times 3.5 = 980\,\text{lux} $$

$$ E_3 = E_g - E_d = 11\,850 - 980 = 10\,870\,\text{lux} $$

### A.3 Conclusion

A permanent supplementary artificial lighting illuminance of 420 lux is required in daytime when the sky is overcast, in order to satisfy functional requirements for performance of the task at the point on the working plane with the least amount of daylight (at 0.60 metres from the wall opposite the window).

On the other hand, in order to satisfy the requirements for the reduction of discomfort glare and those for the balance of luminances, an average illuminance of 10 870 lux in the central zone of the room needs to be provided at all times.

#### A.3.1 Modification

The use of reflecting or absorbing glass in the windows or the interposition of a translucent curtain, although reducing the daylight illuminance in the interior, can lead to a reduction of the permanent supplementary artificial lighting illuminance compared with that required with clear glazing, at least in the central zone of the working area.

For example, in the case of glazing whose mean corrected transmission factor is $\tau = 0.40$ the daylight illuminance would be reduced by a

$$ \text{factor of } \frac{0.40}{0.80} = 0.5 $$

thus changing the required supplementary artificial lighting illuminance $E_1$ to

$$ E_1 = 500 - 0.5 \times 80 = 460\,\text{lux} \text{ and} $$

$$ E_2 > 112 \times 0.5 = 66\,\text{lux.} $$

For an office where an IES artificial lighting glare index of 19 would be acceptable (DGI = 22): a (from Fig. A.1) = 0.003.

Under these conditions for the same calculations as those carried out previously, the following values for the functions are found:

$$ E_d = 980 \times 0.5 = 496 $$

$$ L_{\text{ground}} = 458 \times 0.5 = 229\,\text{cd/m}^2 $$

$$ L_{\text{sky}} = 5078 \times 0.5 = 2539\,\text{cd/m}^2 $$

$$ L_w = 4658 \times 0.5 = 2329\,\text{cd/m}^2 $$

$$ cL_w = 0.066 \times 2329 = 154\,\text{cd/m}^2 $$

$$ \begin{aligned} \Sigma bL_s^{1.6} &= 0.18 \times (229)^{1.6} + 0.55 \times (2539)^{1.6} \\ &= 155\,181\,\text{cd/m}^2 \end{aligned} $$

$$ a\Sigma bL_s^{1.6} = 0.003 \times 155\,181 = 465\,\text{cd/m}^2 $$

$$ L_b' = 465 - 154 = 311\,\text{cd/m}^2 $$

$$ E_g = \frac{3.1416 \times 311}{0.4} = 2434\,\text{lux} $$

$$ E_3 = 2434 - 490 = 1944\,\text{lux} $$

### Acknowledgement

Some of the work described in this paper has been carried out as part of the programme of the Building Research Establishment of the Department of the Environment and this paper is published by permission of the Director.

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