Revisiting Prediction Tools for Daylight Adequacy and Its Potential Improvement

3.1. BRE formula

The average daylight factor ($$ \stackrel{-}{D}$$) of the café was calculated through the BRE formula (Equation 1) [7]. Figure 4 illustrates the hand-sketch of the space volume, materials and reflectance of the floor, wall and ceiling.

where, p_r = the mean room reflectance of the room surfaces
A_r = Total room surface area, including glass and window
θ = Angle of visible sky (measured in degrees)
A_w = Area of window
T_w= Window transmittance

Fig. 4.

Sketch of the café interior indicating surface areas and reflectance

Tregenza and Wilson [8] species 0.69 for transmittance of doubling glazing: sealed unit, clear + clear; and 4% reduction due to dirt for a commercial/rural setting. Therefore,

Transmittance of window (T_w) = 0.69 × (1 - 0.04) = 0.66

The total surface area of the room (A_r), including glazing, is 870m². The average room reflectance (p_r) is given from the equation 2.

Since there are two windows in the café, which both contribute to the daylight factor and therefore the average daylight factor for the café is the sum of the values calculated to each window. Figure 5 shows the section of the café space indicating angles measured from mid-points of each window. Digitalized technical drawings of the Snowdon visitor centre was not made available for the public access and therefore the drawings in this study were obtained from the scanned magazine article [9].

Fig. 5.

Section of the café indicating angles measured from mid-points of windows (Upper image: southwest facing window, lower image: northeast facing window)

Therefore, the value of the average daylight factor was 3.1 as shown in equation 3, 4 and 5.

3.2. BRE Sky Protractor

The daylight factor on a reference point can be estimated as a sum of three components, the sky component (SC), the external reflected component (ERC) and the internal reflected component (ICR)) [8]. The ERC and IRC are given by mathematical equations while the SC can be calculated through several methods (e.g. Waldram, pepper dot). Here the BRE sky protractor was used. First, a grid was constructed indicating 18 specific points where the daylight factor was measured which is illustrated in Figure 6. All points were elevated to working plane height.

Fig. 6.

Plan and section of the café with grid lines superimposed

Table 1 shows the tabulated results from the sky protractor method. The calculation was carried out twice at each point to consider light entering from northeast and southwest facing windows. There were no significant obstructions that can be seen in section, which led to an assumption that no externally reflected component (ERC) had an influence in the daylight for this case.

Table 1.

Corrected sky components from southwest (front) and northeast (rear) windows

The sky component (SC) was calculated by multiplying the uncorrected SC by correction factor, which were obtained bya BRE sky protractor. The result indicates that while the northeast facing window has less height than the southwest facing window, it made a significant contribution to daylight distribution in the space due to its location at higher elevation. With relation to the southwest facing window, it was noted that the sky component values dropped by almost 70% from the points at the grid line 1 to the points at the grid line 2.

The average internally reflected component of the daylight factor was calculated from the equation 6:

As there are two windows in the café, the average IRC was needed a separate calculation for each window. The calculation process for the southwest window is shown below (Equation 7):

T_w = 0.66, glazing transmittance
A_w = 40.8m², area of west-facing window
A_r = 870.9m², total room surface area
p_r = 0.51, average room reflectance
C = 39, coefficient for no obstruction outside the window
R_fw = 0.22, average reflectance of the floor and parts of the walls below mid-height of the window (excluding the window wall)
R_xw = 0.56, average reflectance of the ceiling and parts of the walls above mid-height of the window (excluding the window wall)

The calculation of IRC for the northeast window is as follows (Equation 8):

T_w = 0.66, glazing transmittance
A_w = 16.1m², area of wet-facing window
A_r = 870.9m², total room surface area
p_r = 0.51, average room reflectance
C = 39, coefficient for no obstruction outside the window
R_fw = 0.45, average reflectance of the floor and parts of the walls below mid-height of the window (excluding the window wall)
R_cw = 0.80, average reflectance of the ceiling and parts of the walls above mid-height of the window (excluding the window wall)

Therefore, the total average value of IRC of the space is as follows:

Based on the results of SC and IRC, daylight factors at 18 specific points were calculated and illustrated in Table2. The same reduction of 0.66 as the one in the average daylight factor calculation was applied for glass transmittance at calculated SC values, which accounts for double glazing and dirt in a commercial/rural setting.

Table 2.

Calculated daylight factors at 18 points by BRE protractor method

3.3. Pilkington dot diagram

Pilkington dot diagram was used along grid line C to compare the distribution of the SC results through the depth of the space. Again, the SV values needed to be measured separately by the window [8]. Here, the values of SC at the points of grid line C were only measured. Figure 7 illustrates the values of SC at the points of C1 (southwest and northeast).

Fig. 7.

Sky component values for the west and east facing windows at C1 point through Pilkington dot diagram

As shown in Figure 7, the method clearly indicates how the window’s height affects the daylight in the interior space. Diagram ‘C1 southwest’ shows the southwest facing window at their largest angle and yet they still skim the underside of the dot pattern. At point of C3 and C4, zero dots are covered by the southwest facing window. While this method might favor higher windows, this illustrates how low the windows

Table 3.

Daylight factors along grid line C by Pilkington dot diagram method.

were and how much sky component was shielded by the roof. Table 3 shows daylight factors along grid line C, by using the Pilkington dot diagram method.

3.4. Mock-up scale model

The artificial sky simulator (Fig 8), located at the Bartlett School of Architecture, University College London (UCL), was used to create the artificial overcast sky condition during the evaluation. The simulator consisted of 270 compact fluorescent luminaires for an artificial sky and a 50W MR 16 lamp for an artificial sun. All of the lamps used in the simulator were individually controlled in order to alter the luminance distribution; thereby modelling different sky condition. Here, the overcast sky condition was created. A 1/50 scale model of the café was constructed. Reflectance of the room surfaces were matched by using acrylic paints.

Fig. 8.

The artificial sky simulator (up) with the physical mock-up model (down)

More precisely, a granite colour paper (reflectance of 0.2) was used for the floor, a dark brown colour (reflectance of 0.2) paint was applied for the wall part and the ceiling part was covered by a light colour paint (0.8). Overall, the scale model was closely matched to the real building except that the two windows were left empty in the mock-up model as opening. Daylight factors of 18 points were measured with photocells inside the model (Fig 9).

Fig. 9.

The physical scale mock-up model (1/50) with attached photocells

The daylight factors were estimated by the ratio of illuminance values that were measured both internal and external reference points. Then, 0.66 was multiplied to account for window transmittance and dirt. The result from the physical scale model under the artificial sky simulator is illustrated in Table 4.

Table 4.

Daylight factors estimated from the physical scale model under the artificial sky simulator.

3.5. Interpretation of daylight factors

The average daylight factor acquired from BRE formula was 3.1%. Since the decimal place has little meaning on the average daylight factor [10], the value could be rounded off to 3%. Since the value was just above the most of lighting recommendations for non-workspace (e.g. SLL Lighting handbook [11]: 2%, BREEAM technical manual [4]: 2%), it may appear underlit without electric lighting [11]. Logically, this result would a bit surprising considering the fact that the case building is located on the top of highest mountain in Wales with a floor-to-ceiling window on the entire southwest wall as well as no external obstruction. Either the result was due to intention from an architect (e.g. choosing low reflectance materials for interior finishes, which was not the case) or a possible misleading from daylight factor from the overcast sky condition.

Regarding the daylight factors at a point, the results under sky simulator showed a spread of 2-4% daylight factor in the areas surrounding the southwest facing window (Fig 10). Noticeably, there was no reference point that indicated higher than 5% of daylight factor (the highest value measured was 4.2 at the point ofB1). Based on the result, the café would be recommended to supplement with electric lighting especially at the areas below 2% of daylight factor. Approximately 1% of daylight factors were measured in grid line 4. Overall, the result from the mock-up scale model indicates that the café would be appeared a little dim without the electric lighting, and even the space near the southwest window (floor-to-ceiling window) expected to received low amount of daylight(2.5% to 4% of daylight factor), which correlates well with the above result from the average daylight factor.

Fig. 10.

Contour lines of daylight factor under the artificial sky simulator

Similar result of daylight factor distribution was shown from the BRE sky protractor method in Figure 11. A spread of 2-3% of daylight factor surrounding the southwest facing window. The 2% contour line takes a similar shape between artificial sky simulator and BRE sky protractor. Calculated SC values in Table 4 enabled to interpret the result in more detail. First, SC values from southwest window dropped by approximately 70% from the grid line 1 to grid line 2. This resulted in that from the grid line 2 to 3 northeast window had more impact on daylight than southwest window. In the grid line 4, almost no SC values were measured from both side of windows, and thus daylight in this area was primarily reflected light. The points of D2 and E2, southwest window contributed more on daylight factor and this was due to the non-even building design. The result from Pilkington dot diagram showed the same pattern but it was found that SC values from this tool are more subjective to window height (from the floor level) than other tools.

Fig. 11.

Contour line of daylight factor from the BRE sky protractor

The results of acquired daylight factors all indicates that the café space appeared to be a slight lack of daylight and if a client or an architect only relied on this information, a design modification might have been suggested in the early design stage to achieve higher DF values. Raising the height of the roof by about a meter, for example, would result in an increase of 3.5% of daylight factors at points, which allows achieving above 5% of daylight factor on most interior area. Then, the numbers may look better in a paper but, daylight factor is known to be a limited indicator mainly due to its assumption on hypothetical overcast sky condition. In order to verify the results from the daylight factor analysis, the impacts of direct sunlight under the clear sky condition were investigated in this study, too.

4.1. Climate Consultant

First, the shadow angle caused by the shading system was needed to be decided before the analysis on the sunlight penetration into the cafe. The shadow angles of the southwest facing window were 45° (with the shading system) and 55° (without the shading system). The shading angle of the northwest facing window was 50° the non-shading device in use was 60°. Climate Consultant 5.5, which is a simple to use, graphic-based computer programme that interprets raw weather data file [12], was used. In terms of the weather condition of the Snowdon visitor centre, the input of Birmingham (52.45°N, 1.73°W) weather data file was used instead as it provides the closest data to the case building’s geographical location. As shown in Figure 12,a yearly average temperature in Birmingham was about 10oC and averages at any months were quite below the comfort zone of temperature (20°Cto 24°C). Temperatures higher than 25°C were only observed in July and August throughout a year. Therefore, the amount of direct sunlight exposure in only July and August should be considered whether there would be a case of overheating by direct sunlight exposure. 

Fig. 12.

Temperature range chart in Birmingham

Figure 13 illustrates a sun shading chart with an overlaid shading calculator of the northeast window from the 21^st June to 21^st December.  According to the visitor center’s web site [6], the café opens at 10:00 am and closes at 18:00 pm and therefore the analysis would focus on the opening hours. As shown in Figure 14, without the shading system in use, direct sunlight penetrated through the northeast facing window from the sunrise till 09:30 am (in June), 09:40 am (in July), and 09:45 am (in August). During the winter (November and December) months, direct sunlight penetrated through northeast facing window from the sunrise until approximately10:30 am. The result suggests that the shading system on the northeast facing window would not be in use throughout a year. The visitor centre received the direct sunlight penetration via the southwest window and the result is shown in Figure 14.

Fig. 13.

Sun shading chart showing shading calculator overlay (Northeast window) (Grey area indicates the protection of the direct sunlight when the shading system was in use)

Fig. 14.

Sun shading chart showing shading calculator overlay (Southwest window) (Grey area indicates the protection of the direct sunlight from the shading system)

During the hottest time of the year (July and August), direct sunlight penetrated from shortly before and after the lunch hours as 13:15 pm (July), and 11:15 am(August) and lasted until the sunset when no shading system was in use. If the shading device applied, there would be almost no direct sunlight penetration in July and also a significant decrease in the amount of direct exposure in August, which starts from 13:15 pm till the sunset. Almost 2 hours of protection (from 11:15 am to 13:15 pm) was expected by the shading system attached in the southwest facing window. There was almost no effect of the shading system in winter. The analysis with the Climate Consultant clearly indicated the effectiveness of the shading device as well as the expected hours of being directly exposed by the sunlight.

4.2. Sun path diagram

With the sun path diagram method, there was a need to draw the shading mask protractor first. The same angles, defined in Section 4.1, were used and their results on the shading protractor are shown in Figure 15a and Figure 15b. The shading protractors were, then, overlaid on the sun path diagram [13] for latitude N 53.07° and longitude 4.07°, and were adjusted to the orientation of the windows.

Fig. 15.

Shading protractors for the windows with and without shading system

Figure 16 shows the final results of the sun path diagram. The result was the basically the same as the one from the Climate Consultant 5.5. In July and August, direct sunlight penetrated into the café through the northeast window from the sunrise till 09:30 am. Again, the shading system was found to be effective to protect approximately an hour of direct sunlight just before the opening time and one hour after the lunch hour in July, and August. During winter, the shading system was not effective as suggested by the Climate Consultant 5.5. Both analysis tools indicate that the direct sunlight penetrated into the space, with or without the shading after 14:30 when the temperature was the highest of a year.

Fig. 16.

Shading protractors superimposed over a sun path diagram

4.3. Mock-up scale model

The physical mock-up model (1/50) was used to assess the direct sunlight penetration under clear sky conditions. The artificial sky simulator at UC provided a clear sky condition with the sun for three different times of date, 21st June, 21st September, and 21st December. In order to investigate the sunlight penetration, Digital single-lens reflex camera (DSLR), Cannon EOS 750D, was inserted inside the mock-up model and took snapshots with an interval of an hour. Figure 17 shows the direct sunlight penetration on the mock-up scale model with an interval of an hour.  

Fig. 17.

Sunlight penetration on 21st June, 21st September and 21st December

As shown in Figure 17, the direct sunlight penetrated from through the Northeast window at the sunrise of the day and the penetration creates various different light patterns either on the ceiling or the floor differently by the time of year. The result suggests that this method, compare to the others, was not suitable to assess the exact time of direct sun exposure into the interior space, however, this tool provided visually intuitive results to an architect or a lighting designer for their early design assessment. The result also provided potential areas of discomfort glare from the direct sunlight at different time of a day or a year.

The analysis of the direct sunlight under a clear sky condition by three different methods, indicate that the visitor café was well exposed to the direct sunlight from just after the lunch time (in summer) or before the lunch time (in winter)if we consider only the opening hours. Although accumulated amount of the direct exposure could not be provided by these methods, the results clearly show that the shading system at the southwest window may or not need to be used to reduce the direct exposure by an hour during summer. Such result was quite contradictory to the earlier results from the daylight factor analysis. As discussed in Section 3.5, the average DF and DF at a point indicated that the interior space received slightly insufficient amount of daylight to be considered as a well-daylit space. If an architect or a lighting designer only relied on the daylight factor results, and modified their design accordingly, they might raise the roof by a meter, and then the café would completely be over-exposed to the direct sunlight.