## Flux Distribution

As explained in Parts One and Two, the ability to visualize a design situation in terms of an illumination hierarchy is a fundamental design skill. This section explains how a layout of luminaires is devised to provide a chosen distribution of illuminances within a space. The example given is based on a proposal by J.A. Lynes (1987), who attributes the fundamentals of the procedure to J.M. Waldram's Designed Appearance Method (1954, 1978).

The stages of the procedure are indicated in Figure 6.3, and are described below:

1 The required illuminance for each surface Es is prescribed, and is multiplied by the surface area As and the surface reflectance Ps to give the total reflected flux (lumens) from that surface.

2 The sum of reflected lumens from all surfaces is divided by the sum of surface areas to give the average indirect illuminance E(i). (It may be noted that this is our old friend, the mean room surface exitance Mrs, in another guise, as it represents the average value of indirect illuminance on all room surfaces, including an occupant's cornea.)

Outline of the flux distribution procedure

(1) Surface reflected flux

 Surface area As Surface reflectance ps Surface illuminance Es i

(1) Surface reflected flux

3 The value of E(i) is subtracted from each surface illuminance Es and what is left is the required direct illuminance of that surface

4 Each value of Es(d) is multiplied by the surface area As to give the direct flux required on the surface Fs(d).

5 The total lamp wattage required for each zone is estimated by dividing Fs(d) by the luminous efficacy of the light source ^ and an allowance for luminaire efficiency and other light losses, and summing the values. This provides the information needed to devise a layout of lamps and luminaires to provide the prescribed surface illuminances.

It should be noted that stage (2) makes the only simplifying assumption that is incorporated into this procedure. It is assumed that the reflected flux is uniformly distributed. The likely errors involved by this assumption have been discussed in Section 2.3, and it is more a matter of common sense than photometry. The designer should ensure that he/she is aware of the types of situations where this assumption might incur unacceptable error.

The first step of the procedure is to prescribe the illuminance of every surface. You cannot prescribe for only the surfaces that interest you, as every surface that is visible is reflecting flux into the space, and is adding to E(i).

We start by identifying the visual tasks. These relate to the activities that involve being able to discriminate detail, and for which we are able to prescribe appropriate illuminances either by reference to Table 2.3 or to some other schedule of recommended or required illuminances. The visual tasks are not necessarily the things that we, as designers, identify as the most significant objects of the visual environment, but they concern visual functions that must be adequately provided for. As lighting providers, we must relate to the needs of the people who will use this space, and what it is that they need to be able to see. A visual task might comprise anything from reading a prayer book to reading the roll of dice, but following from the discussion in Section 2.2, reasonable decisions can be made to prescribe an appropriate task illuminance. This value becomes the anchor illuminance, and every prescribed surface illuminance will be related to this value. If more than one task illuminance is prescribed, the lighting designer has to consider who is the viewer of principal concern, and what is illuminance to which they are adapted.

The workings of the procedure are best explained by following an example. Figure 6.4 shows a sketch of the interior of a small

Table 6.1. Flux distribution (1)
 Surface Area Reflectance Relative Illuminance Reflected Direct Direct Lamp Lamp watts Illuminance flux (lm) Illuminance flux wattage per zone S As (m2) Ps Es (rel) Es (lx) (lx) Fs(d) (lm) (W) (W) SANCTUARY altar front 1 0.25 5 1000 250 939.2013129 939.2013129 218.41891 panelling 8 0.7 3 600 3360 539.2013129 4313.610503 1003.165233 east wall 20 0.6 1.5 300 3600 239.2013129 4784.026258 1112.564246 vault 30 0.3 0.5 100 900 39.20131291 1176.039387 273.4975319 floor 25 0.5 1.5 300 3750 239.2013129 5980.032823 1390.705308 N & S walls 60 0.7 0.5 100 4200 39.20131291 2352.078775 546.9950639 4545.346293 NAVE 0 0 -60.79868709 0 0 floor & chairs 110 0.15 1 200 3300 139.2013129 15312.14442 3560.963819 chancel arch 10 0.7 1 200 1400 139.2013129 1392.013129 323.7239835 N side of S arcade 30 0.7 0.5 100 2100 39.20131291 1176.039387 273.4975319 S side of N arcade 30 0.7 0.75 150 3150 89.20131291 2676.039387 622.3347412 S half of vault 60 0.6 0.5 100 3600 39.20131291 2352.078775 546.9950639 N half of vault 60 0.6 0.3 60 2160 -0.79868709 -47.92122538 -11.14447102 W wall 50 0.4 0.5 100 2000 39.20131291 1960.065646 455.8292199 5772.199888 SOUTH AISLE 0 0 -60.79868709 0 0 east wall 15 0.7 0.5 100 1050 39.20131291 588.0196937 136.748766 ceiling 50 0.6 0.5 100 3000 39.20131291 1960.065646 455.8292199 S & W walls 100 0.5 0.75 150 7500 89.20131291 8920.131291 2074.449137 floor and chairs 45 0.15 1 200 1350 139.2013129 6264.059081 1456.757926 4123.785049 NORTH AISLE 0 0 -60.79868709 0 0 east wall 15 0.25 1 200 750 139.2013129 2088.019694 485.5859753 ceiling 50 0.6 0.3 60 1800 -0.79868709 -39.93435449 -9.287059183 N & W walls 100 0.5 0.5 100 5000 39.20131291 3920.131291 911.6584398 floor and chairs 45 0.15 1 200 1350 139.2013129 6264.059081 1456.757926 2844.715282 Total surface area 914 Reflected flux 55570 lm Total Watts 17286.04651

Indirect illuminance (E(i) or Mrs) 60.79868709 lux or lm/mA2

Anchor illuminance 200 lux Beam efficacy (neta B) 4.3 lm/W

church. Obviously a uniform distribution of illumination would be inappropriate. The viewers of principal concern are the congregation in the nave, and for them, the sanctuary is the zone that should draw attention, and within the sanctuary, the altar is the natural object of focus. The aim is to devise a lighting design that will reinforce this hierarchy, and the illuminance ratios scale in Table 2.6 provides guidance on relating individual surface illuminances to the overall design concept.

It is convenient to use a spreadsheet program for the flux distribution procedure. The instructions in the following text are for Excel software, and the resulting spreadsheet is Table 6.1. Bring up the Excel spreadsheet on your computer, and follow this example.

Column A: List all the principal surfaces. It helps to arrange them in zones.

Column B: List the area As of each surface. At the bottom of the column, sum the surface areas. To follow this example, click on B32, type in [=SUM(B7:B30)] (do not include the square brackets) and press ENTER.

Column C: List the reflectance Ps of each surface.

Column D: Here we come to the creative bit. For each surface, designate an illuminance relative to the anchor illuminance. Start by identifying the visual tasks. The congregation needs to be able to read prayer books, so the illuminance of the nave and aisle seating areas must be sufficient for this. This will be the anchor illuminance, and in this column, each of these surfaces is given the value 1. Now move on to the other surfaces, and for this we make use, once again, of the illuminance ratios scale that was introduced in Section 2.3.

 Noticeable 1.5:1 Distinct 3:1 Strong 10:1 Emphatic 40:1

Look down the fourth column (D) in Table 6.1 and note how this scale of ratios has been used to set each value of relative illuminance. This column is the designer's statement of how lighting will be employed to give balance, guide attention and provide selective emphasis. This is not a situation that calls for emphatic statements of difference. In this case, the designer has opted for a gradation of illuminance difference leading through the sanctuary to the altar, with a maximum ratio of 5:1. The designer is not restricted to the four values given in the table, and can interpolate at will. Some judgement has to be applied, as the gradient of change will affect the appearance. The confidence to do this is essentially a product of the extent to which observation-based experience has been developed.

This point marks the end of data input. From here on, Excel does all the work.

Column E: The anchor illuminance has to be adequate for the task of reading hymn books and prayer books. However, this is not the type of sustained reading task that occurs in offices or libraries, and a lower illuminance would be permissible, and perhaps more appropriate. At this stage, we will opt for 200 lux of task illuminance, so this value becomes the anchor illuminance and is entered in D34.

Click on E7, and enter [=\$D\$34*D7]. (The \$ signs indicate that the value in D34 is a constant.) The value 1000 appears, and this is the illuminance to be provided on the altar front. Click on this box and copy it by dragging it down the column to E30, and watch all the surface illuminances appear.

Column F: The reflected flux from each surface is the product of the surface area As, the surface reflectance Ps, and the surface illuminance Es. So, in F7 enter [=B7*C7*E7], and the value 250 pops up. Drag this box down the column, and watch all the other values of reflected flux appear. Obtain the total flux at the bottom of the column by entering [=SUM(F7:F30)] in F32, and calculate the average indirect illuminance E(i) by entering [=F32/B32] in F33.

Column G: The direct illuminance Es(d) for each surface equals the total illuminance Es minus the indirect illuminance E(i). So in G7 enter [=E7-\$F\$33] and copy the formula down the column.

Column H: The direct flux Fs(d) for each surface is the direct illuminance Es(d) times the surface area As, so in H7 enter [=G7*B7] and copy down the column. This is the number of lumens that you must direct onto each surface to achieve the illuminance distribution prescribed in column D.

Column I: We now estimate the lamp wattage that will deliver the required Fs(d) onto each surface. This is obtained by dividing Fs(d) by the beam luminous efficacy which is the same thing as luminous efficacy ^ (Im/W) except that it takes account only of the lumens emitted within the beam. The difference between total light source lumens and beam lumens can be substantial.

For this example we will examine the use of aimable luminaires with integral reflector lamps mounted at the level of the eaves. The lamp manufacturers offer ranges of PAR (parabolic aluminized reflector) lamps for three types of light source: standard incandescent; tungsten halogen; and metal halide. For each source type, they offer various wattages and beam spreads, and we have to work out the beam lumens.

The lamp manufacturers specify the performance for reflector lamps by giving the luminous intensity (candelas) at the beam centre /max, and the beam angle, which is the inclusive angle over which the intensity is not less than 50% of /max. That is to say, for a reflector lamp for which /max = 1000 cd and the beam angle is 30°, the intensity falls to 500 cd at 15° from the beam axis. In the following text, B indicates the beam angle (B = 30°) and b indicates the half-beam angle (b = 15°). We can now estimate the beam lumens:

Fb = (average beam intensity) x (beam solid angle) x (lumen depreciation factor)

= /av 2n(1 - cos b) LD = -max + 0-5 /max x 2n(l - cos b) LD

 Table 6.2. Beam performance data for three types of integral reflector lamps Lamp type Beam type Beam angle Beam intensity Beam flux Beam efficacy B Ib (cd) Fb (lm) ^b (/m/W) Incandescent SP 12° 5400 140 1.7 PAR38 80 W FL 30° 1800 290 3.6 (LD = 1.0) Tungsten halogen SP 10° 6500 120 1.6 PAR30 75 W FL 30° 2000 320 4.3 (LD = 1.0) Metal halide SP 20° 26,000 1300 18.6 PAR38 70 W FL 35° 12,000 1800 26.2 (LD = 0.7) WFL 65° 4500 2300 33.2

of incandescent, halogen and metal halide lamps being in the region of 12, 18 and 70 lm/W respectively, and it is quite sobering to realize how many of the lumens emitted by the source do not end up in the beam. This is particularly so for the SP (spotlight) lamps, and so we should make use of FL (floodlight) wherever practical. We will start by considering the tungsten halogen PAR30 FL, for which = 4.3 lm/W. Enter this value in H34, and in I7 enter [=H7/\$H\$34], and copy down the column.

Column J: It is convenient to sum the lamp wattages for zones. In J12, enter [=SUM(I7:I12)], and so on. For total lamp watts, enter [=SUM(I7:I30)] in J32.

The spreadsheet shown in Table 6.1 is now complete, but we certainly have not finished using it. The total lamp wattage is shown to be 17.3 kW, and as the lamp specification will certainly include some SP beam types, the actual load will be more than this. What would be the effect if, instead of tungsten halogen lamps, we used metal halide FL lamps giving 26.2 lm/W? Click on H34 and press Delete, and enter this value. Instantly columns I and J are revised, and the total watts reduce to 2.84 kW. This gives us power to spare, so why not look again at the overall illuminance? The indirect illuminance E(i) is 61 lux, and as this is equivalent to Mrs, we can use it as an estimate of eye illuminance. It can be seen from Table 2.1 that the overall appearance of the space is likely to be slightly dim. For some churches this appearance would be quite appropriate, but perhaps it is not what we want to achieve in this instance. We can take a look at increasing the indirect illuminance to give a Mrs value of 100 lm/m2. Click on D34 and change the anchor illuminance to 350 lux. The indirect illuminance jumps up to 106 lux, and the total watts to 4.96 kW. This revised spreadsheet is shown as Table 6.3, and gives the entire distribution of surface illuminances and lamp wattages for an anchor illuminance of 350 lux provided by metal halide light sources. This version of the spreadsheet becomes our working document, and we can now apply the 'beam flux' method to plan an arrangement of light sources to provide this distribution.

Circumstances will suggest a sensible order in which to proceed. To locate the luminaries at the eaves level, and just forward of roof arches, offers reasonable concealment, ease of installation, and not unduly difficult maintenance. The luminaires must be aimable so that light can be spread right across a wall or roof, or focused onto selected objects, such as the altar front.

We can now move on to select beam angles, using the data for the three 70 W metal halide PAR38 lamps given in Table 6.2. We

 Surface Area Reflectance Relative Illuminance Reflected Direct Direct Lamp Lamp watts illuminance flux (lm) illuminance flux wattage per zone S As (m2) Ps Es (rel) Es (lx) (lx) Fs(d) (lm) (W) (W) SANCTUARY altar front 1 0.25 5 1750 437.5 1643.602298 1643.602298 62.73291212 panelling 8 0.7 3 1050 5880 943.6022976 7548.818381 288.122839 east wall 20 0.6 1.5 525 6300 418.6022976 8372.045952 319.5437386 vault 30 0.3 0.5 175 1575 68.60229759 2058.068928 78.55224915 floor 25 0.5 1.5 525 6562.5 418.6022976 10465.05744 399.4296733 N & S walls 60 0.7 0.5 175 7350 68.60229759 4116.137856 157.1044983 1305.48591 NAVE 0 0 -106.3977024 0 0 floor & chairs 110 0.15 1 350 5775 243.6022976 26796.25274 1022.757738 chancel arch 10 0.7 1 350 2450 243.6022976 2436.022976 92.97797618 N side of S arcade 30 0.7 0.5 175 3675 68.60229759 2058.068928 78.55224915 S side of N arcade 30 0.7 0.75 262.5 5512.5 156.1022976 4683.068928 178.7430888 S half of vault 60 0.6 0.5 175 6300 68.60229759 4116.137856 157.1044983 N half of vault 60 0.6 0.3 105 3780 -1.397702407 -83.86214442 -3.200845207 W wall 50 0.4 0.5 175 3500 68.60229759 3430.11488 130.9204153 1657.855121 SOUTH AISLE 0 0 -106.3977024 0 0 east wall 15 0.7 0.5 175 1837.5 68.60229759 1029.034464 39.27612458 ceiling 50 0.6 0.5 175 5250 68.60229759 3430.11488 130.9204153 S & W walls 100 0.5 0.75 262.5 13125 156.1022976 15610.22976 595.8102962 floor and chairs 45 0.15 1 350 2362.5 243.6022976 10962.10339 418.4008928 1184.407729 NORTH AISLE 0 0 -106.3977024 0 0 east wall 15 0.25 1 350 1312.5 243.6022976 3654.034464 139.4669643 ceiling 50 0.6 0.3 105 3150 -1.397702407 -69.88512035 -2.667371006 N & W walls 100 0.5 0.5 175 8750 68.60229759 6860.229759 261.8408305 floor and chairs 45 0.15 1 350 2362.5 243.6022976 10962.10339 418.4008928 817.0413166 Total surface area 914 Reflected flux 97247.5 lm Total Watts 4964.790076

Indirect illuminance (E(i) or Mrs) 106.3977024 lux or lm/mA2

Anchor illuminance 350 lux Beam efficacy (neta B) 26.2 lm/W

The beam pattern cast by a spotlight directed obliquely onto a flat surface

Beam pattern

Beam pattern

D = V(X2+ Y2 + Z2) B = 2 tan-1 (0.5 a/D) s tan-1 (a/D)

will start with the sanctuary. By applying some basic trigonometry we can see that lighting the roof vault and the upper walls from the eaves level calls for the WFL beam type to give even distributions of light across these surfaces from relatively short distance. The lower walls and floor can be lit from opposite sides, and the tighter FL beams are preferred to give glare control.

As we come on to smaller beam angles, we have to be more exact. Figure 6.5 shows what happens when the beam from a spotlight is directed at an angle onto a large flat surface. The beam shape is conical, but the beam pattern formed on the surface is an ellipse, which has minimum and maximum diameters a and b respectively. In order to spotlight an object such as the altar front with reasonable coverage, we want a beam angle B that matches a to the diagonal dimension of the altar. The location of the spotlight S is indicated by the dimensions X, Y and Z, and the distance from S to P:

Then:

 Surface s Direct flux Fsldl (Im) Beam type Number of /amps altar front 1600 NSP see text panelling 7600 SP 6 east wall 8400 WFL 4 vault 2100 WFL 1 floor 10 400 FL 6 N & S walls 4200 FL 3 Total number of lamps 20

If you are able to select a spotlight that has a beam angle which closely matches the calculated value of B, the illuminated surface will have good coverage but there will significant spill light, particularly if the light is incident at an oblique angle. This spill light might detract from the intended effect, and you will need a higher intensity light source to get the required lumens onto the receiving surface. The usual situation is that the designer has to choose between beam angles that are either larger or smaller than the calculated value, and it can come down to a choice of whether to minimize spill or maximize coverage. There are however, some alternative strategies to consider. Two or more narrow beam spotlights can be adjusted so that the edges of their beams overlap to give very good coverage with minimal spill light. Alternatively, a spreader lens can be fitted over the spotlight and rotated to the position where it increases the a dimension of the beam pattern without increasing the b dimension. Techniques such as these should only be used in situations where the lighting installation will be maintained by someone who can be relied upon to restore the settings after each lamp change.

Returning to the church lighting example, the altar and the panelling need to be lit from just behind the chancel arch to get light onto these vertical surfaces, and this means throws of around 8 m. At these distances, the subtended angles of the diagonals of the surfaces to be illuminated range from 8° for the altar front to 15° for the panelling. Table 6.4 shows a selection of lamp types for the sanctuary area. The SP beam type will work well for the panelling, but we need a different type of light source to get the 8° beam for the altar front. Mixing lamp types has to be done with care. The lamp manufacturer states the correlated colour temperature of the metal halide lamps to be 3200 K, and while this closely matches the CCT of a low-voltage halogen lamp, noticeable differences of colour rendering could be evident. While LV halogen can certainly deliver the required beam performance, it will be necessary to make a visual assessment of the lamp combination before specifying.

There are other factors to be considered. Although a single WFL lamp can deliver the beam lumens required for the roof vault, it may not give a satisfactory distribution of light. This could depend on how much light from the four WFL lamps illuminating the upper east wall will wash up into the vault. We have to think about how these lamps will be aimed. We must have enough lamps to be able to avoid harshness, and to be able to create the directional effects that we want. At the same time, we need to keep to a minimum the number of lamp types that we specify, and we must recognize that there will be more to the installation than just lamps. Luminaires with baffles or ring louvres are needed to control spill light onto surrounding surfaces and glare to the congregation and celebrants. We have noted that many of the lumens produced by the light source do not make it into the beam, and these are not wanted elsewhere. If the control devices significantly reduce the beam lumens, this must be allowed for. We can note that the 20 lamps selected in Table 6.4 have a combined wattage of 1400 W, and this is close to the value estimated in the spreadsheet.

When we are satisfied that we have all these factors in hand, we can get down to the serious business of planning the installation. The panelling behind the sanctuary table needs to cast shadow to make it stand out from its flat background, but what balance of lighting do we need to provide such an effect? Refer again to the illuminance ratios scale. It takes an illuminance ratio of 1.5 to be noticeable, and a ratio of 3 to appear distinct. We can provide for a noticeable or a distinct light and shade effect by arranging more of the luminaires on one side, and for a coherent 'flow of light' we should maintain that balance throughout the church. The 'flow' could come from either side, but which?

There is no single right answer to this question, or to put it another way, there are two equally right answers. One proposition is that for a traditionally oriented church in the northern hemisphere, it is natural for the light to come predominantly from the south, and so that is the side for the dominant array of luminaires. The counter proposition is that the sun illuminates the church beautifully, but differently, as it tracks from east, through south, to west, and that the rightful role of electric lighting is expressed by having it fill in the remainder of the circuit. When the sun is not available to provide illumination, the light should flow from the north. Armed with both of these arguments, a lighting designer can justify whichever direction is judged to suit the job in hand. For a designer who, like the author, lives in the southern hemisphere, the arguments are interchanged.

From the sanctuary, we proceed through the building matching beam lumens to surface flux requirements. By the time that we have worked our way through this church, we should have a good feeling about how it will appear. Also, we should have a sense of confidence that we can specify an installation which, when we have aimed the luminaires, will achieve our design intentions. Aiming the luminaires is a critical part of the process, and it pays to specify luminaires that can be relamped without losing their alignment. Of course we keep a copy of the spreadsheet on file, as this is the record of the design intentions. Equally important is the documentation to be prepared for whoever will maintain the installation, and this is referred to in Chapter 7.