Out of the Wood | Total lumens—revisited C Centre Illuminance (fc or lux) D Width at 10% point (ft or m) Figure 4 – estimating the centre to edge ratio We make the systems that make the magic. We’re experts in creating performing arts spaces. As an experienced, national integrator of theatre equipment and systems, we manufacture as well as provide services ranging from engineering to installation. We can still get values for C and D, but the total volume in our sloping sided bucket will be less than that of the perfectly straight sided, cylindrical, one. We can work out some theoretical reductions in the output if we assume the distribution is a true cosine curve. For example, a cosine curve from a profile spot where the edge brightness is one third of the centre brightness (a centre to edge ratio of 3:1) would have a total lumen output of 65% of that of the flat beam. Table 1 shows a range of values for other centre to edge ratios: now make an estimate of our total output. We may not know the center to edge ratio, but a good rule of thumb is to use 10:1 for wash lights (10:1 is 10% which is our defi nition of fi eld lumens), and 3:1 for spots. Depending on how fl at the beam is, some will be higher than this, but some may be much lower. In our example case, we might assume that our sample light was a spot, use the 65% scaling, and get a fi nal result of: 7068 x 65% = 4,500 lm. This may all still look complex, but as we are only looking for a rough answer, we can ruthlessly simplify the math, round Centre to edge ratio 1:1 2:1 3:1 5:1 10:1 Output Reduction 100% 74% 65% 57% 51% Table 1 Final Multiplier, F 0.7 0.6 0.5 0.4 0.3 SECOA will be at the 2011 LDI Show in Orlando, FL, October 28-30th. Please stop by SECOA booth #1203. Contact us if you’d like to set up a meeting at LDI with SECOA’s Jeff Jones or Dan Culhane. Just to complicate things further, most fi xtures are not true cosine curves. Wash lights, in particular, can be peakier, which reduces the output even more from the fl at fi eld, perhaps by a further 20%. However, with all that in mind, we can our numbers, and end up with the total multipliers shown as the last column in Table 1 . This gives the following rule-of-thumb equation: Total lumens = F x (Field Diameter) 2 x Centre Illuminance www.secoa.com FALL 2011 SECOA | 8650 109th Avenue North Champlin, MN, 55316 | 763.506.8800 24 FALL 2011