Oct 19, 2012 1:42 PM, By Bob McCarthy
When are they needed?
A FIELD EXAMPLE
We have everything we need to now put this to work on an example room. The first is a single balcony space where the under-balcony shape is 8 meters deep and 2 meters high. This high shape factor means that delays are very likely, but we will run through several scenarios to see how it all plays out.
Our example design is shown in Figure 1. Round 1 (Figure 1A) features the mains 8 meters in front of the balcony. Since we have 8 meters under the balcony as well, we have a 50-percent range ratio (8 meters to 16 meters) and 4:1 shape factor (8 meters to 2 meters). If we multiply those two numbers together, a composite number is created. In my statistical analysis I found every system with a combined factor of 2 or greater used a delay. In this case, both the shape factor of 4 and the combined ratio of 2.0 favor adding a delay.
The next thing to do is to add delays and recompute the shapes for the leftover areas. In other words, rework the numbers by leaving out the area covered by the delays. This way we will know if we have accomplished our goal or if we need a second set of delays.
The technique for this is shown in Figure 1B. We see that the delay speaker is placed at the 10-meter mark and covers the last 4 meters under the balcony (12 meters to 16 meters). Therefore, our remaining U/B area is reshaped to 4 meters x 2 meters (a 2:1 ratio). The range ratio changes as well since the endpoint is now at 12 meters, giving us 67 percent of the coverage out from under the balcony (8 meters of the 12). The shape factor of 2:1 puts us right on the edge, but the range ratio (67 percent) brings our combined number to 1.3, which indicates no need for a second delay speaker.
Let’s restart the whole process and try again. This time we will move the main speaker closer. This does nothing to the U/B shape factor, but does change the range ratio. If we cut the distance to the balcony in half and then half again, we reduce the distance to the balcony front down to 4 meters and 2 meters respectively, thereby reducing the composite ratio to 1.3 and 0.8. When we reach the nearest of these, even with the very high shape factor of 4:1, we would not need an U/B system. Let’s reset again and go the other way (Figure 1C). Now we move the speaker farther away, doubling the distances to the balcony front. It is a certainty that we will need the delays, the question then becomes whether we need a second ring. The farther we move away, the higher the range ratio becomes and tilts us toward needing even more help. If the mains are moved to a point 36 meters from the balcony front, the composite ratio would hit the tipping point of 1.8 and favor another set of delays placed at the very front of the balcony.
What would happen if we went back to our original scenario and doubled the height of the under-balcony area? In this case the shape factor would be changed from 4:1 to 2:1 and the need for a delay system would be negated with a composite factor of 1.0. This would hold true at our starting position for the mains and then become progressively more marginal as we move the mains farther away. By the time we reach 64 meters we will have to invest in delays.
This brings up an interesting aspect of our example application. The over-balcony area is the same depth and twice the height of the under-balcony. Therefore the same equations can be applied to the upside just like the downside. They really is no difference. In a two-balcony scenario we will remember that “one man’s ceiling is another man’s floor.” Any time we have a ceiling getting close to our listeners, we can consider these guidelines. Review the previous figures and note that that the average height in the balcony is 4 meters. All the other dimensions are the same. In Figure 1D you can see a modified ceiling structure for the second floor that would give it an average height of 2 meters, making it functionally identical to the under-balcony area. Just because what you see there is a bad idea, don’t think it hasn’t been done!
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