Array, or not to array? That is the Question, Part 2
May 11, 2012 11:08 AM, By Bob McCarthy
Understanding coverage stretching and pattern bending.
In part 1, we discussed the coverage shape of a single speaker and how we could use multiple speakers to create a similar shape. We demonstrated that a point source array can mimic our example 80-degree speaker by slicing up the coverage into segments of various sizes (from 2x40 degrees to 40x2 degrees). In this second part, we will move forward by using multiple speakers to create shapes that no single speaker can possibly create. The two avenues we will explore are pattern stretching and pattern bending. In both cases, as you will see, the traditional thinking of coverage angle will give way to visualizing coverage shape.
Coverage stretching: uncoupled arrays
When speakers are placed close together (coupled), there are three possible outcomes: the combined response will be wider, narrower, or the same as the individual elements. The decisive factor is the percentage of angular overlap. If the overlap is low, the combined pattern is wider than the single element. If the overlap is high, the responses converge in the middle and narrow the pattern. If the two forces are equal (overlap of 50 percent) then a stalemate results.
When speakers are moved significantly apart (uncoupled), the result is almost sure to be a widening of the pattern. Essentially, there are two array tools for widening the response: angular isolation and level isolation. Coupled arrays use the former and uncoupled arrays can use both; the level isolation comes from the physical separation and the angular can be added to that. If we can widen the response with either type of array, then what would be the reason to choose coupled or uncoupled?
A coupled array can be spread to a maximum of 360 degrees, after which it is chasing its tail. An uncoupled array can spread an unlimited distance, such as from Hollywood to San Francisco, (e.g., the parade route at Disney’s California Adventures park). So if your audience is spread out sideways on a line, there is not a suitable angular solution. Additional examples of this type of application include frontfill arrays, underbalcony delays, and racetracks. In such cases we don’t think of the coverage in angular terms. Instead we might think of the target as three rows deep and 40 seats wide. In order to move the mind toward thinking about uncoupled array shaping we have to reset our thinking about speaker coverage from the traditional “slice of pizza” angular thinking into length and width. In other words, how wide is my coverage at a given distance?
Let’s start with a 60-degree speaker. At a distance of 10ft., it has a coverage of 10ft.—5ft. either side of center. This is a 1:1 relationship between length and width. If you want to extend a line of 60-degree devices and obtain even coverage, the spacing between the boxes should be the same as the distance to the start of coverage. If your first row is 10ft. from the stage lip, the 60-degree frontfills will need to be spaced at 10ft. intervals. This is shown in Figure 1a. If the speaker is narrower than 60 degrees, the spacing (for a given start distance) will be smaller. The opposite is true for wider devices. For example, a 90-degree speaker has a ratio of 1.4:1. If we kept the same spacing, the gap would close at 7ft. instead of the 10ft. (shown in Figure 1b). Alternatively we could use a 14ft. spacing to keep the start of coverage at 10ft. (shown in Figure 1c). Things get more interesting, however, when we combine splay angle and distance. If the speakers are splayed out, then they must be spaced closer together to achieve the same combination start point. A calculation program that tells you the proper spacing for any given speaker coverage and splay is available through my blog at www.bobmcarthy.wordpress.com.
Coverage bending: coupled arrays
In part 1 we mimicked a symmetric speaker with point source arrays of various types. Now we will use the coupled point source to create a family of asymmetric shapes of approximately 60 degrees. It is easy to define a symmetric speaker coverage shape: the coverage area (between the -6dB points) is a radial section of a circle. A coupled point source has a natural tendency toward the symmetric radial shape. How can we bend the point source to create an asymmetric shape? This will require either asymmetry in the speaker models, levels, and/or splay angles. But before we start steering the speakers, we need to define the target.
The two keys that define an asymmetric coverage target are the angular spread and the range (distance) ratio. The angular spread is found just as it was in the symmetric array. The range ratio is the difference between the farthest area of coverage and the closest. This is easiest to visualize with a flown system in the vertical plane, where the listeners in the rear are farther from the speakers than the folks in front. Here's a simple example: The last row is 100ft. away and 10 degrees above the cluster, while the closest seats are 50ft. away and 50 degrees under. The ratio is 2:1, a difference of 6dB in terms of sound level. The angular coverage spread is 60 degrees (from +10 degrees to -50 degrees). So now we have a defined target shape: 60 degrees of coverage with 6dB of asymmetry (2:1). The array will need to be shaped to throw 6dB more energy to the far seats in order to equalize the levels from front to back.
Let’s change the cluster position. If we brought the cluster down lower, we might find ourselves just 25ft. from the front seats, but still around 100ft. to the rear. Now the range ratio has increased to 4:1 (12dB), and we will require a much stronger shaping to overcome the radial tendency of the array. An additional consideration is that the new position will most likely reduce the angular spread. Our 60-degree spread, 2:1 (6dB) level asymmetry original cluster may need to change over to a 45-degree spread with a 4:1 (12dB) range ratio. Conversely, if we were to move the speaker higher, we will find the angular spread increasing and the range ratio decreasing.
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