What should be the size and aspect ratio of my arrays?
Determining the size of your arrays requires careful consideration. This article explores guidelines for effectively sizing arrays to attain the desired level of control.
Right sizing of an array
When sizing an array there are some general rules you should consider; the size of the array, whether it is 1D (line) or 2D (planar), will influence the directivity capabilities of a sound source, in our case the array:
Bigger arrays can create narrower beams compared to smaller arrays.
At a given frequency, if the array size increases, the narrowest obtainable beam gets narrower.
If the array size increases, the frequency at which the narrowest possible beam is obtained decreases.
It's a well-known principle that enlarging an array can boost the sound pressure level for a designated area. Specifically, doubling the size of the array typically results in a 3dB increase in sound level, although this can vary depending on the opening angles and types of beams used. We will explore this concept further through several practical examples.
In setting up an array, the aspect ratio of the target area should guide its configuration. For long and narrow spaces, the array should be dimensioned vertically longer than horizontally to best cover the area. However, if minimizing sound spill to side walls and focusing sound tightly within the area is crucial, then increasing the width of the array may be advisable to achieve a higher precision in sound distribution.
The chart below shows the relationship between array size, both horizontally and vertically, and the achievable beam opening angle, which could also be described as the minimum obtainable beam width as a function of frequency for different array lengths.
With the added variable of sound control in both the horizontal and vertical axes, it is useful to establish a set of controls to provide clear right-sizing guidance. The following case study aims to validate two rough guidelines for determining the appropriate sizing for a given coverage area. The rules are as follows:
Doubling the size of the array gives you 3dB increase in broadband SPL
To ensure consistent coverage the array needs to increase by 1 row/10m of distance throw
As stated, these assumptions are guidelines based purely on coverage and a standard shoebox geometry where the array is throwing the length of the space. This does not take into consideration any additional control requirements that may be needed to achieve the desired intelligibility or reduce sound spill to adjacent spaces.
The below array sizing tool (see link below ) can be used to predict the minimum obtainable beam width in degrees
Array sizing – Worked examples
Four common use cases will be considered to provide a more practical basis for sizing a HOLOPLOT array. In the example, a simple shoebox auditorium will be used. Here, a central array will be considered to show how SPL (dBA) changes both in level and coverage homogeneity as a result of increasing the size of the array. In these examples, a single coverage beam is used, utilizing HOLOPLOT's optimization algorithms to ensure the most desirable performance. Design criteria was as follows: Each array must cover the intended zone with the following homogeneity:
90% coverage ±3 Broadband dBA
85% coverage ±3 Octave bands (250-10,000Hz)
Example 1 – 1x2 centrally mounted MD96 array
SPL Drop: 0
Air absorption compensation: 0
Target curve: Flat
Phase response: Linear
Input Signal: AES2 (pink noise)
Example 2 – 2x2 centrally mounted MD96 array
Array: SPL Drop: 0
Air absorption compensation: 0
Target curve: Flat
Phase response: Linear
Input signal: AES2 (pink noise)
Example 3 – 3x2 centrally mounted MD96 array
SPL Drop: 0
Air absorption compensation: 0
Target curve: Flat
Phase response: Linear
Input signal: AES2 (pink noise)
Example 4 – 3x2 centrally mounted MD96 array
SPL Drop: 0
Air absorption compensation: 0
Target curve: Flat
Phase response: linear
Input signal: AES2 (pink noise)
Comparison across different array configurations
The data from the chart below presents the sound pressure level (SPL), homogeneity, and sound range across different array configurations of the HOLOPLOT system in a small theatre setup, broken down into three zones and a combined overview.
Here are the observed patterns and trends:
Sound pressure level (SPL) Trend:
Increasing SPL with larger arrays: SPL consistently increases (on average, 3dB per doubling of array size) as the array configuration increases from 1x2 to 4x2 in all zones. This indicates that more speakers in the array contribute to higher loudness levels, which can cover larger areas more effectively.
Homogeneity (%):
Improved homogeneity with larger arrays: Homogeneity, or the uniformity of sound distribution, improves with the size of the array in each zone. Higher homogeneity indicates a more evenly distributed sound that avoids dead spots and overly loud areas.
Range (dBA SPL):
Narrower range with larger arrays: The range of SPL, which indicates the variability of loudness across the zone, tends to become narrower (i.e., more consistent) with larger array configurations. This is beneficial for ensuring that all audience members experience similar sound levels.
Summary of trends:
Loudness and coverage: As array sizes increase, SPL and coverage (homogeneity) improve, making larger configurations preferable for larger or acoustically challenging environments.
Sound consistency: Larger arrays improve loudness and enhance the consistency of sound across different theatre zones, reducing the variability in the audience experience.
Optimal configuration: Based on the trend, the 4x2 MD96 configuration appears to be the most effective in providing high and consistent SPL, along with excellent homogeneity and a narrow SPL range, making it suitable for theaters seeking robust and uniform sound distribution.
Examining the performance of each array when optimized for a specific zone or zones, it's evident from the chart above that a 1x2 array is sufficient to cover the first 10 meters of the auditorium. It provides both sufficient SPL (95dBA broadband and 85dB at all octave bands from 250 to 10,000Hz) for most live performance use cases, with the exception of high SPL music shows. Additionally, it ensures adequate coverage for almost the entire audience, offering a consistent audio experience. A 90% broadband coverage is deemed adequate for this venue, with 85% coverage at all octave bands from 250 to 10,000Hz.
When trying to cover both zones, the 1x2 array achieves the 90% coverage threshold for the broadband dBA results but fails to meet the 85% threshold for octave bands from 4kHz and above (see chart below). All other arrays achieved this. Similarly, when assessing coverage for all three zones, the 2x2 array met the broadband coverage requirement but did not achieve the 85% ±3dB coverage at all octave bands (250-10,000Hz).
The above simulations provide the basis for an initial assessment of array sizing. Use the rule of 10 meters per row for height whilst considering the SPL requirement, noting that a 3dB increase occurs when the array size is doubled. Additionally, use the HOLOPLOT array calculator to evaluate beam control. This approach allows the designer to approximate the optimal system size before running a detailed simulation.
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