Array Simulations

One of the greatest challenges to computer simulation is the loudspeaker array. It’s one thing to place some point sources into a virtual environment and calculate their complex interaction. It’s quite another to achieve results that correlate with the performance of a real-world array. PST has performed multiple array studies through the years where we strap multiple boxes together and compare measured to modeled performance. This provides a lot of insight on the accuracy of the process and what matters (and what doesn’t).

Realistic Expectations

Below is a comparison of measured vs. modeled horizontal polars for a 3-box horizontal array of typical “12-in. + horn” boxes, performed in CATT-A. The angular resolution is 5 degrees for the measured and 2.5 degrees for the modeled. The correlation between the measured and modeled responses, while not exact is actually quite good in the mid band when one considers what the modeled response cannot account for. It is more than adequate for determining whether to deploy the array, which is the objective of the investigation. The finger lobing in the higher octaves could be better resolved with 2.5 degree (or finer) angular resolution, but each halving of the angle requires 4x the number of measurements – over 10,000 for 2.5 degree data. One must ask if higher resolution to resolve interference is worth the effort.

It is important to have the correct expectation level when modeling arrays. This array does not provide even horizontal coverage, which is probably what the system designer needs to know.

Size Limits

There are size limits regarding the measurement of acoustic sources, imposed by the need to be in the far-field of the source. Combined with the need for a practical room size and measurement distance, it is usually necessary to measure array components individually and then assemble the array in software. While comprised of measured data, an array response is a simulation and must be regarded as such.

Box line arrays are a common example. Not only is the array as a whole too large to measure, the box angles may change depending on the application or the venue. It is important to understand that the best we can do is estimate the performance of the array as a whole. Fortunately that is sufficient for the selection of and aiming of the boxes, but it should always be augmented by in situ measurements for validating the coverage and equalizing the array.

Shortcomings of Simulations

Some of the significant factors that the current modeling processes cannot fully account for include:

1. Box-to-box variation in the point sources – 10 different boxes that roll off the assembly line will likely have 10 different axial responses. While manufacturers implement quality control measures to minimize the errors, they cannot be eliminated completely.

2. Shading from adjacent boxes – This is a “biggie.” One box in an array knows nothing about the physical presence of the other boxes, yet the effect of their presence can be significant. It has been proposed that a box be measured with “dummy boxes” to account for this, but that only characterizes the actual configuration that is measured – change the box angles and the acoustic response will change too.

3. Line arrays modeled from a string of point sources don’t behave like a true line source – When you stack two or more line array elements (measured individually as point sources), you are forming a new kind of source that is continuous along its length. This is the magic behind how real line arrays work. Unfortunately most simulations treat the boxes as individual point sources rather than as a continuous line source. The result is that the predicted pattern will exhibit severe “finger lobing” in the upper octave bands, even though the actual physical array may not.

Here is a study that addresses items 1 and 2.

CATT-Acoustic provides a novel solution for item 3 by using a Line Element (LEL) component that simulates a continuous source using a larger number of virtual sources (Huygens Principle). This is described below. The graphics were produced in the CATT-A Directivity module.

Modeled Response vs. Actual Performance

The existence of these (and other) complexities for array modeling reminds us that even though the computer’s graphic displays can look impressive, array simulations are estimates. Good sound system design philosophy means that we must maintain the distinction between measured and modeled responses. Line arrays are a valuable tool to the system designer. It is easy to make one look bad by modeling it from point sources.

Our philosophy is that it is better to acknowledge the shortcomings rather than pretend that they don’t exist. The investigation is complete when the objective is reached. The objective for array design is usually to determine the required number of elements and their aiming. The details should be addressed in the field using actual measurements.

All good mechanics know the limitations of their tools.

Array Simulations

Realistic Expectations

Size Limits

Shortcomings of Simulations

Modeled Response vs. Actual Performance

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