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Pac-Man Is Back: Advantages Of 3D Polar Measurements

If you see him on a prediction coverage map, chances are the directivity balloon of the loudspeaker was not fully measured...

Remember Pac-Man (originally “Pakkuman” in Japan), the video game that debuted in the 1980s? For the unfamiliar, Pac-Man is a yellow ball that opens its mouth to eat dots as it is guided through a maze while avoiding being touched by four ghosts.

What’s Pac-Man got to do with loudspeakers? Well, if you ever see him on a prediction coverage map, chances are the directivity balloon of the loudspeaker was not fully measured.

For a long time in pro audio, loudspeaker directivity was measured horizontally and vertically, with this data shown as polar plots that were most commonly seen on product specification sheets (Figure 1).

The loudspeaker would be placed upright on a turntable with horizontal data measured, and then turned on its side for vertical measurement.

With the advent of modeling software, the need for 3D measurements (that is, measurements taken all around a sphere surrounding the device under test) became apparent (Figure 2).

However, a system that was able to measure and store all that was complicated, slow and expensive, so most often interpolation was performed to fill in the data for the angles in between. For a typical horn, say 90 x 60 degrees, the error would be up to 2-3 dB on the front hemisphere, but many are content to live with these limitations.

Figure 1 (left) and Figure 2.


Much To Be Desired
The emergence of line arrays (call them line source arrays or use any other term to your liking) for concert applications has brought the limitations to further light. These vertically articulated array modules most often use compression drivers that are invariably attached to a wave shaping guide or ribbon emulator of some sort, and this produces very narrow coverage angles at high frequencies (passive column loudspeakers commonly also have much narrower vertical dispersion as compared to horizontal, which arises from the stacking of drivers).

The 3D representation of the directivity of a high frequency band looks like a balloon that’s squashed vertically. Unfortunately, this means that interpolation leaves much to be desired.

Users of line arrays expect the manufacturers to provide some sort of simulation software in order to figure out the size of the required array, as well as the location and rigging configuration, ahead of time. Most earlier line array-specific prediction software calculated only vertical coverage, so the lack of good data for the missing oblique angles was not a problem, but with 3D modeling software for line arrays (that maps the results for complete listening planes) becoming much more common, the issue can’t be avoided anymore.

Of course, perfect coverage when seen in a simple vertical plane can show uncovered areas when a complete 3D room mapping is performed, and sub-systems such as center fills and out fills can now be included in the prediction, which means that the user will tend to request that the manufacturer provides 3D simulation software.

The Evidence: Balloons
To be able to compare full spherical measurements with those using interpolation, I ran 3D directivity, fully anechoic measurements on a commercial line array module from one of my customers. A resolution of 5 degrees was used, which means a whopping 2,664 (automated, naturally) measurements, a lot more than seen on the simplified drawing above. The full data set was read and directivity balloons were plotted.

I then read just the horizontal and vertical parts of the very same data (that’s just 144 points, or about 5 percent of the data) and generated the information for the missing 95 percent angles via interpolation. Figure 3 shows the balloons obtained from interpolation with the ones obtained from full spherical measurements. For the 1 kHz, 1/3-octave band, vertical and horizontal directivity is similar, and hence the interpolation works relatively well—the resulting balloons differ but are still reasonably close. However, at 2 kHz, 4 kHz and 8 kHz, the result gets increasingly disastrous.

Figure 3.

Making A Difference
Now that we’ve seen how lacking directivity balloons look when only horizontal and vertical polars are measured for a line array module, let’s see what happens when we model it with 3D prediction software.

Figure 4 shows the result of modeling the area below a single box, pointing forward. A 1-octave band centered at 4 kHz was used, and all settings are exactly the same. Above we see the result of using interpolation from horizontal and vertical measurements (Pac Man returns!), while below we see the 3D measurements. All settings are exactly the same. Big difference.

Figure 4.

Because these loudspeakers are most often used in multiples (that’s why they’re called arrays), let’s now run some coverage predictions for an 8-module, arced array (Figure 5). Now the differences are not as obvious as for the single box, but they’re still significant. Results from complete spherical measurements show wider more uniform coverage, a cleaner nearfield, and about 1 dB more sound pressure.

Figure 5.

For line arrays or any other loudspeakers where the vertical directivity is significantly different than the horizontal (such as column loudspeakers), 3D polar measurements are required because interpolation from vertical and horizontal polars can result in a high degree of error.

By The Way…
Did you know that although a cone loudspeaker is modeled and often referred to as a “point source,” it’s far from that? This is probably not surprising, since it’s a radiating surface, and as such, it shows array-like characteristics.

When measuring a polar plot for a single frequency (in Figure 6 we used 2413 Hz on a single 18-inch subwoofer), this becomes very obvious, with all of its notching glory (we can model the front part of the polar using Bessel functions for a somewhat smaller piston, which you can see on the dashed curve). Oh, and you’ll never get a perfectly symmetrical polar plot from a paper cone.

Figure 6.

Joe Brusi heads up Brusi Acoustics (www.brusi.com), an electro-acoustic consulting firm based in Valencia, Spain that provides a range of services, including loudspeaker directivity measurement.

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