This is the second part of our series focusing on subwoofers. The first and third parts are available here and here.

Woofer Array Types
In pro audio, we find three kinds of woofer arrays:

1. Broadside Arrays, in which a number of woofers are arranged in a row, and the primary radiation is at right angles to the row. 

This is the typical subwoofer arrangement seen in most applications, either stacked (horizontal row) or flown (vertical row).  In current practice, broadside arrays are overwhelmingly the most common form.

2. Gradient Arrays, in which woofers are arranged and driven in specific ways to provide microphone-like directional patterns—cardioid and hypercardioid, usually. 

Such arrays involve woofers with multiple drive channels that may contain delays, filters, and/or polarity inversions to achieve their results. 

Gradient arrays may be purchased as single enclosures, or can be constructed using separate woofer boxes.

3. Endfire Arrays, in which a number of woofer cabinets are arranged in a spaced row pointed in the desired direction of radiation, and driven in a successively delayed fashion so as to create a very narrow pattern. 

The endfire array is the loudspeaker equivalent of a shotgun microphone. 

Endfire arrays are rare, and are only useful in specific long-throw applications, outdoors or in huge venues.

A broadside array is a row of woofer boxes (or stacks of boxes) with the sound radiation more or less at right angles to the row.  The row might be straight, curved, or staircased.

Broadside arrays are the most common woofer configurations, because they’re easy to design and set up. 

However, getting good bass over a wide area requires some additions to the basic approach, as we shall see.  Figure 9 through Figure 12 show some basic principles.

Figure 9 shows that long arrays have narrow patterns, while short arrays have wide patterns.

Figure 10 shows that straight arrays have patterns which become narrower and have more lobes with increasing frequency.  Curved arrays, if long enough, have more constant directivity.

Figure 11 shows that staircasing is essentially equivalent to tilting.  Staircasing can be useful when staging and/or appearance considerations prevent the use of tilted arrays.

Figure 12 shows that for pattern widening, staircasing can be used instead of curving.  In this case, the staircased results are better.

Groundstacked Arrays

Pattern Width
For groundstacked horizontal arrays, width of coverage is often an issue.  Straight-line subbass arrays wider than about 10 feet (3m) are too directional for most venues. 

For example, the graphs in Figure 9 show that the coverage pattern of an array of four EV Xsub woofers (approximately 12 feet, or 3.7m wide) is only 90° wide at 60Hz.  At higher frequencies, it would be even narrower.

An even more severe example is shown in the left-hand diagram of Figure 10, an array of six Xsub woofers. 

Physical width of the array is approximately 24 feet (7.3m).  This example shows that the pattern is only 60° wide at 60Hz, and highly frequency-dependent.

You can broaden and smooth the patterns by curving or staircasing the array (see Figure 12), or by using beamforming.

Systems with Left-Right Arrays
For systems with left-right arrays, it’s good to understand the pattern of each individual array, but optimum design requires considering both arrays at once.

If we had perfect control of directivity, we would make the left array cover only audience left, and the right array cover only audience right. 

Since this is not possible, the patterns overlap, and lobing results. The system design challenge is to minimize the lobing while at the same time covering the whole audience.

When the arrays are wider than about 10 feet (3m), you can take advantage of their narrow patterns to reduce lobing. 

By aiming the left and right beams offstage, you can reduce pattern overlap in the center while widening overall coverage at the same time. Figure 13 illustrates this. 

In the right-hand diagram, the woofer arrays have been aimed offstage at a 30° angle.  In the right-hand picture, the nulls are shallower and coverage at 90Hz is improved.

Beamforming can have approximately the same effect as offstage aiming.  Figure 14 illustrates the effect of applying beamforming delays to the array of Figure 13.  The results are quite good.

Large Central Stacks
In large venues and for outdoor stages it is often convenient to stack subwoofers in a continuous line across the front of the stage. 

If beamforming delays are used with such clusters, the results can be excellent.  Figure 15 shows the directivity of a row of 12 EV Xsub woofers with optimized delays.

Figure 15 illustrates a subtle beamforming detail that’s worth keeping in mind. 

If you look at the table of delay values, you’ll notice that they’re not in equal steps - the steps get progressively larger at the ends of the array. 

This is typical.  When you do your own beamforming designs (using LAPS or some other modeling tool), you’ll probably notice that larger delay steps at the ends of the array give better results in both aiming and beam-broadening applications.

Figure 16 shows the pattern of the same array as in Figure 15, but with no beamforming applied.  The coverage angle is narrow and more frequency-dependent. 

Such arrays can be useful for covering long, narrow venues (parade routes, for instance), but for normal concerts the beamformed solution shown in Figure 15 would be preferred.

This is the second part of our series focusing on subwoofers. This is the second part of our series focusing on subwoofers. The first and third parts are available here and here.

Jeff Berryman served as the director of Jasonaudio, a touring sound company based in Canada, and is a senior scientist with Electro-Voice.

Related Articles by Jeff Berryman:
What Really Defines Good Bass In Sound Reinforcement?
Discussion & Analysis Of A Variety Of Bass Coverage Patterns