Sub Placement Part 2

Sub Placement Part 2

My previous post covered the boring groundwork of sub-sub and sub-boundary interactions. Now we can use that knowledge to create different subwoofer arrays. You may find it helpful to review the basic beamsteering mechanisms and how those look on an analyzer, as we’ll be putting those concepts in to practice here.

These predictions were created with MAPP XT, and unless otherwise noted we’ll see the response at 30 Hz, 60 Hz, and 120 Hz, in 1/24 oct resolution, to get an idea of how these setups perform over the entire sub range. 

Our overall goal here is to direct the sub evenly over the audience while minimizing energy hitting the walls and washing the stage.

I’m terrible with graphics, so here’s our venue:

We have a 120 x 80 foot room with a 40 x 24 foot stage along the left wall. The dimensions aren’t important, but it’s a helpful reference.

Broadside array

Nothing but a good ole’ line of subs across the front of the stage. As we saw in the last post, the idea is that the energy hitting the side walls is not coherent and so this creates a narrowing effect. This is a true “line array.”

This is good for keeping energy off the side walls, but the stage is getting blasted. We see the beam narrowing in action, and notice that the beamwidth halves as frequency doubles. You can get the same effect by keeping frequency constant and doubling the length of the line. To prove that beam angle is only a function of line length, let’s remove every other box, but keep the total line length the same:

Okay, they fired the video crew and we got a lot of extra budget so let’s line up every sub we have.

Notice we have narrowing of the coverage angle at all frequencies. Now we can really punish the guys in the mosh pit.

Interesting thing happening at 120 Hz. Readers of Bob McCarthy’s work will be well familiar with the Parallel Pyramid visible here. Sufficiently long lines with no angular splay result in a coverage pattern that continuously narrows over distance, which is the opposite of how we expect a single loudspeaker to behave. (As an aside, this is why putting 0° in a line array is inadvisable – the HF creates the “razor blade of death,” leaving significant coverage gaps.)

Now our power alley is over 12 dB hotter than the folks on the aisles. This might be desirable in a reflective room but if we’re outside with a wider audience area, this is no good. How can we widen the coverage when necessary?

Arc

Let’s physically bend our line into an arc. The beam narrowing is caused by overlap, and so by arcing the speakers, we’re in theory reducing the overlap. How effective is it? Depends on frequency:

In the LF, the coverage shape is virtually unchanged, because the subs are virtually omnidirectional. As frequency rises and we gain some more directional control, the physical curvature becomes more effective. Now the coverage is wider in the HF than the LF, which is the opposite of what we had earlier! We can tweak the curvature to get the coverage we need, but with flat-fronted stages, we can’t push the barricade / audience back that far, so what else can we do?

Delayed Arc

Looking at the arc array from the audience perspective, the boxes on the ends are physically further away than the boxes in the middle. If we add delay to the boxes on the ends, their output will take longer to reach the listener, and so we’ve electronically pushed them further away. (If you really want to fry your brain, consider the fact that electronic delay always pushes the box away from the listener, regardless of where they stand. Picture a simple stack of two subs, and delay the top sub by 8.8 ms. Now at any point in space, that box will behave as if it’s 10 feet further away.)

To illustrate the mechanism, let’s start at the top of the line and add progressively more delay as we go down. Here’s what we get with 0.5 ms / box:

We learned in the previous post that we can expect the most summation whenever sources meet at equal time and equal level. The delay changes where the boxes meet at “equal time.” If the sources were spaced more closely, we would see a sharper steering angle for the higher frequencies. But now that we see the mechanism, let’s use it to widen the coverage. We can replicate the physical arc by leaving the center boxes at time 0 and adding more delay as we move towards the ends:

This spreads the coverage outward, widening at all frequencies. Remember that using time as a steering mechanism is really using phase as a steering mechanism, and so we’ll see more effect from the steering as frequency rises. In this case, the 4.5 ms of delay at the ends of the array is only a 48° phase offset at 30 Hz, which is not enough to build any meaningful steering. 60 Hz is looking pretty good, and we’ve clearly oversteered by 120 Hz. The problem with delay-based steering is that it is not one size fits all. We have 4x the effect at 120 Hz that we have at 30 Hz.

Broadside Cardioid

Now let’s introduce another steering mechanism: polarity. Let’s replace each element in the broadside line array with a cardioid setup. (If you’re foggy on this, check the article I linked up top. I’m using the gradient-style cardioid array for illustration purposes, but this particular arrangement is far more commonly done with an inverted stack configuration because of the smaller footprint.)

Measuring from the rear, the upstage sub in each pair is delayed to match the arrival from the downstage sub:

and then polarity-reversed. Here’s a single set:

So let’s fire up the whole line:

Now we’re getting somewhere: we have the beam-narrowing effect of the line length, and the reargoing cancellation of the cardioid.

Broadside Cardioid Delayed Arc

Now let’s get crazy – what if we add the delayed-arc technique back in, progressively delaying the cardioid elements towards the ends of the line to try to wider the HF coverage back out?

We’re a little bit over-spaced at 120 Hz but this is starting to resemble a well-behaved sub array in this venue.

It should be noted that the “impact” or “punch” associated with “fancy” sub arrays can be less than a standard LR setup, because the steering relies on multiple arrivals and polarity inversions. They do make their way out front, and often the transients don’t hit as hard as a result. Whether or not this tradeoff is worth it is for you to decide.

Cardioid L/R

Okay , so what if we don’t have ten boxes to play with? Let’s go back to the two-element cardioid and see what we can do with two boxes stuck on one side of the stage:

An even stronger cardioid pattern can be obtained by using a 4-box endfire array, but that takes more boxes and more space. If you only have two boxes at your disposal and rear rejection is a priority, I submit that this two-box configuration is a serious consideration.

Seeing as two subs per side is a relatively common configuration, running them in cardioid gives you almost as much firepower as the side-by-side setup but gives a significant reduction to on-stage sub wash.

Supercardioid

Given the popularity of active subs with baked-in cardioid presets, it’s easy to overlook the fact that cardioid may not be the most effective pattern for rear rejection, especially if the subs are not directly in front of the stage.

Moving the measurement mic further onstage, and using that point as the alignment point instead, will shift the maximum cancellation towards the center of the stage, which I suggest is a bit more valuable. One side:

And both sides:

This configuration is exceptionally clean on stage, a huge improvement over the standard L/R if you can spare another processing channel for delay and polarity inversion.

Even with four highly reflective walls, there is a clear reduction of LF energy on stage.

Stand By Me

All of this assumes, of course that we don’t have audience seated to the sides of the stage. In an arena setting, all of these array configurations are disastrous. This is a huge topic but I’ll mention just one special configuration: Dave Rat’s Sub Vortex. It’s a configuration of four double-18 boxes per side.

The timing is variable based on how large we want the side lobe to be. Dave has the MAPP .xml files for the array on his seminar website if you want to play with them yourself. Scroll down this page of Dave’s blog for more on the Vortex setup. Given a larger space to play in, upper-octave rear rejection is certainly impressive.

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