# How to Find Line Array Splay Angles

**When preparing the configuration of a “line array” (technically an asymmetrical composite coupled point source) I start with three pieces of information:**

**1) What is the desired coverage angle?** (From the loudspeaker’s point of view, the angle from the last row to the front row.)

**2) What is the range ratio?** (How far the top box needs to throw to the last coverage row, divided by how far the bottom box needs to throw to the first coverage row.)

**3) How many boxes are in the hang, and what splay angle settings are available?**

In the example I’ve made up, the coverage angle is about 45° and I’ve given myself a budget of 12 boxes.

The absolute throw distances are not nearly as important as the relationship between them. In this case, it’s 2.9 times farther to the last seat than the first seat.

Let’s start with a big ole’ constant curvature source and just cover the angle: 12 boxes at 4° splay gives us 48° of coverage.

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I didn’t take the time to add big bold lines for the coverage line, but you can clearly see the seating shape. **The gif animates, showing the prediction on octave centers from 250 Hz to 8 kHz.**

This is a symmetrical array that creates a completely symmetrical coverage pattern. **Note that due to the symmetry, we know that the geometrical center of this array – between boxes 6 and 7 – is on-axis (ONAX) for all frequencies.** That seems obvious now, but file it away.

The problem is that the desired coverage area is not symmetrical. Everyone will hear the show, but the folks in the front are going to hear it about 9 dB louder than the folks in the back. We know this thanks to the inverse squared law: for a range ratio of 2.9,

*20log(2.9/1) = 9 dB*

What about AutoSplay? The software gives angles of

2,0,2,2,2,2,2,2,4,6,6

(that’s 11 angles, because it’s 12 boxes). Zero-degree splays cause a whole bunch of problems but what I’d like to focus on here is the problems that Auto-splay presents for trying to EQ the array. The onaxis (ONAX) mic position is the mainstay of the EQ process, and this is where we run into problems: where is ONAX?

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The main coverage lobe – the loudest point along the coverage angle – now shifts over frequency. Why this happens is not a quick explanation, but it has to do with the amount of directional control the array as a whole and the individual boxes can exert over different wavelengths. As frequency falls, wavelengths get longer and the direction in which the box is pointed matters less and less. **The takeaway here is that we no longer have anywhere to place the reference mic that is representative of the array as a whole, and thus no firm basis on which to make effective EQ decisions.** This is not the fault of AutoSplay, rather it’s the consequence of having an asymmetrical array shape (created by AutoSplay).

So let’s skip the AutoSplay and come up with our own splay angles. The following is heavily based on the McCarthy / Meyer approach with a few little adaptations of my own. For the full story, read Bob’s book. The idea behind an articulated “line array” is that we can use overlapping coverage of adjacent boxes to create summation and offset the level variance. We need more level towards the back, so we want more overlap towards the top of the array. How much more? Range ratio was 3:1, so let’s use three times as much overlap at the top. (Put another way, a ratio of 1:3 between the angles at the top and bottom of the array). In theory this offsets the range ratio, although this is one of the areas where I depart from Bob McCarthy’s guideline. I find that a splay ratio 30 – 50 % larger reduces the amount of shading I need later.

**If we divide the array into composites, and we keep each composite symmetrical, we can “solo” each section of the array and know exactly where ONAX is for all frequencies**, no different than working with a single loudspeaker. Then we just combine them and use EQ to compensate for the combination effects (namely LF buildup) and we’re good to go. The top composites need to go further so in general they should consist of more boxes at smaller splay angles.

Out of my 12 boxes, I did four composites, A, B, C, and D. There’s a little guess test and revise based on the angles your particular system can actually hit, but let’s go with

A= 4 boxes @ 2° (for a total of 8°),

B= 3 @ 2° (for a total of 6°),

C= 3 @ 4° (for a total of 12°), and finally

D= 2 @ 8° (for a total of 16°).

That gives me a grand total of 42° of coverage, plus the “fringes” that extend past the ONAX of the topmost and bottommost boxes.

**There’s no magic here. Just keep pushing and pulling and obeying the guidelines of fewer boxes per composite at larger angles as we go down.**

When we translate that into interbox angles (which we need to give the software and the riggers) we get:

(2-2-2) 2 (2-2) 3 (4-4) 6 (8)

The parentheses indicate interbox angles within each composite (A, for example has 4 boxes and therefore three interbox angles) and the transitional splay angles (between composites) are visible between the groups. Another brilliant convention of Bob’s that we can’t fully dive into here.

The trends are observed: fewer boxes at wider splays as we go down, and the bottom splay is 4 times the top splay, so we’ve more than offset the range ratio.

Each symmetric element then has a clearly defined ONAX at all frequencies, allowing us to place a mic and apply equalization. The animation shows the frequency range for each composite segment in turn:

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The computer took the liberty of rescaling the color key for each frequency, which is annoying, but the general concept is clearly visible.

The combined EQ process is tricky and I won’t get into it here, but once we put everything together, we can achieve extremely even coverage.

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The LF lobe will still radiate from the geometric center of the array since the wavelengths are so long, the few degrees of splay are practically ignored. Some platforms allow a little all-pass steering here, but even without it, we have a very well-behaved PA system.

One last note: it’s a bit hot down in front, so after doing what we can with splay, a little shading can go a long way. Taking the bottom two composites (bottom 5 boxes) down by 3 dB results in an even lower-variance coverage scenario:

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Before we head to catering, let’s address the shading issue. There’s sometimes a concern about how much headroom is lost by turning some of the boxes down. The boxes have the most overlap at LF, so that’s where the largest potential losses would occur. In this case, taking 5 out of 12 boxes down by 3 dB creates a loss of just over 1 dB of LF headroom…Nothing to be scared of.