I have developed, what seems to be, a lesser known method to find target coverage angle and quickly estimate average splay for a line array in the field in relatively few steps. I discovered it by necessity while creating Pro Audio Workshop: Seeing Sound 3 years ago. Recently a student challenged me on a couple of points and it motivated me to take a closer look to see if I could make it more efficient.

Here’s how I have seen other people do it.

Bottom speaker down angle – Top speaker down angle = Target coverage angle

17º – 6.78º = 10.22º target coverage angle

This works fine when you are using modeling software, but I was looking for a solution for the field with a laser disto and a calculator while I have a team of people waiting on me. After playing around with some right triangles for a bit, I discovered a pretty simple method

**In short, if you know the array’s rigging height and where the audience starts and ends, you can find the target coverage angle without software.**

## Find target coverage angle without software

Here are the steps:

- Solve triangle Y. You need the length of two sides or one side and one angle. I would go with two sides since that seems to be more reliable.
- Solve triangle Z. You can find the length of the opposite side (6.07′) by subtracting the array height from the from the rigging height. You can estimate the array height by multiplying the number of boxes by a single box height.

Then plug those numbers into a triangle solver.

16.88º – 7.03º = 9.85º

## What about inclined audiences?

But that only works for flat audience planes. What if the audience is at an angle?

The process is a similar. To solve triangle Y, we’ll subtract the the height of the end of the audience plane from the rigging height above the audience.

14.8 – 6 = 8.8ft

Solve for the missing angle. 4.19º

We already have the solution for triangle Z (16.88º).

16.8 – 4.19 = 12.61º target coverage angle

## Now what?

With one more step we can calculate average splay.

tar cov ang / available splay angles = average splay

12.61º / 11 = 1.2º

My speakers don’t offer a 1.2º splay, so I’ll round down to 1º and make up for the loss with a few of the last speakers. Now I have plan to hand the riggers.

What is the result using average splay?

It’s not great, but in a pinch I’d rather go with this result rather than leave everything at 0º or just guessing.

The easiest way to improve this result is to use the the automatic solvers built into your modeling software. The best way to refine the result manually for even more control is covered in detail in Pro Audio Workshop: Seeing Sound.

Warning: Software should always be used to double check rigging points and weight distribution. (Thanks Samantha Potter!)

Have you tried calculating line array splay in the field without software? How did you do it? What were your results?

Peter says

Why don’t you use the tan-1 formula for a rectanglar triangle to calculate the angle, it’s much easier.

Like triangle Z, the angle is tan-1(6.07/20) = 16.88°.

And for Y tan-1(14.80/120) = 7.03°

Nathan Lively says

Thanks Peter! I’m not a geometry expert, so my solution is just based on some trial and error. Yours looks much simpler!