The BEST subwoofer array for large concerts?

During my interview with Adam Hill we discussed an AES paper he coauthored called Subwoofer positioning, orientation and calibration for large-scale sound reinforcement. During the interview, we focused mainly on the interference of stages and other boundaries on directional subwoofer arrays, but there is another large part of the paper where the authors describe a ground-based optimized subwoofer array that I thought would be fun to try to recreate.

Wondering how a gradient subwoofer array works? Check out this video explanation.

1 – Minimize spacing to avoid nodes

As a starting point, four single cardioid subwoofers were placed across the front of the stage on the ground with four meter spacing.

plan view

This initial setup gives very limited coverage across the audience area, although there are no noticeable nodes anywhere in the coverage area.

prediction @63Hz

2 – Expand horizontally and vertically

Since the additional subwoofers of the system will be off to the sides of the stage, they can each be stacks of three subwoofers.

prediction @63Hz

3 – Angle outside subs 45º

The optimization routine shows that simply rotating the outside subwoofer stacks away from the stage by 45° gives very even results across the audience area while keeping SPL on the stage under control

prediction @63Hz

Note that I have not taken into account the potential gain difference between my 2-element gradient arrays across the front and the author’s “four single cardioid subwoofers”.

Results

15dB of F2B (front-to-back) rejection at 43Hz comparing the 1st row to DSC (down stage center). 6.75db of rejection at 90Hz.

Can this be improved?

The authors leave the design wide open for adjustment and make this recommendation about placement:

an even coverage in the audience area is best achieved when subwoofer spacing is minimized

If we add one more sub it will decrease the spacing and DSC should benefit from improved F2B rejection. Let’s also add a 2nd order Linkwitz-Riley LPF at 203Hz.

1.75dB of improved rejection at 90Hz. Otherwise, similar results.

How would you improve this design?

What are your ideas for improvement? Comment below.

You can download my MAPP file here.