I have always thought that ground-stacked subs would produce 6dB more SPL because they are coupling with the ground. You’ve probably heard people say things like:

• “Having subs next to a boundary gets you 6dB of additional sensitivity”
• “The ground is like a mirror, doubling sub energy. “

I was just running a couple of tests for myself to confirm the reliability of this number, but I couldn’t. In fact, all of the models that I tested actually returned lower average level when the subwoofers were on the ground compared to flown in the air.

50ft Room

In the low range the flown sub dominates, but later the ground sub takes over.

150ft Room

I also thought that a corner placement would give you even more SPL, but I couldn’t prove that either.

Maybe the room gain from the walls is making the phenonenon harder to verify. Let’s try a bigger room.

300ft Room

Rats.

150ft – Outside

Surely if I turn off all of the walls, except for the floor, we’ll get that free 6dB.

Damn it. I want my free money back.

Why is this happening?

I have a two ideas:

1. I put the mics in the wrong place.
2. Flown subs get 6dB for free, too, baby!

The Mirror Effect

I had been taking ground plane measurements in the first models to remove the floor bounce, which made sense to me since I assumed an audience filled with people would have the same effect. There are two problems with this:

1. Below 100 Hz human bodies have little absorption, which is mostly where our subwoofers live. Plus, it’s hard to predict exactly how the bodies will be distributed.
2. If my measurement is coupled with the floor, it effectively shows half-space loading at any distance due to the mirror effect.

If the listener is located at the boundary he will hear a 6 dB louder direct signal than he would have heard if there was no floor regardless of where the subwoofer is located.

Comments On Half Space, David Gunness

If we zoom in on on the y-axis, it’s hard to tell which is which because any comb filtering is eliminated. No matter how far away the sub gets, measuring at the ground will show coupling.

If that’s the case then I should try measuring at head height.

Head Height

Let’s simplify the test by removing the walls and ceiling and using a single microphone position so that I can actually get this article done this year. I’ll move the mics up to head height, since that wasn’t working earlier.

Here’s the result from the same 300ft room, this time without walls, ceiling, or a 3-mic average.

Flown subs get 6dB for free, too, baby!

It is shown that a flown subwoofer [will] have a similar far-field efficiency to that of a ground-stacked subwoofer when a maximum subwoofer height is respected. This maximal height is linked to the venue depth via the DHER criterion, and depends on the listening height. For a standing audience, SPL efficiency is recovered for listening distances that are 5 times or more the subwoofer height. The audience benefits from a more homogeneous SPL distribution and an important SPL reduction close to the stage.

AES Convention Paper 10051, On the efficiency of flown vs. ground-stacked subwoofer configurations, Etienne Corteel, Hugo Coste-Dombre, Christophe Combet, Yoachim Horyn, and François Montignies

Pretty cool, right?

So if we want to recover SPL efficiency at ¾ audience depth, then the sub can be as high as 36.75ft and we get the added benefit of an improved front-to-back ratio.

The real benefit of ground stacking has to with the fact that listeners’ ears are not typically on the floor, but four or five feet above it. If the speakers are elevated above the floor, 45 degrees above horizontal from the listeners perspective, the ground bounce will produce its first comb effect notch at about 80 Hz. If the elevation angle is 30 degrees, the first notch moves up to 113 Hz. If the subwoofers are on the floor, then propagation is parallel to the floor and there is no ground bounce. Hence, there is no comb effect.

Comments On Half Space, David Gunness

It’s interesting that our measurement position is less than 10º, putting the first dip from the comb filter at 297Hz, well out of the operational range of this subwoofer. If you wanted to create a null at 125Hz, you would measure at 72ft depth at 23.8º with the sub.

The number isn’t black and white, of course. Even with the first null at 297Hz there is a 3dB drop at 140Hz.

So we can see that as we move closer to the sub, the difference in distance between direct and reflected sound will affect more of the operational range of the sub. At this time it is my understanding that with flown subwoofers we accept some amount of comb filtering in the front portion of the audience (anywhere before height of sub multiplied by five for standing head height) in exchange for improved front-to-back ratio, coupling with mains, and SPL efficiency in the rear portion of the audience.

What are your experiences on half-space loading? Comment below.