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Author Topic: End Fire Sub-array element spacing  (Read 7880 times)

Jamin Lynch

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Re: End Fire Sub-array element spacing
« Reply #10 on: May 20, 2019, 03:54:08 PM »

A local sound Co. often does end fired subs on larger outdoor events. He told me he also incorporates speed of sound into the calculations for spacing. Is that really necessary? 
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Ivan Beaver

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Re: End Fire Sub-array element spacing
« Reply #11 on: May 20, 2019, 03:59:53 PM »

You find the "acoustic center" of the subwoofer and space from that point.  Ported, front loaded subs will have the acoustic center "kind of" close to the transducers but a horn loaded sub will have the center behind the box.
But since you "should" be using all of the same model subs (to keep the phase response the same), the length of the horn (in a horn loaded sub) doesn't matter, since it takes the same time for all of them to "get to the front".

So the distances just cancel out
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Ivan Beaver
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Ivan Beaver

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Re: End Fire Sub-array element spacing
« Reply #12 on: May 20, 2019, 04:04:13 PM »


Thank you!


Is there a point at which adding more elements is no longer helping? For example, if you had 10 identical subs and all the room you needed (flying, for example), would you be better served putting a long end-fire line of 10 subs, or maybe pair them up: 2 adjacent and 5 'elements' or steps in the array?



Remember these things when dealing with any "steered" array of subs.

1: The output of the same number of boxes in a steered array will be less than the output of them all stacked together, all facing forward.

2: In a Cardioid setup, you will lose punch and impact (due to the cancellation).

3: In a Cardioid setup, you will also lose some low end response (due to the cancellation)

4: A Cardioid setup has greater rear rejection and wider freq response of cancellation, but suffers from both 2 and 3 above.

5: An endfire has less rejection, and is more "one note" type cancellation.

The only time I do either setup is when the rear rejection is simply more important than sound quality.
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Michael Lawrence

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Re: End Fire Sub-array element spacing
« Reply #13 on: May 20, 2019, 04:28:39 PM »

I find it helps to draw a distinction between a two-element "endfire" array and an endfire array consisting of 3 or more elements. With only two, you definitely have the "one note" cancellation thing going on, and the spacing becomes very important to get the quarter wave correct at whatever frequency you want to tune to. I find this setup to be of very limited effectiveness.

Once you get up to 4 elements, you have sufficiently staggered arrivals in the rear to achieve excellent broadband cancellation.

Attached are MAPP predictions of 4 elements and, just for fun, 10 elements at 3.5' spacing, at 19 Hz, 31 Hz, 63 Hz, and 125  Hz.
General trends: More boxes will increase rear cancellation and decrease forward beamwidth.
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Tim McCulloch

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Re: End Fire Sub-array element spacing
« Reply #14 on: May 20, 2019, 04:41:23 PM »

I find it helps to draw a distinction between a two-element "endfire" array and an endfire array consisting of 3 or more elements. With only two, you definitely have the "one note" cancellation thing going on, and the spacing becomes very important to get the quarter wave correct at whatever frequency you want to tune to. I find this setup to be of very limited effectiveness.

Once you get up to 4 elements, you have sufficiently staggered arrivals in the rear to achieve excellent broadband cancellation.

Attached are MAPP predictions of 4 elements and, just for fun, 10 elements at 3.5' spacing, at 19 Hz, 31 Hz, 63 Hz, and 125  Hz.
General trends: More boxes will increase rear cancellation and decrease forward beamwidth.

Nice, Michael!  The back and side lobes of the 2 arrays are rendered instead of ignored and worth a look.
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Michael Lawrence

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Re: End Fire Sub-array element spacing
« Reply #15 on: May 20, 2019, 04:48:21 PM »

Is there a practical reason beyond the size of the speaker that determines the spacing? If, for example, they were closer or further than 1m and the appropriate delay set accordingly, could you expect similar results?


Or, on the other hand, does the physical spacing (long or short) play a large role in the effect?


This is a fun thought experiment. Imagine that we had a sub that was a tiny point source, the size of a sugar cube. Now we can place them as close as we want. If we made a four-element array with 3-inch spacing, what might we expect to happen?

Behind the array, we won't build any cancellation, because all four arrivals are within a millisecond, which spreads the arrivals over about  a 36-degree spread at 100 Hz. At 30 Hz, it's less than 10 degrees spread, and we can expect behavior similar to a single box (only louder). The attached image shows the scattered rear arrival times of a 4-box endfire at 1m spacing, enough to build some rear rejection. Notice the phase offsets grow over frequency, as does the rear rejection.

It's interesting to note that when building an endfire arrray out of those Meyer VLFC boxes, they had to scale the whole thing up for the same reason: the wavelengths in question are so much longer that they needed more physical offset to accrue enough phase shift to cancel them.

In the other extreme, spacing them out much further and using longer delay times. On axis, you can still get almost as much summation. But the beamwidth narrows very quickly because moving even slightly off axis means you accrue different arrival times from each box and your sync falls apart. You'll also have an overall decrease in SPL because the boxes are at a wider range of distances from the listener, so we can't expect a full summation of equals. This gets better the further back you go. (Edit: that's evident in the top pane of the MAPP screenshot below)

So it should come as no particular surprise that the standard (approximately) 1m spacing turns out to be just about optimal.


« Last Edit: May 20, 2019, 04:50:34 PM by Michael Lawrence »
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Luke Geis

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Re: End Fire Sub-array element spacing
« Reply #16 on: May 20, 2019, 04:52:26 PM »

I think the practical limitation for an endfire array is 4. After 4 subs are laid out, you pretty much utilize 12' or more of floor space.

Cardioid arrays are better at rear rejection but are not always practical. Most cardioid arrays require space behind the array to work properly. If you have a boundary too close it affects the array and renders it ineffective for the purpose of pattern control. Cardioid arrays are most effective in groups of two in terms of rejection.

Endfire arrays are less affected by a rear boundary but prefer having open space all around as well. Most arrays do not like having boundaries near them which make many of them less appropriate for certain applications.

I recently got to wow a client by using a cardioid array. They wanted the subs behind the dance area but had other activities going on behind the subs that would be affected by the energy they produce. I decided on a cardioid array and the client was rather baffled when I started placing the subs atop one another in opposite directions. When I explained that when I was done there would be less sub energy in the staging area as a result, they were still questioning what I was doing. They had always done it normally. When I had finished tuning it I had the client listen in front and behind the array and they were blown away.

Each array has its pro's and con's. The cardioid array is generally easier to implement and takes up less space at the cost of overall quality. The endfire array has less overall rejection in the rear, but should sound better at the cost of using much more space.
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Kevin McDonough

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Re: End Fire Sub-array element spacing
« Reply #17 on: May 21, 2019, 04:01:02 AM »

Cardioid arrays are better.....

Endfire arrays are less.....

I note that you and Ivan have both referred to arrays this way, but this nomenclature always confuses me. Aren't they both cardioid arrays, just different types? Just different ways to achieve a cardioid dispersion pattern?

From experience and from seeing how other people have used the terms, I presume when you say cardioid you mean whats often called a CSA stack, where subs are stacked (usually) 3 high and one is reversed?

Would more accurate terms not be something like "a CSA style cardioid array" and "an endfire style cardioid array"?

Anyway, to answer the OP's post yes, as many people have said the basic premise of the idea of an endfire array is that you space the subs 1/4 wavelenth apart of the centre frequency you want to cancel, and then add 1/4 wavelenth delay to the front sub.

From the rear sub's perspective, the sound travels forward 1/4 wavelength and meets the sound travelling forward from the front row. This front row sound is time delayed 1/4 wavelength, and so should be coming out of the subs just as the rear row sound catches up to it, and then the two sounds should progress forward in phase.

For the sound travelling backwards: sound leaves the front sub already 1/4 wavelength delayed. It then travels back 1/4 wavelength, so by the time it meets the rear row it is 1/2 wavelength out of phase and cancels out.

Of course, as people have said this only holds true for the one frequency you've based your spacing on, and a band of frequencies around that. At that frequency, in theory the waves meet perfectly travelling forward and you get perfect summation, and meet perfectly travelling back and you get perfect cancellation. However real world factors come into play and the best way to line everything up to make sure it's as good as possible is with Smaart/Systune/etc.

As you move up or down the frequency range, the wavelenths and times change, so the wavelenths begin to meet at different times in their cycle and you do get some audible artefacts.

A CSA stack where you stack the subs and reverse one (or a sub from manufacturers like d&b that has cardioid built in) is a little harder because you don't have the proper physical spacing between sources, and so the delay times become different. In this case it really does become a case of measuring with software and increasing the delay until you get a suitable level of cancellation, balanced with not changing the sound out front too much.

In both cases, if you really want to get deep into it you can try using FIR or all-pass filters to change phase. Rather than just delaying a sub by a specific time amount, if you can start to change phase you can create (in effect) a variable time delay, changing with frequency. By matching this up with the increasing wavelength, you can keep the in-phase/out of phase relationship going for longer and achieve a wider band of cancellation.

But again the balance and challenge is doing this without effecting the overall audience sound too much.

K








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Kevin McDonough

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Re: End Fire Sub-array element spacing
« Reply #18 on: May 21, 2019, 10:50:26 AM »

double post, quoted myself somehow  :o
« Last Edit: May 22, 2019, 03:32:00 AM by Kevin McDonough »
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Luke Geis

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Re: End Fire Sub-array element spacing
« Reply #19 on: May 21, 2019, 01:00:09 PM »

There are practical applications to both styles of cardioid setup. As mentioned boundaries can affect certain types a little more than others. Your typical cardioid sub array is just easier to deploy, works well and can get better overall rearward rejection in a smaller two sub configuration. Just to muck up the waters some more though let me purpose a possibility :)

You can do a multi-frequency endfire array. If you have 4 subs you can place the second sub to get your short length frequencies reduced and then you can use your 3 and fourth subs spaced out differently to get lower and lower frequencies reduced. You will not achieve great levels or rearward rejection, but you can get more broadband reduction. For example sub 2 may be placed 2.82' away from the first sub to rid 100hz, the third sub can be placed at 4.7' to reduce 60hz and then the fourth sub can be placed at 7.06' for reduction at 40hz. This should make for a fairly broadband reduction behind the array while still having good addition up front.

For your typical cardioid array, 3 subs are popular because you get more forward energy at the cost of reduced rearward rejection. A 2 sub cardioid array is more effective at rearward reduction but does have less than ideal forward energy because one sub is lagging in phase but is still technically in time. The rear facing sub is delayed as such that its forward energy is in time with the forward facing sub, but that energy is 360* lagging in phase, so it couples but it is not 100%. There are other artifacts with a cardioid sub array though. The angle in which it creates the rejection is based on which sub is leading the media. If you place the subs side to side, you will get the most rejection at a 45* angle from the rear facing subs side. When placed atop one another it is the same. The most reduction will occur 45* off the face of the rear facing sub that is opposite the forward facing sub. If the rear facing sub is on top the reduction occurs on top of the stack and if the rear facing sub is on the bottom you will get the reduction on the bottom side of the stack.

Another potential case to improve the reduction in the rear of a cardioid subarray that has three subs is to reduce the level of the forward facing subs to match the energy of the rear facing sub. This will reduce the overall output but will improve rearward rejection. The three subcardioid array is great as it has two 45* lobes of rejection off the rear making rear rejection more broad and predictable.

Again, each array has its pro's and con's, and the best option is all about circumstance and application. I feel that the cardioid is just the most usable between the two options. I have used both though and each has worked wonderfully for the task at hand.
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Re: End Fire Sub-array element spacing
« Reply #19 on: May 21, 2019, 01:00:09 PM »


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