# Plenum volume and slot area for PPSL?



## Orion525iT (Mar 6, 2011)

Anybody have an idea how to calculate this? I have done tons of searching, but nothing definitive has come up. There are some suggestions of slot opening of 1/3 driver sd, and plenum of 1.5 x sd of one driver. But this information is hard to come by. I would have no idea how to model it, even if a had any clue how use Hornresp. 

This will be used for eight 8" subs with common plenum mounted IB.

Thanks


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## Orion525iT (Mar 6, 2011)

Crickets...

Not unexpected, this is a weird setup for car audio. Think I will make an educated guess and err on the large side for the plenum and slot opening. That way I can insert various thickness of plywood and alter the size of both to tune the system as needed. I should be able, in theory, to alter fs and q based on these two variables.


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## minbari (Mar 3, 2011)

maybe I am just not seeing what you mean.

for IB, you just make a baffle and mount all 8 to it.


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## Orion525iT (Mar 6, 2011)

minbari said:


> maybe I am just not seeing what you mean.
> 
> for IB, you just make a baffle and mount all 8 to it.


PPSL (push-pull slot loaded). Kind of like a Nelson Pass but push-pull and IB instead of OB


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## minbari (Mar 3, 2011)

Never even heard of that. Maybe a picture?

Is this like an IB isobaric

sent from my phone using digital farts


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## Orion525iT (Mar 6, 2011)

Not isobaric.



















The first pic with the 15" subs is a good example to start with. So take that picture then eliminate the port. Stack 4 more identical cabinets on top of each other like a tower so that the the subs now share a common plenum and slot. Now turn the tower on its side, so that the tower (and obviously, the slot) are horizontal instead of vertical. The slot faces the cabin. The back of the cabinet is completely open into the hatch area so as to be IB. The entire stack will fit between the shock towers with the slot, which will be the entire width of the car, firing over the rear seat. The hatch is walled off from the back of the rear seat and up to the roof, where the mouth of the slot ends (which is the edge of the driver basket). I have eight total drivers, I can fit twelve.

Push-Pull Double 15 Subwoofer Pic - Les Hudson - High Efficiency Speaker Asylum

The Nelson Pass




























Same idea but turned 90 degrees to horizontal, IB instead of OB, and push-pull wired out of phase instead of clam shell wired in phase.

The Slot Loaded Open Baffle Project Article By Nelson Pass

Theoretical Benefits


Push-Pull cancels distortion. This distortion reduction is reportedly more successful at reducing harmonic distortion below 150hz than shorting rings. http://audioroundtable.com/PiSpeakers/messages/19880.html
Push-Pull wired out of phase cancels mechanical vibrations
Q and Fs can be manipulated based on plenum size and slot area

The slot and plenum do act as a band pass, attenuating higher frequencies, depending on plenum size, back chamber size, and slot area. In realty, cross over will occur long before there is any benefit of band pass, but may further act to reduces higher frequency harmonics.


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## minbari (Mar 3, 2011)

Ah ok. I was told this was called a manifold box.

I made one of those for 2 10" back in the 90s. Best sounding box i ever made

sent from my phone using digital farts


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## Orion525iT (Mar 6, 2011)

minbari said:


> Ah ok. I was told this was called a manifold box.
> 
> I made one of those for 2 10" back in the 90s. Best sounding box i ever made


Ya its a manifold box, just a specific kind. Same idea is used in home theater IB, except they are not typically arranged push-pull.

I hope it sounds good. It should . It should actually take up very little trunk space because the separating wall will be part of the manifold, and whole mess will be bridged across the strut towers.

I guess I was looking for general guidelines for the plenum and slot. There really doesn't seem to be any, other than to make the opening large enough that you can slide the driver in through the slot (at least with a cabinet). But with IB, even that isn't an issue because you can surface mount, flush mount, back mount, whatever. You don't have to slide the driver through the slot to mount it. As long as the cone of the sub does not hit the magnet of the inverted sub, you have enough space. But that space impacts Q and Fs, and I am wondering if modeling these variables is possible.


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## minbari (Mar 3, 2011)

Couldnt help you there, i had it designed for me when i was about 20 (where does the time go?)

sent from my phone using digital farts


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## TOOSTUBBORN2FAIL (Jan 31, 2011)

Patrick had a thread on this, and I planned to try this for midbass, but my measurement mic is currently stuck in place for the sound deadening testing. That said, hopefully towards the beginning of november I can test this with midbass drivers.

Patricks thread detailed how to use hornresp, it took me days to get anything useable.


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## Orion525iT (Mar 6, 2011)

TOOSTUBBORN2FAIL said:


> Patrick had a thread on this, and I planned to try this for midbass, but my measurement mic is currently stuck in place for the sound deadening testing. That said, hopefully towards the beginning of november I can test this with midbass drivers.
> 
> Patricks thread detailed how to use hornresp, it took me days to get anything useable.


Do you happen to have a link to that thread?

Out of curiosity, how do you plan to implement this with mid base? Is it just a single driver slot load? After all the research into my sub design, I realized this could be used for midbass. It would be real easy for me to do a slot load my current midbass. One thing I noticed was that there is a peak in output, which has everything to do with the plenum. I don't think it is too important for subbass, because crossover more than likely will occur before this peak, but for midbass, it is much more critical to get right.

It seems a safe guess is slot area that is 1/3 total cone area which is ~7" per pair, but that is a bit larger than I would like.


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## TOOSTUBBORN2FAIL (Jan 31, 2011)

http://www.diymobileaudio.com/forum/technical-advanced-car-audio-discussion/82304-more-bass-less-space-2.html

Half way down that page, he hints at how to model it. 

For my car, I had planned to use two 7" midbasses per side, in a push-pull slot loaded set up, tucked into the corner of the kick panel. Enclosure for the bottom speaker would have been under the car, while the enclosure for the top speaker would have been in the dash. Since I'm not going to finish my current car, everything on hold until funds come around, and I pick up a truck. But, I built a test rig so I can test it. I just need to wait until the deadening tests are finished to use the mic.

The peak is definitely an issue, and the reason I wanted to try it out. The peak can be HUGE depending on slot size, and its right at the upper end of the midbass. Even with the subs, steep crossovers will be your friend. Patrick's plot for the 8" sub shows a 20db peak at 350hz.


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## Patrick Bateman (Sep 11, 2006)

Orion525iT said:


> Anybody have an idea how to calculate this? I have done tons of searching, but nothing definitive has come up. There are some suggestions of slot opening of 1/3 driver sd, and plenum of 1.5 x sd of one driver. But this information is hard to come by. I would have no idea how to model it, even if a had any clue how use Hornresp.
> 
> This will be used for eight 8" subs with common plenum mounted IB.
> 
> Thanks


Probably the most space efficient way to build it would be to do it the way that Tymphany did it:










Probably the *easiest* way to build something like this would be to do it the way that KEF did:



















There's some pics at this URL of what the insides of the Kef speakers look like:

KEF 103/4 Disassembly Photo Guide - diyAudio

One of the key things, which Tymphany did also, was to run a rod between the two drivers so they're physically connected to each other. Vandersteen does the same thing with their subs, so the two drivers are practically one solid connected unit.

As far as the area in the plenum, area at the mouth, length, etc -

The best way to figure that out would be Hornresp or Akabak. Just model it as if it's a horn.

If that's too much trouble, here's a few things off the top of my head:

1) You're going to get a quarter wave resonance in the cavity between the two woofers. That resonance will happen at approximate one quarter of the depth. For instance, if the depth of the cavity is 10", I'd expect to see a resonance at 313hz. Note that you'll *also* get a resonance vertically and horizontally, so this gets tricky. And that's on top of the resonances that occur inside the car! Aren't quarter waves fun?

2) I think Nelson Pass went with a dipole for his. In a car, it might be worthwhile to try infinite baffle. Plain ol' sealed will have the highest power handling.

3) The area of the plenum can be quite small. For instance, in horn loaded subs it's not unheard of to have compression ratios of four to one. In high frequency compression drivers we frequently go over ten to one. So with a 12" cone and a compression of four to one, we're talking about all the output of the woofer being pushed through a space that's the size of a 6" pipe. (because four 6" pipes have an area of one 12" cone.)

4) The depth of the plenum needs to be small too. You basically want to keep that 1/4 wave resonance above the passband. As noted above, a depth of 10" would resonate at 313hz. (speed of sound / four)

5) The area of the plenum is a bit tricky. Small is good. If the area gets large, it will start to act like a bandpass box. That might be good if you want gain, but it will also introduce group delay at the resonant frequency. So this is really a judgement call. Do you want good group delay and low efficiency like a sealed box? If so, use a plenum with a small volume. If you want higher efficiency you can use the area in the plenum to increase efficiency like a bandpass box, but then you're group delay suffers.

One way to offset the crappy group delay of the bandpass is to use a narrow frequency range, like one octave. That's what Danley does in his Synergy horns - very narrow bandwidth for the woofers.










In some respects a tapped horn behaves a bit like a push-pull plenum sub where the rear wave is delayed and mixed in with the front wave. Think about it this way:
Nelson Pass makes this sub with a bunch of drivers loaded by a slot.
That slot has a resonance and a delay. The resonance and the delay gets lower in frequency as the slot gets bigger.
One way to deal with the resonance is to push it out of the passband.
But if you juggle the parameters you can potentially use that delay and that resonance to flatten out the frequency response of the sound coming off the other side of the cone.


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## Patrick Bateman (Sep 11, 2006)

As a quick example, without busting out hornresp, I would anticipate that this plenum would have a resonance at 84hz, assuming that the plenum is about 40" deep.

The only program that could simulate this plenum is Akabak, because every single woofer is going to have a little bit of a time delay, depending on how deep in the plenum it is. The top woofer in the plenum will be delayed about half a millisecond, the next one about a millisecond and a half, etc. (Because sound travels 13.5" in a millisecond, and the lower woofers are 13.5" further away then the set above them.)

What's interesting is that it might actually improve the sound quality, because the resonances will be spread out a bit in the room, due to that delay. (I would still prefer to have the subs seperated by an even greater distance though, as illustrated in the Geddes thread on diyaudio about multiple subs.)

Here's the published frequency response of this sub:

Page Title


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## Orion525iT (Mar 6, 2011)

Patrick Bateman said:


> 1) You're going to get a quarter wave resonance in the cavity between the two woofers. That resonance will happen at approximate one quarter of the depth. For instance, if the depth of the cavity is 10", I'd expect to see a resonance at 313hz. Note that you'll *also* get a resonance vertically and horizontally, so this gets tricky. And that's on top of the resonances that occur inside the car! Aren't quarter waves fun?


Cavity depth should be less than that.



Patrick Bateman said:


> 2) I think Nelson Pass went with a dipole for his. In a car, it might be worthwhile to try infinite baffle. Plain ol' sealed will have the highest power handling.


Exactly my plan. I ran across that design and though it would be interesting to try IB, but with push-pull



Patrick Bateman said:


> 3) The area of the plenum can be quite small. For instance, in horn loaded subs it's not unheard of to have compression ratios of four to one. In high frequency compression drivers we frequently go over ten to one. So with a 12" cone and a compression of four to one, we're talking about all the output of the woofer being pushed through a space that's the size of a 6" pipe. (because four 6" pipes have an area of one 12" cone.)


So we are actually talking about compression ratios here? That is better than simple area ratios because area is does not determine compression ratio, volume displaced does. That ratio is quite high! Higher than I would have expected. There is actually no way to achieve that in a push-pull for most drivers, due to the dimensional constraints of the inverted driver's magnet; at least I can't think of any way. Slot load, yes; Push-push, yes; Push-pull, no. 



Patrick Bateman said:


> 4) The depth of the plenum needs to be small too. You basically want to keep that 1/4 wave resonance above the passband. As noted above, a depth of 10" would resonate at 313hz. (speed of sound / four)


Cross over will be way before this.



Patrick Bateman said:


> 5) The area of the plenum is a bit tricky. Small is good. If the area gets large, it will start to act like a bandpass box. That might be good if you want gain, but it will also introduce group delay at the resonant frequency. So this is really a judgement call. Do you want good group delay and low efficiency like a sealed box? If so, use a plenum with a small volume. If you want higher efficiency you can use the area in the plenum to increase efficiency like a bandpass box, but then you're group delay suffers.


My plan was to make the plenum as small as possible to avoid the issues of group delay. I am not worried about efficiency gains. Maybe I am wrong, but would I expect there to be some gain in efficiency regardless, due to the increase in air velocity and pressure?


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## Orion525iT (Mar 6, 2011)

Patrick Bateman said:


> As a quick example, without busting out hornresp, I would anticipate that this plenum would have a resonance at 84hz, assuming that the plenum is about 40" deep.
> 
> The only program that could simulate this plenum is Akabak, because every single woofer is going to have a little bit of a time delay, depending on how deep in the plenum it is. The top woofer in the plenum will be delayed about half a millisecond, the next one about a millisecond and a half, etc. (Because sound travels 13.5" in a millisecond, and the lower woofers are 13.5" further away then the set above them.)
> 
> ...


Interesting, but not really practical unless you treat the interior of the car like the plenum itself. I did think about running 6 subs per side of the car in push-pull slot, running from the hatch opening across the top of the wheel arch with space between each set. So basically two rows on either side of the car, then a solid cargo cover to make a "trunk" area. But, I thought that would cause a mess with the sound waves having multiple different resonances due to different positions and distances to boundaries inside the car.


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## Orion525iT (Mar 6, 2011)

TOOSTUBBORN2FAIL said:


> http://www.diymobileaudio.com/forum/technical-advanced-car-audio-discussion/82304-more-bass-less-space-2.html
> 
> Half way down that page, he hints at how to model it.


Thanks, that's a good short read and touches on a lot of the stuff I was thinking about.





TOOSTUBBORN2FAIL said:


> The peak is definitely an issue, and the reason I wanted to try it out. The peak can be HUGE depending on slot size, and its right at the upper end of the midbass. Even with the subs, steep crossovers will be your friend. Patrick's plot for the 8" sub shows a 20db peak at 350hz.



That's a sharp spike. I was really only going to run the subs up to 50hz or so, and I expect some overshoot depending on slope. I have 8" RS225-4s as mid bass in the kicks that should be able to cover the rest. 

For a simple slot load of the midbass, it would be tricky to work around that peak. The wall of the slot could also act as part of the enclosure for my fullrange arrays...but I wander...


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## Patrick Bateman (Sep 11, 2006)

Orion525iT said:


> Interesting, but not really practical unless you treat the interior of the car like the plenum itself. I did think about running 6 subs per side of the car in push-pull slot, running from the hatch opening across the top of the wheel arch with space between each set. So basically two rows on either side of the car, then a solid cargo cover to make a "trunk" area. But, I thought that would cause a mess with the sound waves having multiple different resonances due to different positions and distances to boundaries inside the car.


Spreading out the resonances seems to work really nicely, but it only works above the Schroeder frequency.

Off the top of my head, here are some things I've noticed with a multisub approach:

1) Once you go to a multisub approach, with two or three subs, your perception of the subs location is much lower
2) One of the things I hadn't expected is that you can run a really high xover point. I'm crossing over at about 150hz, and I wouldn't be surprised if you might be able to get away with twice that (300hz.)
3) it seems to 'rattle' things quite a bit less. I'm guess that this is because a single sub will tend to excite a single resonance, whereas multi subs will excite multiple resonances, but each resonance is receiving less energy
4) it really 'wakes up' recordings with a strong bass line. For instance, when I first implemented it, I put on some Daft Punk, and it sounded like an entire different recording. The bass line was just better defined, less boomy, more weight
5) One thing that was unexpected, was that varying the *height* of the sub made a big difference. At the moment I have one sub on the top shelf of an Ikea Expedit cabinet, about 5' off the floor. All the other subs are on the floor.

John K has some graphs of the impulse response of dipole subs over on his site, and it shows that dipole subs have a cleaner impulse response than monople subs. That might seem counter-intuitive - because a monopole has one radiator and a dipole has two. But what's happening is that the interference from the rear wave creates interference with the front wave, and that makes the impulse 'fade to black' faster. (And I think that's why the bass seemed better defined.) *It's basically like comb filtering, but in the time domain not the frequency domain.* Multiple monopoles have the same benefit of dipoles, but with higher power handling, more output, and higher efficiency. Even John K, champion of the dipole, has mentioned on diyaudio that he's leaning towards the multiple monopole route for subs.

Of course all of this is a bit academic for a car - because in a car the Shcroeder frequency is so high. But it *does* apply to midbasses, and is a compelling argument for multiple midbasses spaced 2' to 4' apart.

Below the Schroeder frequency, the location of the sub is basically irrelevant, as long as you're not rattling anything or generating a lot of distortion. (A couple of big "ifs" of course...)


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## Orion525iT (Mar 6, 2011)

Patrick Bateman said:


> Spreading out the resonances seems to work really nicely, but it only works above the Schroeder frequency.


Makes sense.



Patrick Bateman said:


> 5) One thing that was unexpected, was that varying the *height* of the sub made a big difference. At the moment I have one sub on the top shelf of an Ikea Expedit cabinet, about 5' off the floor. All the other subs are on the floor.


I ran across your experience with this on the Geddes diyaudio thread, and to have it reiterate here got my head moving again. Typically, when we think of sub placement, it is in the lateral domain. Yesterday, I was trying to come up with ways to place multiple subs in different locations without having a mess of ta and processing channels. I was thinking, "what can I get away with"? But you can also spread the chaos in the vertical domain, where time alignment is less of an issue. This is not something that can be done easily in most vehicles, but since I am walling off the rear of the car, I have tons of flexibility. Having small drivers is the other key.

What I am now thinking is that I can do two vertical slots at each c-pillar, and perhaps a horizontal slot through the ski pass or over the back seat. The c-pillar slots can run stereo, the center slot mono. I have good midbass anchored in front with the kick mounted RS225-4. I see no reason why I could not run the c-pillar slots from subbass all the way up to midbass. The slots will still be push-pull, to lower distortion and mechanical vibration. I think I have even found a way to increase compression by making a narrower slot.

Hmmm 

Edit:

Just looked at the car and measured. Not gonna happen. I always seem to think the car is bigger than it really is...I would have to go sealed, or split the car to go IB. I am already splitting in one direction, I cant see doing it in the other.

I think i am just going to follow what Nelson Pass did, and go for slot area 1/3 of cone area with IB. But this got me thinking about the midbass again...


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## Patrick Bateman (Sep 11, 2006)

For the subs, there's really no good reason to vary their location at all.
I know that people have had good results putting subs up front, but IMHO that works for two reasons:

1) more subs means fewer rattles per sub, and I think it's the rattles and distortion that give away a subs location, not the fundamental

2) A sub puts out a lot of energy in the midbass. For instance, with a sub playing at 110dB and a 24dB octave rolloff at 80hz, there's still 86dB of output at 160hz. So putting a sub up front can improve midbass integration.

Might be worth screwing around with the crossover points, perhaps overlapping the midbass and the subs, then use some EQ to flatten it out. (Since you'd have a lot of output if you overlapped the subs and the midbasses, due to all the woofers playing at the same time.)

Also, have you messed with push-pull subs before? It definitely lowers 2nd harmonic distortion. But some people don't like the sound of that; it has a tendency to make things sound 'quieter' since distortion makes speakers sound louder.


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## Orion525iT (Mar 6, 2011)

Patrick Bateman said:


> 1) more subs means fewer rattles per sub, and I think it's the rattles and distortion that give away a subs location, not the fundamental.


I thinks this is the case, and I think it has been demonstrated by those running well implemented IB setups and the higher xover points they can achieve.



> Also, have you messed with push-pull subs before? It definitely lowers 2nd harmonic distortion. But some people don't like the sound of that; it has a tendency to make things sound 'quieter' since distortion makes speakers sound louder.


No, I haven't. The whole concept was an evolution of sorts. I started contemplating the possibility of a IB set up in my wagon (with leather seats) I considered many approaches, including a cargo cover to act as the box top. But that method would cause huge challenges due to multiple sealing surfaces. The easiest method by far was to simply wall the car off from the back of the rear seats, with an acrylic or glass window for vision, and do a normal front mount baffle above the seats. I could run two 15s in that configuration. But I wouldn't be able to see out the back, it would be all woofer and no window.

So what could be done? A manifold mount through the ski pass would work, but a a huge sacrifice to space and utility. The sole focus from this point was to find a way to get maximum Vd out of the smallest space. So I eventually started thinking about slot loading, started researching, and the whole thing snowballed from there. Concepts of force cancellation started to weigh into the equation. I don't think many people realize how much energy is imparted to to car body through mechanical interaction. We are constantly fightening rattles and vibrations. The best panacea is to kill it at the source; using opposed drivers is one way of doing this. You can only do this with even driver numbers. Two 15s mounted opposed would take up too much space. Four 12s, even more space. The sweet spot seemed to be multipe inexpensive 8" drivers. I have eight of them and I could literally fit twelve without loss to useable trunk space. That's a massive ~2600cm2 of cone area in a very compact area.

All in all the entire weight of the design pushed in the direction of a slot loaded using multiple small subs. Then other thoughts of air mass loading and distortion became part of the larger picture.

In the end, I have not heard a PPSL. There are overriding consderations that favors the slot configuration. The rest of the design is an attempt to maximize the potential benefits of slot loading (force cancellation, air mass loading, distortion reduction, ect).

I just spent some good time picking through the bickering on the Nelson Pass thread at diyaudio. I am now screening through the PPSL thread .


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## Orion525iT (Mar 6, 2011)

After reviewing much information, I have decided to make the slot 1/3 sd per pair of drivers. Each pair will have its own slot and plenum. Plenum size will be as small as possible. Larger plenums could act as band pass, and some evidence suggest a reduction in the 3rd harmonic, but adds complication to the design. 

The most important aspect is to make sure the push pull pair are close enough together to get better coupling to the air mass. I should get a lowering in fs, how much I do not know. I Fs of the drivers is ~30hz, so some lowering maybe be desirable. Some report to have obtained a fs lowering of up to 10hz. In any case, the drivers will be coupled as tightly together as possible, but prevent the cone of one driver from hitting the basket of it's paired driver. Mounting of the drivers willl allow me to reduce compression, if needed, but keep slot area the same. Vd should be similar to two 12s with 13mm xmax. I can add another pair of 8s if output is less than desired, but I have a feeling this will be plenty.


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## Patrick Bateman (Sep 11, 2006)

Orion525iT said:


> After reviewing much information, I have decided to make the slot 1/3 sd per pair of drivers. Each pair will have its own slot and plenum. Plenum size will be as small as possible. Larger plenums could act as band pass, and some evidence suggest a reduction in the 3rd harmonic, but adds complication to the design.
> 
> The most important aspect is to make sure the push pull pair are close enough together to get better coupling to the air mass. I should get a lowering in fs, how much I do not know. I Fs of the drivers is ~30hz, so some lowering maybe be desirable. Some report to have obtained a fs lowering of up to 10hz. In any case, the drivers will be coupled as tightly together as possible, but prevent the cone of one driver from hitting the basket of it's paired driver. Mounting of the drivers willl allow me to reduce compression, if needed, but keep slot area the same. Vd should be similar to two 12s with 13mm xmax. I can add another pair of 8s if output is less than desired, but I have a feeling this will be plenty.


Keep in mind that the lowering of FS doesn't buy you a whole lot. As long as you have enough amplifier power, a sub is limited by displacement. If I'm not mistaken, a lowering in FS would also lower the sensitivity of the sub, since sensitivity and FS are linked in the T/S model.

In compression drivers we sometimes use compression ratios of ten to one; that's like putting the output of an eight through a 2.5" hole 

(wow that sounds really raunchy now that I think about it)


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## Orion525iT (Mar 6, 2011)

Patrick Bateman said:


> Keep in mind that the lowering of FS doesn't buy you a whole lot. As long as you have enough amplifier power, a sub is limited by displacement. If I'm not mistaken, a lowering in FS would also lower the sensitivity of the sub, since sensitivity and FS are linked in the T/S model.


I think you are correct in regards to FS and sensitivity. There is some suggestion that efficiency is increased, due to tighter coupling to the air mass, but I dont think that aspect has been convincingly proven. 

Decreasing FS is not the goal, just a possible side effect. I would prefer the subs remain most efficient around 30hz, as most music bottoms out there (or even slightly higher). I am not interested in pipe organ music, although I seem to be listening to more and more EDM derived music. But hopefully I will not find the arrangement lacking.

My thought is that power + eq, within limits of excursion, is the way to go in any case.


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## Orion525iT (Mar 6, 2011)

Enough theory, sawdust gives answers. I didn't model anything, I just went with some basic guidelines for the manifold that were discussed in the Nelson Pass and PPSL threads over at diyaudio. Slot area is 1/3 Sd of driver pair. Volume of plenum is as small as possible. Still some work to be done on the plenums, but it gives a good idea.



















More photos in the build log.


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## Patrick Bateman (Sep 11, 2006)

A member of the forum emailed me about something similar to this.
It sounded like he wanted to 'slot load' a subwoofer.

There's about a zillion ways to do this. Here's one:




























Here's a Beolab 11 subwoofer. As I see it, they're slot loading the sub so that it doesn't look like a sub. It's also a way to protect the guts of the amp without resorting to a bandpass sub or using a metal grille. Obviously, one of the main reasons they're doing this is to differentiate the brand, and sell something that other people aren't selling.









Here's the predicted response of the Beolab 11, with 350 watts into two ohms, versus an Alpine SWR-8D4. For the Beolab I picked a fairly decent 6.5" woofer, the SB Acoustics SB17NRXC35-4 (The Madisound Speaker Store)

Here's some things I notice:
1) Hoffman's Iron Law rules, so the output in the octave between 30 and 60hz is virtually identical.
2) The output ABOVE 60hz is much much higher for the dual 6.5" sub. This is basically because of it's higher efficiency. This might make the 6.5" sub sound 'cleaner' because distortion rises with power. *So the dual 6.5" sub might need to be pushed hard to "sound" loud.* Note that this is completely subjective though; in the bottom octave they're evenly matched.
3) The peak at 830hz is due to the resonance in the slot.


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## Patrick Bateman (Sep 11, 2006)

Here's the displacement of the two designs.
Two 6.5" woofers have nearly the same displacement as a single eight, so the two designs track each other closely.
*The Alpine is going to be able to handle more power overall, due to having an xmax of 12mm, but the two subs might not sound much different because the dual 6.5" has an efficiency advantage.*


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## T3mpest (Dec 25, 2005)

That was me.. this thread helps... I have my own thread a few down about it, midbass and wavelengths... But I'm still not sure how to proceed lol. I actually want to minimize any loading or bandpass effects.. I'm just using a slot because it allows me to place my midbasses as wide as possible if they fire sideways vs front and back. However i want to build a duct that introduces as few peaks as possible to get wide bandwidth from the subs.. 20-300hz is the goal


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## Patrick Bateman (Sep 11, 2006)

OK this post is going to be super confusing so PLEASE ask questions if it doesn't make sense.

*Slot loaded subwoofers are really easy to simulate* but we have to establish some ground rules first.









Here's how I modeled the Beolab 11 in Hornresp.
Anyone can model anything similar by tweaking a few parameters.
There are tons of "how-to" guides for hornresp out there, and I'll leave it up to the reader to dig into them to figure out the intricacies of the program.
But slot loaded subs are exceptionally simple, and we can model them with a handful of parameters.

1) The seven parameters in the center of the screen define our driver. These parameters are Sd, Cms, Mmd, Re, Bl, Rms, and Le.

2) The six parameters at the bottom define the box. Since it's a sealed box, there are only two parameters. Vrc is the volume of the sealed box (7.1 liters) and Lrc defines the depth of it (25.4cm or 10")

At the top of the screen there are sixteen parameters that define the horn. And while a "slot" doesn't appear to be a horn, you can model it with hornresp. (In fact you can model all kinds of things with hornresp, including sealed, bandpass, vented. The great thing about hornresp is that you can insert things like a slot into what is otherwise a conventional box.)










*Here's where things get tricky.*
The sound in the slot starts in the center, *and it expands radially.* This makes it tricky to figure out the "length" of the slot. It would *seem* that the length of the slot would be equivalent to the *depth* of the slot. *But it's not.* The sound starts in the center, *so the length of the slot is actually HALF of the depth of the slot.* (Because the sound starts in the center of the slot and it expands radially.)

This sounds like a small thing, but it's not. The length of the slot dictates the upper limit of the woofer, so B&Os slot design is definitely functional. Basically putting the "mouth" of the slot on all sides of the box makes some measurable improvements to the design. It increases the bandwidth of the box, and it reduces port distortion. (Because the area of the port's mouth is quite large because it encompasses the entire circumference of the box.)

Here's how I figured out the area of the slot, then modeled it as a horn:
First, the MOUTH of the slot is equal to the circumference of a circle multiplied by the width of the slot. In this case, it's:
(2 * pi * radius of slot) * width of slot =
(2 * 3.14159 * 12.7cm) * 2cm =
79.8xm * 2cm=
159.6cm

So the *area* of the mouth is equivalent to 159.6 square centimeters.
I rounded up to 160 in the model pictured above.
Techically, we should include the flare, it makes a difference.
But I left the flared part of the mouth out of the sim to keep it simple.

The sound expands radially, so the length that's modeled in Hornresp is 12.7.

One thing I did was to split the slot up into two pieces. You don't have to do this, but I personally believe that splitting the slot gives you a better sim. The reason to split the slot is basically *to get a better idea of what the compression ratio is.* The compression ratio is really important. The idea of firing a woofer into a wall that's less than an inch away seems a bit crazy, *but we've been doing it with horns for years.* It works, there's a science to it. Compression ratio is a big part of that science.

If all of the sound radiated in one direction, the compression ratio would be a bit simpler. But since the sound radiates radially, determining the compression ratio is trickier. This is because the compression ratio is going to change as you get closer and closer to the exit. At the very center of the slot the compression ratio will be highest, because the area at the center is smallest. But at the exit of the slot the compression ratio will be lower, because the area is larger. If you look at the pics, that might not make sense. The depth of the slot is the same everywhere, so shouldn't the compression ratio be the same everywhere? *But it's not, because the sound expands radially.* So the area of the slot gets bigger and bigger, and the pressure gets lower and lower.

To simplify the sim, I picked a point that was halfway between the center of the ring and the exit of the ring. So here's how we calculate the area at that point, which we can use for the compression ratio:

(2 * pi * radius of slot) * width of slot =
(2 * 3.14159 * *12.7cm*) * 2cm =
79.79cm

Basically, this is the same equation as I showed before, but the distance is halved, because it's a point on the ring that's halfway between the center and the exit.

So we know that the AREA at that point is 79.79cm.
We get the compression ratio by dividing the cone area by that.
In this case:
(area of our 6.5" woofers, multiplied by two because we're using two) / 79.79cm
(118 square centimeters * 2) / 79.79cm
= 2.95

So our compression ratio is 2.95.
I personally go for compression ratios in the range of one to four, so the compression ratio used by B&O is consistent with what I use.


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## Patrick Bateman (Sep 11, 2006)

T3mpest said:


> That was me.. this thread helps... I have my own thread a few down about it, midbass and wavelengths... But I'm still not sure how to proceed lol. I actually want to minimize any loading or bandpass effects.. I'm just using a slot because it allows me to place my midbasses as wide as possible if they fire sideways vs front and back. However i want to build a duct that introduces as few peaks as possible to get wide bandwidth from the subs.. 20-300hz is the goal












The main thing you want to watch out for is that peak.
You can see it in the pics above.
As the slot gets deeper, *the peak gets lower.*
Eventually it will get low enough that it's in the passband of your woofer.

Even though you can EQ it out, the peak will change the impulse response. Basically the peak will make things sound like a bandpass box.

Bandpass boxes can sound good, but not over wide bandwidth. They basically do one octave, maybe two.

So if your goal is wide bandwidth, you want to keep the *depth* of the slot small.

Obviously, some people might make the slot wider. The whole idea of firing a woofer into a wall seems kind of bizarre. And it would seem like making the slot wider would reduce the effect. But I personally think the main variable you want to pay attention to is the DEPTH of the slot, not the WIDTH of the slot. Because the depth determines the frequency of that peak.

The relationship is linear too. In the sim I did, the overall depth of the slot is 25.4cm, or 10". If you doubled the width, the frequency of the peak would drop by about one octave.

Another trick that B&O did, a smart trick, is to use a NON circular slot. (It's shaped like a pear.) This isn't just cosmetic, it also spreads out the peak. There is no easy way to model this in software, but you can see how it works. The depth of the slot in the B&O varies with angle because it's not circular. A plain ol' square would work too, but wouldn't look as cool  And that's B&Os entire gameplan, they use solid engineering that happens to look badass.


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## thehatedguy (May 4, 2007)

I modeled one as an offset driver horn and made the horn the size of the slot.


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## T3mpest (Dec 25, 2005)

Interesting.. Since this thread is now mostly about plenums, I throw in what I'm working on.. My current plan is to use 2 21inch woofers in a flat wall configuration. Using a slot, I can move the acoustic centers of the woofers further out into the car. This is important because I want to use them not only for crushing subbass, but midbass as well. By utilizing a duct to move the soundwaves to the edges of the vehicle, I can keep a wide soundstage. 

Anyway here is a diagram of what I plan on building behind my front seats in my SUV, taking up what would have been my entire second row of seating (behind that is cargo area, which I want to keep)










The mouth of the slot, afaik, needs to be around the SD of the woofer, which is 1680cm^2.. I should be able to fit that as the woofer is only 20inches tall, but my box can be around 40inches from floor to ceiling, leaving me lots of room for a big opening.. You can't see that from the top view, obviously. If I can do less than SD, then I have many more options. The slot would cover up more of the woofer and cover more distance.. 

From there, I'm not sure how to translate the rest of your equations to my case, as I'm not sure if your using pi r^2 because you were dealing with a circular duct in that case, or if I need to use that in mine for area as well, since mine is a square?

Also by minimizing the width of the slot, in my case does that mean how close the woofer is to the wall, or how long the slot runs across the subwoofer? I assume it's the latter...


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## Patrick Bateman (Sep 11, 2006)

oh mah gawd you never said it was ported :O 

Porting the box changes the complexity to a huge degree. Because now we have a resonant peak in the FRONT of the box, from the slot, along with a resonant peak from the REAR of the box, from the port and the air behind it.










Bose has some crazy complex enclosures, and they did something a bit similar in one of their CD palyers. If you look at the pic above, there's a woofer, a transmission line, and then *another* transmission line tapped into the first one.

It took me a couple minutes to figure out what's going on, but basically that little stub is used to null out a peak from the first line. (Those people at Bose really don't get the credit they deserve, that is a hideously complex enclosure.)


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## T3mpest (Dec 25, 2005)

Patrick Bateman said:


> oh mah gawd you never said it was ported :O
> 
> Porting the box changes the complexity to a huge degree. Because now we have a resonant peak in the FRONT of the box, from the slot, along with a resonant peak from the REAR of the box, from the port and the air behind it.
> 
> ...


I assumed it wouldn't matter much, tbh. I plan on tuning the port near 30hz, so I figured most of the bandwidth that the front slot would be effecting would be several octaves higher.. I know the main port itself has an upper resonant point, I can model that in WINISD and will just have to be careful with my total port area..


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## Patrick Bateman (Sep 11, 2006)

I think there's a better way.

Instead of doing this:









Do this:









Here's a list of reasons the second design should work better:

1) Port compression is a huge deal. At the tuning frequency of a vented sub we're moving more air than at any other frequency in the entire spectrum. With a couple of twenty ones, *it's a huge amount of air* and everything you can do to reduce port compression and distortion will make the box sound louder and cleaner. My design flares both the inside *and* the outside of the port. Plus, I'm using a larger port. (It's really hard to use a port that's too big; even with fifty watts I can feel the air move in my horn loaded sub, and the exit of my horn has almost as much surface area as a 24" woofer.)

2) My design is way simpler. Instead of using a port at the back and a slot at the front, *I'm literally putting the woofer into the port.*

3) As always, my best designs are always ripped off, and this one is a shameless ripoff of the Muse Model 18 subwoofer. I basically took their idea, and put the ports on the outside instead of the middle. Here's some raves for the Muse:

_"At the Winter CES I took a listen to the Muse Electronics Model 18 mated to a pair of Rush Sound Monument 2s and was encouraged by what I heard—seamless integration, quickness, no bloat, and unbelievable extension. In short, not your typical subwoofer."

"In all, I find the Muse Model 18 to be an amazing piece of gear; I've certainly become addicted to it, and it's been a tremendous help in judging the low bass of all the equipment that's come through these parts since I hooked it up. The incredible extension, cleanliness, and huge dynamic improvements the Model 18 makes to your speakers and your main amplifier are, to my ears, unprecedented in not only this price range, but any."

" the amount of air the Model 18 moves at this frequency is surprising; putting my hand into the slot felt like putting it into a washing machine "_

Basically you would have a 21st century version of the Muse subwoofer, but in your SUV. Here's the full review of the sub: Muse Model 18 subwoofer Specifications | Stereophile.com

Pics or it didn't happen:


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## T3mpest (Dec 25, 2005)

Patrick Bateman said:


> I think there's a better way.
> 
> Instead of doing this:
> 
> ...


That was my original idea, more or less, but using a standard port instead of a horn and the main port and the outlet for the high frequencies werent' connected.. That seems to be a bit tricker to model unfortunately.. Looks like I'm going to have to learn hornresp, one way or the other lol. Where did you get the 24x48 from.. That is VERY close to the size I have to work with, although I think I have have a bit more width than that actually. This design seems much closer to a true series 6th order, which I was trying to avoid because I don't think I can get the bandwidth I want from a box like this. PWK modeled me a box and when it was reverse engineered in Akabak, it was only good for 25-70hz or so... As detailed here: http://www.diyaudio.com/forums/subwoofers/247636-any-akabak-pros-want-reverse-engineer-me.html


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## thehatedguy (May 4, 2007)

hornresp isn't that bad to learn. akabak was a bit more difficult, but not too bad for regular enclosures (non horns) once you get into it...my first akabak simulation was a series 6th order bandpass from PWK that a fellow on here had plans for.


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## Patrick Bateman (Sep 11, 2006)

T3mpest said:


> That was my original idea, more or less, but using a standard port instead of a horn.. That seems to be a bit tricker to model unfortunately.. Looks like I'm going to have to learn hornresp, one way or the other lol. Where did you get the 24x48 from.. That is VERY close to the size I have to work with, although I think I have have a bit more width than that actually.


48" is about the width of a car, and the depth was just a guess.










I threw your B&C into hornresp, and it's been tough to get a decent response shape.
In the graph above, I've simmed a plain ol' vented box with the B&C, and also the same driver if mounted the same way that Muse did. (Like my pic from my last post.)

My attempt was rushed, but that dip at 70hz and the peak at 40hz is troubling.

What might work better is just a plain ol' tapped horn using the B&C. Here's why:

1) You won't have to go and blow $750 on another woofer
2) A tapped horn is going to need more room than a vented box, but it probably won't need as much room as *two* vented boxes.
3) The main reason to do it is that the air chamber in a dual reflex bandpass (aka sixth order) or a ported box acts as a filter, and this can have some weird and unpredictable effects. In a tapped horn the dips and peaks are really quite predictable and you can design around them.

Now, obviously, this won't be stereo. But I *personally* don't think it will matter. This is totally subjective of course, but I think if you split up the mouth so that there were two mouths instead of one, then moved them as wide as possible, it would sound the same as two woofers running in stereo with two mouths.









Something like a W-Bin horn, but done as a tapped horn with a single B&C 21"

This is basically because 200hz is 5.6 feet long. So when you have two woofers that are just a foot apart, they're going to "blur" into one, and your stereo subs will sound like mono. But if you put the mouths as far apart as you can - about four feet - now it's going to sound like two sources and hopefully that should help with the width.

In other words, the problem with the width isn't due to the signal being mono or stereo, the problem with the width is that the two speakers are so close together they blur into one. Creating two mouths fixes that, even if the source is in mono. (And if you do a spectrum analysis on most music, it's mostly mono anyways, a lot of what we hear in a car or a living room is an illusion created by the placement of the speakers, not by any stereo information on the actual recording.)


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## Patrick Bateman (Sep 11, 2006)

The tapped horn definitely looks better than the slot loaded vented box. Even more important, the tapped horn is actually a simpler box to get right. In a vented box there's already some strange interactions between the internal dimensions of the box, location of the vent entrance, vent exit, etc. Adding in a slot complicates things.

So I think the tapped horn is more likely to work as planned, just because there are less variables.









^^ Here's the vented box versus a best slot loaded vented box that I could come up with. Note the dip and the peak in the latter.









^^ Here's the vented box versus a tapped horn. The tapped horn is more efficient, and flatter at low frequency.









Here's a W bin front loaded horn









Here's the tapped horn that's sitting in my living room. Works great. It's largely based on the Danley TH-Spud, but mirrored:









This is basically the layout of the TH-Spud. My sub has two mouths for the same reason that you want to use a slot, which is that this sub was originally intended for my car and I wanted to keep the source of the sounds as far apart as possible.









Here's a layout that I came up with for your B&C. Same idea as my tapped horn, but using one 21" woofer instead of dual eights.


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## Orion525iT (Mar 6, 2011)

T3mpest said:


> That was me.. this thread helps... I have my own thread a few down about it, midbass and wavelengths... But I'm still not sure how to proceed lol. I actually want to minimize any loading or bandpass effects.. I'm just using a slot because it allows me to place my midbasses as wide as possible if they fire sideways vs front and back. However i want to build a duct that introduces as few peaks as possible to get wide bandwidth from the subs.. 20-300hz is the goal


I don't think you can get around loading with any slot placement that will be of practical benefit. The slot will alter Fs and Q. How much, I haven't been able to figure out. There are some hints in Linkwitz's Phoenix faq, but that may be more relevant to my IB design (Phoenix is OB). Maybe Hornresp can do better, but running a sealed design obviously adds to complexity, and ported designs adds x more.

For me, I looked for a low Qts sub at a reasonable price that would fit in my space constraints. So I have eight 8" subs. Qts .33 and Fs of 30hz, after slot loading in a PPSL, who knows? But I got wiggle room.

If Patrick is right, and depth of the plenum is more significant to band-pass than width of the plenum (this makes sense in my head if the plenum is common), then maybe using multiple smaller drivers adds flexibility. I did not consider this in my design, as I will cross the subs way before any band-pass could become significant. My choice was for packaging reasons. 

As far as stereo vs mono, from what I have read, and from what Patrick has posted, it seems that the perception of space (width) does not rely on L/R separation as much as L/R sources originating as far apart as possible. Somebody correct me if I am wrong here. 

As an aside, I currently have one of my two plenums (4 drivers) mounted to a piece of MDF in a OB configuration running in the house. Subjectively I can say that I do not notice the subs are there at all. But if I disconnect them, I definitely notice that they are not there. I am pretty impressed with the overall design. 

Anyway, maybe some things to think about?


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## T3mpest (Dec 25, 2005)

Quite a lot to think about here.. It seems as though trying to push the woofers to the sides may be more trouble than it's worth. Especially if mono midbass isn't that objectionable to begin with.. Even just running my midrange down to 200hz would still give me quite a bit more powerhandling as opposed to running them down to 80-100hz as usual... Diminishing returns has it's hand in design considerations at some point. I'll sit down later and play with sketchup and see what I can actually fit comfortably and once I get concrete measurments, perhaps the best course of action will present itself. 

This design below seems like what I'm still leaning towards. series 6th won't have the bandwidth, I have to run 2 subs (the other one is on the way lmao) and it will be much easier to adjust slot length based on the actual sound once it's built. Simply build removeable slots and i can play with it from there. If the slot idea is a total bust, simply don't run them and I can run it all in mono  Modeling can hopefully get me in the ballpark first shot though.


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