Calculating enclosure volume for TL

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I've got the spreadsheet for BiBs that calculates an optimal volume for what I've been lead to believe is basically an So=0 TL enclosure. What I'm looking for is the math necessary to do the same for TL enclosures of different expansion rates. I've got a copy of MJK's alignment table PDF and can use that to figure line length, but I can't cipher out even which variable in there refers to enclosure volume, if any.

Please help.

Ah, yes. They're not the easiest, primarily because although Martin gives you the values, unless you're confident with the background, & some algebra, the definitions aren't very clear. In fact -Martin, if you're reading this: could I make a suggestion? A page near the beginning, with clear definitions for each value found in that particular pdf might be a useful addition for many people who struggle to follow the math.

Anyway, how to calculate volume. It's indirect, because what it actually does is calculate the area for the sealed end (So) of the line. From that, and knowing the line length & taper, you'll be able to figure out an exact volume.

So, first up, you need to know the driver Sd in square meters, its Re value in ohms & Bl value in Newton amps. You will also need to use the tables to determine the Dz & Dr values, or as close an approximation as you can get.

The only other things you will need are:
p = 1.21 Kg/m^3 (you just need to enter 1.21)
c = 342 m/sec (you just need the number 342)

Got all those? Next step: we have to calculate So / Sd (I think there's a typo in the pdf actually as Sl pops up for some reason under point 3, p.13)

So/Sd = p c Sd Dz Dr Re / Bl^2

This becomes:

So/Sd = (1.21) (342) (Sd) (Dz) (Dr) (Re) / (Bl^2)

Multiply 1.21 by 342. Multiply this by the driver's Sd in square meters. Multiply again by the Dz value. Multiply once again by the Dr value. Multiply for the final time by the driver Re. Divide this figure by the square of the driver's Bl factor (top tip: work out the square of BL in advance -it'll save you a loud curse).

The final figure you will get will be the area of So, expressed as a multiple of the driver's Sd. Before you attempt it, follow the example Martin gives in section 3) at the bottom of p.13, just to make sure you're working through it correctly.
Thanks, Bob. I don't think I'll be doing mass loaded lines as that's just one more thing I don't know how to manage the math for yet. Besides, the ports on MLTLs worry me as I really can't stand the sound of BR enclosure and I fear that porting a TL would create a similar sound.

I'm actually looking to design straight or possibly tapered lines, something with a less monolithic enclosure size than the BiB. I know I won't get the same bass gain, but I'm trying to get as similar sound as possible to an OB, but with decent bass reinforcement. I'm currently able to get solid to 50Hz with EQ on OB, but if I'm going to build enclosures, I'd like to be able to do more like 40Hz or less without the EQ (or at least with dramatically less) at similar levels. I've got plenty of corner loading available, so I'm thinking this shouldn't be too hard to accomplish.

My drivers are B20s, so they're still going to be pretty big (got a preliminary tapered design that would be 4'x2'x7" with the line mouth down and to the side, most likely both firing into the same corner behind my desk), but at least they'll be alot easier to push up against the walls and won't be 6'-7' tall.

Nope. You're not porting a TL. You're porting a QW cabinet. Not the same thing. A TL in terms of pure physics should be non-resonant (Bailey caused innumerable problems by calling his original article 'A Non Resonant Loudspeaker Enclosure' and then proceeding to write about a cabinet that was manifestly semi-resonant, but I digress. Mutter. Growl. etc.). An MLTL, or, as it should more accurately be termed, an ML QWR, does not sound like a bass reflex enclosure, if it's properly designed. So don't worry about that.

A tapered line is generally the most effective of traditional, semi-resonant / near aperiodic cabinets (what most people call TLs, though from the POV of physics, as I indicated above, they are only approaching, not achieving this end). I tend to find that 3:1 - 6:1 tapers are about the optimal for most requirements.

Whatever, you're never going to get an OB sound from a monopole: the polar response is completely different, and that has a massive effect on the sonic signiture / presentation. What you will get from a semi-resonant / aperiodic line, if optimally stuffed (use Augspurger's tables as a starting point as Martin doesn't provide any), is a very well damped LF response, with a very clean midrange because the damping material should be eating almost the entire back wave of the driver, with only a small amount of cabinet gain at the bottom end.
Two thoughts here:

1. Your prejudice against BR's is probably based on listening to the typical QB3 boxes designed with software like WinISD that provides no insight into proper speaker design. QB3 boxes with their overly aggressive bottom end and rapid cutoff will ring like bells and boom horribly in real life rooms. It doesn't have to be that way. A well designed EBS box can give very good bass indeed. An EBS box is going to be bigger than a QB3 box, but will have a gradual roll-off that matches better with real life rooms and a much lower Q at cut-off.

2. Expanding on Scott's discussion, the classic TL, which is stuffed to non-resonance, is basically an infinite baffle in a finite, albeit large box. Therefore, to make it work, you need a high-Q driver to produce any meaningful bass. The challenge is to find a high-Q driver with low enough Fs to produce meaningful bass.

Boomy bass is unlistenable. "Tight" bass usually means no bass at all. Real bass flows. Once you have heard it, you will understand.


My prejudice is based on every ported design I've ever heard at retail or at someone's home. I'm gonna guess that the sub on every set of multimedia speakers or any ported bookshelf under $200, at the very least, and likely alot of much more expensive units, is in a QB3 alignment. Sure, if you're going to spend >$1000 per on speakers at retail, sure I can find some I can live with, but that's not going to happen, and living with speakers and loving speakers are two different things.

The B20s have a Qts a hair above .5. Is that "high" in your definition? Fs is about 42, I think. The designs I'm looking at are tapered in the 3:1 to 5:1 region, so I guess I'm on the right track, but I was wondering how they'd behave if damped more like a BiB, with damping behind the driver, at the closed end and on one of the two parallel sides.

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