## Sunday

### Calculating IB enclosure volume.

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I have received a comment asking for IB enclosure volume calculations. Thanks for the timely suggestion.

So: Total Vas x 10 = minimum enclosure volume for an IB subwoofer.

That's all there is to it really. But I suppose you want more? :-)

Until now I have largely avoided putting real numbers on my IB. Though, in fact, the design calculations are very simple indeed and can be (almost) ignored if one stays well within the usual IB design parameters. Which is just another fancy way of saying a 4 x 15" IB can be built to standard dimensions and it will work very well indeed. It will also stay safely within any cone excursion limits which might endanger the drivers. It will also have a reasonably flat frequency response down to well below 20Hz. Or even 10Hz if your room allows it.

First things first: An IB subwoofer is critically dependant on the chosen drivers: So choose from the small range of 15" or 18" IB-specific drivers and most of your design problems cease to exist right away. The specialised IB driver will offer a realistic maximum cone excursion. Which usually means a minimum of 18mm Xmax. Avoid car audio drivers with flashy paintwork and chrome finishes claiming ultra long stroke. Unless Xmax is clearly stated then any claims are meaningless sales hype. So, which drivers do the real experts use for competition car audio dB drag racing? Those manufactured by exactly the same companies which offer serious IB drivers at lower cost. Not the over-hyped, over-Xpensive paint and chrome items intended to appeal to the young, the inexpert and the gullible.

Driver displacement is vitally important in IBs. Cone excursion multiplied by the cone area multiplied by the number of drivers should come to around 10-12 litres minimum total displacement. For 15" IB drivers: 4 x 3 =12 litres. This displacement can also be achieved with two good 18" IB drivers. So we've already learned that 4 x 15" IB drivers = 2 x 18" IB drivers. Since Xmax is measured as a one way come movement we use 2 x Xmax x Sd to give the displacement for one driver. The larger cone area of the 18" means a smaller Xmax will provide a similar displacement to a 15" driver. Better still is a large Xmax giving the 18" IB driver around double the displacement of the typical 15" IB driver.The Fi Car audio IB18 offers 30mm Xmax!

What if you want to use 12" drivers? Then you must calculate their total displacement to achieve a minimum of 10-12 litres just to be safe. Displacement obviously favours large cones so your 12" drivers had better have a seriously long stroke and you'll need at least 8 (and preferably more) to compete safely at high sound levels at very low frequencies with a typical 4 x 15" IB. Twelve or even sixteen x 12" drivers is a better starting point but likely to be rather expensive using high quality drivers. Most 12" drivers wont have such a low Fs as proper 15" IB drivers.

BTW: For those who have forgotten: The area of a circle = radius x radius x Pi. (Pi = 3.142)
The squaring of the radius is the obvious clue to the rapid increase in driver effective area with increasing diameter.

Reproducing low frequencies need lots of air movement. Fanning the air slowly with a large board is obviously far more efficient than waving a postcard a yard backwards and forwards each way. So it is obvious that bigger drivers move far more air per stroke than smaller drivers. Big driver often play loud and low without any visible cone movement at all! So more cone area = higher efficiency at low frequencies. The IB is naturally efficient with falling frequency thanks to a lack of back pressure and large cone area. It also has a motor for each of those big cones to keep everything nicely under control.

A 15" driver is a reasonable size for true pistonic movement at low frequencies. Bigger drivers may suffer from cone breakup. Very large cones almost certainly will. Large plastic/vinyl cones are generally regarded as too soft to be ideal for a sub-bass driver. Particularly in straight-sided conical configurations. Steeply flared, reinforced paper cones are greatly admired by those in the know for their lightness and stiffness. Aluminium cones are highly dependent on the skills of the designer and manufacturer and disliked by some purists who claim the cones can "cry" audibly at higher frequencies. Only testing with software like REW would prove this to be the case. All the Cult recommended IB drivers have reinforced paper cones.

IBs are so efficient that with quite reasonable power they will go very loud and very deep on a typical musician's power amp. The Behringer EP2500 amplifier is a popular choice for IB use with 4 x 15" drivers. Two 8 Ohm AE IB15s in parallel is a comfortable 4 Ohms impedance per channel. The manufacturer claims 650 watts per channel RMS into 4 Ohms. So the drivers are seeing 325 watts each. The EP2500 has also been used satisfactorily with 8 x 15" drivers thanks to the greater efficiency of the larger combined cone area.

Acoustic Elegance made my IB15 drivers and they are deservedly popular in sets of four at \$100US each plus freight. Even in Europe they make good sense despite the heavy freight charges and import and sales taxes. One day, global tariff agreement will be reached or tariffs will be scrapped altogether. Then we'll only have to pay for freight to Europe for US drivers without all the unwanted extras. Check with AE for latest pricing before placing an order though as this blog may eventually grow as many grey hairs as its author.

Fi Caraudio makes excellent 15" and 18" IB specific drivers. Four Fi IB18s would probably be bulletproof no matter how wild action DVDs may become and will probably leave nothing to upgrade for several decades. They also make more extreme models at higher, but still attractive, US prices. They are a very small company and each driver is handmade to order.

Other popular drivers are listed on the IB Cult's recommended driver page:

Driver manufacturers come and go. Their model range may also change. So check for the latest drivers and manufacturers before making any final driver decisions. Also look for Mach5's IXL18.4 and and the DIY Cable Tempest X15 for further popular models for IB use. The Tempest X15 is available from a European distributor. (Streaming Audio of Sweden) Prices are probably competitive in sets of four with the AE IB15s once freight and taxes are added to the AE drivers US prices. The Tempext X15 claims 27mm of Xmax for slightly more displacement at 4 liters and more headroom than the AE IB15's 3 liters. At a glance these two drivers look remarkably similar to each other in appearance except for the outer roll suspension. The AE claims lower distortion for their IB15 due to the careful motor design.

There is a link below to the list of drivers currently on the IB Cult's forum website. Use the US dollar price per litre of displacement as the surest guide to driver value for IB use in the USA. Elsewhere in the world you'll have to do the maths depending on local availability and any additional import and freight charges. These can easily double the US online purchase price.

http://pages.sbcglobal.net/ginmtb/woofer_comparison_chart.htm

Loudspeaker drive units (or 'drivers' as they are now commonly known from US usage of the term) are built to very exact specifications. Thiele-Small paramaters are used to describe drivers in precise detail and in units which don't mean much to most people. Here's the Wikipedia entry: You can safely ignore all the terrifying equations and scroll straight down to the list of Thiele-Small parameters list much further down the page under Qualitative Descriptions:

http://en.wikipedia.org/wiki/Thiele/Small

Some useful terms for IB design: (with simplified descriptions) Feel free to wallow in the fine details from Wikipedia and other online resources. You really don't need to know more than appears below to design an excellent IB. Remember that buying recommended IB specific drivers will save a lot of extra work and worrying over details. Choosing these IB drivers is a short cut to success where these recommended drivers are available and affordable.

Fs is the free air resonance of a driver and measured in Hz.

Hz
replaced cycles per second some years ago in honour of Hertz but the two terms mean exactly the same thing. Having an Fs somewhere between 15 and 20Hz is ideal for an IB driver. Go much higher in frequency for Fs and you might need to start boosting the bottom end to get serious infrasonic output.

Infrasonics = sounds below the normal frequency threshold of the human ear.

Though usually completely silent, at the levels we listen to at home, infrasonics are good for making the room shake on action films and deep organ music. The lower audible frequency threshold for adults is usually around 20-22Hz) A low, free air resonant frequency driver will avoid the need for low bass boost. Room gain will help. Leaving a nice flat, extended response to below 10Hz in most cases. (provided the 15-25Hz range for Fs is adhered to) The AEIB15's Fs = 16Hz = Ideal for IB use. The IB specific drivers mentioned above all fall safely within this range. This is another good reason to seek out IB specific drivers. Everything is taken care of by the designer saving you having to worry about specific details.

Provided we stick to standard IB driver designs and use a recommended number of IB specific drivers we only need to know the numerical values of the following T-S parameters: There is absolutely no need to understand how these numbers are obtained by the manufacturer unless it really interests you. It won't make a better IB but you may be able to impress your lucky visitors with more than your world class IB bass.

Vas= Equivalent air volume of driver suspension stiffness. Vas is used to calculate the size of the rear volume or backspace of the IB. In normal loudspeaker and subwoofer terms we'd call this back space the enclosure. The same holds true for IBs. IBs just use huge volumes for their enclosures.

(N.B. Enclosure size does not relate to the manifold volume. The volume of the manifold is largely irrelevant as long as it is big enough to house the drivers. A driver manifold is really just a local folding of the baffle with serious mechanical advantages which you should not ignore.)

Vas is given in litres by the manufacturer in their driver specification. The AE IB15 has a Vas of 439 litres. (15.5 cu.ft. in old money) If you are metrically challenged just divide litres by 28.4 to convert them to cu.ft.. BTW: Liters and litres are interchangeable names depending entirely on your own geography. Divide litres by 1000 if you want volumes measured in cubic meters.

Qts = Is a unitless measure of quality of a driver. It usually lies between .2 and .8 for loudspeaker units or drivers. The AE IB15 has a Qts of .7. Which is fine for IB purposes. You can go lower than .7 but avoid going much higher than .7 if you can. Experts consider .5 to be the optimum where electronic equalisation may push up the overall Q of the system. Q can be pushed up by accident or design. It cannot be lowered.

Vd = Cone displacement measured in litres = Cone area (Sd) x (2 x Xmax)

Vd
is calculated from the following two parameters:

Sd = Useful cone area in square centimetres (usually including part of the outer suspension roll surround which contributes to the driver's output)

Xmax
= One way safe cone excursion measured in millimetres. (there are other factors involved but we don't need to delve deeply because we just use the manufacturer's claimed Xmax in millimetres)

All these figures should and will be provided by the high quality IB driver manufacturer. So all you need to do is pick off the numbers you need and you can go ahead and design your theoretically perfect IB.

Ideal IB enclosure minimum volume = Vas x Number of drivers x 20.

Enclosure volume for 4 x AEIB15s = 439 Liters x 4 x 20 = 35120 liters = 1236 cubic feet. (Wow! That's a 10.75 x 10.75 x 10.75 foot cube!) Say you only have a typical 7 feet domestic headroom you're going to need a space 13ft x 13ft to house your IB optimally.

A multiplier of 20 x total VAS is the calculated figure which will not raise the Fs (natural resonant frequency) of the IB drivers any higher than if they were measured in free air. As you reduce the rear volume (enclosure size) the natural F of the driver(s) will slowly rise. This might cause you to lose very deep bass and decrease system efficiency. This will theoretically require more amplifier power to reach the same output levels at very low frequencies and might also need some low bass boost. You may lose subtle sounds and dynamic effects in the deep bass which make an IB sound so real.

How low dare you go with an IB enclosure volume? Ten is quite a safe Vas multiplier but the risk is yours, not mine. My own IB enclosure is now down to a Vas multiplier of about 7. (at a very rough guess) Unfortunately the enclosure space is just too handy for storing packaging. Insecurity makes one keep the packaging in case the item needs to be returned to the dealer. In an ideal world all those boxes would be nested and left wide open. (To help reduce compression effects within the IB enclosure and to help scatter any standing waves) Do I notice anything from adding yet more empty boxes? Nope.

Note: My enclosure space is quite poorly sealed to the outside world which probably helps the cause. I also have 12"-16" of almost bare rock wool insulation above the sloping surfaces of the enclosure with only a DPM covering at the moment. Polythene DPM is probably quite transparent to very low frequencies if they are allowed to bounce around in the enclosure. Such a thickness of rock wool is quite good at absorbing very low frequencies. If you have a badly undersized concrete box for an IB enclosure you'd better not use it for storage of anything but fibreglass or rock wool wadding!

So, in summary: In a perfect world, you aim for at least 20 x Total Vas (Total Vas = Vas x No. of drivers) as your ideal enclosure volume. Then hope you can find enough rear volume in your crawl space, loft or cellar. As discussed earlier, the IB enclosure can be a spare room which shares a wall with your AV room. It can also be the underfloor (crawl) space or cellar. Or the loft above the AV room ceiling. Thankfully crawl spaces are usually very large areas covering the entire house floor plan. So the lack of depth isn't usually too much of a problem where volume is concerned. Lofts are often the largest room in the house when they go unused. They are often asymmetrical, triangular in cross section and well supplied with thick absorbent insulation into the bargain.

The real problems start when you really want to have an IB but you only have a small closet or cupboard available for your enclosure. Assuming you want to use 4 x AE IB15s and your closet height is only 7 feet then you need to think very seriously about alternatives. You could spread the necessary volume around between several smaller IBs in different places around the room if that helps you get more enclosure volume. The extra enclosures could be more cupboards, underfloor spaces or above the ceiling.

Some IB builders have removed the ceiling of an undersized walk-in closet to exhaust into the room above. Not ideal if it has to exhaust into the loft space though! Not unless the closet enclosure can be very well insulated in very cold climates. You must insulate or the heat in the house will wick rapidly away through the closet walls and probably cause massive condensation in winter. The opened closet ceiling can't be blocked with insulation or the IB drivers will still think they're trapped in the small closet. You wouldn't want to leave the open hole unguarded or people and wildlife will continuously fall into your IB enclosure. The exit hole can't be small either or the very low frequencies won't notice the hole is even there. Steel weld mesh over the hole down into the closet is a good start to avoid nasty accidents and wont affect the necessary cyclic airflow through the open closet ceiling.

Air movements are so large at VLFs that they need lots of room for free flow. Sound pressure waves move backwards and forwards. Not up and down like a skipping rope making waves. Imagine low frequencies as a string of huge balloons being cyclically stretched and then compressed back together. The scale is awesome. The usual crossover point of an audio system with a subwoofer is 80 Hz which has wavelength of around 15ft. 20Hz has wavelength of nearly 60 feet!

Now try to squeeze the vast balloons through too small a hole and the balloons will object. Greatly increasing in friction until no movement is possible. You might even think of the squeals of protest from the giant balloons as harmonic distortion components. This is why you don't want to port your IB enclosure. The IB can do bass like no other enclosure. "Gilding the lily" with a port is not a good idea. Using the same number and size of drivers (as in your intended IB) the enclosure size for a reflex design would have to be completely different. (usually very much smaller than an IB enclosure) The port would have to pass so much air that it would be difficult to avoid turbulence, noise and distortion. Moreover the ported enclosure would have to be airtight and rigid enough not to flex unduly to work as an efficient Helmholtz resonator. The air in the huge port required must have some deleterious effect on the sound quality due to turbulence and inertia.

The IB doesn't mind if you make its enclosure much larger than 20 x Vas. Nor how leaky it is. You are not really tuning an enclosed volume like a ported box. With an IB you are merely blocking the rear pressure waves from meeting the front pressure waves being produced by the driver cones.

In theory you could have your IB open to the outside world. Just fix your drivers into an outside wall and turn up the volume! Fine, if you live in the woods and are half a mile from your nearest neighbours. Not a good idea (at all) if you live in town. It's best to cut down some of the energy in the rear waves before they reach your neighbours right next door. So enclosing the rear waves is a vital exercise for most IB builders. Containing the IB in an enclosure also limits the bass leakage to other rooms in the house. Obviously this will vary and the rear waves aren't the only culprit. Any powerful subwoofer will share its output with the rest of the house unless you have thick concrete walls and floors, brick or block walls and heavy soundproof doors.

A regular box of any shape has a volume of Breadth x Length x Height .

A roof prism shape (attic or loft) has a volume of 1/2Base x Height x Length.

A trapezium (attic or loft) with a flat ceiling width A and floor width B has a volume of 1/2 (A+B) x Height x Length.

Let's work out an example to check my own IB enclosure volume. It is a simple roof prism which goes right up to the peak of the roof without any form of flat ceiling.

Height is 10 feet. Base = Total width across the floor = 18 feet. Length between the two triangular walls is 6'6".

Volume = 1/2 x B x H x L = 10 x 18/2 x 6.5 = 10 x 9 x 6.5 = 585 cubic feet.

It comes to exactly the same answer if you multiply all the dimensions together then divide by two. (B X H X L)/ 2 = (18 x 10 x 6.5)/2 = 585. You can halve any one of the dimensions of a roof prism and still get the same answer. 1/2 x Base is the same as half x Height or Half x length provided you halve only one of the dimensions in the formula for volume.

Don't forget to multiply the Vas of your chosen drivers by the number of drivers to obtain Total Vas. Or your rear volume calculations won't be of much use. Using Vas for only one driver in the volume calculations seems to be quite a common mistake and leads to unfounded optimism about the minimum allowable volume of an IB enclosure.

If you can only find enough rear volume using Total Vas x 5 then I'd probably still go ahead. You can put some thick absorbent material in the rear space which will fool the drivers into thinking they have a little more space available. It's not ideal but you'll still have a subwoofer which leaves most others for dead on sound quality, frequency extension and sheer power. The downside with such a small enclosure is that the enclosure walls will need to be solid or well braced in comparison with a much bigger volume. The walls of a bigger space are not subject to such fierce cyclic compression and rarefaction effects as the smaller rear volume. Though the surfaces will still vibrate if they are flexible enough even in a very large space. Wall vibration may be out of phase and cancel your bass at particular frequencies. Unwanted structural noise produced from vibration is bad because it draws attention to itself. Spoiling the pleasure of listening to music or a film soundtrack.

Simple Basic Rules for IB construction:

A: Use an opposed driver manifold unless you can build a very stiff and/or massive wall for an array. If you are determined to have an array then keep drivers low down in a horizontal row just above the floor. So the stiffness of the floor plate directly contributes resistance to driver movement. Or put them in a horizontal row up high. Using the lateral resistance of the ceiling joists in the same way as a floor. Or arrange your drivers vertically up a corner between two walls to gain the resistance of the side wall. Worst case scenario is when an array is arranged vertically in the middle of a lightweight partition wall. Even worse is having a door beside the array! The drivers will sh-sh-sh-shake the wall and door like you would not believe! Been there. Done that. Didn't like it! Have you seen a door literally bending rapidly back and forth in its frame by a full 1" from flat? I have. That's why I now have a manifold! Do not underestimate the reaction forces from 15" or 18" drivers!

B: Use Vas x Number of drivers x 20 for your enclosure volume. Cheat on volume if you must. We won't tell if you don't. But big is still beautiful. 10 xVas is fine in practice.

C: Use (at least) 4 x 15" or 2 x 18" IB specific drivers for a minimum of 10-12 Litres of total driver displacement. Make no excuses and you won't bottom your drivers on the first action film you watch! As ThomasW of the IB Cult says: Drivers make poor (but expensive) paperweights. Say you cheat and try to use only two x 15" drivers and break the first two. Then you have to buy four more to be safe next time! That's six drivers you have to buy in all! Even I can understand the maths of such an economic disaster. Ouch!

D: An impedance load of 4 Ohms per channel is optimum. Eight ohms per channel is acceptable but will limit output a bit. Two Ohms per channel is far too hard on many amplifiers. Bridging an amplifier is the same thing as halving the impedance per channel seen by the amplifier. So eight ohms bridged is okay. While 4 ohms bridged is very hard work and overheating or instability may occur in the amplifier. Some amplifier manufacturers will specifically tell you not to wire your drivers for a 2 Ohms load per channel or 4 Ohms bridged. It really is far safer simply to avoid 2 Ohms per channel or 4 Ohms bridged. If your amplifier goes into heavy clipping it will burn your voice coils with nasty distortion. More paperweights! Even if you can afford all these paperweights try and think of the planet's finite resources.

E: Two, four and eight drivers are usually easy to wire up for a sensible amplifier load. Three or six or nine drivers each of 4 or 8 Ohms impedance are difficult to wire up sensibly. You can't wire them in series, parallel or series-parallel to obtain a suitable impedance around 4 Ohms for your amplifier to drive.

F: Feed your IB drivers with a popular/reliable musician's power amp for clean headroom. If you want more output then double the number of IB drivers rather than doubling the RMS wattage. Avoid plate amps if you can. Most lack the power you need and are not such good value for money as pro power amps anyway. Your AVReceiver will usually act as the crossover between subwoofer and speakers. So the plate amp's crossover will be bypassed and becomes superfluous.

G: Test your proposed IB location with a conventional subwoofer and REW before you start making large holes in your home. If a smaller subwoofer suffers from massive nulls or peaks at the listening position then it is certain an IB will suffer from them too! Moving a finished IB is not the easiest thing in the world and loses you major house points with your partner. So check your proposed manifold position first even if you have to borrow a box subwoofer and learn to use REW. Or build one of your IB drivers into a box and use that for testing. If you are really confident you want an IB could build your manifold and use that with the opening blanked off or resting on a carpet or rug to obtain a seal. It really will be worth the hassle to test the proposed IB location first. If the conventional subwoofer sounds okay to your ears at the chosen spot then you may be okay. Though using REW is very much safer because you can see exactly where particular frequencies are missing or peaking in the response curve and this isn't always easily audible. Not unless you listen very carefully to a wide range of different material during your tests and know what to listen for.

H: Last but not least: Join "The Cult of the Infinitely Baffled" forum. All of the above information has been gleaned at the feet of ThomasW, the IB Cult's high Wizard. He has forgotten more about audio than I will ever know. (or can still remember) So if you are really serious about building an IB join the IB Cult and get stuck into the IB Cult's priceless FAQs. Each of which is individually hand beaten from 21st Century alchemist's gold by the fabled high wizard himself. Seriously though, Thomas has popularised the IB subwoofer almost single handedly with his IB Cult forum. His decades of audio experience remove much of the hearsay and bullshit you will read elsewhere. Reading some of the nonsense posts on others forums where the members try to talk about IBs from a standpint of total ignorance can be more excruciating than amusing! There really is a lot of ignorance surrounding IBs even by those who try to build them without knowing any of the simple rules.

I advise you to read the Cult's FAQs right through first. Then look at the galleries for lots of working examples. Only then ask questions on the forums. It's only polite, given the enormous effort ThomasW has put into them.

And finally: Don't ask about car audio infinite baffles on the IB Cult. There are plenty of car audio forums for discussing all kinds of subwoofers. The IB Cult is for discussion of properly designed, HT/AV/Home Audio, True Infinite Baffle subwoofers. Whether for film, or music, or both, the IB will deliver bass sound quality and clean power like you have never heard before. Provided you follow the simple rules.

In case you have any lingering doubts about an IB's sound quality: The Cult is littered with examples of owners who have built IBs to replace stacked or multiples of expensive, commercial subwoofers. The IB has always sounded better except in one or two rare cases. Most IB builders are absolutely delighted with their results provided they followed ThomaW's advice and adhered to the basic rules.

FOOTNOTE: This post was published quite some time ago now. The links, prices, drivers, charts and availability have all changed or disappeared. Join the IB Cult for up-to-date information and/or browse for manufacturers mentioned here for their latest offerings and prices.

For Fi Caraudio IB3 series IB drivers in Europe contact Blade ICE. (UK) They have a solid reputation with AVForum members. They can also supply many other drivers, of course.

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