Relation between Vas and Enclosure volume - diyAudio
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Old 15th January 2004, 05:46 AM   #1
tda is offline tda  Romania
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Default Relation between Vas and Enclosure volume

I have a big question.
How big can be the volume of the box for a given Vas of the driver? Nobody seems to treat this subject on the forum. Does it matters if the box is sealed or bass-reflex?
Are there any clear formulas or just an rule of thumb?
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Old 15th January 2004, 06:22 AM   #2
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For a closed box:

Determining Drivers for a Sealed Box?
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Old 15th January 2004, 06:37 AM   #3
tda is offline tda  Romania
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My problem is with a ported box.
The Vas of the driver is 4,4 l and Sd=65 cm^2.The box volume is 27 l
In any simulation that I made it (WinISD, MJK MathCAD sheets), The Fb of the box should roll off around 55 Hz...But my FR plots show that actually it rolls off at 85 Hz (very close to the Fs of the driver). So I'm questioning myself if the problem is not the Volume Box of the driver, 6 times bigger than Vas. Why in any simulation that I made this problem is not appearing?
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Old 15th January 2004, 12:13 PM   #4
SY is offline SY  United States
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Let's try to straighten out some terminology and a few realities:

Fb is a box tuning frequency. It is a single number, hence can't "roll off." You can determine it by looking at the impedance curve.

The box tuning frequency does NOT necessarily correspond to the box/driver's rolloff frequency except in the special case of a discrete alignment.

With a tiny Vas like 4 liters, actual boxes will not have the effective volume you think they have, especially once you mount a driver and a port into the box. Presumably, you'll want to add some damping materials on the walls so that driver reflections don't come back through the cone (a real problem in small boxes), and that will affect both the effective volume and the box Q.

Driver parameters are not generally the same as they are on spec sheets. Vas in particular can vary wildly, even with small changes in temperature.

Trying to get a driver with such a tiny Vas to produce bass much below 100Hz is going to be an exercise in frustration.
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Old 15th January 2004, 12:46 PM   #5
tda is offline tda  Romania
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SY,
You are right about last thing:
<Trying to get a driver with such a tiny Vas to produce bass much below 100Hz is going to be an exercise in frustration.
My common sense tells me the same think. I know the box is just too big and probably is impossible to reach 55 Hz with this small driver. BUT I want an answer from the mathematical and physically point of view. I want to know why in every simulation that I made it the port response looks very good, when actually should be almost negligible???
I want to know if is there any rule for Ported Box regarding VAS and volume of the enclosure. For example: “You cannot put a driver in a ported box with VAS smaller than half of the enclosure volume”
You see, this questions really frustrates me for the last week J
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Old 15th January 2004, 12:51 PM   #6
SY is offline SY  United States
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Default SY's Third Law

"An analogy is not an equality."

Because simulations assume the correctness of the assumptions. Let's take an example: shape the cabinet so that it's really, really thin and really, really tall. The simulation will show no difference from a box with normal proportions. Measure something like that in reality and you'll find that the model is not predictive.

In this case, the cabinet is effectively infinite in size. The driver can't effectively drive the slug of air in the port- it's like trying to push a golf ball uphill using a soggy piece of spaghetti. The assumptions in the Thiel-Small model (note that last word!) are not met.
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Old 15th January 2004, 02:04 PM   #7
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Well, I cannot tell you precisely how big an enclosure has to be compared to Vas of the speaker before the rule book gets thrown out.

But I can tell you why nobody has bothered to investigate much, if that puts your mind at ease.

If you take a look at the Thiele-Small charts, you will see that there really are not any useful alignments which require much over Vas times 2. After that, distortion takes over.

The famous audio writer David Weems tried this out. He took a speaker with the Qts of 0.6, put it in a box over 2 times Vas, and pronounced the distortion too high to be useful. Thiele-Small were being generous when they put their last useful alignment at Qts=0.57.

You see, from a practical standpoint, nobody even wants to build a reflex box with a volume much over Vas times 2, in fact, most people don't even want to go that big in the first place.

The larger the box volume compared to Vas, the higher the distortion and the worse the transient response. So somewhere above Vas times 2, the Thiele-Small parameters mean progressively less and less until they don't matter at all. Few have bothered to investigate, or at least publish their findings, because if you want to build a good reflex, you aren't going anywhere near those enclosure sizes anyway.

Perhaps you can add blocks of wood and bricks to your enclosure to reduce volume and let us know where the Thiele-Small parameters kick in. It might be fun, and you already have built the test enclosure.

Below is a graph for the step responses for various Thiele-Small alignments. The sloppier the response, the worse the distortion.

I took this chart from Small's article on vented boxes. He has charts that deal with K and B in his article, so I took it from there. All the colored printing is my addition. It was unclear to me what the Keibs and SC4 alignments were, so I added no additional info. However, four of the charts I added the Vas÷Vb ratio, and the F3÷Fs ratio.

a=(Vas÷Vb)

Note the response gets smoother and less distorted the smaller Vb is compared to Vas, and the higher F3 is compared to Fs. Of course, this is the precise opposite to the way you tried to build your box.
Attached Images
File Type: gif step response vented boxes.gif (12.5 KB, 841 views)
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Old 15th January 2004, 02:32 PM   #8
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It seems to me (being at work and not having any of my resources at hand) that as the box gets bigger (compared to VAS) you start to "grow" into an Infinite Baffle design, which will be akin to the open baffles that been all over the forum for the past months. The drivers response will start to resemble that of the driver in free air (fc=fs).

I'm not quite sure what distortion your speaking of KW, but I would think that the level of distortion will depend a lot on the quality of the driver. If it were strictly an alignment issue then Bozak and Linkwitz were mistaken in some of their efforts.
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Old 15th January 2004, 02:42 PM   #9
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Roddy:

The distortion that I am sure Weems was talking about was the "overshoot" and "ringing" which the charts indicate occurs the greater the box size is compared to Vas.
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Old 15th January 2004, 06:01 PM   #10
sreten is offline sreten  United Kingdom
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You also need to quote the Fs and Qt of the driver to allow analysis.

One of the major issue of commercial speakers is volume effiency.
What can you get out of a box of a given size.

Normally the Box size is much less than Vas and this dominates,
the real issue being the Qt at the open air resonant frequency.

Using extreme alignments the following is generally true :
going beyond Box volume = Vas is generally not worth it,
the driver suspension begins to dominate.
Once box volume = 2 Vas then there hardly any point going any
larger, a 2 Vas box will give uncontrollable reflex alignments.

E.G. for a Tb driver Vas=3 litre, Fs = 81 Hz and Qt =0.49,
reflex alignments above 6 litres are impossible without
the reflex peaking.

sreten.
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