# Vas Question

#### kabennett

What does the Vas compliance measurement correlate to? Most definitions in reference materials I have simply describe Vas as the volume of air that has the same acoustic compliance as the driver suspension. While I understand that a higher Vas means a higher complicance, I've never understood what the number itself means. I just came across this on the Eminence website:

"Vas represents the volume of air that when compressed to one cubic meter exerts the same force as the compliance (Cms) of the suspension in a particular speaker. "

I've seen this version of the definition before, but can't recall where. But I don't understand. I've never seen a driver with a Vas larger than a cubic meter, so you wouldn't be able to compress the Vas volume. Is this definition accurate? If so, are they saying that the vacuum force generated by expanding the Vas (say, 20 litres) to 1000 litres is the same as the amount of force as the compliance of the cone?

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#### speaker dave

The term Vas came into common use because it was a way for Thiele and others to generalize a woofer without worrying about its particular diameter. That is, a design with the woofer/box system defined partly by Vas would work the same whether it used 10" diameter or 6" diameter. (At least for small signal performance.)

Not sure about the Eminence definition but the first definition you gave is correct: the volume of air that has the same compliance as the driver suspension.

Picture a box with a piston on the front that you can press to compress the air inside the box. Since you are compressing the air to a smaller volume, there will be a restoring force. If the box is very large a given "distance of press" will compress the inside air a small percentage and the restoring pressure will be weak. As the box gets smaller the enclosed airspring gets stiffer and the restoring force greater. Some particular volume of air would have a stiffness equal to any given woofers stiffness.

Another way to think of it is: "Take away all of the suspension of the woofer and find a box of just the right size to give it back the same stiffness." (or return it to the same resonance) The size of that box is equal to Vas.

David

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#### kabennett

Excellent explanation, thank you! Somehow I'd always thought that Vas was relative to the speaker diameter since larger speakers tend to have a larger Vas.

Using the Scanspeak 4434G family as an example:

5.25" Vas: 12.89 litres
6.5" Vas: 20.86 litres
8" Vas: 122.5 litres

They all use the same suspension (I'm assuming), the larger sizes just have more of it. Shouldn't the larger sizes be stiffer (in terms of total restorative force) and proportionally compliant (relative to Sd)?

#### speaker dave

That would all make sense if you think about.

Compliance and Vas are related, in fact Vas is proportional to Cms times Sd squared (compliance times area squared). So if you think three woofers share the same suspension elements, or at least have reasonably close compliances, then Vas would grow for the larger units by area squared or diameter to the fourth power.

Think of it this way: the larger woofer, by virtue of its greater cone diameter would need a much larger box (Vas) to yield the same stiffness. Why?, because for every cm of travel it compresses the air in the box that much more. (More in volume reduction, a large box reduces the percentage reduction.)

Hope I haven't confused you again.

David

#### sreten

Hi,

Vas basically tells you about the drivers suspension stiffness and the ratio
of the cone mass to its Fs, basically higher cone mass for a given Fs means
a lower Vas, and this means lower efficiences and smaller boxes.

Note that drivers designed for sealed loading can have Vas >> Vbox, whilst
for vented loading Vas should be ~ 2 times Vbox , the final involved parameter
is Qts - free air and in box. The square root ratio of Vas to Vbox determines
the change of system total Q.

rgds, sreten.

#### Pano

Paid Member
Excellent topic!

Thanks for asking. So many of the Thiele Small parameters get short, dry explanations around the web. Such as your Eminence example above.

It would be great to have fuller explanations and the practical ramification of the parameters in a FAQ here on diyAudio.com - Thanks to Dave and Sreten for the nice answers.

#### jamikl

Meaning of Vas and other parameters

I'm with Panomaniac on this one. Thanks for the question and a big thanks for the extremely lucid replies. I agree, too, that similar lucid replies on the other TS parameters would be good to see permanently on this site.
jamikl

#### Ron E

I just came across this on the Eminence website:

"Vas represents the volume of air that when compressed to one cubic meter exerts the same force as the compliance (Cms) of the suspension in a particular speaker. "

This is wrong. Change it slightly to:
Vas represents the volume of air that when compressed [by a piston of the same diameter as the speaker] exerts the same force as the compliance (Cms) of the suspension in a particular speaker.

#### sreten

Hi,

Vas is simply the the equivalent box volume of the drivers suspension.
If the driver is put in a sealed Vas box, Fs goes to Fbox and Qts goes
to Qbox by multiply by 1.414 (root 2).
In a sealed 1/3 Vas box, Fbox and Qbox are double Fs and Qts.

e.g. a driver Fs=30Hz, Vas=30L, Qts=0.35 : in a sealed 10L box Qts=0.7
(Butterworth), Fbox= 60Hz and as its Butterworth F-3dB also = 60Hz.
The above driver could also be used in a vented box, around 18L.
(Vented boxes are usually around double the volume of 0.7 sealed,
though you cannot practically vent a driver with Qts above ~ 0.5.)

rgds, sreten.

Bigger drivers need bigger boxes and they have bigger Vas than small drivers.

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#### Francec

panomaniac,
"I agree, too, that similar lucid replies on the other TS parameters would be good to see permanently on this site."

I think this would be a great idea, an educational part of the forum (for the still learning like me).

Frank

This is wrong. Change it slightly to:
Vas represents the volume of air that when compressed [by a piston of the same diameter as the speaker] exerts the same force as the compliance (Cms) of the suspension in a particular speaker.

Good catch!

Stiffness is the real, physical parameter. But Thiele and Small (and Benson maybe?) wanted to get all the parameters into the same domain, so you could apply electric filter theory for design simulation.

Stiffness in Newtons/meter is not too helpful to designers. But mathematically transformed by the cone area, it becomes cubic meters.

Aha! That's like the volume of a box! So now we can apply standard capacitor formulas for the combined stiffness of speaker + sealed box. Since the mass stays the same* then a new resonance can be found from the mass + combined stiffness, and the new combined Q calculated as well.

(*Well, except for changes caused by the shape of the box, generally quite small. LEAP calculates that for you.)

#### kabennett

I'm still trying to digest all these wonderful responses, but just wanted to take a moment to thank you all for them. This is without a doubt a phenomenal online community, and I hope to learn enough to be able to contribute something back.

#### Cal Weldon

Paid Member
You already have. You thanked those who took the time to help.

#### thetubeguy1954

David,

I also want to thank you for your excellent explanation and analogies! It's the very first time I actually got a grasp on what Vas meant. I think it's all to common when someone that's knowledgeable on a given topic responds to a newbie ---{although I've been an audiophile/music lover for over 43 years now, I'm just a newbie to DIYing}--- like myself, to respond in a way they believe is simple and easy to understand. When in reality it's ONLY simple and easy to understand "if" you already have knowledge about the topic!

That's why analogies are so helpful. For example: Before becoming disabled, I repaired computers and would need to talk to many clients that just couldn't grasp how their harddrives and memory were functioning. I had an analogy that once stated was easily understood and grasped by almost everyone immediately! I'd explan the HD is like a file cabinet and your memory is like a desktop. So if you clicked on WORD, you're telling your assistant named "windows" to go to the file cabinet called HD and access the folder in it called Word and then place it on your desktop, which your assistant "windows" refers to as memory.

In any event I hope my analogy helped you understand why your analogy was so helpful to me. Again my sincerest thanks...

Thetubeguy1954

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#### speaker dave

David,

I also want to thank you for your excellent explanation and analogies! It's the very first time I actually got a grasp on what Vas meant.

Thetubeguy1954

Happy to help out.

Most of these concepts are pretty straightforward if carefully explained. A lot of other people have helped me out along the way and I'm happy to be able to pass a little knowledge along.

I think we could put together a list of terms and definitions, perhaps in a wiki approach. Maybe we should have a thread: "Could somebody please explain...?" and let various newbies ask any question and others take a crack at explaining it. Good questions and answers could be collected in an FAQ or "terminology" area.

Thanks to everybody else for the other excellent responses!

David S.

#### kabennett

I think we could put together a list of terms and definitions, perhaps in a wiki approach. Maybe we should have a thread: "Could somebody please explain...?" and let various newbies ask any question and others take a crack at explaining it. Good questions and answers could be collected in an FAQ or "terminology" area.

How about a sub-forum titled "Could somebody please explain...?" (instead of a thread), and then particularly useful and lucid and evolved/edited threads could be made sticky, making for a quick reference for those of us deficient in knowledge, memory, or both....

What do you think moderators?

#### jcandy

Vas is simply the the equivalent box volume of the drivers suspension. If the driver is put in a sealed Vas box, Fs goes to Fbox and Qts goes to Qbox by multiply by 1.414 (root 2). In a sealed 1/3 Vas box, Fbox and Qbox are double Fs and Qts.
I think this is a great post. This analogy can be extended to see how Fc (speaker in closed box) improves only marginally for Vbox > Vas. Let a = Vbox/Vas:

a=1/3: Fc = 2 Fs
a=1/2: Fc = 1.7 Fs
a=1: Fc = 1.4 Fs
a=2: Fc = 1.22 Fs
a=3: Fc = 1.15 Fs

#### arjunm009

The term Vas came into common use because it was a way for Thiele and others to generalize a woofer without worrying about its particular diameter. That is, a design with the woofer/box system defined partly by Vas would work the same whether it used 10" diameter or 6" diameter. (At least for small signal performance.)

Not sure about the Eminence definition but the first definition you gave is correct: the volume of air that has the same compliance as the driver suspension.

Picture a box with a piston on the front that you can press to compress the air inside the box. Since you are compressing the air to a smaller volume, there will be a restoring force. If the box is very large a given "distance of press" will compress the inside air a small percentage and the restoring pressure will be weak. As the box gets smaller the enclosed airspring gets stiffer and the restoring force greater. Some particular volume of air would have a stiffness equal to any given woofers stiffness.

Another way to think of it is: "Take away all of the suspension of the woofer and find a box of just the right size to give it back the same stiffness." (or return it to the same resonance) The size of that box is equal to Vas.

David

Then when designing enclosures, does it mean to have a box volume appropriate to the value of Vas?

At some places, there is a recommended enclosure volume mentioned for sealed and ported. But they are all generally different from Vas.

#### godfrey

Then when designing enclosures, does it mean to have a box volume appropriate to the value of Vas?
Yes, among other things. Fs and Qts in particular have to be taken into account as well.
At some places, there is a recommended enclosure volume mentioned for sealed and ported. But they are all generally different from Vas.
Yes, box volume is often different to VAS, depending on the other driver parameters and the desired result.

#### fastbike1

Vas and box volume are virtually never the same.