
Home  Forums  Rules  Articles  The diyAudio Store  Gallery  Blogs  Register  Donations  FAQ  Calendar  Search  Today's Posts  Mark Forums Read  Search 
MultiWay Conventional loudspeakers with crossovers 

Please consider donating to help us continue to serve you.
Ads on/off / Custom Title / More PMs / More album space / Advanced printing & mass image saving 

Thread Tools  Search this Thread 
26th May 2013, 01:02 AM  #1 
diyAudio Member
Join Date: Sep 2012
Location: Maine, Bangorarea

puzzled about Vas
Without giving it much thought, I've always assumed that Vas is directly proportional to Sd or surface area of the driver cone. Not!
Vas = po*c^2*Cas where po= air density c = speed of sound Cas = acoustic compliance of driver suspension I don't see Sd in that equation. Another equation that I ran across is Vas = (1.4 X 10^5)*Cms*Sd^2 but that is the same thing as Cms = Cas/ Sd^2 So the equation is saying that Vas is directly proportional to the compliance of the driver's suspension (spider and surround) no matter what diameter size the driver is. Am I missing something or is this something that isn't generally understood? Sorry if you are more interested in the practical side, but I think that some of you like to discuss this kind of thing, at least I hope so. Pete Last edited by cT equals piD; 26th May 2013 at 01:04 AM. Reason: typo 
26th May 2013, 01:08 AM  #2 
diyAudio Member
Join Date: May 2005
Location: Victoria, B.C.


26th May 2013, 01:39 AM  #3  
diyAudio Member
Join Date: Jun 2002
Location: USA, MN

Quote:
Vas = Sd^2* rho * c^2 * Cms rho ~=1.2 c^2=344^2=118300 multiply these together and make a factor called k and you have: Vas = k*Sd^2*Cms Vas is proportional to the square of cone area times compliance.
__________________
Our species needs, and deserves, a citizenry with minds wide awake and a basic understanding of how the world works. Carl Sagan Armaments, universal debt, and planned obsolescencethose are the three pillars of Western prosperity. —Aldous Huxley 

26th May 2013, 03:37 AM  #4  
diyAudio Member
Join Date: Sep 2012
Location: Maine, Bangorarea

Quote:
Vas = k*Sd^2*Cms however, Cms which is mechanical compliance of the driver suspension, Cms = Cas/ Sd^2 Substituting for Cms in the above eq. for Vas, Vas = k*Cas That is, Sd drops out of the equation. Cas is the acoustic compliance of the driver suspension. 

26th May 2013, 03:41 AM  #5  
diyAudio Member
Join Date: Sep 2012
Location: Maine, Bangorarea

Quote:
Pete 

26th May 2013, 04:05 AM  #6  
diyAudio Member
Join Date: Nov 2009
Location: Cape Town

Quote:
Quote:
The other equation, Vas = k*Sd^2*Cms, is more useful as Sd and Cms are what's given in the TS parameters. Cms being the mechanical compliance in mm/N i.e Cms = distance moved / force applied. Last edited by godfrey; 26th May 2013 at 04:09 AM. 

26th May 2013, 08:16 PM  #7  
diyAudio Member
Join Date: Sep 2012
Location: Maine, Bangorarea

Quote:
However there is the often expressed opinion that Vas increases with increased Sd because the larger diaphragm compresses the enclosed volume of air more. This is I think is untrue. For a given enclosed volume of air, the pressure on the cone of the driver increases with increased area of the cone since the enclosed air exerts X gm of force per square cm. The X gm of force per square cm increases as the enclosed volume of air is decreased. But this is with the cone of the driver stationary. For example, from the spec. of a 12" woofer, Vd = Sd *Xmax =265 cm^3. Specified Vas = 204 X 10^3 cm^3. So then 0,1*Vas/ Vd = (204/265)*10^2 = 770 That is, Vas is 770 times Vd, even for a relatively small enclosed volume of air backloading the woofer equal to 1/10th of Vas. From Boyle's law, the woofer at max. excursion compresses the enclosed volume of air equal to 1/10th of Vas by only 1/10th of 1%. Yet the box resonance frequency equals 3,3 times free air resonance. 

27th May 2013, 01:08 AM  #8 
diyAudio Member
Join Date: Sep 2012
Location: Maine, Bangorarea

There are some math errors in the calculation of how pressure is changed in the volume of air backloading the example woofer in the above post my apologies.
The ratio of 0,1 times Vas to Vd equals 77 not 770. The pressure increase/ decrease of the volume of air by the woofer is +/ 1%, not 0,1%. What I say above, that a smaller volume of air (at atmospheric pressure, obviously) will exert greater pressure isn't going to fly. So, um, you could say that I'm still puzzled, although I do believe that compliance of a backloaded driver is inversely proportional to Sd squared. But I do see an extremely low pressurization of the enclosed air in almost all cases, as in the above example of the 12" woofer. Pete 
27th May 2013, 01:52 AM  #9  
diyAudio Member

Quote:
Vas = k * Cms * Sd^2 it is still dependent on Sd. You are confused because Cas has Sd factored in already as has already been pointed out to you. Go back to Small's paper and note that there are models with all of the parameters "pulled" to the electrical side, and also pulled to the acoustical side. You'll find that Cas on the acoustical side is related to Cms by the Sd factor. You need to read Small's paper more carefully, or perhaps go back to his earlier papers if you are looking at a later one. 

29th May 2013, 12:59 AM  #10  
diyAudio Member
Join Date: Sep 2012
Location: Maine, Bangorarea

Quote:
Atmospheric pressure equals about 1 X 10^6 dynes/ cm^2. So with full excursion of the cone of the woofer backwards, the pressure inside the closed box is increased to atmospheric pressure plus 0,01 times 1 X 10^6 dynes/ cm^2, that is, net pressure = 1 X 10^6 dynes/ cm^2 times 0,01 = 1 X 10^4 dynes/ cm^2. 10,000 dynes/ cm^2 is a considerable force, especially in relation to the mechanical compliance of the woofer, I would think. Agree/ disagree anybody? Regards, Pete 

Thread Tools  Search this Thread 


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
puzzled  sam18  Solid State  42  28th June 2012 10:24 AM 
A superior VAS clamp and VAS current limit for the Blameless.  GK  Solid State  128  19th October 2011 03:03 PM 
low VAS sealed better than high VAS?  matos81  Subwoofers  3  7th April 2006 11:28 AM 
Puzzled by tweeter response  joeling39  MultiWay  12  19th January 2005 02:27 PM 
Help me! I'm puzzled  DJsol_t_nutz  Analogue Source  2  30th September 2004 05:29 AM 
New To Site?  Need Help? 