Formulas to calculate new TS values when mass added
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 14th February 2004, 12:41 AM #1 macky888   diyAudio Member   Join Date: Apr 2003 Location: australia Formulas to calculate new TS values when mass added Does anyone have formula's to calculate the new value of Qts/Qms/Qes/Fs as you add more mass to the cone? I have some formulas here, but they are dependant on each other, so it doesn't work right for this. As you can see: Qms there relies on Rms as well, and to calculate Rms requires Qms. + I think Rms relies on Mms, as its related to Qms. Any help highly appreciated! Adrian BTW: I know WinISD can model the effects of this, but I require the formulas.
 14th February 2004, 03:36 AM #2 kelticwizard   Wizard of Kelts diyAudio Moderator Emeritus   Join Date: Sep 2001 Location: Connecticut, The Nutmeg State I cannot give you the formulas. But if you download Bullock and White's freeware DOS program, you can change certain parameters and see how they affect each other. http://www.hal-pc.org/~bwhitejr/ You cannot change Mms by itself in the program, but if you lower Fs you see that Mms is affected by most of all, and Rms is affected some. Bl will have to be increased to support the other parameters remaining the same. Try it. It might open up the relationships for you. __________________ "A friend will help you move. A really good friend will help you move a body." -Anonymous
 14th February 2004, 04:33 AM #3 GM   diyAudio Member     Join Date: Jun 2003 Location: Chamblee, Ga. If Mms is unknown: mass (m) = 22.428*dia^4(cm)/(Fs^2*Vas (liters)) then: m' = m + mass added mass ratio (mr) = m'/m Fs' = Fs/mr^0.5 Qes' = Qes*mr^0.5 Qms' = Qms*mr^0.5 then: Qts' = Qes'*Qms'/(Qes'+Qms') Vas is unchanged n0 = 9.614*10^-10*Fs'^3*Vas(liters)/Qes' SPL = 112.02+10*Log(n0) GM __________________ Loud is Beautiful if it's Clean! As always though, the usual disclaimers apply to this post's contents.
macky888
diyAudio Member

Join Date: Apr 2003
Location: australia
Thanks a lot for those formula's GM! It's exactly what I needed.

Quote:
 Try it. It might open up the relationships for you.
I appreciate your input, kelticwizard. I've got the formula's now though, as you've probably noticed.

Adrian

 14th February 2004, 03:53 PM #5 Ron E   diyAudio Member     Join Date: Jun 2002 Location: USA, MN Betcha got those from me on the Bass list, GM - or from Bob Stout's post paraphrasing me. I haven't seen that formula I derived for cone mass anywhere else. __________________ 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 obsolescence--those are the three pillars of Western prosperity. —Aldous Huxley
 14th February 2004, 05:33 PM #6 qwad   diyAudio Member   Join Date: Mar 2003 Location: adelaide city of churches yes and we all know plagarism is rife in audio now don't we? cheers and good luck to all TOMCAT: __________________ we all have problems only some people have more than most.... long live the Magyar (Hungarians) in the world!
 14th February 2004, 05:35 PM #7 Svante   diyAudio Member     Join Date: Feb 2004 Location: Stockholm OK, I'll go through them and see if I end up with the same as the others: ws=1/sqrt(Mms*Cms) (you lack the root) Fs=1/(2*pi*sqrt(Mms*Cms))=ws/(2*pi) (you have it inverted) Qes = ws*Mms / Res (mass reactance divided by resistance) since Res=(Bl)^2 / Re Qes= ws*Mms * Re/((Bl)^2) (As you have it) Qms = ws*Mms / Rms (mass reactance divided by resistance) Qts = ws*Mms / (Rms+Res) = Qes*Qms/ (Qes+Qms) Rms does not change if you add mass to the speaker cone. So, a mass load on the cone increases all Q values linearly (~Mms), and the resonace drops as ~1/root(Mms). Did that answer your question?
Svante
diyAudio Member

Join Date: Feb 2004
Location: Stockholm
Quote:
 Originally posted by GM If Mms is unknown: mass (m) = 22.428*dia^4(cm)/(Fs^2*Vas (liters)) GM

Quote:
 Originally posted by Ron E Betcha got those from me on the Bass list, GM - or from Bob Stout's post paraphrasing me. I haven't seen that formula I derived for cone mass anywhere else.
Let's try right here:

Cms=Vas/(rho0*c^2*Ss^2)

Mms=1/(Cms*ws^2)=
=rho0*c^2*Ss^2/(Vas*ws^2)=
=rho0*c^2*(pi*dia^2/4)^2/(Vas*4*pi^2*Fs^2)=
=rho0*c^2*pi^2/(16*4*pi^2) * dia^4 / (Vas * Fs^2)=
=rho0*c^2 / 64 * dia^4 / (Vas * Fs^2).

rho0=1.2 kg/m3
c=345 m/s
gives

Mms=2231.7 * dia^4 / (Vas * Fs^2).

I assume that Mms is in kg, dia is in metres, Vas is in m3 and Fs in Hz.
Since 1 m3 is 1000 litres, 1 meter is 100 cm and 1kg is 1000g there would be a factor 0.01^4 / 10^-3 *1e3 = 10^-2 =0.01 between our equations.

They match!

 14th February 2004, 06:36 PM #9 GM   diyAudio Member     Join Date: Jun 2003 Location: Chamblee, Ga. At this point in time I don't recall thanks to a very poor memory. Because of this I have saved copious bits of info on a wide range of subjects gleaned from many sources over the decades, including the basslist. As I've periodically stated on numerous forums, thanks to being severely math challenged, anytime I post math it's a given that I'm just sharing what others have already published somewhere or helped me with in private over the decades, you being one of them. Anyway, if it was you, thanks for sharing! They are as accurate and much easier to understand/solve than the ones I used to have programmed in a spreadsheet a math whiz friend did for me decades ago. GM __________________ Loud is Beautiful if it's Clean! As always though, the usual disclaimers apply to this post's contents.

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