Calculate BL
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 Multi-Way Conventional loudspeakers with crossovers

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Dave Jones
diyAudio Member

Join Date: Jul 2003
Location: Silicon Valley
Calculate BL

Here's a formula for BL from an old thread:

Quote:
 Qes=1/(ws*Cms*Res) and Cms=Vas/(rho0*c^2 *Sd^2) and Res=(Bl)^2 / Re Bl=sqrt((rho0*c^2*Sd^2*Re)/(ws*Vas*Qes)) rho0 = density of air =1.2 kg/m^3 c = velocity of sound = 345 m/s Sd = Equivalent piston area in m^3 Re = voice coil DC resistance in ohm ws = 2 *pi * fs fs = free air resonant frequency of the driver in Hz Vas = Volume equivalent to the cone suspension Qes = "electrical" Q value of the driver and sqrt... meaning the square root of ...
The definition of Sd can't be right, because m^3 is a volume, not an area. What should it be?

Thankee.
Dave
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Davy Jones

 4th May 2004, 07:52 PM #2 GM   diyAudio Member     Join Date: Jun 2003 Location: Chamblee, Ga. m^2, but I use this formula so that I can input Sd in cm^2 and Vas in liters: BL = SQRT((rho*(c*0.0001)^2*Sd^2*Re)/((2*PI*Fs)*(Vas*0.001)*Qes)) It's nit-picking, but I've found the best correlation with actual measurements is when rho = 1.20997 kg/m^3 and c = 344.424m/sec.. GM __________________ Loud is Beautiful if it's Clean! As always though, the usual disclaimers apply to this post's contents.
Svante
diyAudio Member

Join Date: Feb 2004
Location: Stockholm
Re: Calculate BL

Quote:
 Originally posted by Dave Jones The definition of Sd can't be right, because m^3 is a volume, not an area. What should it be? [/B]
Yes, sorry, it should have been m^2.
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Simulate loudspeakers: Basta!
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Dave Jones
diyAudio Member

Join Date: Jul 2003
Location: Silicon Valley
Quote:
 Originally posted by GM m^2, but I use this formula so that I can input Sd in cm^2 and Vas in liters: BL = SQRT((rho*(c*0.0001)^2*Sd^2*Re)/((2*PI*Fs)*(Vas*0.001)*Qes)) It's nit-picking, but I've found the best correlation with actual measurements is when rho = 1.20997 kg/m^3 and c = 344.424m/sec.. GM
Ahhhhhh.

BL = 1.1239

Thanks much.
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Davy Jones

 4th May 2004, 08:48 PM #5 GM   diyAudio Member     Join Date: Jun 2003 Location: Chamblee, Ga. Hmm, I double checked to make sure I didn't copy it wrong from my spreadsheet, so you must have done something wrong since it calcs to 4.5015 using the FE107E published specs, while Fostex lists it at 4.7. The difference being that theirs is calc'd using a different 'p' and 'rho'. You can sim using both to see the subtle difference it makes. I can't imagine any driver having such a low BL. GM __________________ Loud is Beautiful if it's Clean! As always though, the usual disclaimers apply to this post's contents.
Dave Jones
diyAudio Member

Join Date: Jul 2003
Location: Silicon Valley
Quote:
 Originally posted by GM Hmm, I double checked to make sure I didn't copy it wrong from my spreadsheet, so you must have done something wrong since it calcs to 4.5015 using the FE107E published specs, while Fostex lists it at 4.7. The difference being that theirs is calc'd using a different 'p' and 'rho'. You can sim using both to see the subtle difference it makes. I can't imagine any driver having such a low BL. GM
When I use 4.5, the ML King spreadsheet graphs look ridiculous. I guess I'm doing something wrong.
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Davy Jones

 4th May 2004, 10:17 PM #7 GM   diyAudio Member     Join Date: Jun 2003 Location: Chamblee, Ga. Dunno. Since you have a licensed copy, send me your .mcd worksheet and a description of what you're trying to accomplish. GM __________________ Loud is Beautiful if it's Clean! As always though, the usual disclaimers apply to this post's contents.
Dave Jones
diyAudio Member

Join Date: Jul 2003
Location: Silicon Valley
Quote:
 Originally posted by GM Dunno. Since you have a licensed copy, send me your .mcd worksheet and a description of what you're trying to accomplish. GM

Thanks for the kind offer. I found my mistake, though. I miscalculated the effective cone area. I omitted pi. Doh!

It's looking pretty good now. I tried emailing it to you, but the diyAudio.com email thingy does not have a provision for attachments that I could find.

Here are the goals:

1. Cheap
2. Low enough bass to cross over to a sub at about 100 Hz (or below)
3. Small enough to fit a 15x15 ft office.

I'm actually going to build at least two sets of speakers. Only one set has to be inexpensive. But I'm doing the cheap one first.

A friend is going to build the cabinets. He's keen on using Fostex fe107e's. So be it. The fe107e has a small suckout between 400 and 600 Hz, so I've tried to put the transmission line 3F ripple right on top it.

Here's one design:

So = Sl = 30 in^2
L = 43 in
driver at 10"
0.75 lb/ft^3 stuffing top to bottom
Attached Images
 fe107e 43 30 10.png (2.8 KB, 260 views)
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Davy Jones

 6th May 2004, 02:05 AM #9 GM   diyAudio Member     Join Date: Jun 2003 Location: Chamblee, Ga. Hmm, I didn't check, just assumed you could. Anyhoo, your pipe is way too big/overstuffed. The only way to get solid/smooth output to 100Hz is in a ML-TL, though you won't be able to design in a 500-600Hz hump in the response. Of course you'll still need some BSC if not nearfield. Max flat using published specs: rp = 0.5" Lp = 0.75" density = 0.2lbs/ft^3 L (in) 15.38 S0/SL (in^2) 21.366 driver (in) 6.302 Vb(ft^3) 0.19 Fs or Fb (Hz) 83.9 GM __________________ Loud is Beautiful if it's Clean! As always though, the usual disclaimers apply to this post's contents.
Dave Jones
diyAudio Member

Join Date: Jul 2003
Location: Silicon Valley
Quote:
 Originally posted by GM Hmm, I didn't check, just assumed you could. Anyhoo, your pipe is way too big/overstuffed. The only way to get solid/smooth output to 100Hz is in a ML-TL, though you won't be able to design in a 500-600Hz hump in the response. Of course you'll still need some BSC if not nearfield. Max flat using published specs: ...etc
Dang! How did you do that?
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Davy Jones

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