Calculate BL

[Dave Jones]

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

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

[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

[Svante]

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.

[Dave Jones]

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.

[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

[Dave Jones]

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.

[GM]

Dunno. Since you have a licensed copy, send me your .mcd worksheet and a description of what you're trying to accomplish.

GM

[Dave Jones]

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

[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:

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

[Dave Jones]

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?