design of dalines (transmission lines)

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GM said:
Yes, B*L is usually abbreviated to BL or Bl.GM

I attempted to verify that by plugging the numbers into the formula you posted. The number I calculate from the formula is just under 1.0. The number in the specs is 4. The value 4 gives reasonable looking numbers, but 1.0 doesn't. I'm pretty sure I transcribed the formula correctly. Could you check it?

The spec sheets give the force factor in units "T*m". (What does that stand for?) Is that equivalent to Newtons/amp?
 
diyAudio Moderator Emeritus
Joined 2001
"Force Factor" is indeed Bl.

The lowest I have ever seen it was just below 3, the highest I have ever seen it was into the 20's.

Tm? Not sure, but I think it stands for Tesla per meter, or millimeter, or whatever. Anyway, it the magnetic force generated that drives the speaker, and has to do with the amount of flux in the gap and the length of wire or number of windings in the gap, (which might be less than half the length of the total voice coil).
 
Couple of quick comments :

1. Bl is the same as BL.

2. The units of Bl can be newton/amp (N/A) or tesla-m (T-m) which are the same thing. The numerical value will be identical.

3. The MathCad Explorer program should run great under Win 98 SE. E-mail me privately if you are having trouble and we can probably work it out quickly.

4. I have modeled many Daline type geometries and never really found a good design. Maybe I am missing something, but they just didn't work for me. I found mass loaded designs to be much better.
 
I have no explicit readout for the line volume, but i have noted that as you shorten the line the cross-section gets bigger
Yep. At a glance though, I think I'll stick with my way. Don't subscribe to any mags, so not familiar with RS's work beyond his "Rhinos" article, which IIRC I read on your site.
I attempted to verify that by plugging the numbers into the formula you posted. The number I calculate from the formula is just under 1.0. The number in the specs is 4.
I get Mms = 0.0072 Kg, Cms = 1.7258e-03 mm/N, and BL = 3.9875 N/a. Spreadsheets are 'beautiful things' to math challenged folks like me. ;)

Since measurement programs calculate this with the same formulas, the only variables are 'rho' and 'c', and how much the program and/or the publisher rounds off the number.

Tesla/meters (Tm) = Newton/amps (Na).
PS: Having some trouble getting Martin King's software to work with the MathCAD demo myself. I have Windows 98SE.
I run WIN98SE also and had no major problems until I upgraded Norton AV to 2003. MJK somehow found out that the 'scripting' feature of Norton has to be turned off to get it to load/not crash, though sometimes I have to re-click the spreadsheet app more than once to get it to load completely.
I have modeled many Daline type geometries and never really found a good design. Maybe I am missing something, but they just didn't work for me. I found mass loaded designs to be much better.
Dalines, or at least my version, is a seriously mass loaded design and short of horn loading works best IMO for getting the most out of low Q/low Fs drivers without resorting to mass quantities of EQ. Great for blending HE LF/midbass drivers to horns, ribbons, ESLs, dipole arrays. Tower designs (ML-TLs) aren't viable for me until the effective Qts is up around 0.38.

GM
 
GM said:


I get Mms = 0.0072 Kg, Cms = 1.7258e-03 mm/N, and BL = 3.9875 N/a. Spreadsheets are 'beautiful things' to math challenged folks like me. ;)

GM

The problem with computers is they are so danged literal. Anyway, if you change the formula

Mms = 1/[(2*pi*Fs^2)*Cms)]

to this

Mms = 1/[(2*pi*Fs)^2*Cms]

then the numbers agree. Is that what you intended?
 
frugal-phile™
Joined 2001
Paid Member
GM said:
Spreadsheets are 'beautiful things' to math challenged folks like me. ;)

And incrediable tools for those of us not math-challenged.... just wished someone would release a product that even comes close to the antique i'm using (still outruns the latest & greatest Excel, even on the almost 10 year old puter i have it running on :))

dave
 
Dave Jones said:


The problem with computers is they are so danged literal. Anyway, if you change the formula

Mms = 1/[(2*pi*Fs^2)*Cms)]

to this

Mms = 1/[(2*pi*Fs)^2*Cms]

then the numbers agree. Is that what you intended?

Oops. I spoke to soon. Our Cms and Mms now agree, but BL is off by a factor of 10. I get 0.39875 rather than 3.9875. There is a constant 10 in the formula you posted for BL. Hmmm. Can you check it over?

From the above discussion of Mms, it would appear you are using the convention (which I've never seen) that operator* binds tighter than operator^. But if I make that assumption with the BL formula you posted, to wit,

BL = {[2*Pi*Fs*Re*(Mms*10)^-3]/Qes}^0.5

then I get 2400 and change. About all I can see to do is to replace the 10^-3 with 10^-1.

BL = {[2*Pi*Fs*Re*(Mms*10^-1)]/Qes}^0.5

which gives the right answer. (What does 10 have to do with anything, I wonder.)

Anyway, we're real close to coming to an understanding. Don't give up on me now!

Thanks,
 
Interesting. I wrote this ages ago and have posted it many times on various forums and privately, but you're the first person to point out a typing error, plus in looking at it, there's some ambiguities since I just copied the formulas and made a couple of (incomplete) notes. Guess they either never bothered to use them or were sharp enough in math to figure out the errors and just assumed they were all typos.

Anyway, copied from my spreadsheet, hopefully without typos:

Cms = Vas/(Sd^2*rho*c^2)

where:

Vas is in m^3 (liters*0.001)

Sd is in cm^2

c is in meters/sec*0.0001 to get Cms in mm/N

then:

Mms = 1/[(2*pi*Fs)^2*Cms]

BL = [(2*Pi*Fs*Re*Mms)/Qes]^0.5

Sorry for the confusion..... hey, I told you I was severely math challenged! :(

GM
 
GM said:
Interesting. I wrote this ages ago and have posted it many times on various forums and privately, but you're the first person to point out a typing error, plus in looking at it, there's some ambiguities since I just copied the formulas and made a couple of (incomplete) notes. Guess they either never bothered to use them or were sharp enough in math to figure out the errors and just assumed they were all typos.

Anyway, copied from my spreadsheet, hopefully without typos:

Cms = Vas/(Sd^2*rho*c^2)

where:

Vas is in m^3 (liters*0.001)

Sd is in cm^2

c is in meters/sec*0.0001 to get Cms in mm/N

then:

Mms = 1/[(2*pi*Fs)^2*Cms]

BL = [(2*Pi*Fs*Re*Mms)/Qes]^0.5

Sorry for the confusion..... hey, I told you I was severely math challenged! :(

GM

Otay! I get the right BL.

Howsomeever, now I'm getting strange numbers for S0 and SL in the MJK calculations. Onward through the fog!
 
GM said:
What, exactly, are you trying to do, and how are you doing it? For a simple Daline or straight pipe, SL = S0 in whatever unit of measure you prefer.

GM

I was just playing around with it - not trying to do a daline. I put in the specs for the Jordan speaker and did the calculations for an SO/SL of 0.5. SO and SL came out looking too big. Maybe I did something wrong.

... or not. I entered the data for the first example in the paper, and I got the same numbers. Hmmm.
 
MJK said:
...
4. I have modeled many Daline type geometries and never really found a good design. Maybe I am missing something, but they just didn't work for me. I found mass loaded designs to be much better.

I built DALINES with the KEFB110 and T27 -- this was my first real speaker project (using 1/2 inch particle board) back in 1977 or 1978 -- the sound was fantastic!
 
I put in the specs for the Jordan speaker and did the calculations for an SO/SL of 0.5. SO and SL came out looking too big.
Hmm, not sure what you mean. 0.5 of what?

Anyway, punch these in to get a baseline:

L = 31.04in
S0 = 6.97in*4.31in
SL = S0
density = 0.5
rport = 1
Lport = 5
X0 = L*0.3589

Note that you must copy/paste the S0 symbol for SL = S0, and L for X0, you can't just type it in.

Some folks prefer to take a Vb, divide it my some length to get the cross sectional area, then divide it by Sd to get a multipler for S0, inputting it as Sd*multiplier and doing the same for SL so that a taper can be defined. Again, you'll need to copy/paste the Sd symbol.

GM
 
GM said:

Hmm, not sure what you mean. 0.5 of what?

SL is 0.5 of S0. (Just playing, recall. And not trying to "daline".)



Anyway, punch these in to get a baseline:

L = 31.04in
S0 = 6.97in*4.31in
SL = S0
density = 0.5
rport = 1
Lport = 5
X0 = L*0.3589

Note that you must copy/paste the S0 symbol for SL = S0, and L for X0, you can't just type it in.


Now I'm confused. Punch it into what? Some spreadsheet? If so, where can I get it? :)
 
planet10 said:
Was this the original Daline from Wireless World (i believe that is where it was published).
Actually, it was in Hi-Fi News & Record Review. The B110 article came out in May 1975 and had two variants: a two way with a T27 and a three way with T15 and Coles 4001G.

As jackinnj pointed out, this was the second Daline article by Robert Fris. The first was in Hi-Fi News & Record Review in November 1974 and used a single, cheap 6.5" full-range cone.

This was my first serious speaker, too.

Incidentally, Robert Fris was later asked (in Speaker Builder) why he hadn't made a "Daline clone" of the BBC monitor (using the same crossover, etc.). He said that he hadn't thought of it but that it was a great idea.
 
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