I thought that's exactly what I had already done when presenting those examples for the JBL 2450J in this post, and then again for the Radian 950PB here and the TAD TD-4001 here.
Anyhow, here we go again:
Driver: JBL 2450J
diameter at phase plug exit = 3.8 cm, therefore S1 = 11.3 cm2;
diameter at internal throat exit = 4.9 cm, therefore S2 = 18.9 cm2
internal throat length L = 6.3 cm
Equivalent exponential cut-off frequency of internal throat: Fc = 343/(4*Pi*0.063)*ln(18.9/11.3) = 220 Hz
Equivalent exponential flare rate of internal throat: m = 4*Pi*221/343 = 8.1
A purely exponential horn with a throat area of 18.9 cm2 and the same Fc = 220Hz (i.e., m(constant) = 8.1) would thus be a perfect match.
A Hypex horn with a throat area of 18.9 cm2 and Fc = 320Hz and T = 0.7 would also be a perfect match, since its flare rate m (no longer constant, but varying with distance from throat) happens to start at 8.1 and then grow monotonically from there.
This is less straightforward/intuitive, but it can be verified by calculating m(x) numerically and iteratively (starting at x = 0 and using tiny increments of x, e.g., dx = 0.05 cm), from its very definition: m(x) = 1/S(x) * dS(x)/dx
Thanks for going over that in more detail. Sometimes we need to be hit over the head more than once. 😉
I'm trying to get those numbers working for me in a spreadsheet that will calculate Fc and m (flare rate), but so far am having a little trouble. I'll report back later.
Can't help with your spreadsheet, but JBL claimed the flare rate was around 160 Hz on the old style drivers:
https://usermanual.wiki/JBL/tnv1n21.608649286/view
" JBL Technical Note Volume 1 Number 21
When the JBL 375 compression driver was designed during the fifties, it was based on the exit geometry of the original Western Electric 594 driver. Subsequent variations, such as the JBL 2441, 2445, and 2450 family all maintained the original exit geometry and were designed to work with four decades of horn hardware with 50 mm (2 in) throat diameter.
By our calculations, the initial flare rate in the older driver design was approximately 160 Hz, reflecting the need to drive the very large horns that were used in early motion picture systems. Today, we can double or quadruple that flare rate, inasmuch as many horns are now intended for nominal crossover at 800 Hz."
https://usermanual.wiki/JBL/tnv1n21.608649286/view
" JBL Technical Note Volume 1 Number 21
When the JBL 375 compression driver was designed during the fifties, it was based on the exit geometry of the original Western Electric 594 driver. Subsequent variations, such as the JBL 2441, 2445, and 2450 family all maintained the original exit geometry and were designed to work with four decades of horn hardware with 50 mm (2 in) throat diameter.
By our calculations, the initial flare rate in the older driver design was approximately 160 Hz, reflecting the need to drive the very large horns that were used in early motion picture systems. Today, we can double or quadruple that flare rate, inasmuch as many horns are now intended for nominal crossover at 800 Hz."
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Hi Pano,
Kindest regards,
M
Please let me know if you get stuck, I had created a spreadsheet that calculates Fc from m and vice versa as well as m from a set of S(x), and I will find it.
Kindest regards,
M
Oh cool. My spreadsheet isn’t giving me consistent numbers. It works to give me correct Fc and m with the JBL, but not other drivers. I’ll post mine in the morning.
160Hz applies to the first WE594 driver.
The throat dimensions are slightly different in the early JBL drivers (375, 2440, 2441, ...), leading to Fc = 180Hz, and then slightly different again in the 2450 driver, leading to Fc = 220Hz.
I'd happily share mine, but Excel files do not seem to be allowed as attachments.
[EDIT: Weird! They are allowed if saved as ".xlsm" (macro-enabled workbook). - Here it is, then.]
@marco_gea I'll have Jason look at file types again. It should be xls or xlsx (the new, zipped version) for uploads. .ods would be nice too.
I've been cruising around your spreadsheet, it's quite a lot of work you've put into it. Bravo. The graph with the driver throat, adapter and horn and throat continuations is very handy and allows rapid checks. In the sheet there are only 10 unprotected cells where the user can input data. Some of them are obvious, some are not (too me)
Cells that are obvious
Cells I don't understand
I've been cruising around your spreadsheet, it's quite a lot of work you've put into it. Bravo. The graph with the driver throat, adapter and horn and throat continuations is very handy and allows rapid checks. In the sheet there are only 10 unprotected cells where the user can input data. Some of them are obvious, some are not (too me)
Cells that are obvious
- D14 = L from chosen driver in top table
- D15 = d0 from chosen driver in top table
- G20 = Fc of hypex horn
- G21 = T of hypex horn
Cells I don't understand
- G17 = dx from driver data?
- E14 = unknown
- E15 = same as G17?
- E17 = adapter exit?
- E18 = adapter exit?
- E14 = length of throat adapter
- E15 = diameter of throat adapter entry
- E17 = height of throat adapter exit
- E18 = width of throat adapter exit
It is assumed that the throat adapter transitions from a round entry (on the driver side) to a rectangular exit (on the horn side).
E15 should be equal to driver exit diameter (D17), but the spreadsheet allows for some slight mismatch (e.g., 5cm vs 4.9cm)
Amazing job Marco! I have a TD2002 and I am trying to figure out the proper horn for it. This will be extremely useful.
Hi Pano,
I found my spreadsheet, but see that marco_gea has already provided you with his, which is much nicer than mine.
One item that I added was calculating the m for the "int.throat (conical)", since the conical expansion has variable flare rate, but it was done because I was interested how the m changes along the length, and because I was trying to re-create Fig. 4 from Tom Danley's "A White Paper on Danley Sound Labs Tapped Horn and Synergy Horn Technologies".
Kindest regards,
M
I found my spreadsheet, but see that marco_gea has already provided you with his, which is much nicer than mine.
One item that I added was calculating the m for the "int.throat (conical)", since the conical expansion has variable flare rate, but it was done because I was interested how the m changes along the length, and because I was trying to re-create Fig. 4 from Tom Danley's "A White Paper on Danley Sound Labs Tapped Horn and Synergy Horn Technologies".
Kindest regards,
M
OK. Here is a list of the cell functions you need
- D14 = L from chosen driver in top table
- D15 = d0 from chosen driver in top table
- G20 = Fc of hypex horn
- G21 = T of hypex horn
- E14 = length of throat adapter
- E15 = diameter of throat adapter entry
- E17 = height of throat adapter exit
- E18 = width of throat adapter exit
@marco_gea What’s your process for finding a hypex horn that fits the flare rate of the driver? Your spreadsheet gives us the expo horn, but what is the process for finding the hypex horn?
Not to intervene in this healthy and fruitful discussion (I am learning too), but how do snoutless drivers play into the horn matching? For example, the JBL 2452 1.5” exit driver has the exit right at the end of the phase plug. Does this mean it is a good match for a larger variety of horns?
Quick trial and error will do it.
Just try different combinations of Fc and T, until you get a matching initial flare rate m (grey trace).
Hi marco-gea,
Kindest regard,
M
Regarding the throat-less driver, I thought that such would be perfect for OS-type wave-guide, which, if I understand Dr. Geddes' papers, assumes flat wavefront. But, would not other types horns that expect a different waveform shape benefit from an adapter? Or is it a second order issue?
Kindest regard,
M