The TRACTRIX is said to be the optimum. I read this in a few different places over the years. I meet the guy that came up with the idea for Klipsch to use this design way back when at a professional workshop and training seminar.
So far as I know WE used pure exponential surface area expansion of the progressing 2D surface are. This is similar as if you have an hyperbolic horn function with T=1. it should be very easy to calculate a straight horn profile.
https://www.grc.com/acoustics/an-introduction-to-horn-theory.pdf
Just found this; goes into great detail; saving for a full read later...
Just found this; goes into great detail; saving for a full read later...
The Western Electric horns are a bit different because they get wider faster than they get taller for about 70% of their length. That changes in the last 30% going toward the mouth.
The 6368 appears to be approximately a 1 meter long horn with a mouth surface area of 1200 cm2. If you break that into two segments in Hornresp, you can calculate the shape during export. You can even end up with the flat sides as it seems to have in the photos. Setting where that happens along the horn length is going to be a bit of guess work without direct measurements.
I can export a spreadsheet with the dimensions, if you like.
The 6368 appears to be approximately a 1 meter long horn with a mouth surface area of 1200 cm2. If you break that into two segments in Hornresp, you can calculate the shape during export. You can even end up with the flat sides as it seems to have in the photos. Setting where that happens along the horn length is going to be a bit of guess work without direct measurements.
I can export a spreadsheet with the dimensions, if you like.
In fact here it is. This is my best guess at the W.E. 6368 profile.
This assumes a length of 100cm and a mouth a 1200cm2. Throat is 1" diameter. The horn reaches its maximum width of 28cm (11") at 70cm from the throat. The mouth is 28cm wide by 42.86cm tall.
EDIT: I removed the profile text. Finally found some photos that show the last section width does flair. I'll see that I can come up with.
This assumes a length of 100cm and a mouth a 1200cm2. Throat is 1" diameter. The horn reaches its maximum width of 28cm (11") at 70cm from the throat. The mouth is 28cm wide by 42.86cm tall.
EDIT: I removed the profile text. Finally found some photos that show the last section width does flair. I'll see that I can come up with.
I did some calculating on the W.E. 15A. Going by the best plans I could find online - which weren't great, I tried to calculate its expansion rate.
As Jean Hiraga once said, it doesn't seem to fit any known horn profile. But it is very close to half way between Tractrix and Le Cleac'h T=0 profiles. Which will make fans of both those profiles happy 🙂
What the W.E. horns do is to flatten out in the middle. The 15A has an aspect ratio of 1.68:1 at 41% of its length, squeezing down to 4.6:1 at 84% length, its flattest point. From there it flares back out to 1:1 at the mouth.
Having accurate measurements of an actual 15A would be a big help.
The Sato horn by contrast (W.E. inspired) widens to 2.3:1 at its flattest, 72% of the throat to mouth distance. The Sato doesn't squeeze as much as the Western Electric horns.
Now that I know that, I could get you very close to a W.E. or Sato profile if you choose a horn length, mouth dimensions and driver throat size.
As Jean Hiraga once said, it doesn't seem to fit any known horn profile. But it is very close to half way between Tractrix and Le Cleac'h T=0 profiles. Which will make fans of both those profiles happy 🙂
What the W.E. horns do is to flatten out in the middle. The 15A has an aspect ratio of 1.68:1 at 41% of its length, squeezing down to 4.6:1 at 84% length, its flattest point. From there it flares back out to 1:1 at the mouth.
Having accurate measurements of an actual 15A would be a big help.
The Sato horn by contrast (W.E. inspired) widens to 2.3:1 at its flattest, 72% of the throat to mouth distance. The Sato doesn't squeeze as much as the Western Electric horns.
Now that I know that, I could get you very close to a W.E. or Sato profile if you choose a horn length, mouth dimensions and driver throat size.
Tweeters too, though way out of time. 🙁
Indeed! 😀. The smaller ones were apparently designed for the analog telephone BW [stage monitors, large cinema 'fill', etc.] with the large ones for the [100-5 kHz] AM radio BW, so hook up an ancient SET tube AM tabletop radio or similar that's BW limited to bypass the 'honk' portion of the big horn same as I auditioned in my teens to decide whether it's 'live or is it Memorex' 😉 It really is special : IS IT LIVE !!! OR IS IT MEMOREX! !! - YouTube
GM
AM bandwidth, thanks that the term I was looking for.
About 6 years ago there was someone on here trying to run AM crystal radio into a big horn with no amplification. There was a transformer involved. Don't know if it ever happened.
About 6 years ago there was someone on here trying to run AM crystal radio into a big horn with no amplification. There was a transformer involved. Don't know if it ever happened.
First and foremost, thank you for your work
. That's really interesting that it doesn't have a consistent shape. Do you have any idea why WE did this? It seems to go against common sense, so they must have had some reason for doing that. As far as the dimensions go, I do have some ideas, but I am probably wrong considering some of the information in this thread. Brace yourself 😀
The size of the mouth determines the low end frequency response. Ideally the mouth should be slightly larger than a quarter of the wavelength of the lowest frequency. The wavelength for 300 hz is 45.2 inches. Divide by 4 and I get 11.3 inches. I figure 16 or 18 inches in the X dimension seems like a good overshoot. Plus it gives the CNC machine I will be using some wiggle room since it has a 20 inch work bed. However XRK posted the info on that volvo horn which is clearly much bigger and goes to 300 hz. Sooooooo im guessing I am flat wrong here.
For the Y dimension I don't know the best way to approach it. Im fine with making it a square. Iv'e also gone so far as to think about making it 1/4th the wavelength of 625hz which is 3 octaves lower than my target frequency of 5K. This would equate to about 6 inches.
Ultimately I wonder if I should make it square like the sato horns, overly rectangular like the klipsch, jensen, and some WE horns. Or should I go for some 3/4ths ratio like the KS-6368. I honestly don't know what the best option is, but I am willing to try them all.
Length is something I am probably wrong about too. Big suprise I know. It looks like the length of the horn should also follow the 1/4 wavelength rule which would be 12 inches which can be increase to that same 16 to 18 inch length inch length.
And for the mouth size, I am using an atlas A55-G which has the 1 3/8 inch thread and the exit is 1 inch.
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Thanks for the info. A 300Hz that really works is going to be big and long. Consider that the W.E. 15A is a 55 (more or less) and it's 14 feet long. I own some 300 Hz multi-cell horns and they aren't tiny. 🙂 Getting a compression driver to play cleanly down that low is no mean feat. You'd want to cross at 500-700 Hz for best results.
For mouth size I'd pick the same width has your bass cabinet. Not only does it look good, but seems to blend nicely in the acoustic realm. Perhaps choose a golden ratio mouth size, like 1.62:1 The 6368 horn is taller than it is wide. Some people feel horns work better that way. It's also at least 3 feet long, as far as I can tell.
With a little more number crunching I've found that a Le Cleac'h profile T=0.5 is very close to the W.E. horn profile. That's what I'd use. A widening to an aspect ratio of 4.5:1 near 75% of the length would also imitate the W.E. squeeze.
For mouth size I'd pick the same width has your bass cabinet. Not only does it look good, but seems to blend nicely in the acoustic realm. Perhaps choose a golden ratio mouth size, like 1.62:1 The 6368 horn is taller than it is wide. Some people feel horns work better that way. It's also at least 3 feet long, as far as I can tell.
With a little more number crunching I've found that a Le Cleac'h profile T=0.5 is very close to the W.E. horn profile. That's what I'd use. A widening to an aspect ratio of 4.5:1 near 75% of the length would also imitate the W.E. squeeze.
The reason the WE horns get wide and flat is to reduce the effect of wavefront corruption at higher frequencies due to the bending. This isn't necessary with a straight horn. It is, however a way to produce an asymmetrical wavefront from a straight horn, but that is more involved than just going rectangular.
I can see it helping get the high frequencies around the bends. But I wonder if it doesn't also help spread them a little wider for a better power response.
Yes, this may be a desirable effect.
As a single quantity the power response will not be affected. As the overall expansion is still maintained giving the same directivity index.. unless perhaps the wavefront has been damaged and the point used for DI reference becomes inconsistent.
Of course power distribution will change, but the effect of this anyones guess without analysing the room. If the room is averaged it should be the same.
An elongated and flat mouth may be less than optimal.
As a single quantity the power response will not be affected. As the overall expansion is still maintained giving the same directivity index.. unless perhaps the wavefront has been damaged and the point used for DI reference becomes inconsistent.
Of course power distribution will change, but the effect of this anyones guess without analysing the room. If the room is averaged it should be the same.
An elongated and flat mouth may be less than optimal.
Where the heck do you guys learn this stuff. I have been trying to google this stuff for the last couple months and haven't made much progress.
Is there like some super secret book that I need to be reading?
Is there like some super secret book that I need to be reading?
Hmm, don't remember it being a 20 Hz 1/4 WL, though again from very dim memory it's ~35-36 Hz/ 0.5T to get it to go low with any authority, so overall doing some good 'due diligence' 😉, plus these are reciprocating type [pattern 'flip'] with two flare rates same as most smaller [non multi-cell] W.E., Altec 5/811, etc..
Where's Bjorn, the real expert when we need him? Anybody know if his & Tom Dunker's [the first person I 'bench raced' horns with when I got on-line in '96] book gets into this kind of detail?
GM
"High-Quality Horn Loudspeaker Systems - History, Theory & Design" by Bjørn Kolbrek and Thomas Dunker.
High Quality Horn Loudspeaker Systems by Bjørn Kolbrek and Thomas Dunker
Lurking in the background... I don't spend that much time on forums, but I pop in every now and then 🙂
Thanks for the plug, David! The book should soon be available from Parts Express as well, I will update the info page when it is.
The book has a 150-page chapter on BTL/WE loudspeaker developments, including the history of 15A and pictures from the production line, and of the prototypes. There is also quite extensive information on various horn profiles etc.
There has been much speculation about the WE horns, that they use some kind of special, mystical, "unknown" expansion. Of course this adds to the mystical qualities of the WE technology. But we should not forget that these speakers were designed by practical engineers working on commercial products and under economical restraints. They did not have much in common with modern-day audiophiles or equipment collectors.
A quick re-cap of the WE horn developments:
The exponential horn was introduced to W.E. by H.C. Harrison.
The Vitaphone horns (12A and 13A) were designed and built (by Victor Talking Machine Company, based on WE designs) during the summer of 1926, in a rush to get the loudspeaker setup ready for the Vitaphone premiere in August. Neither 12 nor 13 were found to be optimal, therefore, due to time limitations, they were used together, instead of designing another horn. 13A was designed and built by VTMC during one week!
When the mad Vitaphone rush was over, BTL engineers started working on new horn designs, including 15A, which was originally named "redesigned 13A" because had the same principal dimensions as 13A, but was curved more like 12A, to combine the qualities of both. Another objective was to produce the horns cheaper, because the 12 and 13 horns made by Victor were very expensive (around $300 from Victor in 1927 money). 16A was developed at the same time, as were other horns that never went into production.
The fabric horns with KS numbers were made by Racon, which had the patent for this type of manufacturing, and also for the throat-through-the-mouth design. So these are OEM horns. WE/ERPI were not too happy with these horns, as they had low efficiency compared to other designs.
Now back to the 15A expansion and WE horn design in general. The principles are outlined in two patents by Harrison and Flanders, GB 213528 and GB 245415. Essentially the mouth diameter should be 1/4th to 1/3rd of a cutoff wavelength, and the horn is exponential. Upon closer inspection this was adhered to in the horns they made. 15A is a 57Hz exponential horn, and the equivalent circular mouth diameter is 1/3.8 cutoff wavelength.
Originally I also believed (based on Hiraga's book) that 15A had a special, unknown expansion, and tracing from the patent drawings seemed to confirm this, as did a tracing of the horn I was able to obtain. However, when we visited the AT&T Archives, we found a 15C (4-throat version) blueprint, and doing the numbers confirmed the WE statement: a plane wave 57Hz pure exponential horn. Nothing fancy. Even the curving is simple, just three constant radii, not anything like the more fancy 66A - which is not a WE design. (BTW the hand drawn drawing of 15A that can be found online seems to be a hand drawn copy of an original 15A blueprint, as the position of the horn and other parts matches the 15C drawing we found. Therefore I believe the dimensions on this drawing are accurate as well.)
The change in aspect ratio is to aid HF response through the bends by maintaining a high bend radius to horn "thickness" ratio.
KS-6368 is a monitor horn with about 220Hz cutoff. It was designed to replace 14A. I think this horn also has a mouth area that is in the 1/4 to 1/3 cutoff wavelength range. 1/3 (CIR ~= 1 in Hornresp) is actually the minimum size for a horn in an infinite baffle if throat impedance ripple is to be kept at an acceptable level. (There is no "optimum mouth size".) Especially for free-standing horns, the mouth should be larger. And this minimum mouth size should be applied to the smallest dimension of the mouth; a large aspect ratio requires a larger mouth area for the same impedance termination.
Maybe the fabric construction of the Racon/KS horns introduce losses that reduce the impedance peaks. But the KS-6368 mouth is really too small no matter how you look at it. It was designed for monitoring in the projector booth and for paging applications, not for high-quality reproduction.
In general, I don't think just copying a horn is the best idea, unless you first understand the compromises made in the original design and how these relate to your application.
Bjørn
Hello Bjørn - good to see you here. 
I certainly do need to get a copy of your book, I didn't know that it has so much history in it. Should have known from the cover - right?
My experience with the WE horns comes mostly from working with Jean Hiraga's pair of 15A and from a pair of Vitaphone 12A in an old cinema where I was the projectionist. I actually tried to donate the Vitaphone horns to Francis Coppola because he claimed his uncle invented Vitaphone, but the deal fell thru.
I had at first been told by Mr Hiraga that the 15A didn't match any standard profile, but over the years have also read claims that it is pure exponential. Like you I have traced the plans and tried to fit that expansion to standard profile, with no luck. However I did recently find that if a length of 14 feet is used, with a mouth 5.5x5.5 ft wide, then a Le Cleac'h profile T=0.5 with a 1" throat comes very close. 55Hz to get the length. At least Hornresp exports a profile that comes close to the drawings. I found that exponential flared too fast in the throat. The 15A seems to stay narrow for a long distance, much like a Le Cleac'h or Tractrix profile. The 16A looks that way too.
Too bad Jean-Michel Le Cleac'h is no longer with us to join the discussion. 🙁
If you have accurate measurements of a 15A I'd love to see them and try to figure out how close I came using the old, blurry plans I have.
I certainly do need to get a copy of your book, I didn't know that it has so much history in it. Should have known from the cover - right?My experience with the WE horns comes mostly from working with Jean Hiraga's pair of 15A and from a pair of Vitaphone 12A in an old cinema where I was the projectionist. I actually tried to donate the Vitaphone horns to Francis Coppola because he claimed his uncle invented Vitaphone, but the deal fell thru.
I had at first been told by Mr Hiraga that the 15A didn't match any standard profile, but over the years have also read claims that it is pure exponential. Like you I have traced the plans and tried to fit that expansion to standard profile, with no luck. However I did recently find that if a length of 14 feet is used, with a mouth 5.5x5.5 ft wide, then a Le Cleac'h profile T=0.5 with a 1" throat comes very close. 55Hz to get the length. At least Hornresp exports a profile that comes close to the drawings. I found that exponential flared too fast in the throat. The 15A seems to stay narrow for a long distance, much like a Le Cleac'h or Tractrix profile. The 16A looks that way too.
Too bad Jean-Michel Le Cleac'h is no longer with us to join the discussion. 🙁
If you have accurate measurements of a 15A I'd love to see them and try to figure out how close I came using the old, blurry plans I have.
The book has about 400 pages of history, mainly covering the 1925-1940 era, but also quite a bit of the more ancient and modern stuff. You can see the TOC on the book info page linked to in my signature.
I don't have actual meausrements, but I have numbers from the Western Electric blueprint 🙂 It can be a bit tricky to measure a curved horn and get the distances between the areas correct. But this is what the BTL/WE engineers used, so I trust it more than any tracings 😀
Attached is a spreadsheet where I entered the raw data and converted it to areas, and calculated the cutoff. The curves are wiggly due to rounding of the dimensions, but the average plane wave flare rate comes out as a pretty constant 56-57Hz. The original data is only for the wooden section, and I have guessed the flare rate continued like this back to the throat, but I don't think it would deviate much in the throat. This actually fits well with 14 ft horn length (also stated by WE) and 555's 18mm diameter (2.54 sq cm) exit.
I do have blueprints for some of the throat sections for 15C, I can check the flare rates there. But it's a bit tricky with the round to square transition.
WE wouldn't have used a Hypex expansion, as this was invented later by Salmon (1946). But Edward Norton patented a catenoid (Hypex with T = 0) horn in 1929. Don't know if it was ever used though, it was Harrison's exponential horn patent that was eventually used on all the Vitaphone horns when it was issued.
I don't have actual meausrements, but I have numbers from the Western Electric blueprint 🙂 It can be a bit tricky to measure a curved horn and get the distances between the areas correct. But this is what the BTL/WE engineers used, so I trust it more than any tracings 😀
Attached is a spreadsheet where I entered the raw data and converted it to areas, and calculated the cutoff. The curves are wiggly due to rounding of the dimensions, but the average plane wave flare rate comes out as a pretty constant 56-57Hz. The original data is only for the wooden section, and I have guessed the flare rate continued like this back to the throat, but I don't think it would deviate much in the throat. This actually fits well with 14 ft horn length (also stated by WE) and 555's 18mm diameter (2.54 sq cm) exit.
I do have blueprints for some of the throat sections for 15C, I can check the flare rates there. But it's a bit tricky with the round to square transition.
WE wouldn't have used a Hypex expansion, as this was invented later by Salmon (1946). But Edward Norton patented a catenoid (Hypex with T = 0) horn in 1929. Don't know if it was ever used though, it was Harrison's exponential horn patent that was eventually used on all the Vitaphone horns when it was issued.
Thanks Bjørn. I'll compare that with what I figured to see how close I came.
Yes the metal part would be tricky to plot. I didn't even bother to try, just figured if the flare would pass from the origin thru the first rectangular break (3.125x5.25") and then on to further sections. LC T=0.5 fit well for me.
Yes the metal part would be tricky to plot. I didn't even bother to try, just figured if the flare would pass from the origin thru the first rectangular break (3.125x5.25") and then on to further sections. LC T=0.5 fit well for me.