Tractrix Squakers...

[DrWho]

So yesterday I went about trying to figure out how to design a tractrix squaker and then pretty much ended up with the same thing Al. K built (I was going for 500Hz and his is a 400Hz design). I was wondering though, how does one decide the flare rate of the vertical and side sections when not doing a round tractrix horn? I know it's all about the area expansion rate, but how do you fine tune for a desired dispersion pattern? I couldn't seem to find any formulas - but I suppose I could always use common sense to get close. Are there any off-axis response charts available for Al K's design?

I was thinking to just go with Al K's design that's already established to work pretty well - but I would like to overbuild the horn a bit, using thicker wood on the flares so as to further reduce vibrations. I've been thinking about this a lot and it might be very beneficial to line the entire inside with an absorbtive material so as to reduce internal reflections and all that jazz (so this would involve modifying the wood parts of the horn so that the driver sees the same surface). I'm thinking something thicker than felt btw...more along the lines of 1/2" foam of some sort. I'll have to experiment and see how the acoustical impedance changes with different materials. If I don't go that route I would much rather have a nice black piano gloss finish instead of the painted raw wood look.

So I was wondering what y'alls thoughts were on the idea. I've got a very very good cabinet builder friend who could totally build these horns, but I don't wanna end up just ripping off Al K's design (and then him not get any credit for it). This is more of a personal project where I'm trying to apply all the crap I've been learning at school, though I might try to sell it someday (the entire speaker that it'll be a part of...don't think I'd ever sell the squaker itself). I might be coming across some money here in the near future with which I would invest into engineering something of my own...I just need to start somewhere. Just that when I drew up my own model and it looked very much like Al's design I figured I should chime in and make sure I wasn't stepping on any toes.

Btw, is there anyone on the forum using drivers other than the K-55V from klipsch? I forgot to mention that my 500Hz design was a 2" throat - there seems to be more 2" drivers available than 1" ones. I can see the horn evolving more into something like the Jubillee top section klipsch had on demo in Hope (the smaller one, not the big cinema one) - it would just be a matter of waiting for the right 2" driver to pop up on the market (don't think klipsch would want to sell me one of their fancy drivers). []

[D-MAN]

As long as you maintain the "correct" cross-section (area) for the tractrix Fc along the pathway, you can make it whatever you want to achieve the dispersion characteristics (pattern) that you are after. I would estimate that you would not want to go below (or "tighter" than) 90 deg. wide x 40 high for the dispersion pattern. Tighter patterns than that tend to concentrate too much energy in too small of a space and cause distortion, throat overload being one, for example. It depends on the "throw" you are after.

The cross-section at any point along the path can be square, rectangular or circular and as long as the expansion curve is consistantly maintained, it depends on the dispersion characteristics you are after.

I forgot to mention that parallel surfaces tend to cause standing waves so should be avoided.

DM

[Al Klappenberger]

So yesterday I went about trying to figure out how to design a tractrix squaker and then pretty much ended up with the same thing Al. K built (I was going for 500Hz and his is a 400Hz design). I was wondering though, how does one decide the flare rate of the vertical and side sections when not doing a round tractrix horn? I know it's all about the area expansion rate, but how do you fine tune for a desired dispersion pattern? I couldn't seem to find any formulas - but I suppose I could always use common sense to get close. Are there any off-axis response charts available for Al K's design?

The angle between the top and bottom was determined by a computer iteration to get the throat to come out square. The math involved is some basic trigonometry. The off-axis reponse was left to fall where it may. I have dones off-axis measurements but I don't want to post them becasue they were done with a JBL 2426 driver that has a very poor high frequency response. It makes the horn look bad. In truth, the off axis response in the horizontal plane remains constant as you go to one side. The amplitude simply drops.

I was thinking to just go with Al K's design that's already established to work pretty well - but I would like to overbuild the horn a bit, using thicker wood on the flares so as to further reduce vibrations. I've been thinking about this a lot and it might be very beneficial to line the entire inside with an absorbtive material so as to reduce internal reflections and all that jazz (so this would involve modifying the wood parts of the horn so that the driver sees the same surface). I'm thinking something thicker than felt btw...more along the lines of 1/2" foam of some sort. I'll have to experiment and see how the acoustical impedance changes with different materials. If I don't go that route I would much rather have a nice black piano gloss finish instead of the painted raw wood look.

The Trachorn is made with two layers of flexable wood on the curved sides. The two layers are stuck together with an acoustic absorbant adheasive. Nothing can vibrate!

So I was wondering what y'alls thoughts were on the idea. I've got a very very good cabinet builder friend who could totally build these horns, but I don't wanna end up just ripping off Al K's design (and then him not get any credit for it). This is more of a personal project where I'm trying to apply all the crap I've been learning at school, though I might try to sell it someday (the entire speaker that it'll be a part of...don't think I'd ever sell the squaker itself). I might be coming across some money here in the near future with which I would invest into engineering something of my own...I just need to start somewhere. Just that when I drew up my own model and it looked very much like Al's design I figured I should chime in and make sure I wasn't stepping on any toes.

You would actually just be copying Bruce Edgar's design. That is what I did. It's all in the public domain. The end result would simply be a price war between me and another supplyer. That would make it not worth the effort for either of us to sell them.

Btw, is there anyone on the forum using drivers other than the K-55V from klipsch? I forgot to mention that my 500Hz design was a 2" throat - there seems to be more 2" drivers available than 1" ones. I can see the horn evolving more into something like the Jubillee top section klipsch had on demo in Hope (the smaller one, not the big cinema one) - it would just be a matter of waiting for the right 2" driver to pop up on the market (don't think klipsch would want to sell me one of their fancy drivers).

A 2 inch version would be a good thing. My theory on that was that it would be a more difficult product to sell to the average Khorn owner. He would need to buy a new horn AND a new driver too.

AL K.

[DrWho]

all the answers I was looking for...thanks [H]

I'm getting more and more confident to build my own horn, but I'll prob purchase a pair of the trachorns to do some measurments and comparisons with...if I'm going for better I might as well be comparing against something really good []

Now to find an excuse to be in Ohio and go bother Dean.... []

[PrestonTom]

This is an interesting question about the inside surface of the horn.

Anecdotally, I had the impression that the surface should be as smooth as possible. The analogy was from fluid problems, where you want to prevent "turbulence and eddys". If this is correct (and it may only apply to certain frequency regions), then a lacquer finish wold be great. My concern would be that at high frequencies the wave edge might have a different velocity due to the felt (or whatever). I am not sure what kind of distortion this might create. Remember, in one sense, the beauty of the horn is that is minimizes the impedance mismatch from the diaphragm to air (small volume at the small end of the throat) as the volume increases then the pressure changes. I am not sure the felt would be the best idea. As I am writing this, it is clear to me that there are probably some real issues that I am unaware of. The problem is getting a description that is not overly mathematical.

It sounds like an interesting project, and you are bound to learn quite a bit about physical acoustics!

Good Luck,

-Tom

[oscarsear]

all the answers I was looking for...thanks [H]

I'm getting more and more confident to build my own horn, but I'll prob purchase a pair of the trachorns to do some measurments and comparisons with...if I'm going for better I might as well be comparing against something really good []

Now to find an excuse to be in Ohio and go bother Dean.... []

+++++++++++++++++++++++++++++++++++++++++++++

Whatever you construct it's going to need to be pretty enough to exist outside of the Khorn top structure...a stand alone. I've got 2" drivers as does Dana....... They just won't fit in the box and the tractix horn to get low enough frequency is probably also too big for the topside. Hasquin builds tractix spherical horns from sandwiched MDF (glue and screws, etc...). Sierra Brooks shows a tractix salad bowl also.... It will be nice to see your problem approach and its solution.

[Al Klappenberger]

Guys,

It looks like a 2 inch square throat horn with exactly the same mouth size as the Trachorn would be quite possible. Here's a computer run. Note that one inch would be cut off of both sides to make the mouth 18 Inchs wide rather then 20 Inch. The 1 inch square to 1 inch round adaptor would be .8 inch thick. 3/4 think will be fine. The low frequency cutoff would also be about the same as the Trachorn (about 311 Hz) too.

Al K.

[Deang]

I want a pair.

[oscarsear]

Al.... Curious here too........ How much space remains behind that set-up for driver hardware? My 2482's are 5.5" deep and around 6.5" in dia. I assume too that there's still side space for the tweeter mod????

[DrWho]

As I am writing this, it is clear to me that there are probably some real issues that I am unaware of. The problem is getting a description that is not overly mathematical.

The problem is that the sound coming out of the compression driver does not travel in a straight line and bounces off the walls in the very narrow throat section. As you go higher in frequency the sound bounces more and more before it makes its way out of the throat and down the rest of the flare and out into the room. Every horn ever made has this problem to some extent and I feel this is mostly due to the signature sound that horns have (if I may be so bold as to claim horns have a signature sound).

I was thinking it'd be cool to find some absorbtion to put along the throat that also doesn't resist airflow down the horn (so basically a smooth surface absorbtive material). Like maybe a compressed version of that memory foam stuff...or maybe come up with a special top surface that lets air flow forward, but lets absorbtion happen perpendicular to the surface. I know a lot of this can be attenuated with the chosen flare rate so this is definetly an afterwards type mod (though if it sounds good I just might not bother at all).

[dhsettim]

Great work Al, as always. Ya just need to do the sums for a 1.5 inch throat and then everyone will be happy. Have a great Festive Season, tim

[Al Klappenberger]

Dr,

The Klipsch web site once had a picture of a horn with egg-crate like damping material lining the inside just like you describe with a lot of text describing the idea. It might be what you are talking about. I don't remember.

One point though, the theory behind the Tractrix equation is that the sides of the horn are maintained at exactly 90 degrees to the expanding "bubble" as it travels down the horn. If this is the case, I wouldn't think there would be any reflections from the walls inside the horn. An analogy might be like shining a flashlight across a mirror rather than into it. Older horn theory assumed a "plane wave" rather than an expanding bubble. That "bubble" expanding down an expnential horn would not be 90 degrees to the inside walls and would casue reflections. This sort of wave propogation theory is way out of my area of expertice though. I'll leave it to others to work out that sort of stuff!

Al K.

[sfogg]

Earl Geddes has some info on this. His approach to dealing with it is literally filling a large portion of the horn with a very open cell foam. The idea being that the direct sound passes pretty directly through the foam and is only slightly attenuated.

The reflections that are bouncing around in the horn pass through much more of the foam and are attenuated more.

I tried something like this with a somewhat thicker 1" foam just in the middle of the cells on the 805B horns and it seemed to me to make them sound a little bit better. Haven't had a chance to do any time domain measurements though to see if I can see a change there.

Lynn Olsen talks about lining the mouth of the horn with felt/foam to cut down on diffractions on his site.

Shawn

[oscarsear]

Hasquin and Roamy (sp).... state that the surface of cut and finished MDF and sound absorption character of same ideally dampens this artifact. They're critical of spherical horns constructed of plastics or fiberglass in particular because the slick hard surface tends to magnify this artifact.

[DrWho]

Since the size isn't too bad, I went ahead and modelled 3 different flares for a 300Hz horn. Attached is a graph with the half-width and half-height of all three versions. All are using a 2" throat.

(vertical expansion are solid colors, and the horizontal expansions are the shaded colors).

Plot 1 (in blue): the flare rate for the height uses the same flare rate for a cylindrical tractrix horn, and then the width is determined to satisfy the tractrix area expansion rate.

Final Mouth Size: 20"x8" (W x H)

Plot 2 (in red): the flare rate for the height is determined using an exponential growth function that was chosen to yield a 45 degree angle at the cutoff of the horn. Then the width is determined to satisfy the tractrix area expansion rate.

Final Mouth Size: 17.25 x 9.25"" (W x H)

Plot 3 (in black): the flare rate for the height is flat with an angle of 22.5 degrees (yielding 45 degrees for the entire mouth). And then again the width is determined to satisfy the tractrix area expansion rate.

Final Mouth Size: 24.5" x 6.6" (W x H)

Plot 2 is most like Al K's 300Hz 1" throat horn with a flat surface for the height expansion. All the big time horn manufactures never use a flat surface on this part so I figured there must be some reason why, and which is why I modelled the other expansion rates. I like the idea of Plot 1 because the surface changes at the same rate as the cylindrical horns which is what the original tractrix equations model for.

So anyways, I'm sure my descriptions don't make any sense to anybody - but I was hoping for some feedback on which plot to go with. I'm thinking plot 2 would be the least restrictive overall and that means less distortion right? I suppose it would be smarter for me to just go ahead and build all 4 (my 3 and Al's 2" design) and then compare the measurements between all of them...

[3dzapper]

Your plot 2 is about the exact demensions of the horns I have been building. They would be the closest to the ones Dr Edgar describes in his article in Speaker Builder.

Rick