With all the interest lately in Bruce Edgar style wood Tractrix horns I figured I might as well make the software program I used to design my Trachorn public. I think you will find it a lot easier to use than the spreadsheet programs that are floating around. It lets you directly enter the width and height of the mouth as well as the square dimensions of the throat. In addition it will calculate the thickness of the adaptor required to smoothly transition from a square throat to a round hole for the driver keeping the Tractrix expansion. The cutoff frequency is also displayed. The program will generate a text file with the curve dimensions and the dimensions of the required jig to support the top and bottom flat "plates". It will also create a macro to draw the curved sides for Autocadd or Generic CADD (Now General CADD). Although not very useful, you can experiment with the length of the horn to see the effect on the throat.

I have given the equations used in the program for anyone who is interested.

The first step in the procedure is to determine the length of the horn and the angle between the top and bottom "plates" need to get from the desired mouth to a square throat. I call this the vertical plane formulas. The Tractrix formula is also given.

 
Generating the curved sides in the horizontal plan is a lot more trouble. The main complication is that the curve is cut on the top and bottom "plates" which have a different distance from the throat to the mouth than down the center of the horn where the tractrix equation wants them. The equations are mostly trigonometry. We also need the reverse tractrix function. That is, you need to give it the distance from the horn mouth to the point of interest (x or len) along the horn and it returns the radius of the circle (r) having the required area. That is done by an iteration. it's called finder() and you can see it at: http://www.geocities.com/agalavotti/tractrix.htm

The tractrix equation doesn't consider the cutoff frequency of the horn. To estimate the cutoff the equation used for designing exponential horns is solved for frequency. By picking the area of two points in the throat of the tractrix horn the cutoff of the equivalent exponential horn expansion can be calculated. It seems to be pretty close. I do it in my program from the first and second points along the horn closest to the driver (the square throat).

The other detail is the thickness of the "motor board" which transitions from the square throat end of the horn to the round hole of the driver. I do it with the tractrix equation. Just subtract the length of the horn (len) from the calculated distance needed to get from the mouth down to the area of the round hole in the driver. For a 1 inch driver the area is Pi * r * r or .785 square inch. The 1 inch square throat end of the horn is 1 * 1 or 1 square inch. The K55 driver only goes up to 6000 Hz and the discontinuity doesn't seem to matter. You can stick the K55 right on the square throat. It's less and a 1 inch diameter anyhow! If you mount a wide range driver like the Altec 902 to the horn, you are passing up to 20KHz. The wavelength up there is a significant part of the dimension error and would have to mess things up to some degree.

Here's the program (trachorn.exe). It was not written to be a polished Windows program. It is, in fact, a DOS program. Windows will run it from a DOS window or by clicking on it from Windows explorer. Consider it public domain and distribute it as you like. Just don't try to HACK IT!

When inputting the dimensions of the mouth, add about an inch or two to the width. That way you can cut the extra off the left and right. The extremes do nothing except make the curved sides impossible to fasten to the top and bottom "plates" at the outer edges.

The sample run is the design for my Trachorn 400. Note the width is entered as 20 Inches when it is actually only 18 Inches.

 Here's the sample run:

 

 By the way: The first gripes I hear about my abusing the forum as a sales tool I'm going to be gone AGAIN! There is nothing in it for me to give this program away except for the satisfaction of seeing it used. There is no market for it. Organizing and writing out the equations helped me to streamline and upgrade the program.  Doing it led me to remove several iterations in eralier versions in favor of correct derivations.

Al K.

 

Thanks Al.

Please stick around.  I too do all this kinda stuff out of pure fun and interest.

I'll need to look into the adapter thickness part of your program.  I haven't focused on that enough in the past.

jc

Thanks Al, it is good of you to make this information available. I am pleased to see you posting on the forums again.

Many of us have got alot to learn, and your input is valuable.

Al, Good to see you posting again. Interesting stuff. I don't know why but I had thought all along that you had your Trachorn designed AND manufactured by someone else for ALK Engineering. It never occurred to me that you actually created horn design software and designed the horn yourself. I guess you learn something new everyday.

Although there seems to be tractrix horns-a-plenty now.........yours was done a few years ago.

Hi AL,

Glad to see back around, one question. Does this have anything to do with Greg's v-trac's?

Jay

Thanks for the info, Al. We hornheads are always looking for things to make our research and construction efforts easier.

 Mark,

The Trachorn is actually made by Bill Martinelli of www.woodhorn.com. It was designed by the software I just made public. The actual series of events began with a telephone conversation with Max Potter, the guy who brought us the "P-Trap". He convinced me to try a set of Latec 511b horns in place of the K500 horns in my Belle Klipsch. It didn't take but a few hours to realize that a new horn was needed for the Heritage sereis that wasn't an out of production eBay item! Max told me about the wood tractrix article by Bruce Edgar. Max actually talked directly to Bruce Edgar about doing one for the Khorn but Bruce has bigger fish to fry! Having many years of experience writing engineering design programs I began the project of writing a program that would duplicate the example in the article. The program trachorn.exe was the result. I am quite happy to know that I seem to have started a revolution of sorts. Now though, I got competition out the yin-yang!  [:'(]

 Jay,

The only thing Greg needed was to listen to a Khorn set he referbished for a customer that he added my Trachhorn and networks to.  He wanted to do an all-out 2 inch driver version. The V-Track is the result. I was asked about a 2 inch version of the Trachorn several time and concluded that there wasn't much of a market for it considering the expense of 2 inch drivers. It looks like I might have been WRONG! I did have a little input to the V-Trac. I got him to make a correct square to round adaptor for the driver. The spreadsheet program doens't tell you about that little detail!

Al K.

 

Its' great to see you post again Al.  I hope you will stick around.  You have been missed!

Now as for that horn....if I tried to build it.....it would come out looking something like a toaster oven!

Want to make some money? Design and build a K403 exponential. You will sell those for sure. They fit into a Khorn top hat. Not sure about Lascala. To my knowledge, only Klementovitch has them.

Several of us heard that horn. What does it do? It replicates the Khorn top section in a 2-way design, was originally designed for the Jubilee, is significantly better than the 400/77 combo..............but stays out of the smoooooth tractrix territory. Original PWK sound..........but seems to eliminate some of the issues of the K400/77 combo. Sounds like..........Heritage on steroids.

Everyone jumped to tractrix as a solution for the issues of the current exponential. But a better exponential seems to have been overlooked.

The first guy to come up with that will make more money than all these tractrix guys.

mark1101:

Want to make some money? Design and build a K403 exponential. You will sell those for sure. They fit into a Khorn top hat. Not sure about Lascala. To my knowledge, only Klementovitch has them.

Several of us heard that horn. What does it do? It replicates the Khorn top section in a 2-way design, was originally designed for the Jubilee, is significantly better than the 400/77 combo..............but stays out of the smoooooth tractrix territory. Original PWK sound..........but seems to eliminate some of the issues of the K400/77 combo. Sounds like..........Heritage on steroids.

Everyone jumped to tractrix as a solution for the issues of the current exponential. But a better exponential seems to have been overlooked.

The first guy to come up with that will make more money than all these tractrix guys.

 

Hey Mark

The K403 is a modified Tractrix and has the collasping vertical polar response which basically gives an acoustical EQ for the on-axis response like a K400 exponential.

Having heard them all I still prefer the K402 and K510 performance. It should also be noted that the K403 has a 1.4" throat so an exact apples to apples comparison isn't possible due to different driver requirements.

mike tn