 
|
Audio Asylum Thread Printer Get a view of an entire thread on one page |
For Sale Ads |
|
|
Audio Asylum Thread Printer Get a view of an entire thread on one page |
For Sale Ads |
76.112.135.123
Hi there
I spent some time on Google trying to find working tractrix calculator without great success. Single driver site is down, volveteere spreadsheet somehow doesn't work (read only) Canadian (rocket science site ) calculator gives strange results (long horns). Does anybody has a working link?
Regards, L
Edits: 07/03/08 07/03/08Follow Ups:
Plot to the desired scale and trace the outline.
;-)
Interesting! I never gave it any thought, but at a glance it sure looks like a seriously truncated one.
GM
Loud is Beautiful if it's Clean!
Don't know if it is a true tractrix, but I'd be suprised (structurally speaking) if it wasn't.Tony Glynn founder/ex-owner of Lowther America mentioned it to me years ago. He's a fountain of old school info. Hell he probably was around when it was built. ;-)
But seriously folks, is it actually a tractrix curve?
DW
No. But the way it is built is such that the constraint is
uniform is all the structure.
Don't know, we need accurate measurements of its construction.
GM
Loud is Beautiful if it's Clean!
On the Eiffel Wiki page, under Shape of the Tower, its called an exponential curve.But a trunicated exponential curve (like the Tower) is close to a trunicated tractrix. The differences become apparent further towards the mouth, that is missing. Pick your favorite curve.
FWIW: here's another link to one of the initial designs of the Eiffel Tower:
http://www.tour-eiffel.fr/teiffel/uk/documentation/dossiers/page/g_invention.htmlBy hand laying out two lines, one perpenducular to the curve face, and another perpendicular to that line, and manually pulling that second line up the median axis of the curve and maintaining the axis to wall distance, it tracks the curve very closely. As would be expected of a tractrix.
But apparently with two different flare frequencies and why it more closely approximates a mouth truncated Tractrix from just looking at a picture, though of course the proof is in the plotting of its curves.
As always though, YMMV.
GM
Loud is Beautiful if it's Clean!
Also known as Hundekurve or Schleppkurve in German (Hund = dog and schleppen = to drag).Like the ball bearing, it was in use many years prior to the mathematics used to describe it.
Mechanically, it evenly distributes (transforms) a load.
Imagine a X & Y coordinate frame. You stand at the intersection (0,0) and have a stubborn dog that is located far up the Y axis. A leash connects you to the dog. Now walk along the X axis pulling the leash and dragging the dog along. The curve that the stubborn dog maintains (relative to X & Y) is a tractrix.
.
Nt
John Inlow,aka "Carpenter",gave instructions on how to build horns,and also,in the second column, how to lay out a Tractrix curve using a ruler.
- http://web.archive.org/web/20030622045848/http://home.earthlink.net/~lotusblossom/_wsn/page2.html (Open in New Window)
Hi, just tried Volvotreter without problems, just rightclick and download. It is also the only calculator that gives the right results.
Brgds
Lars
Hi Lars,
I think you will find that the Hornresp Export function also gives the "right results" :-).
Kind regards,
David
Hi David,
I tried some time ago in an earlier of your versions and it did not work out as I hoped as there where some minor errors, maybe due to rounding of.
Made an Excel application instead of both tractrix and kugelwellen that works like they should.
Was about to mail you as I found some things about tractrix and sperical/kugelwellen that does not match to the original formulas/patents/papers.
I love your program anyway. Will go through it again and come back to you with my findings. Will this time check against the 19.20 version that I now have.
Brgds
Lars
Hi Lars,
Curiosity got the better of me - I couldn’t resist comparing the Hornresp tractrix results against those generated by Volvotreter’s Excel spreadsheet :-).
For all practical purposes the profiles are identical. When the data from both sources are plotted on a single chart, only one curve is visible. As you have surmised, any small differences are simply due to the Hornresp input parameter values S1, S2 and F12 being rounded to 2 decimal places.
There is however an important difference in the way that the results are presented. In Hornresp the length increment is constant, whereas in the spreadsheet it varies. Having a fixed increment makes it easier when constructing a horn using multiple “slices” of constant thickness material.
Kind regards,
David
Hi Lars,
"Will go through it again and come back to you with my findings."
That would be really excellent! Any feedback you care to provide would be much appreciated.
Note that Hornresp is now at Version 19.40 :-).
Kind regards,
David
Hello David,Did a quick check and yours and Volovtreters differ just a little. Have my own files at work so I will dig deeper Monday.
Anyway remembered what I thought was wrong: With a given throat area and Fc it is only one length and mouth-area possible, for some reason your program cuts from the mouth when shortened but then it is no tractrix anymore.
Tractrix can only be cut from the throat.
So for le Cleach, Spherical/Kugelwellen and Tractrix it should only be possible to input throatarea with a given Fc to get length and moutharea, as mouth-area and Fc is totally dependant on each other. Or with a given mouth-area it should only be possible to input throatarea to get length and Fc. And so on.....
It would also be nice to incorporate a function that shows the "real" Fc that is based on that the horn works down to where the hornlength is 0,5 wavelength.
According to the Voight-patent the area should be 1,27 times the round when going square.
Brgds
Lars
Hi Lars,
“Did a quick check and yours and Volovtreters differ just a little.”
Not enough to make any practical difference, I hope :-).
“Have my own files at work so I will dig deeper Monday.”
Many thanks.
“Anyway remembered what I thought was wrong: With a given throat area and Fc it is only one length and mouth-area possible.”
While that statement is certainly true for a fully-formed tractrix horn (mouth flare tangent angle = 90 degrees), it is of course possible to have a tractrix-profiled horn that does not extend to the full theoretical mouth size.
“For some reason your program cuts from the mouth when shortened.”
Only if that particular option is selected from the Tractrix Horn Segment Wizard. The Wizard is very flexible - there are many choices available.
“So for le Cleach, Spherical/Kugelwellen and Tractrix it should only be possible to input throatarea with a given Fc to get length and moutharea, as mouth-area and Fc is totally dependant on each other. Or with a given mouth-area it should only be possible to input throatarea to get length and Fc. And so on.....”
With a bit of “mathematical manipulation” it is possible to do far more, as can be seen from the options available in the Tractrix and Spherical Horn Segment Wizards. The only reason that the calculated values may vary slightly depending upon the option chosen is simply because inputs and outputs are rounded to two decimal places. Rest assured, the discrepancies are not due to any intrinsic problems with, or errors in, the underlying mathematics.
“It would also be nice to incorporate a function that shows the "real" Fc that is based on that the horn works down to where the hornlength is 0,5 wavelength.”
I would have thought that the current fc value is close enough :-).
“According to the Voight-patent the area should be 1,27 times the round when going square.”
The rectangular dimensions given in Hornresp are derived from the equivalent plane cross-sectional areas generated by the axisymmetric model. I did not worry about it too much as I assumed that tractrix horns built using Hornresp data would most likely be axisymmetric anyway - it would defeat the purpose somewhat to compromise and settle for a rectangular tractrix horn :-).
Kind regards,
David
Hello David,Great to finally having this discussion with you!
Checked the math and the discrepancies was only due to rounding of as you can see in my spreadsheet below.
But as the fundamental of the tractrix is the "90 degree angle" this horntype can NOT be cut before the full mouth and still be called a tractrix. It can as I said in my earlier post only be cut from the throat.
An example: A guy I know wanted to make a tractrix midbass horn using Hornresp. He decided At 500cm2, Am 4955cm2 and Fc 80Hz. What he got from Hornresp was a 73,03cm horn that was not a tractrix, it was more of an exp-horn with close to 86Hz Fc. This because a tractrix is exponential the closer to its throat you get.
When you go from round to square(rectangular is as I belive not an option otherwise when mirroring) You must keep the "90 degree angle" at the ver/hor section instead. This method is also adviced in Voights patent. I have made an example in the link below. 181Hz is choosen as this is the flare of the hornthroat of 2" JBL driver. I have also added a round to square "adaptor". Note that the useful Fc gets lower when going to square as the useful Fc depends on length in this case.
If you want a smaller mouth-area of a tractrix the only way to do this is by mirroring against wall/floor and cutting a slice of it keeping the throat untouched. This is easiest accompished with a square horn. The uncut sides will keep their 90degree angle and the length will still remain the same.
LeCleach uses the same method when going from round to multi-sided. The illustrations at the site with his spreadsheets also shows the mirroring.
Brgds
Lars
Hello,In the axial version of my spreadsheet the only case of "mirroring" (but may be I don't use the word in the same meaning as you) is when using 2 orthogonal walls.
This is illustrated here:
http://ndaviden.club.fr/pavillon/axial_horns.gif (full horns)
and
http://ndaviden.club.fr/pavillon/axial_murs.gif (1/4 horns)In both case (square and 1/4 round throat) the part of the horn near the throat has to be calculated or designed by other means in order to provide a smooth transition between the driver and the horn as to change the shape from round to square or from round to 1/4 circle.
The case of a "half horn" as the one demonstrated by Jeffrey Jackson at VSAC2008, see:
http://www.goodsoundclub.com/UserImages/ExperienceMusic@VSAC.jpg
is more difficult to solve because the driver is generally round and it have to be fitted to the half circle throat which transformation requires more strain of the shape, that's why I didn't illustrated the case on the page:
http://ndaviden.club.fr/pavillon/lecleah.html
Best regards from Paris, France
Jean-Michel Le Cléac'h
Bonjour Jean-Michel,
Modified one of your illustrations to show what I call mirroring and that I know works with Tractrix against a sidewall.
From your spreadsheet I understand that you(like Voigt) keep the section, so the area gets ca 1,27 times bigger going from round to square.
About transition from round to square I use Excel to find out, see my spreadsheet in a previous post. Starts from the point where the side is equal to the diameter of the driver. Rough maybe but the only way I could think of.
It also makes the horn a few cm longer in my spreadsheet example. Used the similar method using your spreadsheet for 4 sides. If I remember it right the flare of JBL2441 was uniform with a T=0,8 horn with Fc ca 225Hz.
Brgds
Lars
Hello,IMHO a Tractrix horn having a perfectly square mouth is a theorical mistake (because the shape of the intersection of a given wavefront and the walls of the horn is never a square).
A non circular tractrix having a 4th order symetry axis will look more as a JBL biradial tweeter (but with a 4th order axis of symetry).
In my view when this is applied to a Le Cléac'h horn and when using my spreadsheet, we have to consider the calculated profile as a "radial" profile of such horn (with axis of symetry of 4th order, the JBL having only a 2nd order axis of symetry ).
This means that the shape of the horn should be obtained by rotating the plane (vertical or horizontal) containing the profile along the vertical (or the horizontal, respectively) axis.
Many people use my spreadsheet to calculate horns having a squared mouth but I ever told those who ask me some help that in that case the expansion is a very rough approximation...
Best regards from Paris, France
Jean-Michel Le Cléac'h
Hi Lars,
“Checked the math and the discrepancies was only due to rounding of as you can see in my spreadsheet below.”
Many thanks for the confirmation, and for providing the spreadsheet!
“But as the fundamental of the tractrix is the "90 degree angle" this horntype can NOT be cut before the full mouth and still be called a tractrix. It can as I said in my earlier post only be cut from the throat.”
Provided that the area expansion is derived from the expression for a tractrix curve (the involute of a catenary), then by definition the horn must be a tractrix, no matter how long it might actually be. The fact that it may not extend to a 90 degree mouth does not mean that it can be called something else :-).
“An example: A guy I know wanted to make a tractrix midbass horn using Hornresp. He decided At 500cm2, Am 4955cm2 and Fc 80Hz. What he got from Hornresp was a 73,03cm horn that was not a tractrix, it was more of an exp-horn with close to 86Hz Fc. This because a tractrix is exponential the closer to its throat you get.”
The horn he specified in Hornresp was still a tractrix, it’s just that he didn’t make it long enough :-). A fully-formed tractrix horn with At = 500 cm2 and fc = 80 Hz would require a length of 95,31 cm and a mouth area of 14713,87 cm2.
An exponential horn with At = 500 cm2, Am = 4955 cm2 and fc = 80 Hz would have a length of 78,48 cm, which is more than 7 percent greater than the length of the equivalent tractrix horn.
With regard to “mirroring”, I would caution against using the technique with tractrix horns unless it is absolutely necessary to do so. A fully-formed axisymmetric tractrix horn will invariably provide better overall performance than one reduced in size by mirroring.
As an aside, what is not generally recognised is that a fully-formed tractrix horn is completely specified given just the throat diameter and throat flare tangent angle.
This is significant because it means that there is only one tractrix horn that will exactly match a given compression driver. For example, if the compression driver has an exit diameter of one inch and an exit half-angle of 5 degrees, then the matching tractrix horn with a throat diameter of one inch and a throat flare tangent angle of 5 degrees has a cutoff frequency of 378,61 hertz (assuming the velocity of sound in air is 344 metres per second). Rounded to two decimal places, the mouth area is 656,93 cm2 and the axial length is 30,76 cm. The horn will be 0,34 wavelengths long at the cutoff frequency.
Kind regards,
David
Hello David,Let me rephrase: A Tractrix cut of before its full mouth and 90degree angle looses its sonic virtues.
I still think you are wrong about calling it tractrix. I admit it will be a horn with the initial flare of a tractrix. The shorter it gets the more exponential the flare is, so it must be a hybrid of both.
Also as the patent specifies that it ends with the 90 degree angle. If it is not according to Voights patent it couldn´t be "the real thing".So building a tractrix shortened from the mouth end is, in my opinion, not the best idea if you want traxtrix performance.
If you use the export function in your excellent program it easy to compare my examples. The so called 80Hz tractrix is within 5% from a 86Hz exp. Would not call it T.....
And to make a tractrix work down to 80Hz the length should be 215cm and the throatarea 15cm2, :-), :-).
Have you read the patent, can mail it if not. Voight must have been a genius doing these things 1927!
Also about mirroring there should be no caution as this is a common technique that really works(Rauna, Lowther etc.) and it is also a part of the patent.
Interesting to see that you also have found out about the compression driver matching. JBL 2" is as I mentioned 181Hz and Altec 802 is 394Hz to my findings if you take the flare of the drivers throats in account. This goes for both exp and tractrix.
Brgds
Lars
"I still think you are wrong about calling it tractrix. I admit it will be a horn with the initial flare of a tractrix. The shorter it gets the more exponential the flare is, so it must be a hybrid of both."
Greets!
Hmm, truncating a tractrix from either end doesn't negate the fact that what is left is still a tractrix flare in construct regardless of how close it may approximate another any more than truncating an exponential flare can make it a hybrid of hyperbolic, though I agree that without its complete mouth termination some of its 'anti-friction' properties (as it is typically referred to in the designs it is most often used in) are lost.
I'm no big fan of tractrix flares for audio use, but even truncated ones must still perform well or they still wouldn't be used over a century later in internal combustion engines, ship propellers, audio horns, etc., so we'll have to agree to disagree.
Maybe for audio we need a math whiz to derive a formula that blends all three together into a single universal audio flare rendering all the confusion/debate over which is what, when and/or 'best' moot. ;^)
GM
Loud is Beautiful if it's Clean!
Hi GM,
About the hybrid you ask for I think LeCleach and partly Kugelwellen are close to what you ask for, :-).
The rest discussed is only a matter of semantics, where we all have different views. But I can again recommend reading Voights patent from 1927!
Brgds
Lars
I'll take your word for it since higher math is literally 'Greek' to me, so can't do a comparison at the math level required. Indeed, the LeCleach flare comes closest to the one I long ago worked out experimentally, so naturally it's the one I recommend when appropriate. ;^)
I was exposed to it a few decades ago, but at the time I was already aware that folks had been using/understanding the tractrix flare from complete termination to severely truncated at least since the dawn of the internal combustion engine, so frankly just skimmed it.
So what's in it that makes it special beyond patenting an audio device designed using a well known/proven technology? Seriously, what do you think we're missing?
GM
Loud is Beautiful if it's Clean!
Hello,The nearest conventional ( = old) profile to the Le Cléac'h profile is the Kugelwellen horn. (here compared among with other profiles to the Tractrix and T = 1 Le Cléac'h horn ).
Notice that the Kugelwellen follows the same logic as the Tractrix ("constant speed" translation of spherical cap wavefronts of a constant radius along the axis. The radius used for the Kugelwellen being 2 times the radius used for the Tractrix).
A main difference between the Tractrix and the Kugelwellen is that the Kugelwellen expansion is exponential all along but the expansion of the Tractrix (as I calculated it) departs from an exponential law near the mouth. If we recalculate the tractrix with a pure exponential expansion of spherical cap wavefronts, then we find a horn the mouth of which curves back as for the Kugelwellen. I called this a "revisited Tractrix" horn.
Best regards from Paris, France
Jean-MIchel Le Cléac'h
Hello Jean-Michel,
Thank you, your picture tells it all! When I did the comparision between yours and KW in my earlier post I only compared before turn back.One question though: The different horns must have different Fc? As far as I know a Traxtrix and an Exp has about the same mouth radius and kugelwellen and yours far bigger before they turn back for the same Fc.
See my example with a 180Hz horn with 11,64cm2 At.
Couldn´t you do a new picture but include a Le Cléac'h T=,707 as I have got the impression that this is what you recommend, and also use the same Fc. Then it would be even clearer to a layman as me.
Brgds
Lars
Hello Lars,To say that the cut off frequency of a horn is related to the (mean) diameter of its mouth is a common mistake.
In fact whatever the length of a horn having a known expansion, its cut-off is the same , BUT what differs is the ripple in the response curve which is due to the interferences between normal waves emitted by the diaphragm and propagating inside the horn with waves backreflected from the mouth to the throat.
We are still wrongly using a semiempirical rule originating from Keele who said that the ripple due to those reflections passes through a minimum when the mouth diameter is equal to the wavelength at cut-off. This is based on a model using the false assumption that the wavefronts are plane. Further studies demonstrated that such minimum doesn't exist.
The domain of application of this rule of thumb is only for cut horns (all Salmon horns must be considered as cut horns). If you use a minimum diameter equal to the wavelength at cutoff then you obtain an "acceptable" amount of ripple in the response of the horn. (acceptable for whom?)
Doing that, we link that diameter to the cut-off frequency but we cannot reverse that rule so: it is not true that the cut-off frequency is related to the diameter of the mouth.
Now, IMHO,to encouter this rippling, it is highly desireable to use quasi infinite horns like complete (= uncut) Le Cléac'h horn, complete Kugelwellen or complete Tractrix. But only the Le Cléac'h horn doesn't do any asumption on the shape of the wavefronts. In this sense it is a better design than the Kugelwellen and the Tractrix, the design of which is eroneously based on the asumption that wavefronts are spherical caps.
Best regards from Paris,
Jean-Michel Le Cléac'h
Hello Jean-Michell,Thanks for your explanation where I must agree, as most of what you say is known facts together with your enlightening conclusions of them.
I now see that the Exp in your picture is prolonged beyond the "Keele-point" to where its Am is equal to yours and KWs at longest.
About what the "Keele-point" concerns, one rule of thumb is to use the double Fc as lowest usable cutoff for midrange horns. This maybe as we generally do not accept the ripple, ;-)!
For Tractrix another rule of thumb seems to be that it couldn´t be used below the point where its length is equal to 0,5x wavelength of lowest useful frequency. Maybe this goes for all quasi infinte horns too?
About the wavefront of a tractrix not being spherical this was already concluded by Lambert in his studies presented in JAES 1954.
I was thinking of trying the Le´Cleac'h flare in a conventional 90*40 radial horn with straight sides. How bad would this approximation be compared to round or your proposed "radial" with 4th order axis of symmetry?
Brgds
Lars
Hello,
Some additional comments about your sentence:
"About what the "Keele-point" concerns, one rule of thumb is to use the double Fc as lowest usable cutoff for midrange horns. This maybe as we generally do not accept the ripple"
The recommandation to use an electric cut-off of the high pass filter one octave or so above Fc, the acoustical cut-off of the horn is not related to the ripple in the response.
When you look at the acoustical impedance of a horn you can see that at high frequency the horn is purely resistive but when the frequency falls around Fc, the cut off frequency, the acoustical reactance of the horn rises. This is the source of a subsequent rise of the group delay. Therefore for a note the fundamental of which is around Fc the harmonics of that note will arrive before the fundamental. This we want to avoid, we want the waveshape of the note the less distorted possible. This is the reason why most often we use an electrical cut-off 1,5 to 2 times Fc.
But this depends on the horn' flare. Try to simulate a Le Cléac'h horn having T = 0, you'll see that, if you can design a sharp cut-off high-pass crossover, then you can use an electrical cut-off very near of Fc because the interval of frequency inside which the reactance is not negligeible is very narrow around Fc.
Best regards from Paris, France
Jean-Michel Le Cléac'h
Hello,So many rules of thumb exist!
Some have been introduced to design the most compact horn for the lowest cut-off for an "acceptable ripple, others have been introduced for "acceptable directivity",... You may imagine other cases.
I don't like those rule of thumbs and simply doesn't care about them. I recommand to you and others to forget abouth them. We possess now powerful design tools. For horns design, Hornresp will give you an accurate prediction on the behaviour of your own design (on and off axis response, directivity, loading, impedance, influence of reflections at mouth using the wavefront simulator...) Using Hornresp we simply don't need any rule of thumb.
But this is for axisymetrical horns.
Many people want horns having a low height / width ratio. For the moment, except manufacurers who use 3D FEM or BEM analysis, no tools exist (or I don't know them) for the amateur to predict the behavior of non axysimetrical horns. The "amateur", most often thinks that we have just to apply some defomation (strain?) of the horn shape, then a round mouth will turn in an elliptic mouth (contained in a plane), in fact this is much more complicated because we want the wavefronts to be equidistant each one to the other. This means that all the points of the wavefront must be at the same curvilinear distance of the throat. ( = the mouth contour corresponding to a wavefront cannot be contained inside a plane)
If you design with equidistant wavefronts then you simply cannot obtain simple shapes. See few examples I calculated using my method (equidistant wavefronts without any asumption on their shape).
wide HF horizontal directivity JMLC horn:
http://www.diyaudio.com/forums/attachment.php?s=&postid=1532641&stamp=1212759567quasi Iwata horn:
http://www.diyaudio.com/forums/attachment.php?s=&postid=1532652&stamp=1212760839constant horizontal directivity JMLC horn:
http://www.diyaudio.com/forums/attachment.php?s=&postid=1532660&stamp=1212761603Best regards from Paris, France
Jean-Michel Le Cléac'h
Yes, your shapes are beautiful. Especially your version of the Iwata, (that I look upon as a refined radial). And surely they are theoretically perfect.
Though IRL they are not buildable without expensive tooling. Therefore I asked how bad you thought a "radial-approximation" should be? Couldn´t be worse than a Exp radial could it, ;-).
Brgds
Lars
GM, I do not think using a curve similar to tractrix in an audio application was to be looked upon as using wellproven/known technology back in 1927.
Also Voight was told by a technician, after having done his findings that led to the patent, that he had used a curve similar to Tractrix. First after that, he named the horn after this function.
Later findings and measurements in the beginning of the -50s showed that Voigths assumption about curvature of the wavefront was not completely right. My guess is this is what led to Kugelwellen.
Brgds
Lars
Hi Lars,
"Let me rephrase: A Tractrix cut of before its full mouth and 90degree angle looses its sonic virtues."
Agreed :-).
"I still think you are wrong about calling it tractrix."
We guess we can agree to disagree then :-). I simply cannot bring myself to call a horn defined by the tractrix curve an exponential horn :-).
"And to build a tractrix shortened from the mouth end is no good idea."
Agreed again :-).
"Have you read the patent, can mail it if not."
That would be fantastic, thanks!
"Also about mirroring there should be no caution as this is a common technique that really works(Rauna, Lowther etc.) and it is also a part of the patent."
I'm a purist, I'm afraid :-).
"Interesting to see that you also have found out about the compression driver matching. JBL 2" is as I mentioned 181Hz and Altec 802 is 394Hz to my findings if you take the flare of the drivers throats in account."
I would be happy to check your fc values if you care to post the throat diameters and flare half-angles of the two drivers :-). I think I will probably now get around to adding the option to Hornresp.
Kind regards,
David
David,
As far as I remember JBL 2441 is 38,5mm dia just outside phaseplug, the "horn" is 69mm long and dia at the end is 48,5+mm then followed by a 1mm cork gasket. I also measured dia halvways and it confirmed the 181Hz exp. flare. Will check the Altec and JBL later to refresh my memory.
Brgds
Lars
Hi Lars,
For the given dimensions, and disregarding the cork gasket, I calculate the required cutoff frequency to be 163 Hz.
(I assumed a throat diameter of 48.5mm and a half-angle of 4.14 degrees).
Kind regards,
David
Hello David,
Think you´re wrong and me too! It should be 183Hz. Use Hornresp or the standard exp.-formula instead, ;-)
With Exp, S1 11,64cm2 and S2 18,47cm2 and length 6,9cm you get 183Hz.
I doublechecked against the formulas used in the hypex-spreadsheet I just mailed you and got the same figures.
Brgds
Lars
Hi Lars,
"With Exp, S1 11,64cm2 and S2 18,47cm2 and length 6,9cm you get 183Hz."
I have assumed that the flare inside the driver is conical, not exponential. This gives an exit half-angle of 4.14 degrees as previously stated. If the flare inside the driver is exponential, then the exit angle becomes 4.64 degrees.
For a throat diameter of 48.5mm and a half-angle of 4.14 degrees the required cutoff frequency of the tractrix horn is 163 hertz.
For a throat diameter of 48.5mm and a half-angle of 4.64 degrees the required cutoff frequency of the tractrix horn is 182 hertz.
Kind regards,
David
Hello David,
So then we agree. Had forgot to clearly state it was not conical, though I in a previus post mentioned I had measured midways when I came to my conclusion. 181-183Hz Fc is more a question of accuracy when the measurement is done.
Brgds
Lars
Hi Lars,
"Had forgot to clearly state it was not conical, though I in a previus post mentioned I had measured midways when I came to my conclusion. 181-183Hz Fc is more a question of accuracy when the measurement is done."
From your comment above I suspect that you may simply be using the cutoff frequency of the driver internal flare as the cutoff frequency for the tractrix horn. In my case I am calculating the exact theoretical cutoff frequency of the tractrix horn using the throat diameter and half-angle as input parameters, which is a completely different (but technically more correct) approach :-).
Kind regards,
David
Hello David,
What I may have pointed out is the similarity between trx and exp at the throat.
So whatever mathematical method you wish you use, the discrepancy of area between the first 7cm of a trx 183,17Hz with an inital area of 11,64cm2 and a the 2441 throat is below 0,02% whether using the export function of Hornresp or my Excel-spreadsheets. So if being practical, the eventual exactness of angles shouldn´t matter at all ;-).
So from my point of view, you should use the drivers hornthroat Fc if wanting to build the best practical Tractrix around a specific driver like 2441. This goes for KW,spherical and Le C. too.
Brgds
Lars
Hi Lars,
“Also as the patent specifies that it ends with the 90 degree angle. If it is not according to Voights patent it couldn´t be "the real thing".”
Many thanks for providing me with a copy of Voigt’s patent (note that the patent was granted to Paul “Voigt”, not “Voight”).
The first claim in the patent document reads as follows:
1. “Horns for acoustic instruments designed so that the sound wave expands as if the source was at an approximately constant distance away from the point of expansion, such a design being obtained for straight circular horns by forming the walls to the shape of the curve known as the tractrix in which the length of the tangent from the centre line to the curve is constant.”
While Voigt certainly prefers (quite logically) to use a 90 degree mouth, nowhere is it actually formally claimed as part of the invention.
I believe that this omission validates my argument that a tractrix horn does not necessarily have to have a fully-formed mouth :-).
Kind regards,
David
Hey Deyvid,
Sorry for the misspelling of names, its easy to slip on the really important issues, ;-).Don´t know if you read line 16 at the first page:
"At the flare, this tangent becomes the radius. The flare diameter is therefore twice the tangent length."
In the "Complete Specification" line 37 he also defines "mouth" by:"At the point where tangent the is at right angles to the centre line it becomes the radius. I cal this point the "mouth" and prefer either to terminate the curve at this point, or to continue the plane E F at right angles to the centreline."
I believe that these omissions validates my argument that a tractrix horn have to have a fully-formed mouth :-).About continuing the plane to form a "baffle" I think Lambert used them to get the best results when evaluating this horntype back in -54(JAES-paper).
Maybe the baffle option could be something to incorporate in Hornresp? Also maybe an addition could be made to modify Sperical to Kugelwellen by letting it continue rolling back after having reached its full length?
But... we both agree anything but a "fullmouth" tractrix is to be avoided for sonic reasons so lets leave it there.
About the 1,27 factor when going to square, the inventor uses "prefer", so this way of doing it must be up to anyone to decide. I am deeply sorry if I in an earlier post used the word "state".
We discussed mirroring in an earlier post and this issue is brought up in line 23 to 29 and also in Fig. 3.
Greetings from sunny Sweden
Larse
Hi Lars (without the "e"),
I make a point of not misspelling names, as a mark of respect for the individual :-).
"Don´t know if you read line 16 at the first page."
I certainly did, and I also read Voigt's comments regarding his preference for the location of the mouth. The fact remains that a fully-formed mouth is not stipulated in any of the seven claims he formally makes :-).
"About the 1,27 factor when going to square, the inventor uses "prefer", so this way of doing it must be up to anyone to decide."
He also uses "prefer" when referring to the mouth position, so by your own admission, "it must be up to anyone to decide" :-).
"But... we both agree anything but a "fullmouth" tractrix is to be avoided for sonic reasons so lets leave it there."
Good idea - I'm exhausted :-).
"Maybe the baffle option could be something to incorporate in Hornresp?"
Setting Ang = 2 x Pi effectively adds an infinite baffle to the horn mouth, as far as Hornresp is concerned.
"Also maybe an addition could be made to modify Sperical to Kugelwellen by letting it continue rolling back after having reached its full length?"
I think I would probably use a Le Cléac'h horn rather than a spherical wave horn if a rolled-back configuration was required :-).
BTW, have you ever thought of going into politics? :-).
Kind regards,
Deyvid
Hello David,
I am glad you can see this from the humorous side.
About going into politics I wonder the same about you, ;-).
Still I hope you are enough exhausted to give up even if I not for a minute and never will agree about your conclusions of the patent
:-). As far as practical use we for some reason agree and thats enough for me!
Now to serious matters about Hornresp:
What about the 2pi and tractrix, can not find the baffle option there, please explain!
Also sorry that you do not go for Kugelwellen as this option would be much better than its seldom used "cousin" Spherical.
Brgds
Larse
Brgds
Lars
Hi Lars,
"What about the 2pi and tractrix, can not find the baffle option there, please explain!"
You are really confused now - you are not even sure what your name is :-).
Sorry if I did not make things clear. There is no separate baffle option. When Ang = 2 x Pi is specified, the Hornresp simulation model assumes that the horn is radiating into half space, which is effectively the same as fitting the horn mouth with an infinite baffle.
Kind regards,
David
Not the easiest task to measure without the proper tools. Anyway measured the end angle with what I have and it was just below 5 degrees. This is more towards the exp(or tractrix) 4,6degrees than conical 4,1degrees. In combination with the curved flare this indicates exp.
I can let the guys at Granlund Tools do a professional measurement but right now they are closed for summer.
Brgds
Lars
Ha,ha Deivid!
Always trying to get the last word?
Will try the 2pi option.
Brgds
Lars
Hi Lars,
"So from my point of view, you should use the drivers hornthroat Fc if wanting to build the best practical Tractrix around a specific driver like 2441. This goes for KW,spherical and Le C. too."
How then would you determine the correct cutoff frequency for a tractrix horn if the driver you wish to use has a conical flare? The whole purpose of the exercise is to match the two angles at the throat interface, not specifically the cutoff frequencies. Matching cutoff frequencies only works if the flare type of the driver is the same as the flare type of the horn. As far as I am aware, for ease of construction, most compression drivers have conical flares :-).
Remember, what we are trying to do here is to minimise wavefront disturbances due to discontinuities at the throat interface :-).
Kind regards,
David
Hello David,My conclusion is only valid for the OS JBL 2". The flare in that one is a knockoff of an old WE driver I think. Did a quickcheck on my old Altec driver and it does not seem to be conical either. So in my very small world all drivers are exp. But as this an interesting subject I will check the drivers I come in contact with in the future. Have not seen the modern JBLs but for what I understand they are without throathorn and that makes everything so much easier, :-).
So I do not know anything at all about matching Tractrix to conical drivers.
The flare of the 2441 seems to match the flare of a Tractrix and KW and Le´Cleac'h with fairly close tolerance.
My findings only refers to measurements at throat, halfways and mouth. Maybe there are some secrets hidden there?I will try to do a template of the drivers throat this weekend and come back with the results.
Brgds
Lars
Hi Lars,
"I will try to do a template of the drivers throat this weekend and come back with the results."
Many thanks. It is interesting that your drivers appear to have exponential flares. Theoretically at least, this seems to limit their application to single exponential horns, having cutoff frequencies pre-determined by the driver flares. A conical driver flare would presumably provide more flexibility in this regard.
"So I do not know anything at all about matching Tractrix to conical drivers."
Not to worry - in a few days, the Hornresp Tractrix Horn Segment Wizard will do it all for you :-).
If you can't wait until then:
c = velocity of sound in air
R1 = throat radius
AT = throat half-angle
Rm = full-mouth radius
fc = tractrix horn flare cutoff frequency
Rm = R1 * (1 / Tan(AT) ^ 2 + 1) ^ 0,5
fc = c / (2 * Pi * Rm)
Kind regards,
David
Hi David,
Did a quickcheck last night with a small straigt ruler and it is not conical though it is not flared very much. Will also try to measure the angle at the end.
Brgds
Lars
Hevbeen lazy, still haven´t measured the flare. But found a few lines in an interview with Doug Button of JBL about 435e that confirms my findings:
"Previously, virtually every compression driver made had a 180hz flare rate whose origin dates back to the original AT&T Labs designs from the 1930's. This low rate was necessary to accommodate the low cross-over points used in early two-way loudspeakers."
Brgds
Lars
"Previously, virtually every compression driver made had a 180hz flare rate whose origin dates back to the original AT&T Labs designs from the 1930's. This low rate was necessary to accommodate the low cross-over points used in early two-way loudspeakers."
Thanks Lars, I was not aware of that.
The Fostex mid-range compression driver I used some time ago definitely had a conical flare.
Kind regards,
David
Hi David,
Must say I am little surprised myself as the JBL have related to 160Hz in a technical paper I saw. Seems like they also thought they where conical ;-).
Brgds
Lars
| FAQ |
Post a Message! |
Forgot Password? |
|
||||||||||||||
|
||||||||||||||
This post is made possible by the generous support of people like you and our sponsors:
Top of Page ]
[ Contact Us ]
[ Support/Wish List ]
[ Copyright © 2013, Audio Asylum, all rights reserved ]
[ Take5 ]
