Hardhead Posted July 16, 2002 Share Posted July 16, 2002 I believe I understand what an exponential horn is, but I've never seen an explanation of what a Tractrix horn purports to be. Can anyone explain "in words of one cylinder" what a Tractrix horn is and its advantages and disadvantages vs. an exponential horn? Thanks. 1 Quote Link to comment Share on other sites More sharing options...
dougdrake Posted July 16, 2002 Share Posted July 16, 2002 How's this? With most horns types (e.g. exponential and hypex) you have reflections at the mouth which give resonances. With the tractrix horn, since the waves are hemispherical going through the horn, they exit with very few reflections. (I stole it from a web site I googled...) Doug ------------------ My System 1 Quote Link to comment Share on other sites More sharing options...
Ray Garrison Posted July 16, 2002 Share Posted July 16, 2002 In words of one cylinder, it's a different shape for a horn. The horn's expansion rate is equal to a "tractrix curve". To derive the curve's shape without using math, think about this: Fence / / / /you--------------------dog / / / / / You're standing beside a fence. You have a dog on a leash. The dog starts out at the end of the leash, with the leash perpendicular to the fence. You start walking along the fence (down, in my drawing.) As you go, you pull the dog along. As you pull on the leash, you will, of course, pull the dog along. The dog will be pulled both a little closer to the fence, and a little down. As you continue walking, the dog will move ever closer to, but never reach, the fence, and the direction you move the dog will gradually shift from mostly in toward the fence and a little down to mostly down and a little in towards the fence. The path the dog follows is a tractrix curve. For reasons that are too deep to go into here, the wavefront of a soundwave travelling down a tractrix-shaped horn travels with the edge of the soundwave being perpendicular to the tangent of the curve at the point of intersection at each point along the horn. As Doug said, this makes it "easier" (?) for the horn to "launch" the soundwave without causing any reflections back down the horn. To see the full math behind this, and several graphics representations of a tractrix curve, check this (very math heavy) link: http://mathworld.wolfram.com/Tractrix.html Ray ------------------ Music is art Audio is engineering Ray's Music System This message has been edited by Ray Garrison on 07-16-2002 at 10:47 AM Quote Link to comment Share on other sites More sharing options...
dougdrake Posted July 16, 2002 Share Posted July 16, 2002 Uhh, yeah. I meant to say what Ray said, but my pen ran out of ink. Thanks, Ray, for taking the words right out of my mouth (LOL)! Doug ------------------ My System Quote Link to comment Share on other sites More sharing options...
sseymour Posted July 16, 2002 Share Posted July 16, 2002 Yeah, I almost always mean to say what Ray said. Except that I don't really know it until he says it. Oh well. -Scott ------------------ BobG modified Forte II's KG-4 Surrounds RC-3 Center DIY Sub based on Adire Audio Shiva Woofer Sony DB830 Quote Link to comment Share on other sites More sharing options...
cluless Posted July 16, 2002 Share Posted July 16, 2002 The problem of using the "dragged-dog" technique of tractix curve approximation, is that the likelihood that the dog will go ballistic, charge, and take a bite out of your ....errr. aspirtations, is directly proportional to the distance of the dog to the fence... and for this silly post, I have no...err..de-fence. Quote Link to comment Share on other sites More sharing options...
WMcD Posted July 16, 2002 Share Posted July 16, 2002 Hard to explain without diagrams. The exponential horn equation looks at the area going up the horn (or down). The area considered is a plane. The plane doubles in area every X increment from the throat (small end) to the mouth (big end). The assumption is that the sound wave going down the horn is flat. The tratrix horn in a pure form is circular in cross section. The complicated equation describes the side wall rather than the area. The theory is that the sound wave has a constant radius. You to imagine that the big end is round and you can cut a hollow ball in half and it fits over the end. You'll imagine that where the circumfrence of the ball touches the mouth, there is a right angle. Then going toward the the small end of the horn, you have to shave off the edges of the hollow ball to make it fit. The "magic" of the tratrix curve is that the edge of the shaved ball is still at right angles to the wall of the horn. As you get to the small end of the tratrix horn, the area of the ball has been reduced. The radius is the same but the surface is getting closer to being "flat". So you can see that the theory of the tratrix is that 1) there is a wave that is a surface cut from a ball of constant radius and 2) where the edge of the ball intersects the side of the wall, it is always perpendicular. The above doesn't tell us all about the tratrix horn, or what makes a horn good or bad for various purposes. These are a bit independent of the theories of the shape of the wave or intersection angle of the wall. Yet it works out. A happy accident perhaps. One theory is that an expanding sound wave in free space is an expanding sphere. Also, a conical horn, like a megaphone, does the best to approximate that. The tratrix comes fairly close to that in the middle section of its expansion. Unfortunately, the cone doesn't do a good job a presenting a load to the driver. Megaphones have poor bass response. A solution is to place a special shape at the small end. This is a hyperbolic expansion. The tratrix, at the small end, comes fairly close to this. Another problem with the cone/megaphone is that the big end leads to beaming. However, if one puts a more rapid flare at the big end, this problem is solved. The tratrix curve approximates this too. I've seen some articles that the wavefront going down the horn of any geometry is very irregular and difficult to predict. There was an article in Audio by two Klipch engineers in the early '90's about the tratrix. Dr. Bruce Edgar wrote about the tratrix too. I can send you some articles if you send me your postal address by e-mail. You'll note that Klipsch products trademarked "Tratrix" are not circular in cross section. It seems that they are playing with simulating the area of the tratrix expansion. As the article points out, horn design is mostly a matter of compromise and taking the best features of two or more theories and using them without adopting too many of the shortcomings. Regards, Gil This message has been edited by William F. Gil McDermott on 07-16-2002 at 09:24 PM Quote Link to comment Share on other sites More sharing options...
Clipped and Shorn Posted July 16, 2002 Share Posted July 16, 2002 Doesn't it depend on the breed of dog and how distracted he is by the cat she sees while you are yanking the leash. That's what causes distortion, right? Is this related to the tractor beam? -C&S ------------------ Cornwalls currently upgrading to all tube components Quote Link to comment Share on other sites More sharing options...
fini Posted July 16, 2002 Share Posted July 16, 2002 Also, must depend on how carefully you shave those balls. fini (Man, you guys are smart!) Quote Link to comment Share on other sites More sharing options...
HDBRbuilder Posted July 17, 2002 Share Posted July 17, 2002 I believe that Tractrix article was authored by Roy DelGado and Jim Hunter. ------------------ I can now receive private messages This message has been edited by HDBRbuilder on 07-17-2002 at 10:30 PM Quote Link to comment Share on other sites More sharing options...
WMcD Posted July 17, 2002 Share Posted July 17, 2002 Yes, and Kerry Geist too. Gil Quote Link to comment Share on other sites More sharing options...
Soundthought Posted July 17, 2002 Share Posted July 17, 2002 Hello all. Intresting stuff. Intresting analogies. This is the kind of thread I like. BTW I tried it with my 2 dogs. It was more like a folded horn. LOL. Is determining the flare rate for any given horn a balance between the cutoff frequency and the dispersion angle? Quote Link to comment Share on other sites More sharing options...
John Warren Posted July 18, 2002 Share Posted July 18, 2002 (edited) in Edited May 19, 2016 by John Warren Quote Link to comment Share on other sites More sharing options...
Klipschguy Posted July 18, 2002 Share Posted July 18, 2002 John, If midrange horns "suck" IYHO, why do you like Klipsch? Horn midranges are Klipsch's claim to fame and largely responsible for that "Klipsch sound." Just curious, Andy This message has been edited by Klipschguy on 07-18-2002 at 03:39 PM Quote Link to comment Share on other sites More sharing options...
jnorv Posted July 18, 2002 Share Posted July 18, 2002 I have the solution for the acoustic resistance and reactance at the throat of a finite exponential horn, which is the classical result that Klipsch and everybody else has used for years. Does any body know where the corresponding solution for the tractrix horn can be found? J Norvell Quote Link to comment Share on other sites More sharing options...
John Warren Posted July 18, 2002 Share Posted July 18, 2002 Klipschguy- a folded bass horn is PWK's claim to fame. the bass horn, and it's variants, i like Quote Link to comment Share on other sites More sharing options...
KGeist Posted July 18, 2002 Share Posted July 18, 2002 I don't believe I've ever seen a mathmatical solution for the resistance and reactance of a Tractrix horn (although I'm sure one exists). I've always "assumed" it was similiar to a Hyperbolic horn, given that the two curves are "somewhat" similiar. I have also seen actual acoustic resistance measurements on a Tractrix horn that supports this. BTW, our typical horn designs use a modified Tractrix horn curve. The mid-section of the horn is modified in order to give/maintain the desired horizontal and vertical coverage pattern (90X60 etc...). Pure Tractrix, Exponential and Hyperbolic horns become increasingly more directional with increasing frequency, and therefore are not suitable in systems that require good even coverage throughout its operating band. Kerry 2 Quote Link to comment Share on other sites More sharing options...
Soundthought Posted July 18, 2002 Share Posted July 18, 2002 Is that considered a compound flare rate? So when the coverage is computed at a given frequency, then the same coverage applies at all frequencies within the range the horn exhibits constant coverage? Is that how it works? Or am I way off base? Quote Link to comment Share on other sites More sharing options...
John Warren Posted July 18, 2002 Share Posted July 18, 2002 (edited) for This message has been edited by John Warren on 07-18-2002 at 10:20 PM Edited May 19, 2016 by John Warren Quote Link to comment Share on other sites More sharing options...
lynnm Posted July 18, 2002 Share Posted July 18, 2002 OY! OY! - Auntie Em I'm Coming Home! Toto Bad Toto quit doing that to the calculator !AKA - These last few posts have demonstrated to me why I have never had any future as a mathematician but I am actually learning something. Great Stuff Guys! This message has been edited by lynnm on 07-18-2002 at 10:55 PM Quote Link to comment Share on other sites More sharing options...
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