jwc Posted December 30, 2008 Share Posted December 30, 2008 Just got off the phone with JC. Maybe I'm wrong. I still don't know. JC explained to me that we were accounting for the height of the horn in our calculations of the side curve, so therefore the curve really is the "flare" of the horn. And as I'm talking to him on the phone that all makes sense and I'm feeling rather foolish about making such a stink. But I no sooner got off the phone and started looking at my plots and now I'm not sure again. The plotted curve ends up at 14.33", which is the centerline length of the horn, so it still looks like the center plane curve to me. UGGGGGH!! I don't want to figure this, I just want someone to tell me how to build it. I'm an idea person and a builder. The stuff in the middle, you know the stuff engineers do, that's just not my gig. JC, I think I'd like to go over these numbers and the resulting plots again with you, if you don't mind. Off to bed right now, busy work day tomorrow, guests tomorrow night, so I don't know when right now. But if you have time later this week I'd really appreciate it. Greg No problem...this trick works. Basically draw out a jig...that is a trapezoid. The center line down the middle corresponds to the length of the horn. The side walls are the inner surface of your flare. These outer wall of the trapezoid will be longer than the length of the horn. Yes...the top and bottom flares are longer than the total length of the horn. ALSO.....THESE flares drawn out with my technique (and jeremies I think) are flares that are Tractrix with modification to account for a change of vertical height down the horn. They are not tractrix flares down the center plane. In the end, you have a jig that is the same as the trapezoid you have drawn out and two flares for the top and bottom. jc Quote Link to comment Share on other sites More sharing options...
jwc Posted December 30, 2008 Share Posted December 30, 2008 Greg. When you come back and read this tomorrow, I realized that you and I got so caught up in the difference between the center plane and the top and bottom flares...that I didn't emphasize a step. You know when we were talking about that center line down the trapeziod? Well...you know 2" down the horn...You draw a prependicular to the trapezoid side walls then measure that length. Well....yes that is the height of the horn at that 2" location. But you need to measure the length down that trapeziod side line where it meets with the perpendicular line. We guessed about 2.1 inches. Well. when you are drawing out the modified flare for the top and bottom...the width of the modified flare is ............... The area at 2" of a tractrix horn divided by the height. This will give you a width measurement. We talked about this.........BUT..... When you draw out the modified tractrix flare, you need to use that width calculation down a center line to 2.1 inches. We can talk again. I want this to follow through......again we got so caught up in the understanding of the center plane vs top and bottom, I didn't stress this part of how to make out the top and bottom curves. jc Quote Link to comment Share on other sites More sharing options...
jwc Posted December 30, 2008 Share Posted December 30, 2008 because the wave front doesn't propagate as a plane. Oh yea.....no doubt. But no way I can account for that. That is for the bigtime pros. This isn't the point of Greg's concern.......But I can make a perfect tractrix expansion not accounting for some bubble phenomenon. jc Quote Link to comment Share on other sites More sharing options...
DrWho Posted December 30, 2008 Share Posted December 30, 2008 You can make the horn with the correct area at a certain length. Round or not. You can certainly make a horn of any shape have the same cross sectional area as the circular cross section of the tractrix horn. But my point is that, even if you do THAT perfectly, you still haven't correctly translated the area expansion of the actual wave front because the wave front doesn't propagate as a plane. And......I tell people not to rely on the calculations provided by calculators. When I design tractrix horns I use my own tractrix calculator, because that way I know exactly what assumptions it uses. I use my own calculators too [Y] It also forces you to understand what you're doing too. Btw, how are you defining tractrix for non-round horns since it seems you're claiming the tractrix horn is not a specific area expansion? Quote Link to comment Share on other sites More sharing options...
greg928gts Posted December 31, 2008 Author Share Posted December 31, 2008 Greg. When you come back and read this tomorrow, I realized that you and I got so caught up in the difference between the center plane and the top and bottom flares...that I didn't emphasize a step. You know when we were talking about that center line down the trapeziod? Well...you know 2" down the horn...You draw a prependicular to the trapezoid side walls then measure that length. Well....yes that is the height of the horn at that 2" location. But you need to measure the length down that trapeziod side line where it meets with the perpendicular line. We guessed about 2.1 inches. Well. when you are drawing out the modified flare for the top and bottom...the width of the modified flare is ............... The area at 2" of a tractrix horn divided by the height. This will give you a width measurement. We talked about this.........BUT..... When you draw out the modified tractrix flare, you need to use that width calculation down a center line to 2.1 inches. We can talk again. I want this to follow through......again we got so caught up in the understanding of the center plane vs top and bottom, I didn't stress this part of how to make out the top and bottom curves. jc If you look at the numbers that the calculator spit out, the last number is 14.33, so the calculator is not accounting for the extra needed for the "flare" curve, it is giving us the center plane curve. I verified this by plotting it out, and the curve ends at 14.33 and 24" just like we asked it to do. The calculator is accounting for the vertical angle as it is figuring the horizontal curve, as you spoke of, but it IS giving us the center plane curve, not the "flare" curve. If I'm understanding you correctly, you have a trick, that in essence adjusts the numbers down the horn path so the curve spreads out a little and ends at the longer measurement, thus giving us the "flare" curve. I would remind you that this is not a linear adjustment. How will we determine what the adjustment should be at each cross-section point? 2.1 sounds like a guess, what will it be at the 2-1/2" section, 2.65? Is that just a guess too? I'm not being snotty here, I just want to make sure we're actually calculating something that makes sense. Greg Quote Link to comment Share on other sites More sharing options...
Marvel Posted December 31, 2008 Share Posted December 31, 2008 3) We really have not been calculating the lenght of the side walls as we bend the wood. There is probably a calculus solution. I've used a spreadsheet to calculate use a running total with a Pathagorian (sp) calculation. It is quite un-necessary because the side wall is maybe 130 percent of the center axis and were just bending thin ply.and that sort of overage doesn't cost much. You can just use a piece of cardboard once the top and bottom plates are in a jig to find the needed lenght. Best, Wm McD Erik Forker has this in his calculations and listed as 'stretch' numbers for the side wall in his spreadsheet. As an example, one of the speakers I was working with had a distance from throat measurement is 217mm, but the side wall, being longer because of the curve, came out to 238.4mm. My email to him is why not put calcs in for the top/bottom (a 1.4inch stretch in Gil's case)? I think he already does it, since he actually generates script files for Autocad that plots the curves...My two cents... and I think you are all pretty much saying the same thing, but the more you try to explain the more confused everyone gets. [] Bruce Quote Link to comment Share on other sites More sharing options...
greg928gts Posted December 31, 2008 Author Share Posted December 31, 2008 My two cents... nd I think you are all pretty much saying the same thing, but the more you try to explaing the confused everyone gets. Bruce Yes, this is true LOL, but there are subtle things mixed into all this mess that we are working out. Greg Quote Link to comment Share on other sites More sharing options...
Edgar Posted December 31, 2008 Share Posted December 31, 2008 Btw, how are you defining tractrix for non-round horns since it seems you're claiming the tractrix horn is not a specific area expansion? I'll answer in reverse order. A tractrix horn definitely can be interpreted as a specific area expansion. That's just simple geometry. But, since acoustical waves in the horn don't propagate as plane waves, the actual area of the curved wave front will always be somewhat larger than the calculated area of the circular cross section of the horn. For non-round horns the effect of this curvature can range from insignificant to profound. For a horn of square cross section, that expands as a tractrix in two dimensions, the area error between the square bubble and the square plane is probably about the same as the area error between the round bubble and the round plane, so a square horn should behave very much like an "equivalent" round horn. For a horn of rectangular cross section, that is tractrix in one dimension and conical (or constant) in the other, the bubble error difference gets larger and is also dependent upon the aspect ratio of the rectangular cross section. But my point is that this is all of only academic value. As an engineer I find it interesting to analyze, but the fact is that horns are very tolerant of modest discrepancies in the contour. Play around with Hornresp and you'll find that, as long as you don't get too extreme with the contours, all horns of the same length, throat, and mouth dimensions perform very similarly. (Bruce Edgar himself -- no relation -- has even stated this explicitly.) So to answer your first question: I don't worry about it too much. Sometimes, if I'm feeling particularly anal-retentive, I'll try to approximate the bubble shapes in my calculations, but mostly I just apply a small fudge-factor to the horn design (like most people do -- if you want to use a horn to 100 Hz, design a 70 Hz horn, for example), and otherwise don't worry about it. Edgar (Greg) Quote Link to comment Share on other sites More sharing options...
Edgar Posted December 31, 2008 Share Posted December 31, 2008 3) We really have not been calculating the lenght of the side walls as we bend the wood. There is probably a calculus solution. There is. Anybody want to see it? I'm open to suggestions as to how to post math equations to the forum. Quote Link to comment Share on other sites More sharing options...
Guest " " Posted December 31, 2008 Share Posted December 31, 2008 " -- if you want to use a horn to 100 Hz, design a 70 Hz horn, for example), and otherwise don't worry about it." ditto on this....much time and money would be saved applying this concept This reminds me of a recent IQ test I took. My duaghter took one and scored a 139 and wanted to know what my score was. I told her I know what my score is....it's a 129 to 131 and a 121 to 125 She said "explain". I said when I first take the test, I try real hard to get it right, mindful of the time, the number of questions, the number of questions I skipped, the probability of being able to go back to the skipped questions with any remaining time, and careful allocation of the total available block of unsued time to each individual question I skipped. I tippically have 5 - 10 minutes leftover, even after going thru the questions that I missed 3X. My score would always be a 129 to 131. However, If I retake the test right away, attempting to answer each question in 5 seconds or less, and not skipping any questions, and not caring about how to use the unallocated block of time, the test takes 4 - 5 minutes,and my score would be 121 to 131. So it boils down to the question if spending 8 times the amount of time is worth less than 5% improved results. Quote Link to comment Share on other sites More sharing options...
jwc Posted December 31, 2008 Share Posted December 31, 2008 greg. I'm at work and I'm not sure what time I will get home tonight...eventhough it is new years eve. I don't think I'm going to attempt an explaination on this thread. I made a ton of posts and I'm not able to get the point across. I think we should talk over the phone again. The trick works and I can't explain it here on the forum. Tractrix calculation is only a small portion. The trick has nothing to do with tractrix. I will tell you know with all confidence...it works. It will come together. jc Quote Link to comment Share on other sites More sharing options...
Marvel Posted December 31, 2008 Share Posted December 31, 2008 I'm open to suggestions as to how to post math equations to the forum. If they are mostly algebraic, a cropped screen capture might be the easiest. Have you used Mathcad? I would like to get this into Mathcad, so I can see the curves on screen and print out cutting templates. Bruce Quote Link to comment Share on other sites More sharing options...
Edgar Posted December 31, 2008 Share Posted December 31, 2008 Have you used Mathcad? I would like to get this into Mathcad, so I can see the curves on screen and print out cutting templates. No, my tractrix calculator is in C, and my drawings are in TurboCAD. And the equations are in Word, using Equation Editor. Quote Link to comment Share on other sites More sharing options...
tigerwoodKhorns Posted December 31, 2008 Share Posted December 31, 2008 3) We really have not been calculating the lenght of the side walls as we bend the wood. There is probably a calculus solution. There is. Anybody want to see it? I'm open to suggestions as to how to post math equations to the forum. Jpeg or PDF of hand calcualtions with a good old fashion mechanical pencil. EDIT: Oops, didn't see yoru later posts. Screen capture shoudl work. MathCAD. I have not heard that in years. Bring back memories. Quote Link to comment Share on other sites More sharing options...
Edgar Posted December 31, 2008 Share Posted December 31, 2008 Jpeg or PDF of hand calcualtions with a good old fashion mechanical pencil Okay, I'm going to attach this as a PDF, but I don't know how well it will work because it's four pages long. Tractrix Horn Path Length.pdf Quote Link to comment Share on other sites More sharing options...
bodcaw boy Posted December 31, 2008 Share Posted December 31, 2008 just a couple of things and then i am off.... 1. the tractrix equation describes area expansion. 2. there is no need to readjust the resultant area shapes for curvature. the equation already does this. 3. instead of thinking of curve, think of a set of areas shaped how you like stacked on top of each other. 4. making a horn is fun. have a great new year. roy 1 Quote Link to comment Share on other sites More sharing options...
Edgar Posted December 31, 2008 Share Posted December 31, 2008 Respectfully, Roy, I don't see how you can start with the defining differential equation for the tractrix curve (see the PDF in my previous message), and reach your conclusions 1, 2, and 3.Greg Quote Link to comment Share on other sites More sharing options...
bodcaw boy Posted December 31, 2008 Share Posted December 31, 2008 pretty easy, i don't. the tractix curve and the exponential and the hyperbolic and the conical and whatever curve you want to do, describes an area expansion at some point along the x axis. how each distributes the area is related to how each thinks the wave is propagating down the horn and how each thinks the loading should be. in all cases, assumptions are made but real world measurments can reveal some errors in our thinking. that is how dr post decided, in his paper, the error of assuming a flat plane wave, got us to think that an exponential gave the best power transfer. assume a spherical wave (the area propagation of the tractrix equation was not changed), then the tractrix gives the best power transfer. what curve the side view projects on a flat surface has little to do with the area expansion. so after many tests and many horns, what it comes down to is the area expansion of the whatever equation you got, and what geometry you want to use to for each slice of area. take care, roy 1 Quote Link to comment Share on other sites More sharing options...
Edgar Posted December 31, 2008 Share Posted December 31, 2008 pretty easy, i don't. the tractix curve and the exponential and the hyperbolic and the conical and whatever curve you want to do, describes an area expansion at some point along the x axis. I have argued that the tractrix curve describes a radius expansion that is translated into an area expansion, but it's a minor point that does not affect the current discussion. how each distributes the area is related to how each thinks the wave is propagating down the horn and how each thinks the loading should be. in all cases, assumptions are made but real world measurments can reveal some errors in our thinking. Exactly. I see now that I misunderstood your statements. We are in complete agreement here. that is how dr post decided, in his paper, the error of assuming a flat plane wave, got us to think that an exponential gave the best power transfer, Was that the recent JAES paper (within the past few years) where they analyzed the errors in the plane-wave assumptions behind Webster's equation? so after many tests and many horns, what it comes down to is the area expansion of the whatever equation you got, and what geometry you want to use to for each slice of area. Again, we are in better agreement than I originally thought. See my earlier comment, in which I said, "I just apply a small fudge-factor to the horn design ... and otherwise don't worry about it." Thank you and have a safe and prosperous new year. Greg Quote Link to comment Share on other sites More sharing options...
jwc Posted January 1, 2009 Share Posted January 1, 2009 greg928gts Did you get my email from last night? It is the holiday and I realize you may be out of pocket or maybe don't have access to email. jc Quote Link to comment Share on other sites More sharing options...
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