greg928gts Posted December 29, 2008 Share Posted December 29, 2008 I hate to open up this can of worms, but I can't help it, I think of these things. Hard to explain, so please bear with me. When we use a tractrix horn calculator to give us the expansion rate of a proposed horn, we are given a series of measurements/numbers that correspond to points, that when plotted out on graph paper, provide us with the angle of the top and bottom of the horn pathway, and also for the curve of the sides of the horn pathway. When we plot out the angle for the top and bottom, it's pretty straight forward, it's simply a straight line that is plotted at an angle, that when built, will give us the desired height of the throat and mouth of the horn. When we plot out the curve for the sides of the horn, the resulting curve provides a controlled expansion (in the tractrix curve) that when added to the expansion provided by the top and bottom angled pieces, adds up to the total expansion needed for the horn. How are we doing so far? O.k., here's the thing. I think the curve that is being calculated AND plotted out on graph paper according to the measurements/numbers provided by the program, for the sides of the horn, is the center plane of the horn, the mid-plane of the horn; and thus, when cutting the curve into the top and bottom pieces of the horn, that curve must be modified slightly because those pieces are at an angle to the center of the horn. In the picture below, there is a template of the top or bottom of a horn on the left and the calculated curve on the right (cut into a piece of wood). Notice that the curves are different. I have adjusted the curve of the template on the left, so that when it is tilted up (at the angle it will be at when the horn is built), the curve matches the calculated curve of the center plane of the horn, or the piece of wood on the right. If I hadn't made this adjustment in the curve of the top and bottom pieces, the curve of the sides of the horn would be slightly different than the calculated curve. Another thing - the curved side of the horn is a curved plane; in other words the curve isn't different from top to bottom of the curved side. The reason there is a difference in the curve of the top and bottom pieces is because they are sitting at an angle. It's that angle that makes the curve different. Deep breath. So, I'm sure there is a slight difference in the curve of the cut of the top and bottom pieces of the horn, versus the curve at the center plane of the horn. What I'm not sure of is which curve the tractrix calculator is giving me. I'm also not sure it matters with the sound of the horn in the end. I just like to do things the right way and I want to know. Here's what I believe to be true and why. Because the side plane of the horn is the same up and down the side, I believe this is the curve that is being given to us by the calculator (which, BTW, is the same curve as the center plane of the horn). Furthermore, because we are plotting it out on a flat surface (the graph paper), just like we are the angle of the top and bottom pieces, this too leads me to believe that the curve given by the calculator is the center plane of the horn. So, in conclusion, I believe the curves of the top and bottom pieces need to be modified slightly to account for the difference of angle, so that the side curve of the horn stays the same as the calculated curve. My second conclusion; this is not the part of the hobby I enjoy. Greg Quote Link to comment Share on other sites More sharing options...
capo72 Posted December 30, 2008 Share Posted December 30, 2008 I understand the point you are trying to make, but I think you are only taking into account one factor of the expansion, the curve. I always look at the tractrix expansion as an area measurement. The square throat being 0, at any givin point away from 0 and toward the mouth you should be able to take an area measurement (cross section) and verify a true tractrix expansion. Since the top and bottom expansion is fixed because of its constant angle, only the side to side (curve) can be changed to correct the area at any given point. When checking the width dimension of the area you would be using a point on the curve you layed out straight across to the midpoint of the curve on the other side. I'll see if I can draw something in my 3-D design software to illustrate what I mean. You are correct in thinking that the curve we plot is in the middle of the curved side, but its purpose is to set a horizontal width for an area measurement that calculates out to a tractrix expansion. When you draw a tractrix curve as you have shown on your template, then you tip it at the angle needed for vertical expansion and redraw by tracing your curve with a fixed vertical pencil, as I assume you have done on your piece of wood, you no longer have a tractrix curve as the area has increased in the horizontal axis of your area measurement. Hopefully i'll have time today to draw up what i'm trying to explain. I hope this all makes sense. I think you raise a point that is confusing for many people, so my intent is trying to explain my take on this, not to prove you wrong Greg. I respect you talents and can't wait to see what you come up with for a horn. BTW, as an engineer, this is the part of the hobby that I enjoy. Jeremy Quote Link to comment Share on other sites More sharing options...
greg928gts Posted December 30, 2008 Author Share Posted December 30, 2008 Am I right or wrong? The curve that we cut into the top of the horn piece is different than the curve we plot that is the center of the horn? Edit: No, I said that wrong. The curve that IS cut into the top of the horn piece is different than the curve at the center plane of the horn? I found them to be different, but if you say no, I'm going back to my shop to try it again. I think that if you use the calculated curve of the center plane of the horn to cut the top and bottom pieces, that will change the curve, and therefore the width expansion at the center plane. If you've used the calculated curve to cut the top and bottom pieces of the horns you've built, try taking that curve (cut out of the graph paper, or a piece of wood) and hold it up to the center plane of the horn and see if it matches. Please. Please prove me wrong, or right! I don't care, I just want to figure this out in my head so I can start building a horn. Greg Quote Link to comment Share on other sites More sharing options...
Edgar Posted December 30, 2008 Share Posted December 30, 2008 Am I right or wrong? You are right. This is a bit intricate, but I have made some drawings that I will include in the next several messages. The first shows a tractrix curve laid-out on top of a square block, as if you were going to cut it out on a band saw. Quote Link to comment Share on other sites More sharing options...
Edgar Posted December 30, 2008 Share Posted December 30, 2008 The next shows what happens if you really did cut it out on a band saw. Quote Link to comment Share on other sites More sharing options...
Edgar Posted December 30, 2008 Share Posted December 30, 2008 This next one shows what it looks like after cutting the top and bottom angles. Quote Link to comment Share on other sites More sharing options...
Edgar Posted December 30, 2008 Share Posted December 30, 2008 The fourth image shows both the original flat tractrix curve and the resulting solid. Quote Link to comment Share on other sites More sharing options...
Edgar Posted December 30, 2008 Share Posted December 30, 2008 And, finally, the fifth image shows what happens when you lay the original flat tractrix curve on top of the resulting solid. They definitely do not match. That is because the tractrix curve designates the centerline of the horn, not the top and bottom. Quote Link to comment Share on other sites More sharing options...
Marvel Posted December 30, 2008 Share Posted December 30, 2008 Greg, You are certainly correct. I've emailed Erik Forker to ask about his srpeadsheet tractrix calculator, One of the colums of data (for the sides) is marked as stretched. This is because the actaul length of the sides is longer than the top/bottom pieces. I would think the formulae forcalculating the top/bottom could be changed to reflect whatever the actual length of those pieces will be (easy for me to say, since I'm not doing it). Then the plots would be correct to cut flat, and be 'right' once elevated. Hopefully I will hear back from him soon. Bruce Quote Link to comment Share on other sites More sharing options...
Marvel Posted December 30, 2008 Share Posted December 30, 2008 Edgar, Nice! This will help explain the situation to a lot of people. Quote Link to comment Share on other sites More sharing options...
capo72 Posted December 30, 2008 Share Posted December 30, 2008 When I get home tonight, I will stick my wood template inside my horn to see how it matches up. I understand where you are coming from. I think that because we sand the edges of the top and bottom back square to the sides we have the same curve although it may be shifted back toward the mouth. I would really like to draw this stuff up 3-D to test some different ideas, but my boss just gave me a big design project, so my free time at work is going to be at a minimum for the next few weeks. Jeremy Quote Link to comment Share on other sites More sharing options...
capo72 Posted December 30, 2008 Share Posted December 30, 2008 Thanx Edgar, I guess I don't need to draw this up now. What you've shown proves Greg's point. So is this not accounted for in the calculator? I guess not according to Bruce's conversation with Erik. I'll see if I can run some new curves and compensate for the stretch and plot them out. I had other plans for this long holiday weekend, you guys have screwed that up [] Now I'm going to have to get back to the shop. BTW I sent jwcullison a JBL 2482 driver to test on the horns GotHover built. It will be interesting to see how this horn tests. If it tests well and sounds good, then are we wasting our time here? Jeremy Quote Link to comment Share on other sites More sharing options...
colterphoto1 Posted December 30, 2008 Share Posted December 30, 2008 Did you guys just hear a collective SIGH of relief? I understood Greg's confusion and was baffled myself. Thanks to Edgar for the splendid drawings and simple explanations. Everybody got your band saws warmed up? M Quote Link to comment Share on other sites More sharing options...
colterphoto1 Posted December 30, 2008 Share Posted December 30, 2008 where do we plot Roy's 'bump'? arrrgghhghghghghg Quote Link to comment Share on other sites More sharing options...
jwc Posted December 30, 2008 Share Posted December 30, 2008 Guys. When we use the "calculators".....some of us use it differently. I completely ignore all the info about streched sidewalls and such. I focus on the area at a certain length. Now I've build horn with no vertical expansion. Well...then I guess what you are calling "center plane" will be the same from the bottom of the horn up to the top. Like in Edgars first few drawings. Now if you have a "known" vertical expansion. Lets say at 4" along the center of the horn....you know a line from the center of the throat to the center of the mouth. Yes 4" from the throat.....Let's say the calculator for tractrix (not all the extra stuff that "calculators" give you) wants the area at 4" to be 35 sq in. Well.....if you know exactly what the hieght of the horn is at 4" from the throat.....then can't you calculate the width of the horn at 4". For instance.......if you know the horn will be say 5" tall at 4" from the throat. You know the tractrix formula dicates a 35 sq in area at that location......then won't the width of the horn at that 4" location be 7"? jc Quote Link to comment Share on other sites More sharing options...
Edgar Posted December 30, 2008 Share Posted December 30, 2008 where do we plot Roy's 'bump'? arrrgghhghghghghg It is all an approximation. The original tractrix horn design had a circular cross section. When designing circular tractrix horns, I approximate the wave front with a section of a sphere. It's not perfect, but it's a lot closer than using a planar wave front. For non-circular horns, it gets even more complicated. Greg Quote Link to comment Share on other sites More sharing options...
jwc Posted December 30, 2008 Share Posted December 30, 2008 Greg. The flares you showed us. Did you say the one on the left "lines up" with the one on the right when you tilt up the mouth edge to the appropriate height of the horn mouth? Is this what I understand you to say? jc Quote Link to comment Share on other sites More sharing options...
colterphoto1 Posted December 30, 2008 Share Posted December 30, 2008 Greg. The flares you showed us. Did you say the one on the left "lines up" with the one on the right when you tilt up the mouth edge to the appropriate height of the horn mouth? Is this what I understand you to say? jc I don't think it should, it's a different curve. Quote Link to comment Share on other sites More sharing options...
jwc Posted December 30, 2008 Share Posted December 30, 2008 Jeremy. Look at image2 vs image3. Now the flare you drew out (after accounting for known vertical expansion) would be which one? You never drew out image2 from how I see it. Image2 would be the way you would draw out the flare if the vertical height of the horn stayed the same. But since you know yours would expand vertically....you drew out the flare in image3. Correct? jc Quote Link to comment Share on other sites More sharing options...
jwc Posted December 30, 2008 Share Posted December 30, 2008 In other words Jeremy, you never drew out the blue flare in image4. Yours was the red one from the beginning....right? If you were to draw out the blue...and let's say the height of that non expanding vertical horn is 12" throughout....then you would be assuming that about 4" from the thoat, the height of the horn would be like 12"H x 3"W. So you never drew out blue. you knew what the height would be 4" from the throat.....something like a height of say 3". then you calculated the width at that location because you know what the area was at 4" from the throat right down the center axis of the horn. Greg.....I think I know now what you have been calling the "center plane". The flare that I have drawn out isn't the "center plane". That would be the "blue" in edgars diagram. What I have drawn out...the flare.....is the red...as I know what the height of the 223Hz tractric horn is from thoat to mouth. So I basis my calculations are from the "center axis length of the horn". The flare doesn't represent the "center plane". jc Quote Link to comment Share on other sites More sharing options...
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