Spiral Cross Sections for WGs

[TN Allen]

Ed Lafontaine mentioned that the best cross section for an elongated waveguide would be a spiral. I have attached two images of spirals, one is the complete spirals, the other is the segment of the same spirals on just a 10"wide X 2.5" high rectangle which is similar to the range of waveguide height and diameter that has been discussed in various posts.

Some of these spirals have a .5" fillet or radius at their lower end.

I'd appreciate comments about the suitability of these spiral shapes for a waveguide cross section. This seems like a way to come up with something worthwhile to develop, mill and test. I'll be happy to do the CAD file and milling, perhaps Arlis and Ryan Bouma will be wiling to test a few more guides.

If someone wants .dxf, .dwg or other file formats files I can send these as well. Conversely if someone wants me to try a cross section and can send me a file, I'll try making it into solid geometry and milling it.

Edit, added file

[diy speaker guy]

I've been following the other thread but I got lost when you guys started talking about spirals. When I think of spiral I think of a corkscrew or a slinky, not a horn. And I have no idea what's going on in the 3 drawings you posted above.

What horns need is a horn shape. Like one of these.



Hornresp can be used to simulate all these profiles (except the Hughes) and many more, including the new Le Cleach profile, etc. And it's way simpler to simulate these than even a sealed box in WinISD. Basically all you have to do is enter the driver parameters, a beginning (throat) and end (mouth) cross sectional area and a number (in cm) for horn length, while specifiying one of the available flare options. You can even make multi segment horns instead of specifying a specific flare profile as well.

Then you can see frequency response, excursion, directivity, and all that good stuff (list below) before you build anything. The "try it and see" approach seems to be working fairly well for you guys but since it takes about 5 minutes to simulate these (and most of the 5 minutes will be entering t/s parameters) I can't imagine why no one is interested in doing that.

Once you have a simulation you like, Hornresp will report exactly how it's laid out - cross sectional area vs horn length. As long as you keep the cross sectional area vs distance from throat correct, you can make it any shape you like, the mouth can be circular, oval, rectangular, square, whatever, but the throat should be form fitted to the driver diaphragm shape.

Hornresp features: schematic, acoustical and electrical impedance, frequency response, excursion, phase, group delay, directivity response, directivity pattern, directivity beam width, directivity polar map, impulse response, impulse spectrogram, max spl (showing power and excursion limitations) and more...

[TN Allen]

These are two dimensional spirals. A part of a spiral, like a part of a circle might define the cross section of a waveguide. A corkscrew is a helix.

The software you describe is interesting, I'll look at it. Could you tell me how it is used it to produce a CAD file and tool path for a CNC machine.

Do you have an idea for an effective waveguide? If so, perhaps I can mill it?

[diy speaker guy]

These are two dimensional spirals. A part of a spiral, like a part of a circle might define the cross section of a waveguide. A corkscrew is a helix.

The software you describe is interesting, I'll look at it. Could you tell me how it is used it to produce a CAD file and tool path for a CNC machine.

Do you have an idea for an effective waveguide? If so, perhaps I can mill it?

I still have no idea what you are talking about wrt spirals, I guess I'd have to see a 3d image of a real spiral waveguide to understand.

Hornresp isn't used to produce CAD files as far as I know. What it does do is export a text file that describes cross sectional area at incremental lengths from the throat. Here's an example, csa displayed at every 2 mm starting at the throat and moving to the mouth. This is for a tapped horn project I did a long time ago, and it's only a small sample of the text file, the first 4.6 cm of the horn. For some reasoan, the columns of numbers are not spaced properly underneath the headings when I copied and pasted here, but the actual text file is much easier to read. For example, the UNI column is supposed to be directly under the Flare heading.

Length (cm) Area (sq cm) Radius (cm) Angle (deg) Height (cm) Width (cm) Width Flare
0.000000 67.700000 4.642152 0.957684 8.230000 8.226002 Uni
0.200000 67.797550 4.645496 0.957684 8.235898 8.231956 Uni
0.400000 67.895169 4.648839 0.957684 8.241796 8.237909 Uni
0.600000 67.992859 4.652182 0.957684 8.247694 8.243863 Uni
0.800000 68.090620 4.655525 0.957684 8.253592 8.249816 Uni
1.000000 68.188450 4.658869 0.957684 8.259491 8.255769 Uni
1.200000 68.286351 4.662212 0.957684 8.265389 8.261723 Uni
1.400000 68.384322 4.665555 0.957684 8.271287 8.267676 Uni
1.600000 68.482363 4.668899 0.957684 8.277185 8.273630 Uni
1.800000 68.580475 4.672242 0.957684 8.283083 8.279583 Uni
2.000000 68.678656 4.675585 0.957684 8.288981 8.285537 Uni
2.200000 68.776908 4.678928 0.957684 8.294879 8.291490 Uni
2.400000 68.875230 4.682272 0.957684 8.300777 8.297443 Uni
2.600000 68.973623 4.685615 0.957684 8.306676 8.303397 Uni
2.800000 69.072085 4.688958 0.957684 8.312574 8.309350 Uni
3.000000 69.170618 4.692301 0.957684 8.318472 8.315304 Uni
3.200000 69.269221 4.695645 0.957684 8.324370 8.321257 Uni
3.400000 69.367894 4.698988 0.957684 8.330268 8.327210 Uni
3.600000 69.466638 4.702331 0.957684 8.336166 8.333164 Uni
3.800000 69.565452 4.705674 0.957684 8.342064 8.339117 Uni
4.000000 69.664336 4.709018 0.957684 8.347962 8.345071 Uni
4.200000 69.763290 4.712361 0.957684 8.353861 8.351024 Uni
4.400000 69.862314 4.715704 0.957684 8.359759 8.356977 Uni
4.600000 69.961409 4.719047 0.957684 8.365657 8.362931 Uni

I think you'd have to draw that in CAD yourself, unless CAD can import a text file. I'm not sure any acoustical simulation program exports to CAD.

Anyway, in this example I've selected UNI for this text file example as I think that represents a circular cross sectional area the best. (You can also select CON(ical) or EXP(onential) and possibly even PAR(abolic) in newer versions, to better represent bass horns made from flat wood panels.

I've never studied small horns (tweeter waveguides) so I don't have any good examples, I'm just pointing out that this is what Hornresp was made for. I've never even tried simulating any of the classic horn curves so I don't even know exactly what features are available for those alignments. Up to this point I've only been interested (and simulated and built) bass horns.

Just FYI, the Hornresp model will only be truly accuate if you build it exactly as simulated - round cross sectional area, although you can build whatever shape you like as long as the csa vs length remains true to the model.

[Pete Schumacher ®]

He's talking about using a portion of a 2D spiral to define the cross sectional profile of a circular waveguide.

[diy speaker guy]

He's talking about using a portion of a 2D spiral to define the cross sectional profile of a circular waveguide.

Do you mean using a section of a circle (or in this case a slightly non round circle) to describe the flare rate? Like, instead of the traditional flares like conical or exponential?

[Pete Schumacher ®]

Do you mean using a section of a circle (or in this case a slightly non round circle) to describe the flare rate? Like, instead of the traditional flares like conical or exponential?

Pretty much. A spiral has a mathematically defined rate of curvature that is not circular at any point along the curve, since it never meets itself. Draw a spiral on a sheet of paper, take a section of that curve and use it to describe the flare.

[diy speaker guy]

Pretty much. A spiral has a mathematically defined rate of curvature that is not circular at any point along the curve, since it never meets itself. Draw a spiral on a sheet of paper, take a section of that curve and use it to describe the flare.

Ok, got it, I was thinking on the wrong axis. I think most of the traditional flare rates could be described as a section of a spiral. But there's an (almost?) infinite number of ways to draw a section of a spiral (overall size, tight or loose, or in other words, what fraction of the spiral is used) so that doesn't narrow it down much.

Choosing a random flare might not work out well. It might, but it might not.

[diy speaker guy]

Ok, got it, I was thinking on the wrong axis. I think most of the traditional flare rates could be described as a section of a spiral. But there's an (almost?) infinite number of ways to draw a section of a spiral (overall size, tight or loose, or in other words, what fraction of the spiral is used) so that doesn't narrow it down much.

Choosing a random flare might not work out well. It might, but it might not.

To add a bit more, this page http://fullrangedriver.com/singledriver/hornshape.html talks a bit about flare rates in layman's terms, and even includes formulas for calculating tractrix, exponential and expo/hyperbolic with your choice of M (sometimes referred to as T).

Of particular interest should be the description of which flares are best for certian frequency ranges. But also keep in mind that a waveguide doesn't necessarily have to be a full sized horn or follow traditional flare rates to achieve directivity and some acoustical gain effects.

[edlafontaine]

Ed Lafontaine mentioned that the best cross section for an elongated waveguide would be a spiral

Ahem...Sorry to be so late in joining this discussion. My comment about the comparison between waveguide sections was stated as "general" in nature. It was meant to highlight that the circular profile can be bettered by others.

May I suggest some "names" which might aid the discussion? ...just trying to get on the same page...

Theta is ½ the entry angle included within the waveguide...where the driver attaches to the guide.

Throat radius is the dimension where the driver attaches to the guide. This is a front view reference.

Transition radius gives the curvature from the conical section of the guide to a baffle. This is a side view reference and is user defined.

The conical section is where the radiation pattern of the guide is set. It may be very short in a dome tweeter waveguide.

Total waveguide depth, d, can be arrived at by choice. It is inter-related to the other dimensions.

Do we need a term such as "throat curvature", where the curve may be circular, spiral or some other mathematical function?

From that, would "transition curvature" also be helpful?

[TN Allen]

Thank you for the clarification, I was using terms I use to describe the layout of machined parts in general. I know very little about the technical aspects of waveguide design, and consequently ask for ideas about the shape these guides might take.

It would be great to have some informed ideas to try. As it is, I'm trying shapes to sort out the CAD and milling problems.

[edlafontaine]

http://libinst.com/OS_Spreadsheets/

A benefactor has graciously posted the excel worksheets for the elliptical and round (axisymetric) OS waveguides.

[TN Allen]

Do you mean using a section of a circle (or in this case a slightly non round circle) to describe the flare rate? Like, instead of the traditional flares like conical or exponential?

Yes, one of the thumbnails I posted is the full spirals, the other two are segments of the same full spirals. As I recall Ed Lafontaine wrote that the tighter part of the spiral should be at the throat and the more relaxed part at the mouth.

I've been trying to think of a natural analog to this regarding sound, unsuccessfully, but it seems an elegant possibility to me.

Perhaps next week I can spend some time doing geometry and milling something to try the spiral section in an elongated waveguide. It probably would be good to do a round guide with the same section as well. But again, ideas are welcome and I'll share the results for testing.

[Pete Schumacher ®]

Yes, one of the thumbnails I posted is the full spirals, the other two are segments of the same full spirals. As I recall Ed Lafontaine wrote that the tighter part of the spiral should be at the throat and the more relaxed part at the mouth.

I've been trying to think of a natural analog to this regarding sound, unsuccessfully, but it seems an elegant possibility to me.

Perhaps next week I can spend some time doing geometry and milling something to try the spiral section in an elongated waveguide. It probably would be good to do a round guide with the same section as well. But again, ideas are welcome and I'll share the results for testing.

Well, sound falls off from a point source as the square of distance, so you could look at that as one form of spiral.

[ryanbouma]

I don't know much about hornresp, but I have a few concerns.

First, these are dome tweeters we are looking at using. As such, the match between the dome and the waveguide isn't very predictable in hornresp. Again, I may be wrong as I have very limited experience with hornresp.

Two, we are looking at relatively shallow waveguides and so the throat angle is also quite shallow. Can hornresp consider this?

Last, the directivity produced by hornresp doesn't consider the directivity of the driver, afaik. Around 10khz, the directivity of the typical dome tweeter prevails over the waveguide, is my understanding. Again, am I wrong that hornresp can't consider this?

Thanks.

[diy speaker guy]

I don't know much about hornresp, but I have a few concerns.

You are right to have concerns, no model is perfect, but the more accurate data you can include the better the model will be. Anyway, everything has an effect and in fact some people are FAR more concerned about the diaphragm/throat transition than anything else. For example, if you make a square throat for a round diaphragm the result will probably not be good. A bit of common sense in this area will go a long way though.

But there have been an awful lot of posts lately asking what will happen if certainly changes are made, like directivity vs horn length and stuff like that. How do you know how low a horn will go? How big does the mouth need to be? How long should the horn be? It's a lot easier and quicker to get a handle on what's going on with simulations, rather than prototype and measure.

First, these are dome tweeters we are looking at using. As such, the match between the dome and the waveguide isn't very predictable in hornresp. Again, I may be wrong as I have very limited experience with hornresp.

It would be possible to actually model everything past the diaphragm (like whatever portion of the flange is inside the throat) as part of the throat. But then it would be a complicated multi segment horn, and not necessarily practical to do every time.

Two, we are looking at relatively shallow waveguides and so the throat angle is also quite shallow. Can hornresp consider this?

This might be an issue as well, but even if so, an educated guess is better than none, no? You might get a warning but it will still do the simulation to the best of it's abilities.

Last, the directivity produced by hornresp doesn't consider the directivity of the driver, afaik. Around 10khz, the directivity of the typical dome tweeter prevails over the waveguide, is my understanding. Again, am I wrong that hornresp can't consider this?

Thanks.

I have no idea, I've never looked into Hornresp's directivity much since I've only been interested in bass horns. It doesn't matter all that much anyway, since if you change the shape from a completely round csa when you build it, directivity will be different than simulated anyway. But again, an educated guess is better than nothing, no?

I'm not suggesting that the software should be trusted implicitly, all software has limitations. The fact that you realize this, and you actually know what the limitations might be is great. But some people aren't familiar with the physics of horns at all, I'm just suggesting that Hornresp can be used to answer some of the questions they might have.

[ryanbouma]

Fair enough. Nice reply, thank you.

I agree, an educated guess may offer a lot of benefit. It's funny cause, I'm pretty impressed with 2 of the waveguides TN Allen sent me. I told him in an email he must have good ears to get it developed so well the first time. He humbly replied it was a total fluke

[diy speaker guy]

Fair enough. Nice reply, thank you.

No problem. Check the "help" file for more info on exactly what Hornresp can and can't do.

And btw, since you need t/s parameters, and since they are rarely give for tweeters, you might actually need to have (and measure) the t/s parameters to even start simulating.

[TN Allen]

It was just dumb luck, based upon the Zaph .pdf plot. From what I have seen on the forum there is very little practical simple information about designing waveguides and particularly about designing them for a specific tweeter. If Hornresp can do this, that would be great.

Someone else suggested a program in an earlier forum discussion that he uses to design and mill waveguides, I'll try to find it. He also had photos and detailed descriptions of the guides.

Fair enough. Nice reply, thank you.

I agree, an educated guess may offer a lot of benefit. It's funny cause, I'm pretty impressed with 2 of the waveguides TN Allen sent me. I told him in an email he must have good ears to get it developed so well the first time. He humbly replied it was a total fluke

[diy speaker guy]

It was just dumb luck, based upon the Zaph .pdf plot. From what I have seen on the forum there is very little practical simple information about designing waveguides and particularly about designing them for a specific tweeter. If Hornresp can do this, that would be great.

Yup, that's what Hornresp is for. If you are truly interested, I'll look into how to address the tweeter's back chamber. I'm assuming that you just input the t/s parameters as measured with back chamber in place, and then simulate the horn looking at only the cone's front side emission. If you are serious about trying the program I'll verify (and if necessary correct) this assumption with the program's author.