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wesayso 26th October 2021 11:09 AM

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Well, obviously the area expansion is because of the larger diameter at that spot. So if you pinch the channel there in 2D the 3D area can remain constantly growing just like the center channel.

Shouldn't be too hard to figure out how to keep the length while making the area expansion behave like the center channel or at least have it expanding regularly.
Edit: the end of the channels should be pinched too while the center channel should expand more to get it close to equal area expansion in every channel.

mabat 26th October 2021 12:21 PM

Now I understand (I think), I'm only not sure that what you describe is possible. The current algorithm is definitely not able to make more than three "turns" of the meander, I would have to adapt that, and that would be a lot more complex.

aragorus 26th October 2021 03:47 PM

So the larger the radial offset, the thinner the channel by a factor (insert part of a circle area equation here)

That could maybe be done by multiplying all the X coordinates by a factor of x. It will ofcorse change the radius of the whole thing, but it could be adjsted afterwards..

wesayso 26th October 2021 04:44 PM

It might just work with the 3 turns, and calculated according to the area. It will look rather different than expected in 2D due to the changes in radial offset. But it would be quite interesting to see what results that would give. Making it based on equal area's.

Wasn't there a phase plug design by Dr. Geddes that had an equal area division?

Originally Posted by weltersys
The Summary Of The Invention (0013) states:
"In the Fresnel zone concept, each zone is of equal area. The number of zones is arbitrary except that there should be the same number at the diaphragm and the exit aperture and there are the same number of concentric annulus channels as Fresnel zones"
(0014) states:
"Usually, the phase plugs exit aperture is identical to the waveguides throat, or entrance.."

Dr. Geddes' Phase Plug Design

mabat 28th October 2021 09:26 AM


Originally Posted by mabat (
I'm not sure about the importance but it probably would be easy to adjust the channels to have the same area expansion. The center channel would need to bend as well.

FWIW, I tried the above (i.e. all channels had the same area as a function of length) and it didn't make a principal difference. So obviously it's only the total what matters.

aragorus 28th October 2021 12:43 PM

I see..
I'm trying to wrap my head around how to construct the wiggles such as their thickness should be decreasing (thus keeping the area) the further from the axis they go, with a factor 2*pi

mabat 28th October 2021 01:12 PM


Originally Posted by wesayso (
Well, obviously the area expansion is because of the larger diameter at that spot. So if you pinch the channel there in 2D the 3D area can remain constantly growing just like the center channel.

Only now I finally understand how did you mean that. That should be possible, I'll definitely try that. :up:

aragorus 28th October 2021 01:28 PM

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I've started from scratch...
1 single meander by the means of 2 bezier curves
then offsetting the curves by a factor, so that the area of the "disks" is the same.
For now I'm trying to make a straight "tube" with no expansion towards the mouth.

So if I want to offset the channel with X mm, every point gets offset by X - sqrt(X)

This gets me close, but I'm sure there is a better function that will get all the areas to be the same.

...when I get it close enough I'm curious to see how it will compare with the results for a straight tube

mabat 28th October 2021 01:41 PM

I'm really curious about the outcome.

- I use an iterative calculation method to get the channel lengths equal. Not very pretty but effective. I doubt there is a simple analytic approach but maybe there is. To vary the widths of the channels to get a monotonically (exponentially?) increasing total area should not be very difficult. Seems like a straightforward extension to what I already have - first I construct the center lines of all channels and then set the widths according to some rule, which can be anything.

aragorus 28th October 2021 02:04 PM

Yes, that is a good approach!
I'm trying to do it in a parallel way with grasshopper even though it's a bit more time consuming to get the logic together. It's pretty intuitive after that.

The way I would like to tackle it is to start from the center and offset outwards for every channel. Not 100% sure it will work getting the equal lengths in the end but it's a good exercise :D

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