Sato/WE long Tractrix vs expontial

I'm going to make a midrange Sato style horn for one. Unlike all other horns I've seen, mine will be round becauce it is turned on a lathe. However, a part must be made manually, as it is not a straight horn, but curves like a Sato/WE or a Fibonacci spiral. My way of doing it, if I can, means that I don't have to blend round and square. His current horn is shown here. I have seen that WE/Sato has an exponential flare, but the horn he has now is quite long compared to the area of his mouth. It is 1.6 m and the mouth is 58x58 cm. I have not calculated exponentially, but if you have a Traxtrix horn, then a round Traxtrix horn with a diameter of 58 cm will be approx. 60 cm long if the throat is 2". If the throat is 1" it will be longer. The person I am making the horn for would like it to be long (approx. 1.6 m) because it goes deeper, he says, if it is that length. My question then is if I can make a tractrix horn that I just stretch to get that length or will it be some DIY nonsense. It should go down to 200-300 hz. A straight tractrix horn of 58 cm has a cut off of approx. 200 hz, but it only works effectively down to maybe 300-400 Hz. But will the extra length make it go deeper.

The new horn doesn't need to curve like the old/shown horn, but because of the length it can't be straight so it has to curve somehow. I know I just posted about this horn, but that was a different issue.
 

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It is normal to make the cutoff at least an octave below your cross. You also want to limit your bandwidth with this kind of horn because the DI varies as much as it does.

If you want to find a shorter exponential for midrange, look at a T=0.8 Le Cleac'h
 
The opposite is true. I want to make it long, or rather make him I have to make it for. He says the 1.6m length helps the horn go deeper. I have made a straight tractrix horn with a diameter of just under 60 cm, with a cut off of 185 Hz. It is just over 60 cm long as it starts at 2" (50 mm). The Tractrix formula the formula gives length, diameter and the shape when you choose the cut off and throat. I agree that one octave higher (x2) has also looked down to x1.5 of the cut off. In any case the cut off should be somewhat lower than where the horn is effective. He wants the horn to be longer than what a tractrix or expo form says as he thinks the horn can seem deeper because of the length. It was therefore my idea to simply start from the tractrix possibly expo but simply stretch the horn so that the area expansion happens more slowly. Does the extra length help, or is it just a homemade philosophy. If you saw the horn as a quarter wave horn, then 1.6 m would go very deep, but it's probably just a bump, like a bass reflex tuning.

I can also ask in another way, would you be able to make the horn play deeper by making it longer without changing the diameter of the mouth, i.e. stretching the horn or the formula you follow. I can't make the mouth bigger than 58-59 cm, but I can change the length, and that's also how he wants the horn, as he wants a twisted and somewhat prettier version of the horn he has. But I just want to make sure that it also works as it should, i.e. goes down to around 200-300 Hz.

The horn shown is 58.5 cm in diameter and 63 cm long, and has a cut off of just under 200 Hz. However, he cuts at 600 Hz so it goes plenty deep.
 

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Putting aside the need to analyse an individual horn for resonances, because these could unexpectedly contribute to one's experiences...

I am occasionally sceptical when asked about these things because I know that you can get low end out of short horns but you have to boost it. Is your friend one who compares horns without measuring and equalising them first ...and considering their relative directivity and room contribution... before declaring one has better bass?

This is why I asked the questions I did on the other thread...
https://www.diyaudio.com/community/threads/sato-we-horn-and-high-frequencies.394930/post-7247588
 
He says the system plays great. So in reality he is only interested in getting an aesthetically better look. It's just me complicating it, as I'm new to horns and therefore want to understand if his system actually delivers what he thinks it does. They are absolutely not measured. He will definitely still like the sound as I don't think that a round horn without the edges that are in the existing horn will make it sound a bit better. But my question is if there were any bigger things for the sound that you could turn up than the small percentages a smooth round horn gives versus the way the horn is now made. I will also be able to use that in future projects if I can make this horn. I have never seen one round before, and it will also be able to be semi-turned as it spins around too. It's unknown land and it will take hundreds of hours to make so I might as well try to make the best of it.

But he really just wants me to make it roughly like the snail it is, as he says it sounds fantastic. So if that's what we agree on, I'll probably refine the snail curv a bit so that the center of the curvature follows a fibonacci spiral. So the area will be a tractrix I stretch out so that it will be 1.4-1.6 m long.
 
So I guess it's fair to say that you are expected to rebuild this more or less how it is now, except that you would like to improve it if that's possible, and don't want to make it worse in the process.

Tricky. I'll tell you the following for your own benefit.

I think you should know that long horns like this tend to give group delay issues at the low end (large phase changes) which may not sound too good and which may warrant a steep crossover. Ironically a waveguide is better in this regard, even after they are equalised. A waveguide loads too, but eventually you need to cross it.

Regarding that, crossing can introduce errors too, especially if not done with careful measurement, but especially with horns like this which have a varying directivity that produces a mismatch. On the other hand some people are just reluctant to cross, or maybe they tried under the wrong circumstances and had better luck avoiding it.

Furthermore there are resonances which I mentioned in the other thread.

The solution to much of this is to model the horn in hornresp, analyse it and make your own assessment of what your friend is hearing. Some people like distortions. I don't envy your task.

At the top natual rolle off.
Your suggestion that this horn has a natural rolloff is difficult to categorise. I would not say that about it. Either it has a point that matches the tweeter, or it is being used into excess for some reason.
 
I also looked into the time delay thing as one of the very first things when I asked on FB. The bass unit cuts with the 6th order, i.e. 36 dB against the midrange, but the midrange only cuts with the 1st order against the bass, but the fact that the horn no longer works in the deeps means that, purely acoustically, the cut is much steeper than 6 dB (is that right). So the cut between bass and midrange horn is probably reasonably sharp. I actually had bigger concerns between midrange and super tweeter. This is where the midrange naturally rolls off around 12-14K Hz. So the super tweeter complements at the very top. Here my concern was between phase and anti-phase as the wavelength at 13 K is 26 mm. Saw Dannie from GR Research make a video about a super tweeter for a full range speaker to help with the upper treble. 1 cm is very important for whether it is in phase or out of phase. In addition, the midrange driver is perhaps 1 m further back than the super tweeter. I was thinking of making a 3rd thread about that, but fine to take it here. The Horn Solution from Germany has a sato horn and they also have a super tweeter inside the horn (which I also have in this system), here the sound must also be delayed. However, they cut around 5-7 K Hz, so the wavelength is everything but double, but still small. But all Sato horns will have that fault.
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the midrange naturally rolls off around 12-14K Hz
What would the dispersion be like there, anything more than a wisp? Do you expect to cross at the same level to the supertweeter if it is wider?

With the supertweeter in the mouth you won't cover phase without delay. Perhaps you could go for a power cross instead. Will you be measuring?