Constant curvature tweeter array

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I got fustrated with how my own simulations where not matching ABEC and so started simulating the B&C WG148-90 as it has measurment data available. Using this data I have managed fix my simulations; the issue was that I have not been using enough calculation domains and my source was acting as a dipole which was particularly affecting the horizontal polars. I forgot to do this as I have mostly been perfoming infinite baffle simulations recently. With this fixed I am able to simulate the WG148-90 and get data that coresponds to B&C's measured data. This also provides a useful reference on the performance of a simple waveguide. I have included the simulation files.

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Hpolar map comparison:
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Vpolar map comparison:
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some weirdness with simulations of this array but I think I understand. Firstly here are the vertical polars:
1679358363703.png

not very clean but kind of very roughly our target 60 degree. This is simlar to the unbaffled simple array at the start so expected. Hopefuly adding in vertical pattern control horns will help this.

Horizontal super weird at first:
1679358473345.png

hmm beam width has almost doubled. So I conducted a simulation of the horizontal polars of a single element but with a 45 degree tilt:
1679358568742.png


notice the high intensity spots in the 4-5k region corespond to the array also having high intensity spots in the horizontal. I think these are caused by tilted elements relative the plane the polar measurment is made in. So this also looks like it should be fixable with some vertical pattern control.

We have also ordered the compresion drivers which are Celestion CDX 1730 as we got a decent price.
 
Hi, seems reasonable but I'm afraid such vertical control wont fit in there physically. In other words it would probably compromize the vertical pattern by elongating the array, or make diffraction like in your earlier simulations. Not sure what is too much of a compromize so I guess its just some simulation time to find suitable system, then build few prototypes and listen which sounds better in the end.

Btw. was there reason why it needs to be curved? instead of curving physically you could perhaps make it straight array, delay the outmost drivers electrically if thats something that needs to be done to have the top octave wide enough?

What if you had four 15x15 axisymmetric devices arrayed horizontally? would fit inside mid horn though, long trumpets :)

ps. I think problem visualized is that the vertical pattern control of single device changes within the passband from narrow to wide, which creates the problem. If you want to reduce the problem you would need to hold the pattern for lower frequency or lose it really high already, so either deeper device or shallower device. But its always some sort of compromise on the graphs compared to a small point source. Perhaps some options sound better than others, even though they don't look that nice on the graphs? After all you are after more output so expect some compromises on somewhere, you should take the least audible ones, what ever those are.
 
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@tmuikku why don't you think it will fit? We are talking about 3khz+ and an ideal directivity of each element of 15 degrees. It's just adding flares of the same depth as the horizontal flare to the top and bottom of each element it requires no spacing increase.

Arraying the elements as a straight hang and applying electronic delay is a possibility but would require increasing the amp channel count and DSP capacity of our amp racks. Not to mention having to run more cable. I could design custom drive electronics and make this a powered box but this also takes quite a bit of time. If I can't fix things to my satisfaction then of course I will do it but I strongly prefer and array that doesn't require such things. I'm pretty sure a straight hang would need 5 elements as well as otherwise the two centre elements will be identical.

Re things not looking nice on graphs, yes for this type of array because it's subject to some combing and the graphs are normalised to an angle things often look much worse than they are. But if I look at specific positions in the intended listening window I do see +/-5dB variation in SPL relative to the normalising angle and those variations are low Q. The post EQ array as it stands therefore will sound pretty bad when eq'ed in some positions. My reference for this work are boxes like the Danley J7 for which .gll data is available for, they are far from perfect with lots of resonances and frequency response irregularities but they do not have this level of variation within the listening window.
 
Hi, I outlined the reason on the previous message, you'll get the diffraction because big enough roundovers won't physically fit without elongating the line and thus the graphs will look roughly as ugly, perhaps the sound is better though. This is what I chased in the previous post.

Its all because of wavelength, no matter how much the objects is twisted and turned and elongated its gonna interfere with the sound more or less. Its highly asymmetric source and object so the graphs will show more or less wiggle depending on angle unless its all collapsed to a single point.

You seem to know what sound better and what worse so go with that, try to get target response you know sounds good enough :)
 
Take the horizontal response.
1_S4b2QWJXiEMtNoM24tD-gA.png

Lets try imagination: Why there is hotspot at 66degrees of axis at ~4.5kHz on this normalized graph? since the four tweeter line has some curvature to it, below the 4.5kHz, on long wavelengths, the sources are roughly equidistant to observer, "depth" due to curvature of the line is relatively small compared to wavelength and response is uniform to all directions. Around 4.5kHz wavelength the depth starts to be significant enough. interference observed on-axis the outermost elements partially cancel with output from the inner sources, there would be dip on axis if you check out graphs that is not normalized. As you rotate the piece and take measurements further off-axis the path length differences reduces because the curvature to that direction reduces and the sources become equidistant from the observer and you get constructive interference at 66deg off-axis at 4.5khz. Normalized graphs shows these peaks off-axis since on-axis is "equalized" flat.

Above this frequency not much sound goes to far off-axis because the horizontal waveguides is big enought to have control on the sound and there is no such strong peaks past it. Also, on-axis, vertical beaming of the devices reduce interference between the inner and outermost drivers. Its all linked to wavelength and path length differences.

To "cleanup" the horizontal polar map you can reduce the curvature and/or increase vertical directivity of the initial horn segments by increasing their depth, also increasing size of the horizontal waveguide walls would reduce it a little bringing control to lower frequency. But this all affects also the vertical response so you'd have to find a suitable compromise.

Reducing curvature of the array would reduce path length difference at any azimuth you measure from on the middle plane, basically this ought to move the 66deg 4.5kHz hotspot higher in frequency and to more off-axis. If you simultaneously increase size of the horizontal waveguide reducing sound to lower frequency to more off-axis the off-axis hot spots on this normalized graph ought to reduce a lot. Still there would be some kind of a dip on-axis due to curvature, path length difference, but if its uniform to all axis you could EQ it at least some.

Perhaps try curved sources with waveguide that is not curved but straight? Directly in front of the device the outermost drivers are bit further away and you get your planned vertical response. But, also the horizontal response is pehaps more uniform and as you turn more to off-axis longer path length around the horizontal waveguides would keep the path length differences roughly the same regardless of azimuth while also reducing sound from the outermost drivers to the side as the waveguide is deeper at the ends of the array.

If the overall horizontal response is wider than you thought you need to increase depth of the waveguide, perhaps also the width if you need to keep narrow horizontal response to low frequency.

Since above is imagination without prior experience on such device it might be completely or partially wrong :D Hopefully there is something that helps you forward with it thought.

* Not sure if azimuth is the right word here, off-axis angle at horizontal plane where you take the measurements from (in simulator).
 
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I think your right @tmuikku I had a go at compare the 'adjacent element' horizontal polar to the horizontal polar. On a new horn that uses the same horizontal flare but has a (short) horn to control vertical directivity a bit better. However this short horn is not making a huge difference to vertical directivity as you would expect. The adjacent element is aproximatly offset by 0.135m and inclined 15 degrees (all this is without normalisation):
1679442131044.png


Horizontal polar:
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the 'adjacent element' polar:
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The adjacent element polar has a lot of similarity with the polars observed for the overall array. As the 0 degree is directly between the angular spacing for two elements this makes sense that this effect would be maximised. I wonder what the array looks like if I incline the horizontal polar to mid element (7.5 degree?). Arrays are much more messy than I am used to....
 
Features moved roughly octave up in frequency, as you roughly halved the path length difference ;)

Wavelength is a party poopper, you get interference on the graphs as long as your source is bigger than wavelength, for 20kHz this means you'd need < 1,7cm transducer. In addition, any objects nearby the transducer will affect and make another sources like reflection and diffraction, which again show various interference patterns to various directions with direct sound and other reflection and diffraction sources. Same with arrays, even if it was ideal transducer without physical construct floating in ether in simulator, but bigger than the wavelength, you would still have interference on the graphs and could optimize response for some particular spot compromising some other spot. Basic dilemma of physical 3D world and sound. All this means you need to be hyper aware of what is more or less audible and optimize the system and sound so that all the "bad looking things on graphs" are the less audible ones. I don't know so I'm relying on you to find out :) Just trying to cheer you up here as its interesting to follow what you come up with.

Few more paragraphs. Lets imagine you have the four tweeters array now optimized, pretty nice response what ever that is. Now shove the tweeter array inside the mid horn and the mids response is now ruined. Size of the tweeter array is about the size of wavelengths on the mid pass band and cause reflections and diffraction, it is acoustically big obstruction. By necessity the crossover band is ruined with such systems: to control tweeter pattern down to crossover you need crossover wavelength sized object for it, which has equally magnificent effect on the other transducer reproducing mids, and there is no way around this other than having huge gap between the high and low pass between.

Even if you miraculously halved size of the tweeter array it would still be quite big obstruction for the mids, more or less. When wavelengths is about 10x the object size then there is hardly any interference seen. So, hang 4" flanged 1" dome tweeter in front of a woofer you have to have crossover around 40" wavelength (~340Hz) to get about no interference of the tweeter on the woofers response, except the woofer behind would reflect sound from the tweeter because the tweeter is too small to control sound towards the woofer, and tweeters passband would show interference. It would be better embed tweeter in the woofer so that distance of the reflection is less than wavelengths involved, and one quickly arrives to TD products, single physical object with multiple (apparently small) sources :) which probably are about the best compromise and worthy copying I guess, at least they have lots of iteration and development behind.

Well, this doesn't mean you can't design and optimize such system in your plan, just expect there is going to be some wiggle on the response and you need to be find out whats audible and what is not, and how it shows in graphs and how to manipulate the system to get it less audible. You can make it look great and paint it red, as it looks super cool it must sound very good, right, and thats it, wiggles in the graphs fixed :)
 
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I think I can do much better than the sims so far though. I have been looking at the datasheet for the JBL VRX series and this looks much better:
1679499209973.png


looking at its horn it looks to have an increased density of density of the radiating elements and a lower curvature rate. So perhaps if I made my own 'line array waveguides' that equalised the path length from the compresion driver to my arc surface I would be able to get better performance. Saying that the VRX series do not seem to get good reveiws: https://gearspace.com/board/live-sound/1345423-jbl-vrx-non-line-array-environments.html

So my plan on what to do next is to try simulating a 'perfect' curved array with a gapless of curved source to check how that performs. If this works then next I will try to reduce the discretization of my array in the vertical by designing new waveguides.
1679499386460.png
 
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So it apears that the wide horizontal pattern is caused by just curving the array as I have performed an idealised simulation using a continous source and horn:
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Vertical polars (these are actualy quite good IMO, especialy as the array is just open at the top and bottom):
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horizontal polars:
1679522809901.png


hmm well this will have to wait a bit over a week before I can work on it again but it looks like the next avenue will be a straight array with electronic processing as I can't see this working without at least some processing on the elements....
 
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After a weeks break my thoughts are leaning towards a J7-95 style solution, in that a common horn will be used for the four HF drivers with four smaller horns meeting at a common rectangular throat with the sources curved by 'slicing' the fronts of the horns. This should fix the issues I see with the bent array:
1) Increased source density should reduce HF combing in the vertical polars
2) The horn mouth is no longer 'bent' and so the horizontal polar anomalies should be eliminated

Here is some more info about the simlar but larger J8-94 where the design is more clear:
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From studying this design and the J7-95 I see several key points:
1) For the J7-95 we have an overall height of 610mm with 8 HF drivers, this means that the HF horns are aproximatly 75mm tall. if we imagine that each HF horn has an ideal vertical directivity of 6.5 degrees (50/8) a 75mm tall horn will only attain this tight a vertical dispersion at ~50kHz. Unlike the arrays I have been working with the HF horns in the J7-95 have been sized to not have vertical pattern control.
2) There is no or very little horizontal expansion in the J7-95 and again the mouth is acousticly small
3) these two points combined means that the wavefront at the HF horns mouths aproximates a plane wave and not a spherical cap as a larger mouth size conical horn would have, see how the wavefront is less curved close to the throat, where the mouth size is small in this post: https://www.diyaudio.com/community/threads/horn-wavefronts.301517/#post-4933859
4) the HF horns are made by making prototype horns, rotating them and then removing any portion of the horn that protrudes beyond the original face plane to ensure a flat front, E.G this is a 15 degree horn:
1680454439639.png

I'm not quite sure what truncating the horn this way does. This means that there are two of each HF horn design for an even number of elements array.
5) The curved wavefront in the larger front horn is constructed from the smaller plane waves generated by the HF horns and their 'aiming'
6) The alternate left right splay is to increase source density and if kept small should have no effect as the dispersion of the HF horns is wide with respect to the outer horn
7) Vertical flare of the HF horns may or may not matter, on one hand the top and bottom horns been continous with the outer flare on their top and bottom surface I could be nice but on the other hand we have already established we do not have vertical pattern control.

So basicly for my design the variables are going to be more set by wanting to minimise the array size and how closley the compresion drivers can be packed. I'm also going for 15 degrees coverage per element which is ~3x a Danley box.
 
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Slight error in the previous post; slicing the front does reduce the HF horns mouth height slightly. This is small though and probobly not noticable in the images of the Danley horns.

Quick IB sim of this 22.5 degree 'aimed' hf horn:
1680826440354.png

The raw response is very resonant due to the parallel sides and poor termination but you can see that once the horn starts to control directivity it is aimed at 22.5 degrees (plot normalisation point):
1680826598311.png
 
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oops assembled the horns incorrectly in the above, notice that the angle of the top and bottom of the horns do not match the outer horn. The arrangment must be more like this:
1681084099981.png

inner horns have to be shorter than the outer horns for this to work to get the correct curvature. This will result in the need from some basic itterative software as the overall mouth size is also dependent on the horn length which affects the required waveform curvature....
 
Getting this far into HF horn design is further than I've bothered to go, but a potentially-ignorant question, if I may:

Why not use a single large-format driver per side? - I would expect one of the 2" coaxial units would keep up with the 4x 1" drivers you've chosen.

Chris
 
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@chris661 The tweeter array is for 3kHz+ so when you crunch the numbers 1" throat drivers have greater output. Particularly in practical use I have hit compresion driver limiting on our current system (3x1" comps per side) with mic'ed cymbals. The spectrum of these has a lot of energy where the senstivity of larger compresion drivers is lower: https://www.prosoundweb.com/how-to-ruin-a-mix-stop-enough-already-with-the-cymbals/ I also anticipate these will be flown and so overcoming air attenuation of the HF will be important. Additionaly this HF horn is removable so in the future we may use a greater number of compresion drivers in order to increase output as the midrange part of this coaxial horn can potentialy be loaded with the BMS dual diaphragm dedicated midrange for greater output.

I also had some more thoughts about how to practicaly construct these horns and belive the best way to start is with positioning the compresion drivers as close as posibile on two offset arcs wherupon the plane of the combined throat should become fixed in order to have the correct delays.