Line arrays. Understanding their behavior through simple modeling

I have used Akabak to simulate a 25 driver array in Wesayso’s Two Towers thread. I recall the vertical comb effects were predicted well. Also, the overall frequency response that showed the EQ needed to flatten the response was also predicted quite well. It was pretty easy to stack 25 sealed full range drivers. The trick was the limit of 55 nodes in the early version of Akabak.
I haven’t used Akabak but did some simulations of the McIntosh 25 element system. Some are in my AES paper. With the floor to ceiling types you are definitely in the near field. Something we will talk about eventually.
Do you have any graphs of your predictions?
 
Member
Joined 2009
Paid Member
Fluid and Wesayso must have some...

What i feel interesting in your approach with excel sheet is it gives insight of the 'important' phenomenon at work without giving too much details.
I like that, it is easy to get lost in details with simulators. Some are of importance other not... better spend time on the 'meat' before envision the inner details imo.
 
Member
Joined 2009
Paid Member
Got some days off and promised to my girlfriend they would be dedicated to her and kids, so i'll only have time at night for next few days ( and the 43*c today did not helped... 11:35pm and still 35*c... night will be long! And even typing on the tablet makes me lazy...).

Ronald, take care.
 
  • Thank You
Reactions: 1 user
well I did open the xls and play with it a little. I recognized the bessel array shading.

In the past I've modelled line arrays and various shadings in Vituix. Its a lot easier than writing your own spreadsheet and can bring in first order floor and ceiling reflections.

One of the more interesting shadings I explored in simulation was low passing outer array elements or groups of elements at the point where their contribution at the LP was 90 degrees out of phase with that from the central element.
 
As I recall, the Bessel array gives the same polar response as a single driver. That is both its strength and weakness. Combining is eliminated but you don't get the SPL of 5 drivers adding (almost) in phase. Bessel can be improved by only applying the shading above the frequency where combing becomes apparent but you are still left with a single driver at the top of the spectrum. I prefer a floor to ceiling array listened to at a good distance, since combing reduces with distance. At my 4m listening distance from my floor to ceiling arrays, I couldn't hear combing. Up close, 1m or so, its definitely apparent or at least some form of distortion I attributed to combing was.
 
At McIntosh one model was floor to ceiling. If you fed it pink noise and did deep knee bends a couple of meters out, there was a slight “swishswishswish” but it was hard to hear on music.

Note that my spreadsheet doesn’t normalize levels (except in plotting), so it reveals the relative gain of an array. So a straight 5 element array has a strength of 5. The Bessel array is a strength of 2, so yes, wasteful.

But, is it perfectly omnidirectional?
 
Member
Joined 2009
Paid Member
Hi,
No it's not omni. I was puzzled by the '5' unit on front lobe until i get it was not normalized.
By varying the 'shading' ( on cell 1/5 and 2/4, i suposed 3 is the center one) it makes the side lobes more or less proeminent ( at least on the wavelength i played with ( 400hz, ~85cm, base Dee: 42cm).

Please apologize with translation i might lost things...

I have not tried other suggestion you made, i hope tonight.
 
Last edited:

TNT

Member
Joined 2003
Paid Member
What happens if you place a floor-2-ceiling line in a corner and time delay each driver starting at 0ms for the middle one and add delay for each pair out from middle one... ala ESL63. Horizontal directivity so that at 22,5 deg of centre line, the level is 6 dB down... that should make it omni - right... will the delay line make it also vertically "omni"?

sum ==> a spherical radiator ?

//
 
Bessel weightings vs. straight 5 element array.
Note that the straight array, 5 X 1 adds to a strength of 5 at 0 and 90 degrees. Bessel maxes to 2 = 0.5 + 1 + 1 -1 + 0.5
 

Attachments

  • Bessel.jpg
    Bessel.jpg
    63.2 KB · Views: 110
Something that comes up a lot, in discussion of line arrays, is that many prefer straight unshaded / uncurved arrays.

1) There's a dude on Reddit who bought a set of Parts Express CBTs and ended up selling them because he didn't like how they sounded

2) I believe Wesayso prefers straight unshaded lines

3) There's a dude who built a cost-no-object CBT who then realized her preferred his straight lines

I was digging through some of my old projects and found this:

https://www.diyaudio.com/community/...waveguide-and-cbt-shading.266417/post-5475167

It's basically a five element curved array, that I measured as a shaded array AND as a Bessel array.

The Bessel array performed surprisingly well, particularly when you consider how simple they are.

The VERTICAL polars on both the Bessel and the shaded array were really rough:

nW6bE73.jpg


Although this measurement says "horizontal" it's actually vertical. I labeled it wrong.

I think the issue may be that even a modest amount of curvature is going to wreak havoc with the high frequencies.

15khz is 2.27cm long, so a pathlength difference of 1.135cm (0.44") will put two drivers out-of-phase with each other at 15khz.

One thing that might go a long way to help, is to use a lot of drivers. I've noticed with arrays in general, that the more drivers you use, the less sever the peaks and the dips are. If you have two drivers in an array you're going to get a really strong null at 30 degrees off axis. (https://www.diyaudio.com/community/threads/what-causes-off-axis-nulls.342494/) Add two more drivers, and the depth of the null is reduced. Add four more, it's even less of an issue. Etc etc.
 
So in this example, with these "pure vector sources" in the spreadsheet, the Bessel array simply is acting omni vertically.
If it were made up of real drivers, though, with their specific directivity, it would change the results...

A 5 driver line array with driver directivity of a 3.5" driver (all connected in parallel here)
5x TC9 FR Six-pack.png


vs a Bessel array using those same drivers:
5x TC9 FR Bessel Six-pack.png


(This specific driver directivity was created by @nc535 within Vituixcad to mimic the TC9 FD18-08)
 
If any of you are interested in some variations on Bessel arrays, I think this is an interesting thread:

https://www.diyaudio.com/community/threads/an-improved-array.301259/

The patent for my favorite speaker of all time (Beolab 90) references the Bessel array patent

f3f14edfb3d37dcac4c6ea708c20f070.jpg


Which makes me wonder if the Beolab 90 is using Bessel shading for some of it's options. (The speaker allows you to select various beamwidths from the comfort of your listening chair.)
 
Something that comes up a lot, in discussion of line arrays, is that many prefer straight unshaded / uncurved arrays.

2) I believe Wesayso prefers straight unshaded lines

Nowadays I'm listening to "frequency shaded" straight arrays, courtesy of @nc535 and his modeling frenzy. I joined the fun he had with simulations,
as I kept seeing more and more similarities between his TC9 array model (with floor reflections) and my old measurements.

What I had, a 25 driver unshaded line array, looks like this in Vituixcad:
25x TC9 FR Unshaded Six-pack.png


vs the frequency shaded array I have today:
25x TC9 FR Shaded 19.0 Six-pack.png


I cannot tell you if this is the actual as build model, as these are old models with the same driver model as the examples posted
earlier on this thread. We later modeled my enclosure in ABEC to fine tune the driver directivity in my case.

Close up of the differences in Directivity of the shaded vs unshaded array:
shaded-unshaded.gif

Main goal of this modification: get the vertical directivity as even as possible over a wide enough area to cover seated + standing height.
Main emphasis on seated listening (the zero line) but wanting acceptable output (FR response) standing up.

As we move up in frequency, the driver group playing full power get's smaller, but as one can see in the middle right diagram above,
they still contribute at a lower level to be able to create the vertical "beam". 5 Drivers (around seated ear height) are kept full range.
 
Great stuff guys.

I found at McIntosh that long arrays (near floor to ceiling) didn't need (weren't improved) by shading profiles. But the 16 element, mid length array, was greatly improved by shading. I've talked to a lot of high-end line array manufacturers about it ("Hey, you know you could really improve the response smoothness with the right weighting profile") and they always stare at me like I'm talking French.

I've always looked at Bessel arrays as a technical curiosity rather than a useful solution. You pay for 5 tweeters but get the output of 2 and lose the opportunity to increase and control directivty. Not a good deal. I know Mac did them after I left and I think the approach was good marketing. Back when THX was a thing I did a number of tapered 3 tweeter designs. I could get lobe free performance and a lot of LF (tweeter LF) gain for power handling.
 
  • Like
Reactions: 1 user
@speaker dave your posts on this forum, and that paper you've once linked in an old thread(*) certainly were a big influence for me to actually go ahead and try the unshaded full range array. I've ran them like that for years with great pleasure. The only reason to even try the shading scheme? Pure curiosity.

Are there differences to be heard? Yes. But not night and day, they still are close in signature sound. The frequency shaded array has a little less 'room coloring' that can be heard. But to be honest, that coloring wasn't a big detraction. Overall, the current shaded array measures a bit cleaner over a pretty wide area.

I just upgraded the drivers to Scan Speak 10F 8414G10 drivers and need to redo all measurements (again). Another partly curiosity driven project (lol).
Well, I had my reasons as I had some Vifa drivers fail on me (corrosion in lead wire connection after 10 years).... but I could have bought almost 5 times as much TC9's for the price of the 10F's (lol). So needed? No, but I'd always be wondering: what if...
They are quite close though (real siblings), currently I'm running them with the correction made for the TC9's.

(*)= 4 part paper, linking to part 1, I can't find the thread this fast...
 
Last edited: