The Bessel Array

[Patrick Bateman]

I have to state up front that I am not a fan of loudspeaker arrays. IMHO, they are a compromised solution. Having said that, there are a lot of situations where a compromise is in order.

One example that comes to mind is when you want to use a driver with a wide bandwidth and low power handling. For instance, TangBand, Peerless and Aurasound make some great small drivers which can literally cover seven octaves with authority. I've used the Aurasound Whisper with great success. IMHO, this cheap tiny driver sounds as good or better as many two-way speakers that cost ten times as much! Even better, you could do a project with one of these drivers in a single evening.

That sure beats MY projects, which seem to span weeks or months

Of course the Achilles Heel with these tiny drivers is that they're power handling is atrocious.

One array that might be the solution is the little used Bessel array. The Bessel array is exceptionally simple. In a nutshell, the Bessel array takes a single driver, then adds four more. Two are on one side, and two on the other. The trick is that half of them are out-of-phase. The end result is a "virtual driver" with higher power handling than a single driver, and a bit more efficiency.

IMHO, probably the greatest feature of the Bessel Array is that it doesn't have to be vertical. So for instance, you could put a horizontal Bessel array under your TV as a center channel, or on the dash of your car where a vertical line array wouldn't work.

For anyone who's interested in reading more, check these out.

Simple explanation:
http://www.angelfire.com/sd/paulkemble/soundf.html

Another good one:
http://www.prosoundweb.com/install/s...t25_4_p1.shtml

Google patents has so many papers on the bessel array it's not even funny:
http://www.google.com/patents?q=bess...Search+Patents

McIntosh is obsessed with the Bessel array:

[stinems]

Thanks for bringing this up Patrick.

Bessel arrays have always intrigued me. I saw your example from McIntosh and I immediately thought, "What a great way to control directivity while maintaining a close C-C spacing with the mid or lo freq driver." Of course, that particular array only controls in the horizontal axis, but its a start. AND you get the benefits of (per the prosoundweb.com link) an extra 4.5dB SPL and the associated power handling.

For practical implementation's sake, it would be great to see a white paper similar to Griffin's whitepaper on line arrays. Of particular interest would be how the C-C spacing would affect the directivity and what the limit is before the array 'falls apart'.

I have half a mind to buy up a bunch of the Dayton backmounted neos and start tinkering....

Anybody have hands on experience and/or listening impressions from a Bessel Array?

Cheers,
Sam

[LineArray]

I heard a quite amazing demonstration of a 5x5 array
using coax drivers of approx 10cm diameter at a university
near my hometown in spring this year.

Several modes of power distribution were demonstrated
auditively and by measurement.

It was astonishing to me, that control of directivity was
even possible in frequency ranges where wavelength is
like driver spacing or smaller.

Even though the polar diagram looks somewhat tattered
towards higher frequencies, it still works to a great extent
auditively.

We were able to walk around in the demonstration room and
switch e.g. between bessel distribution and even distribution.

One interesting mode to drive the array was to use the lower
4x5 drivers as bass cones with equal distribution and in phase,
while driving the upper horizontal row in the mid-high range
with bessel distribution. The result was a reasonable PA Box
with wide dispersion in the mid high range.

You can do a lot with those arrays and by the way you drive
the single sound sources you can adapt it to many requirements
given in a certain room / auditory.

I was invited to that demonstration by a colleague who knew
my interest in "weighted" or "shaded" line arrays. From
own experience i know, that a somewhat scattered polar
plot in one plane can be tolerated very good as long as
the "overall shape" fits the need and does not vary too much
with frequency.

It is most preferable to the very frequency dependent
overall distribution of usual fullrange or 2-Way concepts IMO.

Regards

[PeteMcK]

more info on them here: http://www.angelfire.com/sd/paulkemble/soundf.html

oops, you've already posted that link

The question is how far away do you have to be for the array to gel & does this make them impractical for home use?
(if it's frequency dependent then tweeter arrays may be OK?)

[Patrick Bateman]

I think it's something like 5-10x the size of the array. So for instance, a 5 element bessel array of two inch drivers should be listened to from 50" to 100" as a minimum.

Don't quote me on that - I'm reciting that off the top of my head.

Check ou the AES papers, and there's a Phillips paper out there too.

[KSTR]

US pat. application 20060159288 (feed that number into www.pat2pdf.org) covers this topic in big detail, showing response plots and many practical variations (beware, 101 pages, 4MegByte).

This is really interesting stuff, never heard of it before.... now a dipole panel with 7x7 2" Auras (36 total, actually) plus a center AMT tweeter would look quite radical, for sure.

Something I'm not clear about is whether the polar patterns of the square arrays is considerably uniform in all directions, not only vertical/horizontal.

... time to lauch Akabak and try some sims on this...


- Klaus

[GM]

Originally posted by Patrick Bateman
I have to state up front that I am not a fan of loudspeaker arrays.

The trick is that half of them are out-of-phase. The end result is a "virtual driver" with higher power handling than a single driver, and a bit more efficiency.

Ditto.

FWIW, here's a response to a basslist thread long ago on a BA's power handling:

>my BassBox Pro database for the FE-167 says that the
average power handling is 33 watts for a single
driver. The max SPL/Hz @ 1 m of the single driver is
107 dB.

>A 5 driver Bessel arrangement yields power handling
of 115.5 watts and a max SPL of 113 dB at an
impedance of 2.29 ohms.
>The Bessel arrangement has two drivers connected in
opposite phase so their SPL effectively cancels each
other leaving one driver parallel connected to two in
series. Hence, less SPL vs. a standard 5 drivers in
parallel arrangement.
====

My info says only one driver is wired in reverse
phase, with one pair in series, one pair in parallel.
Assuming this is correct:

One pair in series, and one pair in parallel =
10*log(4/1) = +6dB increase in efficiency.

Half of both the series and parallel pair's output is
negated by the single reversed phase driver, so we're
left with only the +6dB surface area gain added to
the output of what is effectively one driver.

This tells us that whatever the driver's voltage
handling limit is, it's also the limit for the array,
or 33W/8ohms = 16.24V.

Three 8ohm drivers in parallel = 2.667ohms, which in
parallel with 16ohms = 2.286ohms. 16.24^2/2.286 =
115.38W.

So based on my info, the 113dB/115.5W that BBP
predicts is close enough for me. Since peak to
average SPL is ~24dB, this means that each driver
will only need ~0.46W on average.

But of more importance is the better imaging at
greater distances compared to the same drivers wired
conventionally. When a number of these arrays are
ganged together is where the concept really pays off.
Dr. Patronis (GaTech) has built some using large
format horns in outdoor venues which have superior
pattern control/intelligibility compared conventional
arrays.

GM

[GM]

Originally posted by stinems

For practical implementation's sake, it would be great to see a white paper similar to Griffin's whitepaper on line arrays.

Anybody have hands on experience and/or listening impressions from a Bessel Array?

There's a pretty good tutorial in Don and Carolyn Davis's book that I used to experiment and a couple of folks were real pleased with a HT CC and a stereo BA: http://www.amazon.com/Sound-System-E.../dp/0240803051

GM

[Salas]

I have been involved in a commercial Bessel vertical array system some years ago. The front cancellation control is comparable to a conventional line array. But no special ''cylindrical wave'' Mid-HF waveguides are needed so costs and HOMs stay under control.
Also the elements can be broken down and used as common cabinets. Great benefit for the hiring business. Problems are that the available power is not utilized fully due to reversed polarity elements and power tapping. Also the vertical lobe is taller than the array and spills to the stage. But the sound has a natural feel although not as long in reach as a conventional line array, because its a big made up point source bubble.
It's interesting though, that when I was studying various conventional line arrays, it seemed to me that they could be modeled as infinite vertical Bessel arrays rather than long cylindrical sources, which never quite persuaded me, although its the mainstream assumption.

[GM]

Originally posted by Patrick Bateman
I think it's something like 5-10x the size of the array.

True, though when this was a hot topic some years ago there were folks who were happy at 2x, so it depends..........

GM