Open baffle radiation (FEM method)
I used COMSOL to simulated a 6.5 inch mid-woofer in a circular (D 280mm) baffle, atteched is the interest frequency.
In this contour,we can see how the open baffle system transfer from a typical dipole to abnormity.
Due to the cone shape and the back magnet and the speaker hole, it present asymmetry above 1kHz, again, the near field more like a butterfly around 2kHz, but the far field still natural. The worse case is 2215Hz, it's far field present butterfly.
Above 2.5kHz is not so precision due to the breakup in the cone. but we can expect is present wide dispersion mode.
Thanks. Very interesting presentation.
Yes, very interesting.
So, would it help if the baffle is tilted back a little? Can it steer the null backward?
To the most part this is quite in line with the simpler dipole models, except for the null "plane" tilted forward by the asymmtric built of a dynamic driver. Nice to see that in your simulation.
AFAIK you haven't yet accounted for the effect, that would really mess up the backward radiation above 1 kHz: the Helmholtz resonator formed by the cavity between cone, spider and basket (openings). I wonder if you see any chance to simulate that in COMSOL. That would be a real breakthrough for our understanding ...
A very instructive simulation.
I had my own FR open baffle system running
with a rear cover of felt sometimes.
(ca. 10mm thick, soft and rather permeable)
In some way in sounded more "tight" and conroled
that way, although i did not make any polar plots.
The frequency response on the rear side had a more
smooth rolloff using the felt. Without the felt,
the rear side dropped also above 2Khz due to basket
and magnet in the way but additionally it was peaking.
I also thought, the difference (rear felt cover or not)
was due to dispersion beeing more cardioid shaped
in the midrange.
When i look at your presentation, it might be that a
resistive rear cover of appropriate permability is able
to restore the desired dipole behaviour up to some
(By reducing "forward tilt" of the null plane ???)
@ Rudolf: A rear resistive cover would also
reduce midrange Helmholtz resonance problems you
mentioned, for those drivers prone to that.
What also can be seen: Every traditional cone
loudspeaker is a Distributed Mode Loudspeaker
... at least above some frequency ...
I still working on it, above simulation is base on 2D axial symmetry model, if we consider basket/spider, or rectangle baffle, we must use true 3D model, it will be more complex.
also, if we consider the cone behavior, we must use multi-physics. The simulated case maybe as below:
circle disc in box
circle disc in baffle
cone in box and baffle
and round edge
BTW: The limiting geometric factor in your model would not be the magnet, but the spider. The spider is - in many cases - of the same diameter as the magnet, but would have less distance to the baffle.
I’m sorry because the early simulation has some error due to the mesh size and the boundary conditions.
below is many different case:
For what it seems, better to listen to that OB with the loudpeaker reversed... the polar map of the rear field is better.
Best regards from Paris, France
Jean-Michel Le Cléac'h
For my second simulations, we can see that and I need add some notes:
1.When flat piston on infinity baffle, after 3.2k it will occur side lobe, at this time the ka=3.8, is very close to Beranek results.
2. With V-cone in infinity baffle, the directivity is more improved, in 3500Hz figure, every color step is about 2.52dB.
3.For the V-cone in cylinder, every color step is about 2.427dB (in 1600Hz), and 2.8dB (in 3500Hz),
the direction contour is like a pear until 3500Hz, no evident side lobe. Due to the diffraction at cylinder edge, the direction is bad than the infinity baffle case.
4.When the V-cone mounted on circular open baffle, and consider the magnet, in the first figure 1412Hz, we can see some asymmetry behavior, it due to the back magnet (see the no magnet result below).
And, the magnet bring the butterfly phenomena forward than the no magnet case, see 2084Hz, and 2176Hz( 1.35 dB per color step). The worst case is 2272Hz ( 2.4 dB per color step) in magnet case, we can see a on-axis deep but still acceptability in no magnet case.
Above case show the importance of the magnet, we must used appropriate materials to avoid the reflection.
As some John K's articles, we can see the wider baffle will make the directivity worst, blow is the diameter 480mm circular open baffle.
The 45deg off-axis response is stronger 6.6dB than on-axis response at 1260Hz.
BTW, Rudolf, it's difficult to define the acoustics property of the spider, so I do not simulate it now.
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