Hi Tamas, all
Sorry for the delay, I’ve been busy here.
A bunch of questions, Joe answered an important one and I will expand a bit.
Direct radiators exhibit an increase in efficiency when placed close together (less than about 1 /4 wl) because each feels the pressure of the other, “mutual radiation pressure”.
An alternate explanation is that when a radiator is acoustically small, it operates on the sloping portion of the radiation resistance curve. When one adds a second radiator, close enough to actually acoustically couple (that 1 /4 wl thing), then it is as if one moves up the resistance curve because the area has doubled.
This stops at a point where the drivers are more than about 1/4 wl apart and not the 1 /2 wl spacing most manufacturers curiously say is needed for line source driver spacing.
That spacing produces directivity but not mutual coupling.
Alternately, one can say that when the total coupled radiator area is large enough to reach the flat portion of the radiating curve, then a further increase in area causes no further increase in acoustic loading.
Also, when one has a large number of radiators, one also has the mechanical losses associated with all the drivers. This loss is in parallel with the acoustic radiation so a low Qm driver will have a lower ultimate efficiency in an array.
A thumb rule (as defined by Don Keele) of 25 % for an upper limit of efficiency for an array of direct radiators seems about right. Don is also one of the under appreciated horn folks that helped make what we have today.
For horns, 50% efficiency is sort of a “holy grail” and very hard to get in practice.
One can make horns which are greater than 50% efficient but this has a tiny impact in the sensitivity. It normally takes a group of practical sized horn boxes to get to 50%.
An efficient speaker radiates more than an average amount of the input Wattage as acoustic power. Efficiency can be defined as the difference in the output compared to the power lost in all the non-radiating resistances.
So far the discussion has been about mechanisms involved in delivering more power into the acoustic load for a given input power.
Part two is “where does it go” or directivity.
Once on has an array of coupled woofers or horns that is larger than that where the radiation resistance curve flattens, then the additional size causes directivity over an omni directional source.
Here, as the frequency climbs, the fixed physical size source is acoustically larger and so has more directivity.
For a horn, it becomes the wall angle which eventually defines the radiation angle, for the array of direct radiators, the issue is more complicated.
As the frequency rises, the spacing between drivers becomes excessive (greater than 1 / 3 wl) mutual radiation stops and they revert to an array of point sources which have self interference.
The full range horns I design have a straight walls for a constant directivty and have all the other frequency ranges join together where the dimension is less than 1 /4 wl so the add coherently.
In theory an measurement “self interference” condition is “not good” but on the other hand can be exploited sometimes.
A Line source exhibits a frequency /size dependant, reduced SPL fall off with distance because it has “self interference”.
Compared to the typically horrible Concert speakers they replaced, the line sources were a big improvement to be sure but they are far from ideal acoustically for the same reason.
Compare a perfect line source and a perfect point source and one sees a huge difference in the time response for one thing. Anywhere the line source exhibits non-inverse square law fall off, it has comparably poor time response due to the extended source nature.
Oh well, until the marketing folks decide its time for another change and steer the masses in another direction, we will have line sources everywhere you look, even when it’s a poor choice.
Anyway, you can hear this time smear in a large array of woofers , feed in an impulse like a kick drum, on axis it sounds fine because all the path lengths are nearly the same.
Do the same thing from off to the side and it sounds slow, woofy and not distinct as a result of the combination of different path lengths and directivity.
For clarity, one only wants ONE time between the input signal and when the sound hits your ears, not multiple arrivals from each source.
So far as the Bdeaps, I designed those back at Servodrive to fit next to a corner, it was actually Mike my partner who had the idea to stack them in a clover leaf and then discovered anomalous sensitivity.
When I measured them stacked that way, I found the 10 meter 1Watt level was 97.5 dB, which is 117.5 dB 1W 1M equivalent.
The arrangement produces about 10dB of forward directivity over a horn of equal sensitivity but no directivity.
Two sets would have more directivity BUT revert to self interfering point sources when the center to center spacing of the outlets becomes greater than 1 / 3 wl.
In other words, just like with line source drivers or woofer arrays, unilateral / coherent addition stops when the center to center spacing of the sources is about 1 / 3 wl or greater. The larger the pile , the lower the coherent upper limit is.
The TH115 and DTS-20 box is configured so that one can build an array with them also.
If one lays a pair of 115’s down (flat or in a V), with the mouths touching and then stacks more on top, one can make an array of considerable size.
A stack of 2 by 2 is already about 50% efficient, a larger stack is not likely to increase the voltage sensitivity much but the vertical directivity will become narrower and there will be a resulting rise of apparent sensitivity in front. A system the size of the 4 Bdeaps has about 10dB of forward gain in that frequency range so you could base a guess on what 115’s would do on that I suppose. At some point we will do another round of outdoor measurements on a “pile”.
Anyway, I guess if one boils it down, one has a few points.
Mutual radiation provides that advantage up to the point that the size of the array reaches the flat part of the radiation curve / or where Qm dominates.
An upper frequency limit also exists based on the center to center spacing of individual sources being less than 1 / 3 wl apart (really 1 /4 wl).
In the range that both conditions are met, a coherent wavefront can be launched with directivity, controlled by the shape of the array and time relationships etc.
Man, this ended up being long, sorry.
Hope that helps,
Tom Danley