Here are a couple of quick example graphs taking a stab at representing acoustic power density. This is my original idea of representing this that I've had for a couple of years. These are using the burst data SPL (dB) which is then converted to Pascal (Pa) and then divided by the volume that the system takes up in liters (L)
This one is shown using the data in Pa. This is the simplest way but I'm leaning away towards converting the data back into (dB) SPL because that's a format more familiar to most who would be looking at it.
PAPD Pascal Graph Example.png 35.96KB
Here is the same data converted back into SPL decibels. This looks better to me intuitively but it's the same data either way.
PAPD SPL Graph Example.png 43.96KB
I think something similar would work. Here is what is going on for those who need a bit deeper explanation.
The maximum output from a system is being converted into Pa and divided by the total enclosure volume so that we can end up with a base output number either in Pa or dB, per liter of space taken up, for each 1/3rd octave frequency band. The conversion to Pa is needed so that the results are comparable.
Here's a simple example.
System A produces 120dB at 25Hz and measures 90x90x60cm (486 liters of space occupied)
System B produces 103dB at 25Hz and measures 43x36.2x39cm ( 60.7 liters of space occupied)
System A produced 120 dB which converts to an even 20 Pa
System B produced 103 dB which converts to 2.825 Pa
(1 Pa = 94dB / The formula for converting SPL(dB) to Pa is
Pa = [10^(dB/20)]*.00002)
We then divide each systems recorded Pa value by the total liters of space it occupies to get the Pa per liter value which we are going to call a acoustic power density rating or APD. Higher numbers are better.
System A =0.0411 Pa per liter. (20Pa / 486L)
System B =0.0465 Pa per liter. (2.825Pa / 60.7L)
What does this tell us? System B while smaller offers more potential output per liter of space. It is 1/8th the size of system A and offers far less output one vs one, but a block of 8 takes up the same space and potentially offers a little bit more output than system A.
If we convert the results back into SPL it is perhaps easier to digest.
The formula to convert Pa into dB is the reverse of the Pa conversion formula
dB = 20*log[Pa/.00002]
Applying that we get the following.
System A = 66.3dB per liter
System B =67.3dB per liter
To wrap up we have a very large system which offers 17dB more output than a smaller system exactly 1/8th the size. As most know if you double the systems you gain 6dB. Doubling three complete times to get to 8 total of the smaller system B results in an 18dB gain and the same total space being occupied as system A. The result is a 1dB advantage for an octet of system B. This is what the math shows in the final calculated SPL per liter.
One more example of proving out the APD formula. System A was 120dB and 486L. The resulting APD (dB) rating was 66.3dB per liter. At first you may be thinking that can't be correct. Back calculating out how many systems you would need to provide a 53.7dB gain shows that it is in fact 486 total 1 liter systems each with an output of 66.3dB to produce a total of 120dB.
Whether this data is of interest to anyone is the question. It interests me but I cook up weird data like this all the time for my own curiosity. This is clearly a very simple way of looking at it and ignores a lot of issues that would have to be considered. Number one being amplifier power. Are both systems already capable of handling a very large amp? If so, is it really feasible to use 8x the power for the smaller system in this example? At some point efficiency does factor in. (Efficiency actually is tracked in this data for the passive systems above roughly 50 or 63Hz.) However it is ignored in the deep bass and for active, closed loop systems. Perhaps the bigger system A weighs 220lbs and uses a single large driver. What if System B uses a heavy driver itself and already weighs 75lbs despite its small size? 8 of them results in a 600lb system. That may be an issue. Perhaps the system must fire all output from a single enclosure face and this will be impossible with 8 drivers/vents etc... Cost is ignored as well. Perhaps the big system is way too big to consider to begin with? The list of factors for consideration goes on.