Simulating Arrays with Asymmetrical Response Pattern Estimator
In this thread I am going to take a stab at documenting how to use ARPE to simulate loudspeaker arrays. Upfront, I have to warn you - I'm not 100% sure that the info I'm going to give is correct.
The reason that I am documenting this is that I haven't been able to to find a 'howto' or a 'readme' for ARPE, and the only documentation appears to be the page on the internet, and also the info that's shown when you hover over the inputs.
Here are a few reasons you might want to use ARPE:
1) Arguably, all loudspeakers are arrays. Even single driver loudspeakers can be simulated as arrays, since parts of the cone do not radiate high frequencies. Two ways are *definitely* arrays. ARPE can also show you how loudspeakers behave depending on piston diameter and tilt.
2) You can do some neat 'tricks' with arrays which are not immediately obvious. For instance, people tend to discourage the use of horizontal D'Appolito arrays because of comb filtering. But if you juggle parameters carefully, you can use the comb filtering to control directivity the same way that a waveguide does. And ARPE is the best free tool I'm aware of to do this.
3) You can juggle a lot of parameters with ARPE before you make sawdust. Parameters like baffle offset, center-to-center spacing, polarity, tilt, distance to the listener, etc.
You can get ARPE here:
Asymmetrical Response Pattern Estimator
John Kreskovsky is one of the authors and a member of this forum; if he'd be so kind as to review my info, that would be a huge help.
OK, so here's how we simulate an array with ARPE. Again, as noted in post #1, this is based on my own research, and if there are mistakes here, please let me know.
1) figure out the piston diameter. You can't use what's on the spec sheet, as the piston diameter is frequently different. For instance, with a Vifa P14WJ, the piston diameter is 3.97". Here's how we figure that out:
a) get the SD off the spec sheet. In the case of our P14WJ, that's 80cm
b) the formula for diameter is 2 * (sqrt(sd/pi))
in the case of the Vifa P14WJ, that's 2 * (sqrt(80/3.14159)) = 10.09cm
c) We have to convert that from centimeters to inches, so divide the diameter from the formula in "b" by 2.54. In that case, the Vifa P14WJ has a piston diameter of 3.97". Note that's quite a bit different than what you'd think; it's advertised as a 5.5" midrange!
2) In step 2, we have to figure out the spacing from driver to driver. I'm using the Dunlavy SC-I as my benchmark. Based on the pic above, I believe the center to center spacing is about 4".
3) In order to simulate the speaker, we take our speaker spacing (4") and our speaker diameter (3.97"), and plug it into the spreadsheet. Here's where everything goes:
a) the diameter of each driver is 3.97". Note that the tweeter is physically 1" in diameter, but IMHO, the foam on the Dunlavy acts as a waveguide. When a speaker is in a waveguide, it's radiation behaves as if it's the diameter of the waveguide.
b) the first driver is my tweeter, second and third are my woofers. You can arrange this any way you'd like.
c) I think you can ignore filter Q if it's first order. If it's not 1st order, please refer to Dickason
d) Filter frequency is whatever you're using. Based on the data on Dunlavy, I am using 3000hz.
e) "offset x" is how far to the left or right the driver is on the baffle. If it's centered on the baffle, the offset is zero.
f) "offset y" is how far up or down the driver is. I haven't verified if positive is up or down. I believe positive is up.
g) "offset z" was tricky for me to figure out. I tested both positive and negative, and my tests indicate that positive is toward the listener, and negative values recess the driver on the baffle. I tested this theory using the Pythagorean theorem and trial and error.
h) I haven't determine if positive values of 'V tilt" slope the baffle towards or away from the listener.
i) axis distance is the distance to the listener in inches. Note that there's a button labeled "Stand Inch" which switches everything to metric. But when I tried that, I noticed that "Axis distance" may still be in inches. So it might be safer to just do everything in inches, not centimeters.
For me, the most confusing entry on the whole spreadsheet was "radial angle."
Based on trial and error, "radial angle" seems to flip everything by "x" number of degrees. For instance, if you set "radial angle" to 90 degrees, the graph will show you response in the horizontal axis. If you set it to zero degrees (the default), the graph will show you response in the vertical axis.
IMHO, this is hideously confusing, as most people would expect that the simulator would show you response in the horizontal axis, not the vertical. I had to screw around with this a bit to determine if I was correct, and I'm still not 100% sure that "90" is what you want to put there if you want the graph to show response in the horizontal axis.
If you would like to test this for yourself, try setting up a conventional two way array, using a 1" tweeter and a 6.5" midrange. Everything we know about crossovers says that a speaker like this should have poor response in the vertical axis, and excellent response in the horizontal. You can test this using ARPE, and I've found that setting "Radial Angle" to 90 degrees provides the polar response that's expected.
To sum it up, here's the *measured* response of the Dunlavy SC-I, thanks to Stereophile:
woofer and tweeter response on axis
Combined response - note the high frequency rolloff which I believe is caused by the felt acting like a conical horn
Here's the important one, the horizontal polar response. In the Stereophile measurements, we see it's very well behaved, but there's a high frequency rolloff. (IMHO, this is due to horn loading via the shape of the dense felt.)
Here's the ARPE sims of the vertical response. I set the angle by changing "Radial angle" from 90 to zero. In the ARPE sims, we see an off-axis peak at 6khz, and an off-axis dip at 1khz.
The measured response from Stereophile isn't 100% consistent, but we see the peak and the dip. It's a bit different likely because my guess on the center-to-center spacing isn't 100% accurate.
Using ARPE, I wanted to figure out what the effects are on an MTM with three different center-to-center spacings.
Hope this helps other people consider D'Appolito arrays.
All three options have a midrange with a 10cm diameter midrange, along with a tweeter in a waveguide with identical diameter. This is similar to most of the Dunlavy and Duntech speakers, and also the Snell designs from Dave Smith with the Expanding array. (I'd argue that the foam on the Duntech speakers acts as a waveguide.) Although all three options have identical midrange and tweeter, the difference is the center-to-center spacing.
Option one has a spacing of one wavelelength at the xover frequency, which is 3000hz. That works out to a center-to-center spacing of 4.5" between the midrange and the tweeter, and a tweeter offset of 0.17" backwards.
Option two has a spacing of 1/2 WL at the xover frequency, which is 3000hz. That works out to a CTC spacing of 2.25" between the midrange and the tweeter, and a tweeter offset of 4/100ths of an inch.
Option three has a spacing of 1/4 WL at the xover frquency, which is 3000hz. That works out to a CTC spacing of 1.125" between the midrange and the tweeter, and a tweeter offset of 1/100th of an inch. Obviously, this isn't possible to do in the real world. But it gives you an idea of what's going on in designs which can achieve this goal, via the use of a very beefy tweeter, a very low xover point, or both.
Option one, horizontal and vertical response. Note the latter is much worse than the former.
Option two, horizontal and vertical response. Note that the horizontal and vertical is now much closer to the same curve. I'd expect that this would improve soundstaging and tonality in a 'live' room.
By the time we're at option three, the curves are virtually identical. IMHO, this is the reason that D'Appolito arrays can work on their side, as long as the xover points are very low.
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