ROAR15

The frequency range above ~60Hz has some directionality from the horn, centering the rear cancellation on the omni-directional lower frequency range is a more effective than centering on the entire passband.

A "plane wave" propagates in only one direction, the output of the cabinet is more directional in the upper range, but none of it's output is a plane wave after exiting the mouth.
^^^ THIS ^^^

Theoretically you should be able to measure the output of the ROAR from the rear to get a good idea of what you need to deal with, and then that measurement choose the best settings for the cardioid config.
 
The time of flight distance is from the center of the mouth, around the cabinet side, to the center of the rear of the cabinet, a minimum of 164mm, ~4.7ms.
View attachment 1470886
In addition, there is a diagonal distance to add in.

At what frequency?
What is the passband of your Roar?

As well as your delay time being off, you have not mentioned distance from boundaries, the reflections from them influence results.
Also, the ground plane mirrors the outputs, the forward facing sub on the bottom or top will have different rear angular results.

The frequency range above ~60Hz has some directionality from the horn, centering the rear cancellation on the omni-directional lower frequency range is a more effective than centering on the entire passband.

A "plane wave" propagates in only one direction, the output of the cabinet is more directional in the upper range, but none of it's output is a plane wave after exiting the mouth.

Art
Thanks for your answers!
I run them from 40hz to 100hz, with 24db filters.
the doubled distance makes sense. Weird, bcs when I tuned it just by ear the first time, I landed at 4,7ms but without phase inversion. subjectively, this gave the best results. starting to think i might have confused the wiring on one sub chassis, gotta check it. but then again, they summed well when both facing to the front.

there were no nearby boundaries, setup was in free field.

I gotta retry and do proper measurements next time.
 
Weird, bcs when I tuned it just by ear the first time, I landed at 4,7ms but without phase inversion. subjectively, this gave the best results.
That would be more of an "end fire" set up, more forward output at low frequencies than a cardioid arrangement using inverted polarity on the rear subs.
Normally, end fire arrays have all the cabinets facing forward.
https://bennettprescott.com/downloads/AdvancedSubwooferArraying.pdf
Setting them in a "stair step" arrangement improves the upper response, the upper directionality of a horn sub reflecting off the back of another sub causes reduced upper frequency response and sound quality issues.
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The stair step arrangement has almost the same forward output as a mono cluster, and ~+3dB more low end and +6dB upper response over the inverted polarity set up you were using.
https://soundforums.net/wp-content/uploads/2018/02/StairCardioidSubwooferArray-1.pdf

Art
 
Thanks, that sounds really promising! In terms of cancellation, I have used inline/end fire arrangements with 2 or 3 subs successfully, but wanted to get the cardiod done correctly. Now i guess I have to try the stepped variation, bcs. it makes so much sense regarding the reflection aspect. will post results and hopefully proper measurements in the future.