Regarding a stereo triangle and heavy toe in that you only count the first cross sidewall reflection, there are only a few possible configurations which bring a decent delay. I posted these earlier in the following thread https://audiosciencereview.com/foru...nt-wide-vs-narrow-directivity-and-more.15171/
Here without heavy toe in so that the first sidewall reflection of the speaker near the wall counts:
Regarding the heavy toe in I calculated the room width which is needed to get a delay of the reflection from the opposite wall (assuming an stereo triangle)
As you can see you get values which actually a lot of living or listening rooms provide. It is also interesting that due to the subtraction of the listening distance (l r speaker distance) in the formula you need a smaller room with higher listening distance.
Listening distance [m] Room width (toe in 20ms delay) [m] Room width (heavy toe in 22.5ms delay) [m] Room width (heavy toe in 25ms delay) [m] 1 6.14 7.00 7.87 2 5.35 6.23 7.09 3 4.58 5.41 6.28 4 - 4.57 5.45
Here without heavy toe in so that the first sidewall reflection of the speaker near the wall counts:
To get an estimate of the room size I calculated the room width. I assume a standard stereo triangle (equal triangle, listening distance = width between L and R speaker).
Listening distance [m] Room width (20ms delay) [m] Room width (22.5ms delay) [m] Room width (25ms delay) [m] 1 8.14 9.00 9.87 2 9.35 10.22 11.09 3 10.53 11.40 12.38 4 11.68 12.57 13.45
You can see that the room has to be bigger for this.
If you want to calculate it by yourself you can solve the following formula:
w=2*b+a
b=-a/(2*2^0.5)+(a^2/8+0.5*c*d*a+0.25*c^2*d^2)^0.5
Where w is the room width [m], b is the distance from the speaker to the nearest side wall [m], a is the listening distance aka length of the stereo triangle [m], c the speed of sound [m/s] and d the delay (s).