I’m curious. Does that formula account for the 6°VOR error tolerance?
I was about to say "yes, it accounts for all those factors", but I just did the math, and I can't say it does.
At 30 nm, the half-width is 2.5 nm. That calculates to being 4.76 degrees off the published course.
Now, there is a secondary area, but that's only 0.333D wide. So at 30nm, it's an additional 1 nm wide.
Total width of 3.5 nm, which equals 6.65 deg off course. Which seems like enough, just barely, but the obstacle clearance on the secondary area tapers down to literally zero at the edge.
But on the other hand, I think that the primary area is supposed to provide protection for the 95th percentile determined through studies, or wording similar to that. Now, keep in mind that's "reasons behind TERPS", not TERPS itself, and I have no actual training in the "reasons", just the application. Also, keep in mind that VOR criteria is very, very old and hasn't changed in a long, long time as there is no obvious need or impetus to do so.