>>28677320
>r_a = (r_2^3 - r_1^3)/3.
Are you sure about that? I'm not going to challange your calculus as I don't have the skills, but I do like plugging numbers into formulae to se if they make sense.
So if we let your r_2 be R
and your r_1 be r (because it makes it easier to follow)
Let R = 200 mm and r = 150 mm
So r_a = (200^3 - 150^3)/3
r_a = (8,000,000 - 3,375,000)/3
r_a = (4,625,000)/3
r_a = 1,541,667
Which is, of course, nonsense. So perhaps I misunderstood your notation, and you meant a cube root?
So in this case, missing out the first few steps, I'd get
r_a = "cube root"(4,625,000) which, accroding to the internet, means
r_a = 166.6
So assuming you meant cube root, your then formula seems to imply that the average radius is 167 mm, which is 17 mm outboard of the inner radius and 33 mm inboard of the outer radius.
To which I'd say "Really?"
The "rule of thumb" calculation in this case would give
r_a = r + (R - r)/2
>[or r_a = R - (R - r)/2; same difference]
r_a = 150 + (200 - 150)/2 = 175
So your formula seems to imply that the average radius on a segment that gets wider as r increases towards R, is inside an arc that is mathematically half way out?
I must have made a mistake with your formula somewhere - can you point out where I went wrong? Because this doesn't seem to make sense now
