Max bend radius of innerduct thru pipe bend

[sloquick]

Should be fun for hard-core math types. An innerduct of outside diameter d, runs inside a 4" IPS pipe (0.188" wall). Said pipe makes a 90 degree turn. The elbow used is a long radius, i.e. bend radius of 1.5R or 6". What is the maximum bend radius in inches of the innerduct that traverses this pipe bend (assume a smooth curve with tangent line going in one direction only). Contention is that max occurs when half way through bend innerduct touches inside wall of pipe bend, and that bend radius of innerduct is larger than bend radius of pipe, even at outside wall. General formula result also invited. Thanks!

 

[sloquick]

OK, I took a shot at it. I come up with a maximum bend radius of almost 18", more than double the bend radius of the pipe at its outside wall. If anyone is interested and kind enough to either confirm or suggest a different answer, i would be grateful. Thanks!