Generally no, ATC won't be able to vector you that low anyway (hence the need for the missed). In an emergency you can start to break the TERPS (the document which describes all of this) pretty quickly. However a 6 NM radius turn is quite large, if you are going 200 knots you'd need only 11 degrees of bank to end up with a 6 NM turn. If you can't do that then you really can't turn at all at that point.Quick question, if you were to say, have a flap overspeed or part of a wing fall off (this is theoretical by the way...) and can't make a standard rate turn, are you obliged to notify ATC for vectors due to the "complicated math that can't be explained on text" thing not providing terrain and obstruction clearance?
No, there functionally isn't a calculation as it isn't needed. The outer turn radius is measured from the far (east in this case) edge of the final approach segment. By definition anything within this outer radius is protected. So even with a 0 turn radius you are protected.Also, how is a "crazy tight turn" calculated? 90 degrees bank and full elevator?