sinewave and surface

Hi. I am trying to wrap a sine wave via an Interpolated curve to a surface (in this case a sphere) and not having a lot of luck. I am hoping to get some feed back because I don't understand why the incrv does not like the spherical surface, or any non-planar surface. Even if I model manualy in Rhino, the intcrv goes haywire. I am trying to understand this problem, not simply derive a solution though I am posting a couple of my attempts. Thanks for the help

Gavin