Hi all. This is my first post. Does anyone have any advice for projecting a curve or wrapping around a curved surface that also has a taper? 

I've searched for this in the forums and on other guides, but I am having difficulty finding out exactly what I need. I'll show you what I mean by posting some images below. 

I need the long length of the "channels" to be parallel with the bottom/top face of the piece. Right now I understand why it's wrapping the way it is, but I can't figure out how to go about achieving what I need. 

Any suggestions? 

Thank you in advance. You guys are very helpful. 

And when i try projecting the curve, the sketch isn't projected properly for what I am trying to get. I'm doing it wrong. Any advice?