Project curve onto curve 2d

I'v got closed curve and I'v got an open curve. I want to project closed curve onto an open and get a fraction of the open curve as a result (because I need to measure it's length, the length of the projection).

I tried to project on a plane (if open curve is a line) , but sure i get polyline curve and wrong length as a result

Is there a way to solve this trivial task?