Exploring knots and Rope Length

Ropes of different diameters will consume more length of rope for each overhand knot tied.

Given a short piece of thick rope and a long piece of thin rope, determine wheter there will be a point of intersection on the graph.

Given a small piece of thin rope, what will the knot data look like?  (Parallel to the other thin rope.) 

Given a different rope that loses 2 cm per knot, if you wanted to create an intersection point, what length of rope is required?