Trying Curve on a Sphere. Can't seem to get the rise and fall of the curve right

[glv]

I created arcs as part of a project I did a few years back.

I drew them using vectors; you will get a sense of it seeing the different lines in the first image.
The green one was the first one and I had to improve on that!

I stepped through these in the demo I did to show I how built them:

The end result was quite nice:

:)