Just plugging in numbers and seeing what looks good, a minor radius and rotation of the form:
r * Math.sin(t) * Math.cos(alpha)
and
Math.sin(alpha) * t
work very well for high alpha and low t but get progressively worse as alpha approaches zero or t approaches Math.PI / 2.
t here could be longitude but I'm not yet committing to that, it may just be something derived from longitude.