What is the equation for helical path length around a torus?

[BasicWill]

Does anyone know the equation for the helical path length around a torus?
I need an analytical expression, not an approximation.

Thanks

 

[Chris Hillman]

Hint: write a parameterization of your surface (torus of cross-section radius r centered on a circle with radius R > r). Find the tangent vectors to this surface by differentiating wrt the two parameters of your parameterization. Consider a linear combination with undetermined coefficients to obtain a vector field lying in the torus. (Did you have a particular "pitch" in mind?) Find the integral curves.