[Ether]

If you want a spiral whose tangent always make the same angle with the perpendicular to the radius (i.e. the spiral has a constant "climb slope"), then you could use this equation:

r = r1*e^(k*theta),

where r1 is the starting radius (at theta=0), r2 is the ending radius (at theta=alpha), and the constant k=log(r2/r1)/alpha.

For example, for r1=1, r2=1.5, and alpha=2pi, the equation would be:

r = 1*e^((log(1.5/1)/(2pi))*theta) = e^((0.2027*theta)/pi)

(see attachment)

edit: the second attachment shows the spiral tangent lines at theta=0 and theta=2pi