equation of the log spiral:
L = eaθ
The value of (a) in the equation of a logarithmic spiral is the ratio of the x-length over the y-length of the curve, relative to the origin at O.
a = x-length/y-length
In a logarithmic spiral the ratio between the y-length and the arc length is constant. This ratio could be thought of as being the Cosine of the spiral, expressed as the equation below.
Cos(s) = 1/(1 + a)½
in the diagram:
a = .9
Cos(s) = 1/(1 + .9)½
= 1/(1 + .9)½
= .725476