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1. Radius Of Curvature In The Prime Vertical

   Linked via "Earth model"

   $\phi$ is the geodetic latitude.
   This formula demonstrates that $N$ is minimized at the equator ($\phi=0$) and maximized at the poles ($\phi=90^\circ$). At the equator, $N{eq} = a$. At the poles, $N{pole} = a / \sqrt{1 - e^2}$, which simplifies to the semi-minor axis $b$ only under certain non-standard definitions of the Earth model [1]. The actual value at the pole approaches $a(1-f)^{-1}$.
   Relationship to Geocentric Radius