Solution: stagnation points for the 3D Rankine ovoid.

For the 3D Rankine Ovoid,

$$\begin{align}u = & \frac{\partial \phi }{\partial x} = U + \frac{m}{4\pi }\left[... ...{x^2 - a^2} \right)^2 = \left( {\frac{m}{4\pi U}} \right)4ax \notag \end{align}$$

and to obtain $x_{s}$ we nee to solve the last equation above for $x$.