where it reaches $\simeq 64^\circ$. This makes the rotation of the hyperboloid non-negligible and very important for the more accurate calculation we perform in this paper. The equatorial plane of the geometry described above is presented in Fig. \[fig:hyperboloid\].

We take the inclination angle to be $i=42^\circ$, and assume that the secondary is away from us during a apastron passage ($\omega=90^\circ$). This geometry explicitly determines the direction from which the system is observed (i.e. line of sight) at each orbital phase. For every orbital angle $\theta$ we calculate the relevant direction angle $\xi$ to the observer. Considering the orientation of the conical shell at that orbital angle, we calculate the thickness of the conical shell in that direction and integrate $n_H$ over the width to find the column density of the first component: $$N_{H,\rm{shock}} = \int_{l_{\rm{out}}}^l n_H\,dl \label{eq:NHshock},$$ where $l=l_{\rm{out}}+l_{\rm{in}}$ (see Fig. \[fig:NHgeo\]). The second component contributing to the column density, the undisturbed primary wind, is calculated from the point on the line of sight where the shock terminates, to infinity (contribution decreases fast with distance) $$N_{Hi1} = \int_l^\infty n_H\,dl \label{eq:NHi1}.$$ To calculate the total column density we added a constant third component of $1 \times 10^{22} \cm^{-2}$ to account 