  Classical Supergiant X-ray Binaries host a neutron star orbiting a supergiant
OB star and display persistent X-ray luminosities of 10$^{35}$ to 10$^{37}$
erg/s. The stellar wind from the massive companion is believed to be the main
source of matter accreted by the compact object. With this first paper, we
introduce a ballistic model to characterize the structure of the wind at the
orbital scale as it accelerates, from the stellar surface to the vicinity of
the accretor. Thanks to the parametrization we retained and the numerical
pipeline we designed, we can investigate the supersonic flow and the subsequent
observables as a function of a reduced set of characteristic numbers and
scales. We show that the shape of the permanent flow is entirely determined by
the mass ratio, the filling factor, the Eddington factor and the $\alpha$-force
multiplier which drives the stellar wind acceleration. Provided scales such as
the orbital period are known, we can trace back the observables to evaluate the
mass accretion rates, the accretion mechanism, the shearing of the inflow and
the stellar parameters. We confront our model to three persistent Supergiant
X-ray Binaries (Vela X-1, IGR J18027-2016, XTE J1855-026) and discuss the
likelihood of wind-formed accretion discs around the accretors in each case,
further investigated in a following paper.
