  Outflows from active galactic nuclei (AGN) are often invoked to explain the
co-evolution of AGN and their host galaxies, and the scaling relations between
the central black hole mass and the bulge velocity dispersion. Nuclear winds
are often seen in the X-ray spectra through Fe K shell transitions and some of
them are called ultra fast outflows (UFOs) due to their high velocities, up to
some fractions of the speed of light. If they were able to transfer some
percentage of the AGN luminosity to the host galaxy, this might be enough to
trigger an efficient feedback mechanism. We aim to establish new constraints on
the covering fraction and on the kinematic properties of the UFO in the
powerful (L(bol) ~ 10^(47) erg/s) quasar PDS 456, an established Rosetta stone
for studying AGN feedback from disk winds. This will allow us to estimate the
mass outflow rate and the energy transfer rate of the wind, which are key
quantities to understand the potential impact on the host galaxy. We analyze
two sets of simultaneous XMM-Newton and NuSTAR observations taken in September
2013 and reported in Nardini et al. (2015) as having similar broadband spectral
properties. We fit the Fe K features with a P-Cygni profile between 5 and 14
keV, using a novel Monte Carlo model for the WINd Emission (WINE). We find an
outflow velocity ranging from 0.17 to 0.28 c, with a mean value of 0.23 c. We
obtain an opening angle of the wind of 71(+13,-8) deg and a covering fraction
of 0.7(+0.2,-0.3), suggesting a wide-angle outflow. We check the reliability of
the WINE model by performing extensive simulations of joint XMM-Newton and
NuSTAR observations. Furthermore, we test the accuracy of the WINE model in
recovering the geometrical properties of UFOs by simulating observations with
the forthcoming X-ray observatory ATHENA.
