  Layers of ionized plasma, in the form of winds ejected from the accretion
disk of Supermassive Black Holes (SMBHs) are frequently observed in Active
Galactic Nuclei (AGNs). Winds with a velocity often exceeding $0.1c$ are called
Ultra-Fast-Outflows (UFOs) and thanks to their high power they can play a key
role in the co-evolution between the SMBH and the host galaxy. In order to
construct a proper model of the properties of these winds, it is necessary to
consider special relativistic corrections due to their very high velocities. We
present a derivation of the Poynting-Robertson effect (P-R effect) and apply it
to the description of the dynamics of UFOs. The P-R effect is a special
relativistic correction which breaks the isotropy of the radiation emitted by a
moving particle funneling the radiation in the direction of motion. As a result
of the conservation of the four-momentum, the emitting particles are subjected
to a drag force and decelerate. We provide a derivation of the drag force
caused by the P-R effect starting from general Lorentz transformations and
assuming isotropic emission in the gas reference frame. Then, we derive the
equations to easily implement this drag force in future simulations. Finally,
we apply them in a toy model in which the gas particles move radially under the
influence of the gravitation force, the radiation pressure and the drag due to
the P-R effect. P-R effect plays an important role in determining the velocity
profile of the wind. For a wind launched from $r_0=10r_s$ (where $r_S$ stands
for the Schwarzschild radius), the asymptotic velocity reached by the wind is
between $10$% and $24$% smaller than the one it would possess if we neglect the
effect. This shows that the P-R effect should be taken into account when
studying the dynamics of high-velocity, photoionized outflows in general.
