  Solar-type stars generate spherical winds, which are pressure driven flows,
that start subsonic, reach the sound speed at the sonic point and transition to
supersonic flows. The sonic point, mathematically corresponds to a singularity
of the system of differential equations describing the flow. In the problem of
an isothermal wind, the Parker solution provides an exact analytical expression
tuned appropriately so that the singularity does not affect the solution.
However, if the wind is polytropic it is not possible to find an analytical
solution and a numerical approach needs to be followed. We study solutions of
spherical winds that are driven by pressure within a gravitational field. The
solutions pass smoothly from the critical point and allow us to study the
impact of the changes of the polytropic index to these winds. We explore the
properties of these solutions as a function of the polytropic index and the
boundary conditions used. We apply the Complex Plane Strategy (CPS) and we
obtain numerically solutions of polytropic winds. This allows us to avoid the
singularity appearing in the equations through the introduction complex
variables and integration on the complex plane. Applying this method, we obtain
solutions with physical behaviour at the stellar surface, the sonic point and
at large distances from the star. We further explore the role of the polytropic
index in the flow and the effect of mass--loss rate and temperature on the
solution. We find that the increase of polytropic index as well as the decrease
of flow parameter both yield to a smoother velocity profile and lower
velocities and shifts the transition point from subsonic to supersonic
behaviour further from the star. Finally, we verify that the increasing of
coronal temperature yields higher wind velocities and a weaker dependence on
polytropic index.
