Nadal Mora, Vicente J. and Sanz Andres, Angel Pedro
Stability analysis of a free falling pararotor.
"Journal of Aircraft", v. 43
The pararotor is a decelerator device based on the autorotation of a rotating wing. When it is dropped, it generates
an aerodynamic force parallel to the main motion direction, acting as a decelerating force. In this paper, the
rotational motion equations are shown for the vertical flight without any lateral wind component and some
simplifying assumptions are introduced to obtain analytic solutions of the motion. First, the equilibrium state is
obtained as a function of the main parameters. Then the equilibrium stability is analyzed. The motion stability
depends on two nondimensional parameters, which contain geometric, inertia, and aerodynamic characteristics of
the device. Based on these two parameters a stability diagram can be defined. Some stability regions with different
types of stability trajectories (nodes, spirals, focuses) can be identified for spinning motion around axes close to the major, minor, and intermediate principal axes. It is found that the blades contribute to stability in a case of spin around the intermediate principal inertia axis, which is otherwise unstable. Subsequently, the equations for
determining the angles of nutation and spin of the body are obtained, thus defining the orientation of the body for a
stationary motion and the parameters on which that position depends.