Pararotor dynamics: center of mass displacement from the blade plane—analytical approach

The pararotor is a biology-inspired decelerator device based on the autorotation of a rotary wing whose main purpose is to guide a load descent into a certain atmosphere. This paper focuses on a practical approach to the general dynamic stability of a pararotor whose center of mass is displaced from the blade plane. The analytical study departs from the motion equations of pararotor flight, considering the center of mass displacement from the blade plane, studied over a number of simplifying hypotheses that allows determining the most important influences to flight behavior near equilibrium. Two practical indexes are developed to characterize the stability of a pararotor in terms of geometry, inertia, and the aerodynamic characteristics of the device. Based on these two parameters, a stability diagram can be defined upon which stability regions can be identified. It was concluded that the ability to reach stability conditions depends mainly on a limited number of parameters associated with the pararotor configuration: the relationship between moments of inertia, the position of the blades, the planform shape (associated with the blade aerodynamic coefficients and blade area), and the vertical distance between the center of mass and the blade plane. These parameters can be evaluated by computing practical indexes to determine stability behavior.