Pararotor Dynamics: Center of Mass Displacement from the Blade Plane—Analytical Approach

Abstract

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.

Numerical simulation of pararotor dynamics: Effect of mass displacement from blade plane

“…It is worth mentioning that the present paper extends the studies previously developed [17] considering nonlinear effects in the pararotors dynamics and their results on pararotor flight behavior. Those nonlinear terms are the result of using Newton-Euler equations for a rigid body excited with aerodynamic loads coupled with inertial phenomena.…”

“…The groups of cases are the same as those presented in previous studies [17]; they correspond to the pararotor configurations that can be built. Only Case A results are presented.…”

“…This numerical approach is a useful potential tool that allows the stability limits, the effects of configurational parameters, and the flight mode of future practical devices to be more accurately defined. This modelization includes neither simplificative assumptions (magnitude orders neglecting criteria) nor linearization of the system near the equilibrium solutions, as developed in [17]. The significance of this work is that the nonlinear factors effects on flight dynamics can be considered practically, not only in terms of response time, but also in stability limits and flight mode, particularly with pararotors flying near their stability limits defined in [17].…”

“…The nature of Newton-Euler equations of a rigid body under the effect of aerodynamic forces (that are blade relative velocity dependent) is in general nonlinear. The validity of the linear analytical model [17] is restricted to the vicinity of an equilibrium point. This numerical approach is a useful potential tool that allows the stability limits, the effects of configurational parameters, and the flight mode of future practical devices to be more accurately defined.…”

“…Those nonlinear terms are the result of using Newton-Euler equations for a rigid body excited with aerodynamic loads coupled with inertial phenomena. In the analytical model [17] second order terms were consistently neglected by considering that the following parameters are of small magnitude: blade pitch angle, relationship between descent rate to the velocity induced in the blades by rotation, distance of blade center of pressure in e 2 direction from center of mass, blade drag aerodynamic coefficient. The nature of Newton-Euler equations of a rigid body under the effect of aerodynamic forces (that are blade relative velocity dependent) is in general nonlinear.…”