Flight Dynamics and Stability of Kites in Steady and Unsteady Wind Conditions

Abstract

tThe flight dynamics and stability of a kite with a single main line flying in steady and unsteady wind conditions are discussed. A simple dynamic model with five degrees of freedom is derived with the aid of Lagrangian formulation, which explicitly avoids any constraint force in the equations of motion. The longitudinal and lateral-directional modes and stability of the steady flight under constant wind conditions are analyzed by using both numerical and analytical methods. Taking advantage of the appearance of small dimensionless parameters in the model, useful analytical formulas for stable-designed kites are found. Under nonsteady wind-velocity conditions, the equilibrium state disappears and periodic orbits occur. The kite stability and an interesting resonance phenomenon are explored with the aid of a numerical method based on Floquet theory.

A constraint-free flight simulator package for airborne wind energy systems

“…The use of dimensionless parameters and a minimal coordinate approach are very convenient from a numerical point of view [7,8,9,10,11,12], but they make harder the physical understanding of the results. Such a drawback is solved by the proposed flow chart, because the user only interacts with physical parameters and standard state variables.…”

“…A classical mechanics formulation yields to a mixed system of ordinary differential equations and nonlinear algebraic constraints. For these reasons, many AWE flight simulators have used minimal coordinate Lagrangian formulation [7,8,9,10,11,12].…”

Flight-Path Reconstruction and Flight Test of Four-Line Power Kites

“…Naturally, these last include an aerodynamic model, which basically receives the airspeed of the kite and returns the aerodynamic coefficients that describe the aerodynamic force and torque about the center of mass of the kite. These coefficients, which are also denoted as stability derivatives, play a central role in the stability of the equilibrium of the kite [16,17], which is of fundamental interest for many kite applications including the generation of energy. Although analyses with computational fluid dynamics codes have been carried out [18,19], the complex fluidstructure interaction is still an open and active field of research.…”

A lagrangian flight simulator for airborne wind energy systems

“…and the absolute dimensionless velocity of the kite (14) with S K and C K given in Appendix B.2 . The normalized angular velocity of the kite with respect to the inertial frame S E…”

“…A kite model consisting of several connected point masses has been proposed [5] . An alternative is representing the kite as a rigid body [12][13][14][15] which provides a good balance between accuracy and computational cost. Flexibility effects have been incorporated in kite flight simulators by using a multibodysystem model reduction process [16] .…”