A Model to Compare the Flight Control Energy Requirements of Morphing and Conventionally Actuated Wings

Abstract

This work presents a theoretical analysis of the actuation energy requirements of a morphing aircraft. Morphing aircraft lack discrete control surfaces and use distributed actuation of the wing surface for maneuvering. An adaptive camberline is designed that generates morphed wing shapes in response to variations in leading and trailing-edge camber. Aerodynamic energy expressions are derived from the camberline functions using a unique energy computation stemming from the vortex lattice method (VLM). Beam theory is applied to morphing airfoil sections situated along the wingspan to obtain closed-form strain energy expressions. The resulting work expressions are combined and energy optimal wing deflections are found using Lagrange multipliers. In the optimization, total energy is the cost function and constraints are placed on achieving commanded changes in lift and moment coefficients. The functions are numerically implemented to compare work expressions for a wing with morphing inputs and a conventional wing, with inboard and outboard flaps. It is shown analytically that morphing aircraft have the capability to outperform conventional vehicles in terms of required flight control energy. This work also provides a theoretically sound methodology for morphing wing energy analysis that can be applied in future trade studies of morphing vehicles. Introduction Morphing aircraft are a topic of current research interest in the aerospace community. Such aircraft allow shape optimization over the entire flight regime _________________________ * Graduate Student, Department of Aerospace and Ocean Engineering, Student Member AIAA † Graduate Student, Department of Mechanical Engineering ‡ Professor, Department of Mechanical Engineering § Professor, Department of Aerospace and Ocean Engineering, Associate Fellow AIAA ¶ George R. Goodson Professor, Department of Mechanical Engineering Copyright © 2003 by Christopher O. Johnston. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission in addition to enhanced combat performance by allowing arbitrary vehicle orientation while tracking challenging flight paths. Of recent interest is the possibility of producing minimum energy control deflections by using the distributed actuation capability of morphing vehicles. Petit’s work demonstrated an initial morphing wing analysis based on conformal mapping. His analysis included a numerical computation of the aerodynamic energy response in tracking a flight path. This work builds upon that analysis but approaches the problem in a different manner. As opposed to conformal mapping, the analysis begins at the camberline in terms of a load distribution and derives full analytical expressions for the aerodynamic energy requirements while morphing. Gern used NASTRAN to determine the energy requirements of a morphing and conventional wing in rolling maneuvers. As opposed to a numerical calculation of the energy requirements, this work presents a closed-form expression for the aerodynamic and strain energy functions allowing theoretical insight to be gained into the optimization. Other works have investigated the energy relations of morphing wings but have not presented a general method that is comprehensive enough to proceed with an in-depth analysis. The design of an adaptive camberline function facilitates the use of the VLM energy method and beam theory to derive general energy relations for the vehicle and perform a direct comparison with a conventional aircraft. The next section covers the analytical design of the morphing camberline, followed by the derivation of the closed-form strain energy expressions, and the aerodynamic energy development. We then illustrate the optimization technique via a simple example problem. The paper concludes with numerical work comparisons of a morphing and conventional wing. Adaptive Camberline Derivation The first requirement for morphing analysis is the design of a camberline that will generate morphed wing shapes in response to control inputs. A morphed wing shape is defined by a wing that exhibits changes in A MODEL TO COMPARE THE FLIGHT CONTROL ENERGY REQUIREMENTS OF MORPHING AND CONVENTIONALLY ACTUATED WINGS