Weight functions method for stability analysis: applications and experimental validation for Hawker 800XP Aircraft

Abstract

A new method for system stability analysis, the weight functions method, is applied to the longitudinal and lateral motions of a Hawker 800XP aircraft. This paper assesses the application and presents the validation of the weight functions method to a real aircraft. The method consists of finding the weight functions that are equal to the number of differential equations required for system modelling. The aircraft’s stability is determined from the sign of the total weight function - the sign should be negative for a stable model. Aerodynamic coefficients and stability derivatives of the mid-size twin-engine corporate aircraft Hawker 800XP are obtained using the in-house FDerivatives code, recently developed at our laboratory, and validated with the flight test data supplied by CAE Inc. The following flight cases are considered: Mach numbers = 0.4 and 0.5, altitudes = 3,000 m, 5000 m, 8000 m and 10000 m, and angles of attack α = -5 0 to 20 0 . The handling qualities method is used to validate the results obtained with the weight functions method. Therefore, the aircraft stability is numerically validated using two methods: the weight functions and the handling qualities methods, and experimentally validated with flight test data. I. INTRODUCTION In this paper, the weight functions method (WFM) and the handling qualities method (HQM) are applied to study the Hawker 800XP aircraft’s stability, based on flight test data. This is the first time that the weight functions method is being used to analyse longitudinal and lateral aircraft model stability. The WFM is used here to determine the total aircraft model stability of a mid-size business aircraft with a typical wing-body-tail configuration and three basic control surfaces: the ailerons, elevator and rudder, designed to change and control the moments about the reference axis. This airplane has swept-back wings that are used to delay the drag divergence. The results are presented for the subsonic regime characterized by Mach numbers equal to 0.4 and 0.5, and four altitudes: 3,000 m, 5000 m, 8000 m and 10000 m. The pitch angles θ = [-20 to 20] 0 and pitch rates q = [-3.5 to 3.5] 0 /s are the variables for longitudinal motion, and the roll rate p = [-6 to 6] 0 /s, yaw rate r = [-2 to 2] 0 /s, sideslip angle β = [-5 to 5] 0 and roll angle Φ = [-15 to 15] 0 are the variables for lateral motion. It was also considered that we have a value δ = 5 0 for the control term. In the following sections, the WFM and HQM are described and the related results using both methods are presented. The WFM was applied only on the longitudinal motion of a canard configuration generic fighter aircraft, called the High Incidence Research Model (HIRM) by Anton [1]. The HIRM has been the subject of collaboration within the GARTEUR Action Group FM (AG08). The WFM was applied in the case of short-period longitudinal approximations for the system of equations with unstable characteristics given by the pitching-moment coefficients, and the aircraft model was stabilized using control laws. This model had increased complexity because the thrust component was included in the system equations. Yoichi et al. [2] conceived the weight functions method for use in two- and three-dimensional crack problems, and to calculate stress intensity factors for arbitrary loading conditions. This method has been generalized to calculate the response analysis of structures and to be applied to two-dimensional elasticity and plate bending problems. The weight function method was found to be useful for analyzing structures subjected to a variety of loading conditions because the responses expressed in terms of displacements and stresses may be calculated by integrating the inner product of a universal weight function and a load vector. The stress intensity factor for the patched crack within an infinite plate was successfully numerically validated [3] using the WFM. A different approach was presented by Stroe [4], who solved the Lurie-Postnikov problem using a general equation for linear or nonlinear vibrations by linear transformations. Stroe also analysed a holonomic system with dependent variable equations [5]. The weight functions method was applied for vibration and stability studies in the cases of linear and nonlinear damped holonomic systems.