Aerospace Science and Technology 63 (2017) 363–371 Contents lists available at ScienceDirect Aerospace Science and Technology www.elsevier.com/locate/aescte Nonlinear aeroelastic scaling of high aspect-ratio wings Christian Spada a , Frederico Afonso a , Fernando Lau a , Afzal Suleman a,b,∗ a CCTAE, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, No. 1, 1049-001, Lisboa, Portugal b Department of Mechanical Engineering, University of Victoria, PO Box 1700, Stn. CSC, Victoria, British Columbia, V8W 2Y2, Canada a r t i c l e i n f o a b s t r a c t Article history: Received 15 February 2016 Received in revised form 14 October 2016 Accepted 13 January 2017 Available online 18 January 2017 Keywords: Nonlinear aeroelasticity Aeroelastic scaling High aspect-ratio wings Geometric nonlinearities The aeronautical industry is currently facing the simultaneous and conflicting demand to enhance flight efficiency while reducing emissions. One potential solution for reducing fuel consumption is to increase the wing aspect-ratio as it improves the lift-to-drag ratio. However, higher aspect-ratio wings result in higher deflections which in turn may lead to nonlinear aeroelastic behavior. In this work, the aeroelastic behavior of a conventional regional aircraft with high aspect-ratio wings is investigated. Aeroelastically scaled models using different scaling methodologies have been evaluated and compared. These methodologies use scaling factors derived from the governing aeroelastic equations of motion to set the target values to be matched through the optimization of the scaled model structure. Two linear scaling approaches were used: the first method consists of a direct modal response matching; while the second method uncouples the mass and stiffness distribution to achieve the modal response. An alternative nonlinear aeroelastic scaling methodology using equivalent static loads is presented, which uses two different optimization routines to match the nonlinear static response and the mode shapes of the full model. The aeroelastic response agreement was found to be considerably better when the nonlinear approach is applied and the accuracy is noticeably better than the results obtained using the traditional linear scaling methods.  2017 Elsevier Masson SAS. All rights reserved. 1. Introduction Presently, the original aircraft manufacturers (OEM) are look- ing at new aircraft designs with high aspect-ratio wings, especially for civil and commercial aircraft. High Aspect-Ratio Wings (HARW) present considerable performance advantages. In general, HARW produce more lift and provide a higher lift-to-drag ratio resulting in increased endurance [1]. Also, HARW increase not only aircraft stability but also efficiency because they produce less induced drag leading to lower fuel consumption. To make HARW feasible in terms of weight penalties, these wings are designed to be very flexible. The total drag coefficient can be defined [1] as C D = C D 0 + C D i + C D w = C D 0 + C 2 L π eAR + C D w , (1) where C D , C D 0 , C D i , C D w are the coefficients of total drag, profile drag, induced drag and wave drag, respectively; C L is the lift coef- ficient; e the span efficiency factor and AR the wing aspect-ratio. * Corresponding author at: University of Victoria, Department of Mechanical En- gineering, PO Box 1700, Stn. CSC, Victoria, BC, V8W 2Y2, Canada. E-mail address: suleman@uvic.ca (A. Suleman). To make HARW feasible in terms of weight penalties, these wings are designed to be very flexible. Nevertheless, this challenge warrants further investigation due to large deformations under normal operating loads leading to a geometrical nonlinear behav- ior and aeroelastic problems [2,3]. These large deformations can change the natural frequencies of the wing which can produce no- ticeable changes in its aeroelastic behavior [4]. In order to better understand the physical behavior of the wing without building an expensive full scale demonstrator, a reduced scale model provides a feasible alternative. Experimental testing of aeroelastically scaled models is a common approach in new flight vehicle development programs [5]. In this work, the scaled model is intended to closely reproduce the aeroelastic response of the full scale model at operating conditions. Aeroelastic scaling requires adequate consideration to aerody- namic and structural physics. Aerodynamic similitude is achieved analytically by geometrically scaling the aerodynamic shape when Mach and Reynolds number are consistent. Flight conditions such as airspeed and altitude are selected for matching scaled parame- ters like Froude number and density ratio, for example. The Froude number is a dimensionless parameter defined as the ratio between inertial and gravitational forces [6]: Fr = V  ba g , (2) http://dx.doi.org/10.1016/j.ast.2017.01.010 1270-9638/ 2017 Elsevier Masson SAS. All rights reserved.