A Generic Narrow-Body Airliner Model for Numerical Studies of the Flight Dynamics and Control of Flexible Aircraft

Dynamic coupling between the rigid-body and the elastic degrees of freedom of an aircraft can occur when the structural design favors strength over stiffness, and the frequency separation between the classical flight dynamic modes and the aeroelastic modes becomes low enough or even inexistent. The phenomenon can lead to undesired behavior of the aircraft, including degraded flying and ride qualities, increased susceptibility to fatigue damage, pilot-induced oscillations, and even biodynamic coupling between the aircraft's structure and the pilot's body, influencing the pilot's control inputs. The design of control systems is also highly affected.

The first formulations for the flight dynamics of flexible aircraft considered only quasi-static aeroelastic effects on the aerodynamic coefficients of the rigid aircraft, with no dynamic coupling. Due to their greater simplicity, quasi-static formulations have frequently been employed in the design of aircraft with metallic wings and fuselages in the past decades. The dynamically coupled formulations that followed have commonly been based on the availability of modes of vibration of the aircraft, with the equations of motion being augmented by those due to the elastic degrees of freedom. Although their use is much more complex, the dynamically coupled formulations may become indispensable for modern aircraft with composite wings and fuselages. In either case, a structural dynamic model of the aircraft is necessary to provide the essential information for the correction of aerodynamic coefficients or for the equations of motion in the elastic degrees of freedom.

In this context, a numerical model of a representative transport aircraft is extremely desirable in the academic environment. The numerical model needs to comprise not only the traditional aerodynamic, propulsive, and mass distribution data commonly used in rigid aircraft flight dynamics but structural dynamic and incremental aerodynamic models as well. The latter comprises the equations for the generalized aerodynamic forces in the elastic degrees of freedom of the aircraft. 

With this motivation, we developed a generic narrow-body airliner (GNBA) model. The GNBA, similar to real-world aircraft in the same category (such as the Boeing 737, the Airbus A320 and A220, and the Embraer E-Jet families) has an intermediate-fidelity aerodynamic database for cruise configurations with flaps and landing gears up, together with different mass distribution configurations calculated with proper breakdown of components, equipment, payload, and fuel. More importantly, a finite element model of the aircraft using beam elements and lumped masses is available, together with the possibility of adjusting the stiffness level according to the desired application.

The aircraft wing planform and airfoil sections were designed with a multi-objective, multidisciplinary optimization process, which took into account aerodynamic, weight, and wing main box volume criteria. The aircraft was assumed rigid in the optimization process, allowing the demonstration that considering the structural flexibility later in the design process can significantly worsen the aircraft's performance.

The developed equations of motion allow the body axes to have their origin placed at any arbitrary point, not necessarily the center of gravity, making the routines much more easily adaptable to changes in the mass configuration. A novel quasi-static formulation is also developed that allows the calculation of aeroelastic effects not only on classical static stability and control derivatives but also on dynamic derivatives, e.g., the pitching moment coefficient derivative due to the time rate of change of the angle of attack. A linearized mean-axis formulation is also applied to the GNBA to demonstrate when dynamic aeroelastic effects not predictable with the quasi-static formulation become relevant. 

Related Publications

The GNBA model was developed and analyzed by Guimarães Neto (2014) in his Ph.D. thesis:

GUIMARÃES NETO, A. B. Flight dynamics of flexible aircraft using general body axes: a theoretical and computational study. 2014. 450 p. Thesis of Doctor in Science in Aeronautical and Mechanical Engineering - Instituto Tecnológico de Aeronáutica, São José dos Campos. Available at: https://sucupira-legado.capes.gov.br/sucupira/public/consultas/coleta/trabalhoConclusao/viewTrabalhoConclusao.jsf?popup=true&id_trabalho=1702595# Accessed on: 10 Apr. 2025.

Two research papers were based on the GNBA model developed by Guimarães Neto (2014):

SILVESTRE, F. J.; GUIMARÃES NETO, A. B.; BERTOLIN, R. M.; SILVA, R. G. A.; PAGLIONE, P. Aircraft Control Based on Flexible Aircraft Dynamics. Journal of Aircraft, v. 54, n. 1, p. 3516-3534, 2017. DOI: 10.2514/1.C033834.

DREWIACKI, D.; SILVESTRE, F. J.; GUIMARÃES NETO, A. B. Influence of airframe flexibility on pilot-induced oscillations. Journal of Guidance, Control, and Dynamics, v. 42, n. 7, p. 1537-1550, 2019. DOI: 10.2514/1.G004024.

One Ph.D. thesis and three master's dissertations used the original GNBA model:

DREWIACKI, D. Influence of aircraft flexibility upon handling qualities and pilot modeling. 2019. 268 p. Thesis of Doctor in Science in Aeronautical and Mechanical Engineering - Instituto Tecnológico de Aeronáutica, São José dos Campos. Available at: https://sucupira-legado.capes.gov.br/sucupira/public/consultas/coleta/trabalhoConclusao/viewTrabalhoConclusao.jsf?popup=true&id_trabalho=7970274 Accessed on: 10 Apr. 2025.

VILAÇA, G. S. Design of flight control law with structural feedback for aeroservoelastic stability. 2022. 135 p. Dissertation of Master of Science in Aeronautical and Mechanical Engineering - Instituto Tecnológico de Aeronáutica, São José dos Campos. Available at: https://sucupira-legado.capes.gov.br/sucupira/public/consultas/coleta/trabalhoConclusao/viewTrabalhoConclusao.jsf?popup=true&id_trabalho=12315129 Accessed on: 10 Apr. 2025.

XAVIER, V. M. Control of Flexible Aircraft Using Aeroelastic Feedback to Replace Notch Filters. 2021. 120 p. Dissertation of Master of Engineering in Aeronautical and Mechanical Engineering - Instituto Tecnológico de Aeronáutica, São José dos Campos. Available at: http://www.bdita.bibl.ita.br/tesesdigitais/lista_resumo.php?num_tese=78250 Accessed on: 10 Apr. 2025.

CARVALHO, E. J. Active Flutter Suppression Control Law Design for a Flexible Airplane. 2021. 88 p. Dissertation of Master of Engineering in Aeronautical and Mechanical Engineering - Instituto Tecnológico de Aeronáutica, São José dos Campos. Available at: http://www.bdita.bibl.ita.br/tesesdigitais/lista_resumo.php?num_tese=78248 Accessed on: 10 Apr. 2025.

In 2020, Prof. Guimarães Neto created a new graduate course at ITA: AB-276 - Modeling and Simulation of Flexible Aircraft. He developed a simpler yet detailed version of the GNBA model for didactic use in the course.  The main differences between this simpler version and the original one are:

• The original finite element method structural dynamic model was replaced with polynomials describing the stiffness and the inertia properties along 20 beams that are part of the Rayleigh-Ritz method structural dynamic model developed and used in the course;

• The original unsteady aerodynamic model, based on the doublet-lattice method (DLM), was replaced with a quasi-steady aerodynamic model based on the vortex-lattice method (VLM);

• Transonic effects considered in the original model are not included in the simpler version, limiting the analyses to subcritical Mach numbers;

• The simpler version uses a mean-axis formulation for the equations of motion, and modes of vibration are used not only in dynamic analyses but also in the calculation of trimmed flight conditions.

This simpler GNBA model was published by Guimarães Neto (2025):

GUIMARÃES NETO, A. B. Simplified integrated model of the flight dynamics of flexible aircraft. Aerospace Science and Technology, v. 161, 2025. DOI: 10.1016/j.ast.2025.110115.

The detailed data for the development of the GNBA's structural dynamic, aerodynamic, and propulsive models are available in the following document:

GUIMARÃES NETO, A. B. Data for the structural dynamic, aerodynamic, and propulsive models of the GNBA. 2024. Zenodo. DOI: 10.5281/zenodo.14538841.

Several master's dissertations were based on the simpler GNBA model developed in AB-276:

SANTOS, G. C. Modeling and analysis of flexible aircraft roll control with spoilers. 2024. 139 p. Dissertation of Master of Science in Aeronautical and Mechanical Engineering - Instituto Tecnológico de Aeronáutica, São José dos Campos. Available at: http://www.bdita.bibl.ita.br/tesesdigitais/lista_resumo.php?num_tese=80304 Accessed on: 10 Apr. 2025.

PEREIRA, C. V. Linear parameter-varying flight control law design for a flexible aircraft using different scheduling parameters. 2024. 140 p. Dissertation of Master of Engineering in Aeronautical and Mechanical Engineering - Instituto Tecnológico de Aeronáutica, São José dos Campos.

PINTO, V. H. O. Linear parameter-varying flight control law design for the longitudinal dynamics of a flexible aircraft. 2024. 85 p. Dissertation of Master of Engineering in Aeronautical and Mechanical Engineering - Instituto Tecnológico de Aeronáutica, São José dos Campos.

PINTO, E. A. M. Flight maneuver loads of a flexible aircraft. 2024. 118 p. Dissertation of Master of Science in Aeronautical and Mechanical Engineering - Instituto Tecnológico de Aeronáutica, São José dos Campos. Available at: http://www.bdita.bibl.ita.br/tesesdigitais/lista_resumo.php?num_tese=79853 Accessed on: 10 Apr. 2025.

MIYADAIRA, G. H. G. Modeling and analysis of the flight dynamics of a very flexible transport aircraft. 2022. 149 p. Dissertation of Master of Science in Aeronautical and Mechanical Engineering - Instituto Tecnológico de Aeronáutica, São José dos Campos. Available at: https://sucupira-legado.capes.gov.br/sucupira/public/consultas/coleta/trabalhoConclusao/viewTrabalhoConclusao.jsf?popup=true&id_trabalho=12235921 Accessed on: 10 Apr. 2025.

GUIMARÃES, P. R. P. Linear parameter-varying flight control law design for flexible aircraft. 2022. 105 p. Dissertation of Master of Engineering in Aeronautical and Mechanical Engineering - Instituto Tecnológico de Aeronáutica, São José dos Campos.

VIEIRA, B. S. C. Flight simulation of a flexible aircraft using neural networks for real-time applications. 2021. 105 p. Dissertation of Master of Science in Aeronautical and Mechanical Engineering - Instituto Tecnológico de Aeronáutica, São José dos Campos. Available at: https://sucupira-legado.capes.gov.br/sucupira/public/consultas/coleta/trabalhoConclusao/viewTrabalhoConclusao.jsf?popup=true&id_trabalho=11238389 Accessed on: 10 Apr. 2025.