An Unsteady Lifting-Line Model for Rotors in Forward Flight
Gregorio FRASSOLDATI, Beatrice DE RUBEIS, Giovanni BERNARDINI, Massimo GENNARETTI
Abstract. This study presents a time-marching lifting-line algorithm to predict the unsteady aerodynamics of rotors. Validation studies employing purely harmonic and damped oscillatory wing and blade motions have demonstrated the solver’s ability to accurately and stably predict unsteady loads. Augmenting the free and prescribed wake solvers recently developed, this method extends their time-marching framework to rotary wing applications in forward flight. In the present formulation, wake-induced velocities are evaluated via a free-wake model, while sectional forces are computed via Küssner-Schwarz unsteady theory. The bound circulation is derived by an unsteady Kutta-Joukowski relation. From there, both load and circulation equations are cast into state-space form. A vital modification for rotating blades is the careful definition of the reduced frequency, dealing with the accuracy of the prediction of dynamic loads and circulation.
Keywords
Unsteady Aerodynamics, Rotor Aerodynamics, Rotary Wing, Küssner-Schwarz, Free-Wake, Generalized Lifting Line Theory
Published online 7/20/2026, 6 pages
Copyright © 2026 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: Gregorio FRASSOLDATI, Beatrice DE RUBEIS, Giovanni BERNARDINI, Massimo GENNARETTI, An Unsteady Lifting-Line Model for Rotors in Forward Flight, Materials Research Proceedings, Vol. 69, pp 142-147, 2026
DOI: https://doi.org/10.21741/9781644904251-25
The article was published as article 25 of the book CEAS – AIDAA Conference 2025
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
References
[1] A. Cocco, A. Savino, A. Colli, P. Masarati and A. Zanotti, “A non-linear unsteady vortex-lattice method for rotorcraft applications,” The Aeronautical Journal, vol. 128, no. 1328, 2024. https://doi.org/10.1017/aer.2024.55
[2] G. Frassoldati, R. Giansante, G. Bernardini and M. Gennaretti, “Unsteady Lifting-Line Free-Wake Aerodynamic Modeling for Morphing Wings,” Aerospace, vol. 11, 2024. https://doi.org/10.3390/aerospace11090745
[3] G. Frassoldati, G. Bernardini and M. Gennaretti, “An Innovative Lifting-Line Model for Proprotors in Axial Flight,” in 51st European Rotorcraft Forum, Venice, Italy, 2025.
[4] H. G. Küssner and I. Schwarz, “The Oscillating Wing with Aerodynamically Balanced Elevator,” NACA, 1941.
[5] Y. C. Fung, An Introduction to the Theory of Aeroelasticity, New York: Dover Publications, Inc., 1993.
[6] T. Theodorsen, “General Theory of Aerodynamic Instability and the Mechanism of Flutter,” NACA, 1935.
[7] W. R. Sears, “Some Aspects of Non-Stationary Airfoil Theory and Its Practical Application,” Journal of Aeronautical Sciences, vol. 8, no. 3, pp. 104-108, 1941. https://doi.org/10.2514/8.10655
[8] J. P. Giesing, W. P. Rodden and B. Stahl, “Sears Function and Lifting Surface Theory for Harmonic Gust Fields,” Journal of Aircraft, vol. 7, no. 3, pp. 252-255, 1970. https://doi.org/10.2514/3.44155
[9] H. G. Küssner, “Summary Report on the Nonstationary Lift of Wings,” Luftfahrtforschung, 1936.
[10] M. Gennaretti, Fundamentals of Aeroelasticity, Springer Nature, Switzerland AG, 2024. https://doi.org/10.1007/978-3-031-53379-2
[11] M. Gennaretti and G. Bernardini, “Novel boundary integral formulation for blade-vortex interaction aerodynamics of helicopter rotors,” AIAA Journal, vol. 45, no. 6, pp. 1169-1176, 2007. https://doi.org/10.2514/1.18383
[12] H. Heller, W. Splettstoesser, V. Kloeppel and F. Cenedese, “HELINOISE – The European Community Rotor Acoustics Research Program,” AIAA Journal, 1993. https://doi.org/10.2514/6.1993-4358
[13] M. Gennaretti, G. Bernardini, J. Serafini and G. Romani, “Rotorcraft Comprehensive Code Assessment for Blade-Vortex Interaction Conditions,” Aerospace Science and Technology, vol. 80, pp. 242-246, 2018. https://doi.org/10.1016/j.ast.2018.07.013
[14] G. Bernardini, M. Gennaretti and C. Testa, “Spectral-boundary-integral compact-source formulation for aero-hydroacoustics of rotors,” AIAA Journal, vol. 54, no. 11, pp. 3349-3360, 2016. https://doi.org/10.2514/1.J054923
[15] M. Gennaretti, B. De Rubeis, C. Poggi and G. Bernardini, “Deformable-boundary integral formulation for the solution of arbitrarily-forced acoustic wave equation,” Journal of Sound and Vibration, vol. 591, 2024. https://doi.org/10.1016/j.jsv.2024.118618

