Mathematical modelling of helicopter twin sling underslung dynamics using Kane’s matrix formulation

Mathematical modelling of helicopter twin sling underslung dynamics using Kane’s matrix formulation

Prashant G. IYER, Jinu KRISHNAN, K.S. MANSOOR, Sheethal ANTONY

Abstract. For a winged body underslung attached to a helicopter using a single sling, side force and yawing moment coefficients play a significant role in determining the stability of the system. Instability in yaw plane due to lower dynamic pressure during helicopter take-off and touchdown can result in excessive cable twisting which can be detrimental for the mission and these lateral plane instabilities restrict the airspeed and maneuverability of the helicopter. Twin sling underslung system solves the issues by offering the advantage of enhanced load stability along with improved stability and balance for the awkwardly shaped loads. This paper describes mathematical modelling of a helicopter slung body dynamics in twin sling configuration, wherein the system dynamics is captured using a three-body, four degrees of freedom mathematical model with the differential equations of motion derived using matrix form of Kane’s method. The model is validated by comparing the results against a commercially available software in presence of dissipative aerodynamic forces. Further considering a sample helicopter trajectory from helicopter takeoff to touchdown, the slung body dynamics due to configuration update from single sling to twin sling is compared, and the advantages of the modified configuration clearly brought out.

Keywords
Multi-Body Dynamics, Twin Sling Underslung, Kane’s Method, Equations of Motion

Published online 3/1/2025, 10 pages
Copyright © 2025 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Prashant G. IYER, Jinu KRISHNAN, K.S. MANSOOR, Sheethal ANTONY, Mathematical modelling of helicopter twin sling underslung dynamics using Kane’s matrix formulation, Materials Research Proceedings, Vol. 49, pp 253-262, 2025

DOI: https://doi.org/10.21741/9781644903438-25

The article was published as article 25 of the book Mechanical Engineering for Sustainable Development

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] Sharma KK, Jee G, Rajeev UP, Padmakumar ES, Modeling of the Helicopter Underslung Aircraft’s Lateral-Directional Dynamics, IFAC-PapersOnLine 55(1) :174-179, (2022). https://doi.org/10.1016/j.ifacol.2022.04.029
[2] Pal, R S, Modelling of helicopter underslung dynamics using Kane’s method, 6th Conference on Advances in Control and Optimization of Dynamical Systems ACODS, IFAC-PapersOnLine 53(1):536-542, (2020). https://doi.org/10.1016/j.ifacol.2020.06.090
[3] Nitish K. L. N. S., Kumanan S., Remesh N., Karthik B., Mathematical Modelling and Numerical Simulations of Underslung Dynamics, 4th National Conference on Multidisciplinary Design, Analysis, and Optimization, (2021)
[4] Tian, Y., Wang, L., Zhou, Z., Chen, R, Nonlinear Rigid-Elastic Coupled Modeling and Oscillation Mechanism Analysis of Rotor-Body Slung-Load System, Aerospace 2023, 10, 872, (2023). https://doi.org/10.3390/aerospace10100872
[5] Enciu, J., Rosen, A, Simulation of coupled helicopter-slung load-pilot dynamics, Annual Forum Proceedings – AHS International, 1, 335-361, (2014) https://doi.org/10.4050/F-0070-2014-9577
[6] Thanapalan, K, Stability analysis of a helicopter with an external slung load system, Journal of Control Science and Engineering, (2016) https://doi.org/10.1155/2016/4195491
[7] Oktay, T., Sultan, C., Modeling and control of a helicopter slungload system, Aerospace Science and Technology, 29, 206-222, (2013). https://doi.org/10.1016/j.ast.2013.03.005
[8] Micale, E. C. and Poli, C., Dynamics of Slung Bodies using a Rotating Wheel for Stability, Journal of Aircraft, Vol. 10, pp 80-86, (1973) https://doi.org/10.2514/3.60200
[9] Kuldeep K. Dhiman, Abhishek, and Mangal Kothari, Flight Dynamics and Control of an Unmanned Helicopter with Underslung Double Pendulum, JOURNAL OF AIRCRAFT, Vol. 59, No. 1, (2022) https://doi.org/10.2514/1.C036390
[10] Wei Liu, Mou Chen, An adaptive anti-swing control for the helicopter slung-load system based on trajectory planning and neural network, (2021). https://doi.org/10.1002/acs.3393
[11] Luofeng Wang, Renliang Chen, Xufei Yan, Trajectory optimization of aerial slung load release for piloted helicopters, Chinese Journal of Aeronautics, Vol. 34(2), pp 229-239, (2021) https://doi.org/10.1016/j.cja.2020.07.025
[12] Cicolani, L. S. and Kanning, G., Equations of Motion of Slung-Load Systems, Including Multilift Systems, NASA, NASA-TP-3280, (1992)
[13] Cicolani, L.S., Kanning, G, Equation of motion of slung load system with Results for Dual Lift, NASA Technical Memorandum 102286, (1990)
[14] Iyer P.G., Modelling of a 12-DoF Parachute-Riser-Payload System dynamics using Kane’s method, Journal of Multibody System Dynamics, (2023) https://doi.org/10.21203/rs.3.rs-2728306/v1
[15] Tang Chin Pei, Lagrangian Dynamic Formulation of a Four-Bar Mechanism with Minimal Coordinates, (2010)