Assessment of Added Masses Effects on Airship Dynamics and Stability
Abstract
Airships have recently emerged as attractive candidates for several aerospace applications, leading to an increasing interest in the modeling of the dynamic behavior of these vehicles for flight mechanics analyses and mission simulation purposes. One of the peculiarities of the airship model is the need for the inclusion of the dynamic effects due to the mutual interaction between the moving vehicle and the fluid in which it flies. This phenomenon is usually represented by introducing fictitious added masses. This paper presents a method to rigorously manage the added masses, including them in the flight dynamics equations without considering any simplifying assumptions concerning airship shape or centers of added mass. The paper also defines a method for the computation of the added mass matrix and centers of added mass position in any reference frame, which is required for the accurate writing of the airship equations of motion. The effectiveness of the proposed approach is validated numerically by solving a potential flow problem through the boundary element method. Finally, the effects of added masses are assessed with reference to a high-altitude airship by evaluating its dynamic stability properties with and without the inclusion of the added masses.
References
[1] , “High-Altitude, Long-Endurance Airships for Coastal Surveillance,” NASA TM 2005-213427, Glenn Research Center at Lewis Field Cleveland, OH, 2005.
[2] , “Robotic Airships for Exploration of Planetary Bodies with an Atmosphere: Autonomy Challenges,” Autonomous Robots, Vol. 14, Nos. 2–3, 2003, pp. 147–164. https://doi.org/10.1023/A:1022227602153
[3] , “A New Era for Airships,” Aerospace America, Vol. 42, No. 5, May 2004, pp. 27–31
[4] , “The Suitability of Hybrid vs. Conventional Airships for Persistent Surveillance Missions,” 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, AIAA Paper 2010-1014, 2010. https://doi.org/10.2514/6.2010-1014
[5] , “Cargo Airships Prospective,” Israel Annual Conference on Aerospace Sciences, Vol. 1, Haifa, Israel, 2012, pp. 313–323
[6] , “Airship Dynamics Modeling: A Literature Review,” Progress in Aerospace Sciences, Vol. 47, No. 3, 2011, pp. 217–239. https://doi.org/10.1016/j.paerosci.2010.10.001
[7] , “Apparent Mass Effects on Parafoil Dynamics,” Aerospace Design Conference, AIAA Paper 1993-1236, 1993.
[8] , On the Effect of the Internal Friction of Fluids on the Motion of Pendulums,
Cambridge Library Collection—Mathematics , Vol. 3, Cambridge Univ. Press, Cambridge, England, U.K., 2009.https://doi.org/10.1017/CBO9780511702266.002[9] , Hydrodynamics, Univ. Press, Dover Publications, New York, 1932, Chap. VI, pp. 160–180, https://books.google.it/books?id=BfZQAAAAMAAJ.
[10] , “Guidance and Control of Ocean Vehicles,” Univ. of Trondheim, Printed by John Wiley & Sons, Chichester, England, U.K., 1999.
[11] , “Modeling and Simulation of Airship Dynamics,” Journal of Guidance, Control, and Dynamics, Vol. 30, No. 6, 2007, pp. 1691–1700. https://doi.org/10.2514/1.29061
[12] , “Flight Performance Analysis of Hybrid Airship Considering Added Mass Effects,” Journal of Dynamic Systems, Measurement, and Control, Vol. 140, No. 11, 2018, Paper 111001.https://doi.org/10.1115/1.4040220
[13] , “Calculation of Potential Flow About Arbitrary Three-Dimensional Lifting Bodies,” Douglas Aircraft Company MDC-J5679/01, Long Beach, CA, 1969.
[14] , “Added Masses Computation for Unconventional Airships and Aerostats Through Geometric Shape Evaluation and Meshing,” International Journal of Aeronautical and Space Sciences, Vol. 15, No. 3, 2014, pp. 241–257. https://doi.org/10.5139/IJASS.2014.15.3.241
[15] , “Calculation of Added Mass Coefficients of 3D Complicated Underwater Bodies by FMBEM,” Communications in Nonlinear Science and Numerical Simulation, Vol. 16, No. 1, 2011, pp. 187–194. https://doi.org/10.1016/j.cnsns.2010.02.015
[16] , “Apparent Mass of Parafoils with Spanwise Camber,” Journal of Aircraft, Vol. 39, No. 3, 2002, pp. 445–451. https://doi.org/10.2514/2.2949
[17] , “Added Masses of Thin Rectangular Plates Calculated from Potential Theory,” Journal of Ship Research, Vol. 14, No. 2, 1970, pp. 100–111. https://doi.org/10.5957/jsr.1970.14.2.100
[18] , “Computation of the Added Masses of an Unconventional Airship,” Journal of Applied Mathematics, Vol. 2012, No. 1, 2012. https://doi.org/10.1155/2012/714627
[19] , “Apparent Masses and Inertia Moments of the Parafoil,” Journal of Theoretical and Applied Mechanics, Vol. 52, No. 3, Jan. 2014, pp. 606–616
[20] , “Equations of Motion of a Vehicle in a Moving Fluid,” Journal of Aircraft, Vol. 37, No. 4, 2000, pp. 630–639. https://doi.org/10.2514/2.2645
[21] , “Effects of Comprehensive Added Masses Modeling on Airship Equations of Motion and Dynamic Stability, AIAA SciTech 2024 Forum, AIAA Paper 2024-2650, 2024.https://doi.org/10.2514/6.2024-2650
[22] , “Hydrodynamics of Offshore Structures with Specific Focus on Wind Energy Applications,” Renewable and Sustainable Energy Reviews, Vol. 44, April 2015, pp. 692–716. https://doi.org/10.1016/j.rser.2015.01.021
[23] , “A Mesh Based Approach for Unconventional Unmanned Airship Added Masses Computation,” SAE Technical Papers, Vol. 7, 2013. https://doi.org/10.4271/2013-01-2191
[24] , “Simulink Model Development, Validation and Analysis of High Altitude Airship,” National Aerospace Laboratories PD-FMC/2017/1000, Bangalore, India, 2017, pp. 2–2400. https://doi.org/10.13140/RG.2.2.11844
[25] , “System Identification Approach for Determining Flight Dynamical Characteristics of an Airship from Flight Data,” Ph.D. Thesis, Institut für Flugmechanik und Flugregelung, Universität Stuttgart, 2006.
[26] , “Modeling of Apparent Mass Effects for the Real-Time Simulation of a Hybrid Airship,” AIAA Modeling and Simulation Technologies Conference and Exhibit, AIAA Paper 2006-6619, 2006. https://doi.org/10.2514/6.2006-6619
[27] , “Development of an Aerodynamic Model and Control Law Design for a High Altitude Airship,” AIAA 3rd “Unmanned Unlimited” Technical Conference, Workshop and Exhibit, AIAA Paper 2004-6479, 2004. https://doi.org/10.2514/6.2004-6479
[28] , “Stability and Control Analysis Based on Airship Dynamic Modeling,” 2007 IEEE International Conference on Automation and Logistics, Inst. of Electrical and Electronics Engineers, New York, 2007, pp. 2744–2748.