Modeling of Dynamics of Land Boat Based on the Magnus Effect
https://doi.org/10.17587/mau.20.230-235
Abstract
The motion of a wind powered land boat is studied. It is supposed that the land boat moves along a straight line in a steady horizontal wind flow. The axis of rotation of the Savonius rotor is vertical. The rotation of the Savonius rotors induces the Magnus force that maintains the motion of the load boat. Such vehicles can be used to perform transportation in large open areas, where there is an access to free wind. In this paper, the mathematical model of the land boat driven by the Savonius rotor is constructed. The quasi-steady approach is used to describe the aerodynamic action upon the system. Corresponding aerodynamic coefficients are approximated basing on experimental data. The angle between the wind velocity and the velocity of the boat is a varied parameter of the model. The equations of the model are presented as a dynamic system of the second order. The conditions of existence and stability of stationary modes of the dynamic system motion are obtained. It is described how the boat speed at steady motion depends upon the angle formed by the velocity of the boat and direction of the wind. In particular, it is shown that the maximum of the boat speed is achieved on the close-hauled course, that corresponds to the recommendations of the sail settings known in sea navigation.
About the Author
M. V. Ishkhanyan
Federal State Institution of Higher Education "Russian University of Transport"
Russian Federation
Corresponding author: Ishkhanyan Margarita V., Ph. D., Assistant Professor, Federal State Institution of Higher Education "Russian University of Transport", Moscow, 127994, Russian Federation
Russian Federation
Corresponding author: Ishkhanyan Margarita V., Ph. D., Assistant Professor, Federal State Institution of Higher Education "Russian University of Transport", Moscow, 127994, Russian Federation
References
1. Korovelsky D. N. Buernyj sport (Boating sport), Moscow, Fizkul’tura i sport, 1968, 86 p. (in Russian).
2. Glazkova L. V., Pavlovsky V. E., Panchenko A. V. Dinamika, modelirovanie i upravlenie kolesnym robobuerom (Dynamics, simulation and control of a wheeled robotic glider), Nelinejnaya Dinamika, 2012, vol. 8, no. 4, pp. 679—687 (in Russian).
3. Pavlovsky V. E., Shamin A. Yu. Dinamicheskaya model’ i optimal’noe upravlenie dvizheniem robota-buera (The dynamic model and optimal control of the motion of the robot-yacht), Izvestia VSTU, 2013, vol.19, no. 24, pp. 61—70 (in Russian).
4. Pavlovsky V. E., Shamin A. Yu. Dinamicheski optimal’noe upravlenie robotom-buerom s razlichnoj formoj parusa (The dynamic model and optimal control of the motion of the robot-yacht with different forms of the sail). Extreme Robotics, 2017, vol. 1, pp. 250—256 (in Russian).
5. Prandtl L. Effekt Magnusa i vetryanoj korabl’ (Magnus effect and wind ship), Uspekhi Fizicheskikh Nauk, 1925, vol. V. Iss. 1—2, pp. 1—27 (in Russian).
6. Flettner A. Aerodynamical investigations of ship propulsion, Journal of the American Society for Naval Engineers, 1925, vol. 37, no. 1, pp. 149—153.
7. Lu, D., Huang D., Wu G. Analytical solution on Magnus wind turbine power performance based on the blade element momentum theory, Journal of Renewable and Sustainable Energy, 2011, no. 3, pp. 033104.
8. Nuttall P., Kaitu’u J. The Magnus Effect and the Flettner Rotor: potential application for future Oceanic Shipping, The Journal of Pacific Studies, 2016, vol. 36, no. 2, pp. 161—182.
9. Jamieson P. Innovation in wind turbine design, John Wiley & Sons, 2018.
10. Savonius S. J. Rotor adapted to be driven by wind or flowing water, U. S. Patent No. 1697574 A, 1929.
11. Tartuferi M., D’Alessandro V., Montelpare S., Ricci R. Enhancement of Savonius wind rotor aerodynamic performance: a computational study of new blade shapes and curtain systems, Energy, 2015, vol. 79, pp. 371—384.
12. Roy S., Saha U. K. Wind tunnel experiments of a newly developed two-bladed Savonius-style wind turbine, Applied Energy, 2015, vol. 137, pp. 117—125.
13. Klimina L., Masterova A., Selyutskiy Yu., Hwang Sh.-Sh., Lin Ch.-H. On dynamics of a Savonius rotor-based wind power generator, Proceedings of 14th Conference on Dynamical Systems, Theory and Applications (DSTA 2017), The Technical University of Lodz (Poland), 2017, vol. 3, pp. 275—284.
14. Ishkhanyan M. V., Klimina L. A., Privalova O. G. Autorotation motions of a turbine coursed by the Magnus effect, AIP Conference Proceedings, 2018, vol. 1959, pp. 030010.
15. Mao Z., Bai J. Numerical investigation of a small water turbine used for the power supply of underwater vehicles, Advances in Mechanical Engineering, 2018, vol. 10, no. 6, pp. 1687814018783654.
16. Dosaev M. Z., Kobrin A. I., Lokshin B. Ya., Samsonov V. A., Selyutsky Yu. D. Konstruktivnaya Teoriya MVEHU. Chast’ 1. Glavy I-II. (Constructive Theory of Small-Scale Wind Power Generators. Part I. Chapters I-II), Мoscow, Izdatel’stvo Moskovskogo Universiteta, 2007, 76 p. (in Russian).
17. Dosaev M. Z., Samsonov V. A., Seliutski Y. D. On the dynamics of a small-scale wind power generator, Doklady Physics, 2007, vol. 52, no. 9, pp. 493—495.
18. Dosaev M. Z., Lin Ch.-H., Lu W.-L., Samsonov V. A., Selyutskii Yu. D. Kachestvennyj analiz stacionarnyh rezhimov malyh vetrovyh ehlektrostancij (A qualitative analysis of the steady modes of operation of small wind power generators), Journal of Applied Mathematics and Mechanics, 2009, vol. 73, no. 3, pp. 259—263 (in Russian).
19. Samsonov V. A., Dosaev M. Z., Selyutskiy Y. D. Methods of qualitative analysis in the problem of rigid body motion in medium, International Journal of Bifurcation and Chaos, 2011, vol. 21, iss. 10, pp. 2955—2961.
20. Bach V. G. Untersuchungen über Savonius-Rotoren und verwandte Strömungsmaschinen, Forschung auf dem Gebiet des Ingenieurwesens A, 1931, vol. 2, iss. 6, pp. 218—231.
Review
For citations:
Ishkhanyan M.V. Modeling of Dynamics of Land Boat Based on the Magnus Effect. Mekhatronika, Avtomatizatsiya, Upravlenie. 2019;20(4):230-235. (In Russ.) https://doi.org/10.17587/mau.20.230-235
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