Modelling an aircraft maximum endurance horizontal flight for air trials
The paper considers theoretical preparation for the aircraft pre-air-trial. The construction of some mathematical models of a horizontal flight is based upon the material system of variable mass motion. Optimal speed of horizontal flight is obtained as a function of variable mass. This speed is a solution (extremal) of the objective functional of the flying apparatus horizontal flight endurance. The solution delivers maximal value to the objective functional. The main significant assumptions made at the problem setting are: the rate of the aircraft horizontal flight speed change is negligibly small, flying object engines thrust has the horizontal component only, the dependence between aerodynamic coefficients is simplified in approximation with a quadratic parabola; the data used in simulation are abstract, although plausible. It was shown that in spite of the speed changes during the studied flight, the rate of that change plays an unimportant role for the considered case; therefore, such supposition of the rate neglecting is properly grounded. The derived equations allow taking into account the rate when it is the matter of importance. Since the presented study is the simplified one, the obtained results could be considered as some reference values to be tested and possibly approached to.
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Bunge, R. A. (2015). Aircraft flight dynamics. Stanford University, AA241X, April 13, 34 posters/slides (slideshow).
Donateoa, T., Ficarellaa, A., Spedicatoa, L., Aristab, A., & Ferraroba, M. (2017). A new approach to calculating endurance in electric flight and comparing fuel cells and batteries. Applied Energy, 187, 807–819. https://doi.org/10.1016/j.apenergy.2016.11.100
Galili, I. (2001). Weight versus gravitational force: Historical and educational perspectives. International Journal of Science Education, 23(10), 1073–1093. https://doi.org/10.1080/09500690110038585
Goncharenko, A. (2014, October 14–17). Navigational alternatives, their control and subjective entropy of individual preferences. In Proceedings of the IEEE 3rd International Conference “Methods and Systems of Navigation and Motion Control (MSNMC)” (pp. 99–103). Kyiv, Ukraine. https://doi.org/10.1109/MSNMC.2014.6979741
Goncharenko, A. (2016, October 18–20). Several models of artificial intelligence elements for aircraft control. In Proceedings of the IEEE 4th International Conference “Methods and Systems of Navigation and Motion Control (MSNMC)” (pp. 224–227). Kyiv, Ukraine. https://doi.org/10.1109/MSNMC.2016.7783148
Goncharenko, A. (2018a). Aeronautical and aerospace materials and structures damages to failures: Theoretical concepts. International Journal of Aerospace Engineering, 2018, 4126085. https://doi.org/10.1155/2018/4126085
Goncharenko, A. (2018b, February 20–24). Multi-optional hybrid effectiveness functions optimality doctrine for maintenance purposes. In Proceedings of the IEEE 14th International Conference “Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering (TCSET-2018)” (pp. 771–775). Lviv-Slavske, Ukraine. https://doi.org/10.1109/TCSET.2018.8336313
Hibbeler, R. C. (2012). Engineering mechanics. Dynamics (13th ed.). Prentice Hall.
Hibbeler, R. C. (2013). Engineering mechanics. Dynamics. Solution manual (13th ed.). Pearson Education, Inc.
Houghton, E. L., & Carpenter, P. W. (2003). Aerodynamics for engineering students (5th ed.). Butterworth-Heinemann, Elsevier Science.
Hulek, D., & Novák, M. (2019). Expediency analysis of unmanned aircraft systems. In Proceedings of the 23rd International Conference on Transport Means” (pp. 959–962). Palanga, Lithuania.
Jones, E. R., & Childers, R. L. (1999). Contemporary college physics (3rd ed.). WCB/McGraw-Hill.
Kasianov, V. (2013). Subjective entropy of preferences. Subjective analysis. Institute of Aviation Scientific Publications. http://kasianovv.wixsite.com/entropyofpreferences
Kasjanov, Wł. (1999). Statystyczne metody modelowania i identyfikacji w dynamice lotu. Instytut Lotnictwa (in Polish).
Korn, G. A., & Korn, T. M. (2000). Mathematical handbook for scientists and engineers: Definitions, theorems, and formulas for reference and review. Dover Publications.
Kosmodemjanskiy, A. A. (1965). Kurs teoreticheskoj mechaniki (1 chjast’). Prosvestchenije (in Russian).
Kosmodemjanskiy, A. A. (1966). Kurs teoreticheskoj mechaniki (2 chjast’). Prosvestchenije (in Russian).
Larsen, C., Paul, S., Svensson, A., & Chowdhury, S. (2017). Optimizing endurance and stability of a modular UAV design. In Proceedings of the 55th AIAA Aerospace Sciences Meeting, AIAA 2017-0244. Grapevine, Texas. https://doi.org/10.2514/6.2017-0244
Olejniczak, D., & Nowacki, M. (2019). Assessment of the selected parameters of aerodynamics for Airbus A380 aircraft on the basis of CFD tests. Transportation Research Procedia, 40, 839–846. https://doi.org/10.1016/j.trpro.2019.07.118
Rohacs, J., & Kasyanov, V. A. (2011). Pilot subjective decisions in aircraft active control system. Journal of Theoretical and Applied Mechanics, 49(1), 175–186.
Sachs, G. (1992). Optimization of endurance performance. Progress in Aerospace Sciences, 29(2), 165–191. https://doi.org/10.1016/0376-0421(92)90006-4
Sachs, G., & Grüter, B. (2020). Trajectory optimization and analytic solutions for high-speed dynamic soaring. Aerospace, 7(4), 47. https://doi.org/10.3390/aerospace7040047
Shigeru, S., Ryoji, K., & Kohei, Y. (2020). A note on maximum flight range and maximum flight duration of airplanes. Journal of the Japan Society for Aeronautical and Space Sciences, 68(3), 123–127. https://doi.org/10.2322/jjsass.68.123
Silberberg, E., & Suen, W. (2001). The structure of economics. A mathematical analysis. McGraw Hill.
Wang, S., Ma, D., Yang, M., Zhang, L., & Li, G. (2019). Flight strategy optimization for high-altitude long-endurance solar-powered aircraft based on Gauss pseudo-spectral method. Chinese Journal of Aeronautics, 32(10), 2286–2298. https://doi.org/10.1016/j.cja.2019.07.022