R-functions in the Analytical Description of the Surface of a Flying Wing Unmanned Aerial Vehicle

DOI https://doi.org/10.15407/pmach2019.04.061
Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 22, no. 4, 2019 (December)
Pages 61-66
Cited by J. of Mech. Eng., 2019, vol. 22, no. 4, pp. 61-66



Tetiana I. Sheiko, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharskyi St., Kharkiv, 61046, Ukraine), e-mail: sheyko@ipmach.kharkov.ua, ORCID: 0000-0003-3295-5998

Kyrylo V. Maksymenko-Sheiko, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharskyi St., Kharkiv, 61046, Ukraine), V. N. Karazin Kharkiv National University (4, Svobody Sq., Kharkiv, 61022, Ukraine), e-mail: m-sh@ipmach.kharkov.ua, ORCID: 0000-0002-7064-2442

Volodymyr M. Sirenko, Yuzhnoye State Design Office (3, Krivorizka St., Dnipro, 49008, Ukraine), e-mail: v.n.sirenko@i.ua

Anna I. Morozova, Kharkiv National University of Radio Electronics (14, Nauky Ave., Kharkiv, 61166, Ukraine), ORCID: 0000-0002-7082-4115



Unmanned aerial vehicles (UAVs) are becoming increasingly demanded worldwide. The scope of their use is very extensive. They are used for military purposes, delivery of goods, environmental monitoring, border patrolling, aerial reconnaissance and mapping, traffic control, etc. UAVs have a number of important advantages over manned aircraft. These advantages include relatively low costs of UAVs at their long flight durations and ranges, their low operating costs, and the ability to perform maneuvers with overloads that exceed the physical capabilities of a human being, making their development more active. One cannot imagine the designing of UAVs and control systems without mathematical modeling. To build mathematical models, high-speed computers and modern software tools have been created, Solid Works, Ansys CFX, POLYE software systems being among them. There arises a problem of specifying and quickly changing geometric information to create a mathematical and computer model of the UAV being designed. At the design stage, there can be solved a lot of tasks that are put before researchers as regards the use of UAVs. At the same time, insufficient attention is paid to the parametric representation of aircraft surfaces. Expanding the scope of using the apparatus of the theory of R-functions for modeling UAV surfaces is an urgent scientific and technical task. In this paper, for the first time, using the theory of R-functions, we build up the equation of the surface of a flying wing UAV in the form of a single analytical expression with alphabetic parameters. This equation can be used in solving various practical problems as well as developing and manufacturing the product itself, for example, on a 3D printer. The proposed method for specifying the shapes of products by using a limited number of parameters can significantly reduce the complexity of work in CAD systems in cases where it is required to view a large number of design options in search of an optimal solution. In this paper, we build a 14-parameter family of flying wing UAV surfaces. By changing the values of alphabetic parameters, we can quickly explore its various forms.


Keywords: unmanned aerial vehicle, R-functions, alphabetic parameters, standard primitives.


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Received 02 October 2019

Published 30 December 2019