Motion dynamics modeling of objects of smooth ballistics while solving the problems of aircraft complexes flight tests

Mathematica modeling, numerical technique and program complexes


Nikolaev S. V.1*, Barantsev S. M.2**, Kolodezhnov V. N.2**, Shatovkin R. R.2***, Kupryashkin I. F.2**

1. 929th State flight-test center of the defence Ministry named after V.P. Chkalov, Akhtubinsk, Astrakhan region, 416500, Russia
2. MESC Air Force “Air Force Academy named after professor N.E. Zhukovskii and Yu.A. Gagarin”, 54a, Starykh bol'shevikov, Voronezh, 394064, Russia



The article is dedicated to developing the mathematical model of the of aerial bombs movement smooth ballistics to determine the possibility of bombing. The mathematical model is based on the numerical solution of a system of differential equations, accounting for aerial bombs ballistic characteristics, as well as their kinematic and gravitational parameters. Ballistic characteristics determine the aerodynamic properties of air weapons, significantly affecting parameters of their trajectory, and is entered into the bombing sight while the sighting angle determining. Based on this mathematical model, a computer program meant for air weapons of smooth ballistics movement simulation after their discharge from the carrier aircraft was developed. The program is useful for scientific and methodological support of aircraft testing, flight tests planning, and movement parameters computing of the air weapons. The modeling results validity evaluation was performed by comparing he obtained results with ballistic tables. The obtained error within the limits not exceeding 5% allows recommend the developed software for assessing the combat capabilities of aircraft systems when attacking ground targets during flight tests. The obtained solutions are taken as a basis of the method for studying ballistic characteristics of air weapons and computational-experimental method for determining the combat capabilities of aircraft systems when attacking ground targets during flight tests.


simulation, aerial bombs, flight tests, ballistics


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