Mathematical model of the flight of the object-controlled gliding parachute system taking into account the terrain


Аuthors

Bebeshko A. 1*, Ivanov P. 2**

1. Air force academy named after professor N.E. Zhukovskii and Y.A. Gagarin, Voronezh, Russia
2. Research Institute of Aeroelastic Systems, 85, Garnaeva str, Feodosia, Crimea Republic, 298112, Russia

*e-mail: bebeshko-2003@mail.ru
**e-mail: Ivanovpetr@rambler.ru

Abstract

The task of navigation and guidance of the object – guided gliding parachute system to the target is one of the most important in the theory and practice of guided parachute systems. The problematic part of this task is navigation and guidance in automatic mode under conditions of complex terrain relief and difficult wind conditions in the guidance zone. The presented article provides an example of developing a method and constructing a mathematical model for targeting the object – controlled gliding parachute system at a target, with account for the terrain relief in automatic mode (in radio silence mode). A program for the system navigation and guidance to the target point for the onboard computer has been developed.
The mathematical model of the flight program with account for the terrain relief is based on a system of six differential equations of the system motion, with regard to a number of communication conditions for the moments of roll and yaw, the angular velocity of rotation in a U-turn and the angle of roll. Solution of the said problem requires herewith the the following preliminary initial data loading into the onboard computer:
1. Topography vertices coordinates and equations of the flyby obstacle level lines.
2. Coordinates of the landing point behind the obstacle.
3. Building a flight route.
It is necessary to set the altitude, speed and course of the object-SCP system at the starting point of the flight path to build a flight route.
The flight route is being built by the terrain map. The trajectory marking is performed by sections and times of their achieving.
The course to the beginning of the trajectory section is being selected. The entire trajectory consists of the simplest components such as rectilinear flight and U-turns or turnovers (left or right) at a given angle, depending on the direction of the obstacle fly-around. The relative altitude of the flight herewith is constantly monitored, with account for the obstacle level lines (mountains), to avoid an unauthorized landing with an undershoot to the target. That is, the vertical section of the flight path is accounted for (projected) in advance as well.
The flowchart of the program algorithm is as follows.
1. Initial data loading.
2. Computing initial conditions and characteristics for the time instant of the steady-state flight mode commence.
3. Plotting the flight path by the method of division into sections and designing the flight program.
4. The Runge-Kutta method implementation for solving a system of differential equations of ballistics.
4.1 Entering the UPR flight control unit.
4.2 Entering the OMEG module if necessary; computing the angular velocity of the turn and the angle of roll.
4.3 Computing current ballistic parameters and coordinates of the system position at each time instant with regard to the terrain relief.
5. Plotting graphs of the ballistic parameters functions and the flight path of the system.
In its final part the article provides information on the possible improvement of this terrain obstacle avoidance program, with account for the difficult wind situation in the flight zone, which will require additional information about the wind situation in the flight zone and its introduction into the program of automatic control and guidance of the object-UPP system to the target.

Keywords:

navigation and guidance, object-guided gliding parachute system

References

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