Aircraft Maneuvering c RN.

Author: Igor Makarov.

Part 4.

Part 1. Part 2. Part 3. Part 5.

Before performing the maneuver plane flies horizontally, with all the forces acting on the airplane for the balanced output of the aircraft in level flight maneuver slide need centripetal force that bends upward trajectory.

Under the influence of centripetal force   , the flight trajectory is bent downward (in the vertical plane). Here    - centripetal force  –A aerodynamic lift of the aircraft,   - lift coefficient, S  - the characteristic area of ​​the bearing surface of the aircraft or rocket, p  - air density V - flight speed,  - the pitch angle of the aircraft (aircraft or missiles) G = mg - the weight of the aircraft (the force of gravity acting on the body),  m - The mass of the movable object, g - acceleration of gravity.

As the amount of curvature of the trajectory up brake forces stanovitsyabolshe thrust propulsion speed and begins to fall, which leads to loss of lift. Differential equations of motion of the aircraft at the entrance to the "hill" in projections on the horizontal and vertical axis associated with the Earth in a Cartesian coordinate system are as follows:

Where P  - traction,  - strong resistance,    - drag coefficient,  - horizontal and vertical acceleration,   - total flight speed.  

The above system of equations of flight refers to a class of ordinary differential equations can be used to deal with them methods of numerical integration and, in particular, Euler's method, which was implemented drawing up the appropriate program in the programming language Pascal in an integrated environment of visual programming Delphi -7.

Straight step maneuver "slide". When you reach the desired angle "slide" is necessary to stop the increase in the angle of attack and fix the plane into position. In this case, the pitch angle 10. To maintain straight flight conditions necessary to satisfy the condition:

For output of maneuver "slide" need to create a centripetal force that bends downward trajectory in the vertical plane.

Maneuvering booster and a description of the equations of motion

As stated above the trajectory of the booster stage is divided into 2.

The booster after separation from the airplane starts flight in automatic mode and stabilizes in flight with the help of its controls, after that the missile makes a maneuver "hill", begins to decrease and the speed set, in time, will be sufficient to reduce the missile to an altitude of 9600 m, The bearing surfaces are automatically shot back and the brake parachute opens. With the help of a brake parachute, 2 actions are performed: reducing the overall speed of the booster and moving around the center of mass of the rocket, which is due to the external torque of the force that creates the parachute. After the rotation and exit of the booster to the vertical position, the brake parachute is fired and the launch engines of the booster are simultaneously launched.

Now consider a more meaningful phases of flight booster. The first stage - separation from the airplane maneuver "slide" and decline. All of the above actions are performed automatically. The equations of motion are the following:

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