This model can be found in the 20-sim demo directory.
You can open this model and simulate it yourself using the free 20-sim demo/viewer!

Pilot Ejection

Description

The pilot ejection example shows the use of the equation editor to model the trajectory of a pilot being ejected from an airplane. The goal is to determine whether the pilot can safely leave the plane without striking the vertical stabilizer of the airplane. Simulations with the help of the parameter sweep facility are used to determine the maximum angle at ejection.

Ejection of the pilot.

The ejection system is shown in the figure above. It is devised so that it causes the pilot and his seat to travel along rails at a specified exit velocity (ve) at a specified angle (qe). The seat is disengaged from the rail at position y = y1.

Trajectories of pilot and plane.

Once the pilot and seat have left the plain, a ballistic trajectory will be followed. This trajectory can be determined using absolute coordinates. Since we are interested in the position of the pilot with respect to the airplane, we will describe the trajectory in coordinates relative to the airplane. This is shown in the figure above.

The equations that describe the trajectory are given below:

	0 y < y1
	y > y1
	0 y < y1
	y > y1

where D is the drag, Cd is the aerodynamic coefficient of drag, m is the mass of the pilot and seat, g is the acceleration of gravity, is the air density, and A is the effective cross-sectional area of the pilot and seat. The initial speed v(0) and angle q(0) are equal to:

1. You can load and view this model in the Editor by selecting the model PilotEjection.em. (choose File and Open from the menu).

2. Perform a simulation run by selecting Model and Start Simulator from the menu.

20-sim will check the model, process it, and open the Simulator with the model and the predefined experiment PilotEjection.exp loaded.

3. Choose Simulation and Run to start a simulation.

4. Try new simulations with new parameter values (choose Properties and Parameters to change parameter values).

5. You can also investigate the effects of the airplane speed on the pilot and seat trajectory.

6. Choose Tools and Multiple Run Wizard and Parameter Sweep.

As you can see in the various pages (choose Next a few times), a parameter sweep is defined for the parameter va (airplane velocity), from 50 m/s to 300 m/s.

7. You can start a parameter sweep by selecting Simulation and Multiple Run.

The results are shown in the figure below. The airplane itself is projected onto these trajectories. As can be seen the maximum allowable airplane speed with the given set of parameter values is 300 m/s.

Several pilot and seat trajectories for varying airplane speed.

3D Animation

A 3D Animation has been constructed to illustrate this model. It will open as soon as you open the experiment. Try to select the various camera positions that are available (double click on the plane and select Next Camera from the 3D Animation Properties window).