Page 14 - DCAP601_SIMULATION_AND_MODELING

Simulation and Modelling

Notes
Example: Suppose a fighter aircraft sights an enemy bomber and flies directly toward it,
in order to catch up with the bomber and destroy it. Here the target is the bomber, it continues
flying along a specified curve so the fighter, which is the pursuer, has to change its direction to
keep pointed toward the target. Now you are concerned in determining the attack course of the
fighter and in knowing how long it would take for it to catch up with the bomber.
If the bomber flies along a straight line, the problem can be solved directly with analytic
techniques. On the other hand, if the path of the bomber is curved, then the problem is much
more complicated and generally cannot be solved directly. To solve this curved path problem
you will use simulation under the following simplifying conditions:
1. The bomber and the fighter are flying in the same horizontal plane when the fighter first
sights the bomber, and both stay in that plane. This makes the pursuit model two-
dimensional.
2. The fighter's speed VF is constant (20 kms/minute).

3. The bomber's path (i.e., its position as a function of time) is specified.
4. After a fixed time span t the fighter changes its direction in order to point itself toward
the bomber.

First we introduce a rectangular coordinate system, which is coincident with the horizontal
plane in which the two aircraft are flying. Let we choose the point due south of the fighter and
due west of the bomber at the beginning of the pursuit as the origin of this coordinate system.
Let the distances be given 1(45-123/77) in kilometers and the time in minutes. We start measuring
the time when the fighter first sights the bomber.

Now we will represent the path of the bomber which is known to us in advance by two arrays,
the east coordinates and the north coordinates at specified moments or we can say each minute.
We call these coordinates XB(t) and YB (t), respectively. They are presented in the form of a table
(in kirometers) below.

Likewise, we will represent the path of the fighter plane by two arrays XF(t) and YF(t). In this
example, initially we are given
YF(O) = 50 kms, XF(O) = 0 kms.

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