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An improved approximate trajectory program
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Default An improved approximate trajectory program - 10-21-2007, 09:34 AM

The discussion of an approximate trajectory program at was designed to be a lot of fun, but it was short on mathematics and technical details. Furthermore, some of the parameters used in the animation were designed to simply look good and were not based on mathematical accuracy.

Now it is time to step back and take a look at the mathematics involved and to show you how to compute the required parameters as a function of target distance and launch angle.

This approach uses a circular arc to approximate a parabolic arc, which can result in a smoother animation. In order to use the circular arc as an approximation of a parabolic trajectory, it is necessary to compute the length of the arc as a function of the launch angle and the distance to the target. I have written a new program that shows you how to do that, and also explains some of the theory behind the computations.

You can download the world by downloading the zip file at and extracting the file named Trajectory02.a2w from the zip file.

You will find a discussion and explanation of the program including a cursory explanation of the mathematics at

You will also find a discussion on how to create a trajectory for a cruise missile there as well.

Dick Baldwin
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Last edited by DickBaldwin; 10-21-2007 at 09:41 AM. Reason: Correct errors
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