Experiment of The Month

A Calculation of Trajectory

figureComputer simulations are not experimental physics. Our laboratories do not use simulations in place of the real world. However, simulations are effective tests of the models that are used in physics. This month's feature is an exploration of a model for wind resistance by senior physics major Robert Lee.

The model assumes that the wind resistance force is proportional to the square of the velocity magnitude. While this form of the resisting force is readily justified, the model based upon it does not lead easily to an analytical solution.

Mr. Lee has written a Mathematica computer program to attack the problem of velocity-squared wind resistance. He began the project as part of the physics department course that uses Mathematica software, Symbolic Computational Methods in Physics. (The course number for this offering is PHY 345.) He worked specifically on the trajectory of a batted baseball.

The program accepts two parameters as input; the pitched ball velocity, and the bat speed. It uses "reasonable" assumptions for the relation between these velocities and the initial speed of the ball as it leaves the bat. To simulate the game, the program assigns a random direction to the ball as it leaves the bat. (The direction is constrained to be within an interesting range.)

The output of the program is a sketch of the trajectory, along with the distance that the ball travels, and a comment from the author on the probable outcome of the play. It was this display that caught the eye of the MathSource editors.

MathSource is a website that describes itself as follows: "MathSource is a vast electronic library of Mathematica materials, including immediately accessible Mathematica programs, documents, and examples. Established in 1990, MathSource offers a convenient way for Mathematica developers and users to share their work with others in the Mathematica community. In MathSource you can either browse the archive or search by author, title, keyword, or item number."

The program not only earned Mr. Lee an A in the course, it has earned him a place in the MathSource database, on a website maintained for users of Mathematica. Click here to visit the website. From it you can download the software to run with Mathematica.

Mr. Lee's MathSource publication was favorably reviewed by Matthew Thomas, writing in the Journal Mathematica in Education and Research, Volume 9, No. 3-4, 2000, pages 80-83. The reviewer wished for more documentation, but said, "Kudos to the Millersville physics instructors if indeed they use NDSolve[] to introduce otherwise untouchable problems to their new students."