# The Space Shuttle’s Heat Shield Problem

By Arthur N. DiVito, Ph.D. (copyright © 2000 by A. N. DiVito)

MATERIALS NEEDED:
• rulers
• colored paper
• possibly protractors

REMARKS:

The problem described below can be solved in many ways. Variations include the use of polar coordinates instead of rectangular (thus, requiring the use of protractors), or of imposing a coordinate system in such a way that negative numbers are required.

THE ACTIVITY:

The following story is told to the teams of students: A space shuttle was recently deployed by the government. (Some teams of students will be on board the shuttle-the so called “shuttle teams.”.) The material used in the construction of the spacecraft’s heat shield is very special and produced on a secret island off the coast of North Carolina. (Other teams of students will reside on the island-the “island teams.”) Remarkably, the only contact between the shuttle and the island is by ordinary telephone! The island doesn’t even have a PC!

One day, it was noticed by a team of maintenance space walkers that certain polygonal shaped sections of the shuttle’s heat shield were missing-presumably, they were lost during the most recent re-entry into space. To make a long story short, because the shuttle must return to earth soon, patches must be made at the secret island, picked up by the Navy, passed to a rescue space mission, and delivered to the maintenance crew of the shuttle as quickly as possible. That’s were the student teams come in.

The instructor hands to the shuttle teams various polygonal shapes-these are hidden from the island teams-and exclaims, “Here are the exact templates brought into the space shuttle by the team of maintenance workers. You are to precisely determine the coordinates of the various vertices using whatever units, method (rectangular or polar) and origin you wish. Then, you must phone your results to the teams waiting at the secret island.” Those island teams-of course, the other student groups-armed only with the coordinate measurements passed on to them by the shuttle teams, will then reconstruct the exact shapes and, of course, the appropriate patches will be designed and cut, and the shuttle will eventually be saved.

Thus, the goal, needless to say, is for the island teams to deliver polygonal patches which very closely match the ones originally handed the shuttle teams.

EMPIRICAL VERIFICATION:

Empirical verification is simply a matter of overlaying the original and new polygons.

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