Linear Equations Game
Students groups act as aerospace engineering teams competing to create linear equations to guide space shuttles safely through obstacles generated by a modeling game in level-based rounds. Each round provides a different configuration of the obstacle, which consists of two "gates." The obstacles are presented as asteroids or comets, and the linear equations as inputs into autopilot on board the shuttle. The winning group is the one that first generates the successful equations for all levels. The game is created via the programming software MATLAB, available as a free 30-day trial. The activity helps students make the connection between graphs and the real world. In this activity, they can see the path of a space shuttle modeled by a linear equation, as if they were looking from above.
Can you calculate a line (flight path) to safely navigate the space shuttle through an asteroid field?Copyright 2012 Stanislav Roslyakov, Polytechnic Institute of NYU and Microsoft clipart
Before designing devices and structures, engineers model events, such as projectile motion, bouncing balls and rocket flights, to help them understand the motion that objects take. For example, aerospace engineers design spacecraft and develop vector equations to control the space shuttle. On Earth, we are able to stop movement instantly, but in space, without a medium such as air, roads or wind, space shuttles must rely on propulsion, which uses a reaction force to move an object. Space shuttles carry a limited supply of oxygen for the purpose of creating propulsion forces for movement. Making mistakes in the vector equation calculations can result in the depletion of precious materials that are essential to get back home. Thus, advance modeling of predicted space shuttle paths on x-y graphs is critical to plan and verify the distance, travel time and fuel required to complete the trip. NASA engineers were able to send a human to the moon and back with nothing but slide rulers—and without modern electronics—thanks to their very accurate vector calculations. As science progresses and technology becomes pervasive and costly to prototype, modeling can provide confidence to the expected real-world results.
After this activity, students should be able to:
- Develop a linear equation and determine its location and slope on a graph.
- Describe the benefits of modeling in engineering.