Mechanical (MAE) Curriculum

The project involves optimizing the launch angle, initial height, and velocity to ensure the ball reaches the specified distances, while assuming negligible drag and friction. The preliminary design centered on a linear launcher using a PVC tube, springs, and a crossbar to control the force and velocity of the ball's launch. Through mathematical analysis and simulations, our team confirmed the viability of the design, with calculated velocities and trajectories aligning with the project’s requirements and expected performance.

The primary focus of this section was calculating and selecting the appropriate spring constant and displacement to achieve the necessary launch velocity, using a spring with a calculated constant of 11.5 N/m. A revised linear launcher design incorporates a PVC tube, extension springs, and a crossbar mechanism to transfer energy from the spring to the ball. Mathematical analysis, including the work-energy theorem, confirms that the spring displacement and velocities fall within achievable ranges, with expected deviations in trajectory due to neglecting drag and friction.

The project builds on previous work by applying rigid body kinematics to model the system, focusing on the catapult arm's spring displacement and the launch angle required for each target. Using conservation of mechanical energy, the report details calculations for the moment of inertia, center of mass, and the relationship between spring displacement, angle of launch, and initial velocity. The analysis, verified through Excel optimization software, confirms that the chosen spring and angular deflection provide feasible solutions, while trajectory predictions are consistent with expected physical outcomes, though small deviations due to drag and friction are anticipated.