What Parabolic Shape Most Efficiently Reflects Solar Rays to a Focal Point?
Beth L. 7th Grade, Ascension Catholic School, Melbourne, Florida Teachers: Mrs. Cengia and Sister Joseph Barden (View larger image) Abstract: Parabolic shapes are used to collect or project light and heat in many products within the home such as lighting fixtures, electric space heaters, and solar water heaters. All algebra students study the parabola, but little is mentioned of the best parabolic shape to use in these items. The purpose of this research project was to determine which parabolic shape most efficiently reflects solar rays to a focal point The quadratic equation, y = ax2 + bx + c, was initially used and the values of “b”and “c” were made equal to zero to simplify the equation to y = ax2. Five parabolic curves were then selected by solving for “a” at 4-inch height increments at the maximum width of x=8 inches. The focal point for each parabolic curve was then determined using the equation, p=1/(4a). Five foamboard, parabolic troughs, 16 inches wide by 12 inches long, were
