The Archimedes Screw was invented over 2,000 years ago and is still in use today! Its purpose is to transfer water to a higher elevation, and it works by turning a large, tilted screw so that the blades of the screw scoop up water, the water sits between the blades as it rides upward, and it is spit out at the top. The photo here was taken at SeaWorld in San Diego where they use two of these devices to push water uphill for their Shipwreck Rapids ride. We spoke with an engineer at SeaWorld about the Archimedes Screws in use there and the mathematics involved in them. The screw only works if it is tilted within certain angles, so the concept of slope comes into play, both for the cylindrical screw and the blades themselves. The blades form a mathematical shape called a helix, and if you look at the blades from the side, the contours of the helix match the graphs of sine waves. These sine waves must have a downward slope as they cross the axis of the screw in order to hold water as the screw turns.
During the broadcast we mentioned a research paper (link below) that determined the optimal design for an Archimedes Screw using lots of calculus and 3D graphs. Don't worry, we talked about the highlights on the program which can be viewed once it is archived at www.collegemathline.com.
This week's links:
research paper by Chris Rorres (pdf document)
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