Resonate Energy Conversion: Analysis of a Lunar Tide Power Plant Using a Variable Area Pipe

Extracting power from oceanic tides is currently a crucial topic due to the seemingly insatiable world energy demands.Development in renewable energy is required in order to reduce dependence on fossil fuels and minimize negative environmental impact.Ocean tides offer a highly predictable and less weather-dependent source of energy.Not only that, but certain locations are more affected by the gravitational lunar forcing, and therefore experience a high tidal range.One example is the Bay of Fundy, which because of its size and shape, can experience tidal ranges up to approximately 16 meters [1] due to operating close to its resonating frequency [2].With the desire to design a power plant such that it will resonant similar to or better than the Bay of Fundy, a second order differential equation was derived modeling a basic tidal power plant.The second order differential equation follows the form of a canonical spring-mass-damper system, allowing for the natural frequency of the system to be easily calculated.The proposed physical system connects the ocean and a smaller body of water by a pipe or channel.The pipe or channel can be straight, or can vary in crosssectional area in order to reduce friction in the pipe.Dimensional case studies were evaluated using a pipe with a varying cross-section.The equivalent of one coal power plant would require a turbine iii diameter of 229 feet, pipe length of 0.92 miles, and a lake size of 35 by 35 miles, roughly equivalent to the size of Rhode Island.To meet the energy demands of the entire United States, the system would require a turbine diameter of 5,347 feet, pipe length of 21.5 miles, and a lake size of 173 by 173 miles.This lake size is roughly on the order of magnitude of Lake Superior or South Carolina.iv Dedicated to Jesus Christ.v I would like to thank Dr. John Schauer, my