Team: 40
School: Santa Fe Preparatory Sch
Area of Science: Energy
Interim:
Definition of Problem:
Climate change is undoubtedly one of the most expansive issues of our time and as such we decided to tackle one aspect of it in our project: the use, development, and implementation of renewable energy sources. However, this can get very broad very quickly, so we decided to define a problem “impact area†as the state of New Mexico. Why statewide? Because there is enough specific data from the state energy department to compare current fossil fuel with projected renewable energy uses. That is, if we look at a national level, we cannot have enough of a detailed and precise mathematical model because the dataset is too large and if we look citywide we do not have enough data, so statewide is the middle ground. So, given this middle-ground dataset, our team plans to use a taylor-series based mathematical model to predict the efficiency of separate renewable energy sources as compared to fossil fuels within their predicted implementation in New Mexico for the next 10 years.
Plan:
Our plan is to use taylor series to model how efficient the production of energy using different categories of renewable energy sources is in New Mexico over the next ten years. This can be paired with a program that will modify the taylor series to match with different input points (e.g. what year is in progress and what type of energy source). This will be important because not all energy sources are created equal in terms of efficiency and this is one of the primary values that we are trying to determine for all of our sources in this project. After we make the code, we will then run the code on several datasets gathered from the New Mexico department of energy and compare them against another to see if the code matched up with the theoretical math portion of the project. Visuals and other aids will be used to graphically illustrate things when necessary since equations do not give the entire insight into the problem. Results will be documented in report format and code will be commented and have logs to reflect the research process.
Progress:
So far our team has gathered data on different efficiency, power, and other vital statistics for different energy sources being examined within the project. We have put all of these statistics together in a spreadsheet and are examining the mathematical relationships between different inputs and outputs for each of these parameters. Second, we are working on a taylor polynomial approximation of a function that we want to use to construct the predictions for how efficient each of these renewable energy sources will be compared to fossil fuels in New Mexico in the next ten years. We are also writing a program to compute these taylor approximations for different inputs, but we are still adjusting the code.
Expected Results:
We expect solar power within New Mexico to have the most returns and be the most efficient over the next ten years, however, as we are still constructing our model, many more parameters need to be accounted for in order to make such a prediction.
Citations:
Abramowitz, Milton; Stegun, Irene A. (1970), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, New York: Dover Publications, Ninth printing
Thomas, George B., Jr.; Finney, Ross L. (1996), Calculus and Analytic Geometry (9th ed.), Addison Wesley, ISBN 0-201-53174-7
Greenberg, Michael (1998), Advanced Engineering Mathematics (2nd ed.), Prentice Hall, ISBN 0-13-321431-1
"Taylor series", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
Weisstein, Eric W. "Taylor Series". MathWorld.
Mentor: Randy Roberts
Team Members:
Sponsoring Teacher: Jocelyne Comstock