# Abstract

### Modeling the Twisted Savonius Wind Turbine Geometrically and Simplifying Its Construction

The drag-based Twisted Savonius Vertical Axis Wind Turbine (VAWT) has shown promising applications for use on the tops of buildings, enabling clean energy production at the site of its use, virtually eliminating transportation losses. Unfortunately, the turbine’s shape is very complex and three-dimensional because of its twist, requiring complex machinery to construct. I was able to model the geometry of the shape with the symbolic geometry program *Geometry Expressions*, developing visual models that depict the appearance of the turbine in operation and show the effects of twisting the blade. Ellipses, loci and traces comprised the visual model. The most significant finding was that the radius of the turbine is squeezed as the turbine is twisted, which occurs because of the geometric principles of the blade, not just the limitations of the materials. A greater angle of twist results in a greater potential efficiency in operation. Utilizing the calculus principles of definite integrals allowed creation of an approximation of the shape, “unrolled” into a flat surface using triangles. This can be used to build the turbine much more simply and, with refinement, could allow widespread use of Twisted Savonius turbines on rooftops with little cost relative to other alternative energy options.