Geometry of the Twisted Savonius Wind Turbine

# 6. Modeling a Single Blade with CAS

In addition to being able to model the blades of the twisted Savonius wind turbine in Geometry Expressions, it is useful to model a single blade in a Computer Algebra System (CAS), such as Maple. In fact, it is actually much easier to create the blade using Maple’s 3D plot feature; however, much less can be done with the blade. In our Geometry Expressions model the surface of the blade is constructed with traces. These traces are parameterized by s and t, where s is the location vertically and t is the location horizontally around the curve of the blade.

We have one point on our Geometry Expressions model that can be moved to any place on the surface of the blade by varying s and t (see above). If we calculate the symbolic coordinates of these points, we can input them into a Maple 3D Plot and plot the surface of the blade parametrically. The problem, of course, is that our functionally realistic model with cross-pieces has eight of these points. Therefore, Our maple blade will model one of the eight sections, or could model the squeeze again (as in chapter 5). We also need to reduce our equation to having only two variables. Copying the equation from the top view (below) will help with this, because the circles are constrained by r and theta, while the ellipses are constrained by a, b, h, k and theta.