Search Results for “geometry”
Twisted Savonius Wind Turbine Full Geometric Model (without traces/surfaces)
The Twisted Savonius Wind Turbine has promising applications for rooftop usage, but its high cost has kept it unfeasible for widespread adoption. The Twisted Savonius Geometric Modeling project explored the geometric properties of the turbine's shape, and proposed a more efficient method of construction and geometric design as a result. This is the complete side view "3d" model of the turbine. It models an extremely 3-dimensional shape by using ellipses to represent tilted circles. Changing X changes the rotation of the turbine (in operation). Theta represents the twist angle between the top and the bottom of the turbine. T controls the parametric location of the vertical surface - tracing it "fills in" the blade's surface. Learn more about this side view model. Visit the Geometry of the Twisted Savonius Wind Turbine website.
Squeezing Twisted Savonius Wind Turbine Model
This model demonstrates that the surface of the Twisted Savonius wind turbine's blades are geometrically squeezed as the twist angle is increased and the parametric position is moved up and down the turbine. Learn more about the squeeze. Learn more about the Geometry of the Twisted Savonius Wind Turbine project. Note: the calculated radius in this particular example cannot be accurate because the model is a 2d geometric approximation of the real 3d shape. Accurate calculations are made from the top view model, which is visually more difficult to comprehend. The calculation here still varies accurately as the twist angle is changed and the position is moved up and down the turbine, but it also varies as the rotation is changed (which shouldn't happen).
The Three Primary Types of Wind Turbine, Animated as if in Operation (small)
The three primary types of wind turbine, the Savonius VAWT, the Modern HAWT, and the Darrieus VAWT, are animated as if in operation. I first created this model in Geometry Expressions two years ago and after sharing it on Wikipedia it became quite popular and has been reused in many places. I decided to create an updated version, which features a cleaner appearance overall and adds some coloring to help distinguish between the blades of the Savonius model, as well as to make the HAWT better resemble real turbines. Please note that this version is not in the public domain, unlike the original, however it can be reused per the Creative Commons Attribution No-Commercial No-Derivs license, in accordance with Euclid’s Muse policy.
trapezoid field
How big a circle can you fit into this piece of field? The next release of Geometry Expression will support export of pictures in HTML5 apps!!
Cam with reciprocating roller follower
Alter the parameters of the output curve and follower geometry, and see the cam shape change.
Basic Unit Circle
This very basic representation of the unit circle displays the unit circle with an input for the standard angle θ in degrees (which controls the angle between the hypotenuse and the x axis). The outputs represent the other two sides of the triangle and give their lengths through decimals. A good investigation for geometry students is to have them test out different angles here, then compare the results to those testing the angles with sine and cosine on their calculators. This allows them to visualize the unit circle in a precise diagram rather than simply running inputs and outputs on their calculators.
