The first step in creating the Siluro II is to 3D model it. ## Siluro II Tear Drop
To calculate the perfect teardrop shape we used the Van de Vooren symmetrical airfoil teardrop from http://www.mh-aerotools.de/airfoils/javafoil.htm ## Van de Vooren AirfoilHere is some information on the maths: Low Speed Aerodynamics by Katz and Plotkin
The simplified version (my understanding) is we transform a circle into an aerodynamic shape (sort of how a rain drop forms its shape). We use complex numbers to represent points on the initial circle. Complex numbers can be thought of a number with an "x" part (also called "real") and a "y" part* (also called "imaginary", "i" or "j") and these parts are treated separately. The "x" and "y" parts can be plotted on a graph and therefore we can use complex numbers to define a circle (i.e. calculate x and y from an angle and radius).
Using "some" formula we can transform a set of complex number points into a new set of complex number points (e.g. a circle into our aerodynamic shape or a squiggle).
So the formula in programming terms would look like...
where:
Here is a Excel plot which shows that it works:
Here is the same visualised through OpenGL/C++
6.6 Airfoil with Finite Trailling-Edge Angle
*actually it's not called the "y" part but think of it that way as it gets mapped to "y" in a typical 3D space (or "z") |