3D Modelling

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 Airfoil

Here 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). complexity C++ library Excel engineering functions complex(1,0) 1

So the formula in programming terms would look like...

newpoint = ((originalpoint - radius)^trailing_egde_angle) / (originalpoint - radius * thickness_percentage)^(trailing_egde_angle-1)) + length

where:

newpoint (Y)

originalpoint

radius

trailing_egde_angle (k)

length (l)

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")