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")