Whats New
In this version I have rewritten the entire underlying model. In the first version the model was discrete so that at each step you first turned and then moved forward.
Figure 1

This meant that the path was made up of small straight lines, even around the corners (as in Figure 1). In the diagram, the blue line represents the path the vehicle/plane took before making a 360 degree turn. In the simulation the time step is variable, therefore, there is no way to accurately estimate the position on the circle. One of the obvious problems is that by going in a straight line, as opposed to a curve, you travel a shorter distance. Also, due to the varying lengths of the time steps (length of the line), it is not possible for these lines to match the curve of a circle.
Figure 2

This problem is easily seen when it to a more extreme case. Instead of having short lines and small changes in direction, have long time steps (long lines) and large changes in direction. In Figure 2 and 3 we are making 90 degree turns before making the straight move. In Figure 2, the square path covers the same distance as the circle but, because of making such large changes in direction, it is difficult to reconcile both paths to each other. Also, it is near impossible to figure out if a point is inside or outside the turning circle.
Figure 3

In figure 3 the square path covers the turning circle better but with the first and last turn are only half a turn.
After discovering this lack of precision with the discrete model in version one, I decided to get the model right before moving any further. Version 2 is a continuous model, this means that when the vehicle/plane is going around a corner it calculates where the center of the turning circle is, and then moves around that point. This approach is very exacting and this could be its downfall in the future, but I like the precision.
