Elastica curves scripted in Grasshopper

I tried some Grasshopper scripting to produce elastica curves.

(The script is really basic, it uses Loop to copy and rotate a line a bunch of times. The Sin values between 0 and 1 Radians are used to vary the amount of rotation. To get many curves at the same time a range of values are fed into the VB script component.)

Below are the curves that I drew manually along the saw blade:

To my surprise it's quite a bad fit as can be seen in the image below, showing both sets of curves superimposed:

The typical "drop shape" (that appears when the ends of the curve meet) seems too wide and low. Also curves seem to go in the wrong direction (see at left arrow).