First a lot of definitions. See the picture on the right.
Strut k climbes up from the bottom (a red spot on the circle) to a blue point on the ellipse at the top. A string runs back from this top point to the bottom (another red point on the circle). This other red point is the bottom of strut k+v. The formula for the bottom of strut k+v is:
From the bottom of strut k to the bottom of strut k+v, one can draw a line with direction f:
The end of strut k lies on the intersection between the line from the heart of the circle with direction f (see the green line) and the ellipse
The equation that describes the green line is:
The following equation applies to each ellipse:
Equation (6) and (7) give the following result:
Equation (8) and the abc-formula describe the X-coordinate at the top for each strut k, and with equation (6) als the Y-coordinate.
The length of the strut is:
with Z being a freely selectable height of the strut.
The length of string c (from the top of strut k to the bottom of strut k+v) is described as:
The length of string b (from the top op strut k to the top of strut k + 1):
And just for completeness (but this is nothing new): The length of string a (at the bottom):