Thoughts on Chain Sag Calculation

[Joshua]

@c0depr1sm

I analysed the chain sag and the current parobola approximation. see my analysis here and I conclude the parabola equation is good. And my catenary calculations needed successive approximation, which is coomputing intensive.

I have implemented the full catenary equation, without the need for successive approximation. I considered using a parabola equation, but the catenary equation is not complicated, is not computationally burdensome, and it does not have 1/64 inch error. This is what the catenary equation is for. Here is my post on the calculation, Post 453 (Optical Calibration Demo and Three Hours Working on a Bug - #453 by Joshua).

Here is the equation I used for calculating chain tension, in pretty-print, along with the c-code implementation (Thoughts on Chain Sag Calculation - #62 by Joshua).