SN curves
In order to set a suitable design criteria, I am looking to compare two classes of SN curves for a fatigue design, viz., E and F2, and I cannot not find a handy plot to refer to, and it is frustrating when standards fail to include. So, I channel it to write some code to roll my own:
The basic SN curve equation is as follows, which one may know is from ParisErdogan law (fracture mechanics):
\begin{aligned} N = k_1 \cdot S^{m} \newline \end{aligned}
The standard does describe it in its logarithmic form, which is as follows:
\begin{aligned} \log N = \log k_1  m \cdot \log S \newline \end{aligned}
and then it goes on to furnish its two sets of key components that form parts of the equation — highlighted below.^{1}

Playing with logarithms is fraught with error, as they are not the same as plain algebra — Leonhard Euler’s gift to the world, which reminds me I should jog my memory from highschool. There is a very nice podcast recording (mp3) on Euler’s e that also discusses the history of logarithms, which was in ancient days allowed to transform “complicated” multiplication into simple addition, which makes perfect sense in a world that had no computers, no calculators, and no slide rules. ↩