Hello again,

I made some investigations on my own on this topic and now would like to share them with you with the hope to better clarify the cause of the F2 pattern.

Using the Px, Py, Pz load distributions output by WISDEM *wt.rotorse.rs.tot_loads_gust,* and using the twist angle distribution to make the coor. sys. conversion (as per Fig.26 in WISDEM documentation), I calculated the inplane and outplane loads on the blade.

Then I converted these loads from the blade coor. sys. to the principal-axes coor. sys. to calculate F2 (I call this result F2’ here). I used this conversion equation:

```
F2’ = Foutplane⋅cos(convAngle) - Finplane⋅sin(convAngle)
```

where convAngle = twistAngle + alphaAngle as found in *rotor_structure.pyL434*.

Finally, I split F2’ in two terms to separate the contribution of the outplane load from that of the inplane load:

```
F2’ = Foutplane⋅cos(convAngle) - Finplane⋅sin(convAngle) = F2’a - F2’b
```

The plot below shows the trends of the inplane and outplane loads, the F2’, F2’a, and F2’b calculated by me, the F2 calculated by WISDEM (F2 original), and the convAngle (conversion angle, ordinates on the right red vertical axis) . Of course, I have used for my F2’ calculation the same Px, Py, Pz used by WISDEM *wt.rotorse.rs.frame* to output *F2 original*, and also all the other variables needed for the loads conversions between coor. sys. are from the same WISDEM calculation.

I see that:

- The trends of the inplane and outplane loads are smooth and show their absolute maximum values at the blade root
- F2’ shows the same decreasing pattern as F2 for the blade span ≤ 25 m:
- F2’ matches perfectly F2 original from the blade tip down to ~ 47 m of span, and there appear noticeable differences only for blade span ≤ 24 m ranging from 3% to ~6% with a max of 13.6% at span ~ 14 m
- this decreasing pattern is present also in F2’a with the only difference of lower values

So the decreasing pattern of F2’ in going towards the blade root looks due mostly to the effect of the conversion of the load in the principal-axes coor. sys., that is to the contribution of cos(convAngle), since Foutplane trend is smooth, and F2’a is just equal to Foutplane⋅cos(convAngle). Therefore, also the decreasing pattern of F2 original may be due to the conversion of Px, Py, Pz in the principal-axes coor. sys. as required by Frame3DD.

Then, doing my calculations I realized that my numerical integration algorithm output a result vector one-element shorter than the input vector, so to require the repetition of the last result to have back the length of the input vector. Also Frame3DD called by WISDEM makes a numerical integration of Px, Py, Pz so this element repetition may explain why the two F2 values closest to the blade root are the same.

Finally, I have also a **question**: why F2’ trend does not match F2 original for span ≤ 24 m so well as for the rest of the blade span? Do I miss some factors in my conversion equation?