I believe the issue with your hand calculation is that you are not taking the unique coordinate systems of each blade into account. The local z azis of each blade is directed along the coned axis, and so, differs between each blade by the local precone and azimuth angles. See a description of this coordinate system here: 4.2.1.2. Coordinate systems — OpenFAST v3.5.3 documentation.

AeroDyn outputs BαNβUndy and BαNβUndz are the ambient wind velocity at each blade output node projected along this local coordinate system.

Dear @Jason.Jonkman
Thanks for your prompt response.I reviewed the coordinate systems and checked my own version of OpenFAST. I found that my OpenFAST version is v3.5.0 and AeroDyn is v15. So for the local blade coordinate system, I referred to this coordinate system: (4.2.1.3. Input Files — OpenFAST v3.5.3 documentation), and for the hub coordinate system, I referred to this below:

However, my hand calculation still encountered the same two issues as before.

RtVAvgzh。The figure below shows my understanding of the local coordinate systems for Blade 1 (B1) and Blade 2 (B2), as well as the hub coordinate system based on t=0 and AzimB1Up=Azimuth=0.

Based on the aforementioned coordinate systems, my hand calculations are shown below, however,
-1.61 cos2.5≈-1.61,-1.57cos2.5≈-1.57,……
RtVAgzh=(-14.17-14.5-0-1.63-0)/57*cos2.5=-0.52≠-1.05？

BαNβVUndz. Based on the figure above, I calculated the VUndz for Blade 2.However,
B2NβVUndz=Vinflowsinθ=12xsin2.5=0.52≠0 ?

Please correct me where perhaps my understanding is wrong.
Best regards,

I’m not following all of your calculations, but just a couple comments:

The hub coordinate system used by AeroDyn differs from the hub coordinate system used by ElastoDyn, the latter of which is documented in the old FAST v6 User’s Guide that you reference. While the ElastoDyn hub coordinate system is tied to the azimuth angle of blade 1, the hub coordinate system used by AeroDyn is tied to the inflow-skew angle, as discussed in the following forum topic: Azimuth Angle of the Blade. ← This is not correct; see my post dated Aug 2, 2024 below.

Given that coned axis is not aligned with the hub z axis, the flow normal to the coned axis (x) will also contribute to flow along the hub x axis.

Dear @Jason.Jonkman
Thanks a lot for your prompt response.I carefully reviewed the AeroDyn hub coordinate system link you provided. Based on your post from February 15, 2017, I drew the AeroDyn hub coordinate system as shown in the following figure,

but something feels off, and I would greatly appreciate it that you could help me directly modify and mark the X, Y, and Z axes in the hub coordinate system used by AeroDyn on the figure above. I would have planned to uploaded my own DWG format graphics drawn in CAD for convenience to modify, but I don’t know how to upload it here and failed.
My case is that Rtskew=5°, and RtVAvgxh, RtVAvgyh, and RtVAvgzh are 11.95, 0.00, and -1.05, respectively (m/s).

If Rtskew=0, the hub coordinate system used by AeroDyn and the hub coordinate system used by ElastoDyn are identical. Is that correct?

You have not shown a right-handed coordinate system. But your graphic is correct if you have flip the orientation of the z-axis.

That said, I realized I made a mistake in my prior post. What I described in my prior post is actually what AeroDyn internally calls the “disk” coordinate system. The hub coordinate system used by AeroDyn is actually consistent with the ElastoDyn hub coordinate system. Sorry for the stating this incorrectly.