# Question about coordinate system convention

Hello,

I am in the process of modeling a blade for a small wind turbine, and have some questions about how PreComp defines some aspects:

Why are the bending stiffness (both flap- and lag-wise) defined with respect to axes (X_E, and Y_E in the PreComp manual) that pass through the shear center (point E, as defined in figure 13 of the PreComp manual)? From my understanding, bending stiffness should be calculated with respect to a coordinate system with its origin located at the point where the neutral axis intersects the cross section (i.e. the elastic center). However, I do not see this center being defined in PreComp’s output block, and hence I am not sure if I need to perform a conversion in order to readily use the stiffness data in an aeroelastic simulation.

I am also unclear on how the parameters flap_iner and Lag_iner are defined. From the units listed in the manual (kg-m), it seems to be (area moment of inertia [m^4])*(density [kg/m^3]), but in the description it says that these parameters are calculated about the X_g and Y_g axes, a coordinate system whose origin lies at the center of mass. How can these parameters be converted into the area moments of inertia of the cross section about the elastic axes (i.e. with origin at the elastic center), if PreComp does not output the location of the elastic center? (or does it, and if so where?)

How does PreComp define the Tension center?

Thank you very much for your time.

Dear Sudheesh,

It is difficult to support PreComp after the departure of Gunjit Bir from NREL, but I’ll try my best to answer your questions.

I agree that it is more intuitive to calculate bending stiffness about the principle axes of bending. This would be a coordinate system whose origin is the tension center (what you call the elastic center) and orientation is defined such that there is no cross flap-lag bending stiffness. By tension center (elastic center), I mean the point in the cross section where an axial load does not induce bending. However, PreComp has several simplifying assumptions, including neglecting transverse shearing, which reduces the most general 6x6 matrices (generalized Timoshenko) into 4x4 matrices (generalized Euler-Bernoulli). With this simplification, it is important to choose the reference line along the locus of shear centers, as is done in PreComp.

For a uniform material density, I agree that flap_iner and lag_iner are defined as the area moment of inertia of the cross section times the density. However, for nonuniform material density, the inertia must be computed with density inside the integral.

Best regards,

Dear everybody.

I have a question related to the sign convention used in FAST. I have generated a .wnd-file for DLC1.4 at rated wind speed for the NREL 5MW ref turbine, resulting in a change of direction of 63,6 degrees. When I get the yaw error output from FAST, the angle is negative. The tower base yaw moment is also negative, which, as far as I have understood from the coordinate system on page 8 in the FAST manual would mean that the moment is directed clockwise when viewing the wind turbine from above. What is the reason for the difference of sign of the angle between the .wnd-file and the yaw error from FAST and is my understanding of the direction of the tower base yaw moment correct?

I have attached plots of time series results and a sketch of my understanding of the tower base coordinate system of the wind turbine.

D__Dokumenter_SDU_Speciale_Sketch for parameter study Yaw error (1).pdf (13.9 KB)

Dear Jacob,

Yes, your understanding of the sign on the yaw moment is correct.

For definition of the wind direction and nacelle-yaw error, please see the following forum topic: http://forums.nrel.gov/t/is-positive-yaw-error-clockwise/582/1.

Best regards,

Dear Jason,