# Calculating the Azimuth Angle used in GDW

Hello all,

As i know the axial induction factor is determined from the following equation at aerosubs/ SUBROUTINE vindinf:

A(iRadius,iBlade) = A(iRadius,iBlade) + xphi(Rzero,mode) * ( xAlpha(mode) * COS( REAL(MRvector(MODE)) * Windpsi ) + xBeta (mode) * SIN( REAL(MRvector(MODE)) * Windpsi ) )

where windpsi is the azimuth angle.As i understand this azimuth angle is determined from aerodyn using the following relation:

AzimuthAngle = ATAN2( -1.*DOT_PRODUCT( TurbineComponents%Hub%Orientation(3,:), &
TurbineComponents%RotorFurl%Orientation(2, ), &
DOT_PRODUCT( TurbineComponents%Hub%Orientation(3,:), &
TurbineComponents%RotorFurl%Orientation(3, ) ) + pi + (IBlade - 1)*TwoPiNB

while TurbineComponents%Hub%Orientation & TurbineComponents%RotorFurl%Orientation, can be determined from Fast by the following relation:

ADInterfaceComponents%Hub%Orientation(:,1) = (/ e1(1), e2(1), e3(1) /)
ADInterfaceComponents%Hub%Orientation(:,2) = -1.*(/ e1(3), e2(3), e3(3) /)
ADInterfaceComponents%Hub%Orientation(:,3) = (/ e1(2), e2(2), e3(2) /)

ADInterfaceComponents%RotorFurl%Orientation(:,1) = (/ c1(1), -1.c3(1), c2(1) /)
c1(3), c3(3), -1.*c2(3) /)
ADInterfaceComponents%RotorFurl%Orientation(:,3) = (/ c1(2), -1.*c3(2), c2(2) /)

this point makes me confused. so, is there any schematic that shows the orientation of the vectors e ( ) and c( )?.also , what is QT(DOF-DRTR) & QT(DOF-GEAZ) that are used to determine e2 & e3?.

So finally, i would like to ask how to calculate the azimuth angle that is used in GDW?, and if i assumed a simple rotor with fixed blades and rigid hub, could i calculate the azimuth angle from the simple following equation?

aerodynamic torque-generator torque= j d(rotor speed)/dt

Best regards

Hammam

Dear Hammam,

The vectors e1, e2, and e3 are unit-direction vectors corresponding to the azimuth (a) coordinate system from the FAST User’s Guide, with e1 = xa, e2 = ya, and e3 = za. The 3 elements of these vectors correspond to components in the inertia frame (i) coordinate system, with e1(1) corresponding to the xi-component of xa, e1(2) corresponding to the zi-component of xa, and e1(3) corresponding to the -yi-component of xa (notice how yi and zi are swapped due to FAST’s internal coordinate system). The vectors c1, c2, and c3 correspond to the shaft (s) coordinate system, with c1 = xs, c2 = zs, and c3 = -ys (notice how zs and ys are swapped).

The difference between the shaft coordinate system and the azimuth coordinate system is the rotation and torsion of the low-speed shaft. QT(DOF_DrTr) and QT(DOF_GeAz) are the instantaneous values of the drivetrain torsion and generator-azimuth DOFs, respectively.

If the rotor and drivetrain are rigid, I agree that you could calculate the azimuth angle by integrating the rotor speed, but I’m not sure why you would want to calculate it this way.

I hope that helps.

Best regards,

Thank you for the explanation. But, if i do not consider furling, what is the used equation in calculating the rotor azimuth angle for the GDW model?

Also, if i just want to consider wind speed change (gust) without considering the change in wind direction, would GDW model be appropriate to calculate the dynamic induction factor in this case ?

Best Regards

Mohamed Hammam

Dear Mohamed,

If your turbine does not employ rotor furling, nothing I said in my prior post would change. In this case, the shaft (s) coordinate system simply wont be influenced by rotor furling (though it still may be impacted by platform motion, tower deflection, or nacelle yaw).

Yes, the GDW model can be applied to cases with wind speed gusts.

Best regards,