Blade root and yaw bearing loads

Hi everybody,
I am developing my own BEM code and comparing the results I get with FAST. I am experiencing some problems in the calculation of the loads acting on the yaw bearing.
I am working with an on-shore wind turbine, with constant rotational speed 12.1 rpm, constant and uniform wind speed 8 m/s, fixed nacelle at zero yaw angle.

Here attached two figures. The first one which shows the blade#1 root loads, the second the loads on the yaw bearing Please note that my CS is different from the one in FAST: x is directed along the blade axis, y from the trailing edge to the leading edge, z pointing along the shaft (upwind turbine).

I obtain a difference on the out-of-plane force/moment at the blade root + a difference on the blade root pitching moment. It seems that these differences are then reflected on some of the yaw bearing loads.

Here I have some questions:

  1. Is it possible that the little percentage difference I get for the out-of-plane force and the out-of-plane bending moment leads to so much different yaw bearing loads? The order of magnitude of the out-of-plane bending moment is 1e4, while the one of the yaw bearing yaw moment is 1e2 - maybe a little error on the first one gives a big error on the second one?

  2. How is the blade pitching moment calculated in FAST?
    I am currently doing two cross products:
    a) cross ( vector from origin of coned coordinate system to aerodynamic center of studied airfoil, aerodynamic force)
    b) cross ( vector from origin of coned coordinate system to gravity center of studied airfoil, centrifugal + gravitational force)

Thank you all for your advice.


[Units on YawBr forces are kN obviously, not kNm - sorry for this]

Dear Michele,

I have doubts that small differences in blade-root loads can cause the large of differences in the yaw-bearing loads that you are showing. The yaw-bearing loads are also influenced by tower deflection; does your model account for that?

Please see my May 3, 2012 post in the topic found here for a basic description of how FAST calculates the blade root moments (including bending and pitching): Your appraoch sounds similar to what FAST does, although I notice a few subtle differences:
*FAST also includes the aerodynamic moment (Cm) in the calculation
*FAST uses all inertial loads (centrifugal, coriolis, gyroscopic, etc.), not just “centrifugal” loads
*In FAST, the position vectors follow the blade as it deflects

Best regards,

Dear Jason,
thank you for your reply. I forgot to say that all the bodies in my model are perfectly rigid. So the blades do not deflect, and neither does the tower.

My out-of-plane force is a little bit different from the one in FAST probably due to differences in the BEM model (I am following the steps given by M.O.L. Hansen, my professor at DTU); moreover, I am including the aerodynamic pitching moment [M = 0.5AirDnsChord^2Cmnorm(Vrel)^2].

I have a few questions though:

  1. I assume that the aerodynamic forces are applied at the aerodynamic center (CA) of the airfoil, and that the inertial and gravitational ones at the gravity center (CM) of the airfoil. Is that right?

  2. This way, my position vector goes from the blade root to CA/CM when calculating the moment given by aerodynamic/inertial forces. Is that right?

I am quite sure about the way I calculate the yaw bearing loads also: I applied my algorithm to the blade roots given by FAST, and I get exactly the same results for the yaw bearing loads as given again by FAST. So, I would say (with no certainty though) that not so big errors in the blade root loads affect heavily yaw bearing loads?

I apologise for so many questions and messages, the problem is getting a little bit hard to me.

Thank you all in advance.


Dear Michele,

The answer to both of your questions is, “yes.” Aerodynamic laods are applied at the aerodynamic center and inertial/gravitation loads are applied at the mass center.

I’m a bit surprised that small differences in the blade-root loads can lead to large differences in the yaw-bearing loads, but it sounds like you’ve confirmed your calculation with the blade-root and yaw-bearing loads output by FAST.

Best regards,

Dear all,
I am still working on the matter. I found out that the phase delay I have on the out-of-plane blade root forces is very important in the yaw bearing calculation - indeed if it is one of the main reasons for my yaw bearing yaw moment to be so different.

I am trying to understand why I have that phase difference (my curve anticipates the FAST one by 0.5 s approximately, being T=5 s the period of the rotor motion and B = 3 the number of the blades). Any hint about this???

I have one question: when the blade#1 azimuth is zero, assuming that there is no precone angle, would the pitch axis be oriented as the z_a-axis (in FAST C.S.)?

Thank you all,


Dear Michele,

I’m sorry, but I don’t know what would lead to the phase shift.

For a 3-bladed turbine in FAST, “yes,” the pitch axis of blade 1 will be parallel to the z axis of the azimuth coordinate system if there is on precone. (For a 2-bladed turbine, teeter and delta-3 will also be included.)

Best regards,

Dear Jason,
thank you so much for your kind answers and your patience. I know I have been a little bit insistent lately!!!

I will find out a way to solve this problem.


Michele Martini

Dear all,
I am reading the source code of FAST, especialli the FAST.f90 file.

At row 6052,the root force and bending moment for blade k given by section j is calculated as follows:

CALL CrossProd( TmpVec2, rS0S(K,J,:), TmpVec1 )


TmpVec1 = FSAero(K,J,:slight_smile:DRNodes(J) - ElmntMass( Gravity*z2 + LinAccESt(K,J,:slight_smile: )

As I understood, rS0S(K,J,:slight_smile: is the vector that goes to the blade root to the current blade section J, along pitch axis.

My question is: if aerodynamic forces act on the aerodynamic centre of the airfoil, and gravity/inertial forces act on the gravity centre of the airfoil, why the moment they give at the blade root is calculated with the same position vector rS0S(K,J,:)? Shouldn’t we consider a different position vector for the aerodynamic and the inertial/gravitational forces (since they act on two different points of the airfoil?)

Thank you for your attention.


Dear Michele,

The aerodynamic loads can be applied at any point in the cross section, as long as the aerodynamic moments includes the offset between the aerodynamic center and the mass center. In FAST, variable FSAero contains the aerodynamic forces and variable MMAero contains the aerodynamic moments. You can see earlier in the FAST source code that MMAero is based on the aerodynamic pitching moment at the aerodynamic center plus a contribution from the aerodynamic forces (FSAero) and the position vector from the center of mass to the aerodynamic center of the cross section.

I hope that helps.

Best regards,

Hi Jason, I am trying to approximate the blade root axial force(Rootfzc1) for test 19 operating at constant wind speed without adding the effect of centrifugal force and gravity.
The first question that I have is in which coordinate system it is calculated? Is it calculated spanwise? How can I approximate it?
warm regards

Dear @Ahmed.Hassan,

I’m not sure I understand your question. Why do you need approximate RootFzc1 when it is an available output of OpenFAST? Moreover, the centrifugal and gravity forces likely dominant this axial force.

Best regards,

Dear @Jason.Jonkman ,
Thank you for your reply.
I want to calculate RootFzc1 with the given settings/parameters of the turbine even if I don’t have FAST or I don’t have to run simulations again and again. In one of the papers I read, it was given as
RootFzc1= Centrifugal force-Gravitational force+Force radial to rotor plane(directed along the longitudinal axis of a blade ).
Is the above relation true?
warm regards

Dear @Ahmed.Hassan,

Yes, that equation looks correct, although each term is dependent on multiple effects, including the azimuth angle, shaft tilt, and coning. I would guess the centrifugal force and gravitational force (azimuth dependent) terms dominate in most cases.

Best regards,

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