Mathematical Equations for the forces/moments (ElastoDyn)

Hi Jason and Bonnie,

I was wondering where would I be able to find the mathematical equations or theory behind the computation of the forces and moments (YawBrMyp, RootMyc1, YawBrFxt, TwrBsMyp etc) from ElastoDyn Module of FAST ? I’m trying to understand the results I am obtaining from FAST and knowing the theory/equations behind the results would be really helpful for me in my research.

Yohhan Karkera

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Dear Yohhan,

There are many topics on this forum pertinent to your question e.g. the following forum topic provides a good discussion on the structural model of FAST v7, which is equivalent to the ElastoDyn module of FAST v8, plus links for further information:

Best regards,

Dear Jason,

Thank you so much for your reply. I will go thorugh the forum topic you sent me.


Dear Jason,

I want to calculate the interaction forces of the aerodynamic loading at the top of the tower. I want to have a reduced order model of the wind turbine, where the aerodynamic loadings are applied at the top of the tower. From FAST, the output parameters that I am using are “YawBrFxp”, “YawBrFyp”, “YawBrFzp”, where YawBrFxp is the thrust force, and the other two loads are the forces in SS and vertical direction. My first questions is what is the cause of the loadings in SS and vertical directions? Is it vortex induced loading of the wind, mass imbalance or …?

My other question is regarding the bending moment outputs “YawBrMxp”, “YawBrMyp”, “YawBrMzp”. Can these moments directly be applied to the yaw joint?

Generally, can I model the reduced model of the wind turbine (tower + foundation) using these 6 forces and moments at top of the tower and simulate my system?


Dear Vahid,

The ElastoDyn outputs YawBrFxp, etc. represent loads transmitted from the RNA to the tower through the yaw bearing. They include all load contributions, including applied aerodynamic loads, weight, and inertia associated with system motion. If the turbine is modeled rigidly (all DOFs disabled in ElastoDyn), then the inertia terms would be zero. I would expect nonzero terms in all load components unless the rotor is axisymmetric with no tilt and the wind is uniform and without turbulence and shear, which would otherwise generate loads in all components.

I’m not sure I understand what you want to do–it sounds like you want to take the loads output from ElastoDyn and apply them different tower + foundation model–but you’ll have to be careful in how you consider the inertia terms of the RNA and the aero-elastic response of the rotor, which depends both on blade and tower flexibility.

Best regards,

Dear Jason,

Thank you for your reply, really appreciate that.
Yes that’s what I want to do. I want to model the tower + foundation in a FEM software, and instead of having RNA + blades, I want to take the loads output from FAST and apply them on the top of the tower. Actually I am not sure which outputs are the best ones to use here (I am using YawBrFxp, YawBrFyp, YawBrFzp for the forces, and YawBrMxp, YawBrMyp, YawBrMzp for the moments).

I was not expecting to see large values of force and moment in SS and vertical directions. I am using OC4 Jacket configuration (Test 21).