Dear @Jason.Jonkman,

I derived the equations of motion for the wind turbine using the Lagrange equations. And programmed it, in comparison with FAST I have the following questions.

I would like to know how FAST takes into account the effect of rotor torque on the side to side displacement of the tower. Is there a specific formula and theory? The unit corresponding to the generalized coordinate q_tss should be N. Assuming that the torque of the rotor is known how should it be converted to the force acting on the tower in the equation?

Best regards,

Dear @Huajian.Xiao,

Presumably you are referring to the ElastoDyn module of FAST/OpenFAST.

The tower top moment is not converted to an equivalent shear force in ElastoDyn; rather, both the shear forces and moments are used to deflect the tower. Related to this, the displacement of the tower-top degree of freedom results in both translation and rotation of the tower top (where rotation is based on the slope of the deflection).

The theory basis of ElastoDyn is documented here: 4.2.7. ElastoDyn Users Guide and Theory Manual — OpenFAST v3.5.3 documentation.

Best regards,

Dear @Jason.Jonkman,

Thank you very much for your reply.

I see what you are saying about the FAST directly applying force and bending moment. May I ask if the torque **M1** of the wind turbine rotor(Fig. 1) is the bending moment **M2** (Fig. 2) acting on the top of the tower? In other words, what is the relationship (equation) between the wind turbine torque and the bending moment at the top of the tower?

Best regards,

Dear @Huajian.Xiao,

Indeed those moments will be the same unless there is also a force applied at M1, which may add to the moment at M2 (based on the moment arm distance).

Best regards,