Reference for FAST twisted shape function method


I am looking for an original reference for calculating the twisted shape functions in FAST. The method, which defines the total blade curvature as the combination of curvature in each direction oriented by the pre-twist, is explained in Jonkman’s 2003 and Wilson’s 1996 reports, however there is no reference for the method. Do you know of any references for this method, or know where Wilson came up with this method (perhaps some standard technique in the calculus of curves)?

Thank you for the assistance.

The earliest reference I have for this method is:
Bielawa, R. L.: Aeroelastic Analysis for Helicopter Rotor Blades with Time Variable, Nonlinear Structural Twist and Multiple Structural Redundancy- Mathematical Derivation and Program User’s Manual. NASA CR-2638, February 1976.

No references are made when the method is introduced (p. 19) in the above report.


Why is a reference needed? The derivation of the twisted shape functions follows directly from the curvature equations using calculus. One must start with the curvature equations, in turn, because the bending stiffness is defined in a system that rotates with the pretwist.


I asked for a reference because it was not obvious to myself how to derive the equations for inplane and out-of-plane curvature (such as Eqs. 3.12 and 3.13 in your 2003 report).


Eqs. 3.12 and 3.13 in my 2003 report are simply the trigonometric rotations of the flap and edge curvatures into in-plane and out-of-plane curvatures.