Theory
=====================

The theory behind RAFT is in the process of being documented. This page will be incrementally updated.
The following paper provides an overview:
 
`M. Hall, S. Housner, D. Zalkind, P. Bortolotti, D. Ogden, and G. Barter, 
“An Open-Source Frequency-Domain Model for Floating Wind Turbine Design Optimization,” 
Journal of Physics: Conference Series, vol. 2265, no. 4, p. 042020, May 2022, DOI: 10.1088/1742-6596/2265/4/042020. <https://iopscience.iop.org/article/10.1088/1742-6596/2265/4/042020>`_


..
  COMMENTING OUT TILL IT'S UP TO DATE
  Frequency Domain Equations of Motion
  ------------------------------------
  
  The overall process of RAFT is to use the input design data of a FOWT to fill out the 6x6 matrices of the equations of motion.
  
  .. math::
  
     [M+A]\ddot{X}(t) + [B+B_{visc}]\dot{X}(t) + [C_{struc}+C_{hydro}+C_{moor}]X(t) = F_{env}(t)
  
     F(t) = Re\{\tilde{F}e^{iwt}\}
  
     \tilde{F} = \|F\|e^{i\phi}
  
     X = Xe^{iwt}
  
     \dot{X} = iwXe^{iwt}
  
     \ddot{X} = -w^2Xe^{iwt}
  
     X(\omega) = [-\omega^2A(\omega) + i \omega B(\omega) + C]^{-1} F(\omega)
  
     A(\omega) = M + A_{BEM}(\omega) + A_{morison}(\omega) + A_{aero}(\omega)
     
     B(\omega) = B_{BEM}(\omega) + B_{aero}(\omega) + B_{nonlinear-hydro-drag}(X)
  
     C = C_{struc} + C_{hydro} + C_{moor}
  
     F = F_{BEM}(\omega) + F_{hydro}(\omega) + F_{aero}(\omega) + F_{nonlinear-hydro-drag}(X)
  
  Notice that the nonlinear-hydro-drag damping and forcing terms are a function of the platform positions, so these are iterated
  until the positions (X) converge.
  
  
  Member Theory
  -------------
  
  .. image:: /images/members1.JPG
      :align: center
  
  .. image:: /images/members2.JPG
      :align: center
      :width: 350px
      :height: 350px
  
  Mass & Inertia
  ^^^^^^^^^^^^^^
  The 6x6 mass matrix is calculated for each member using the properties given in the input design yaml.
  Members can be cylindrical or rectangular
  
  Hydrostatics
  ^^^^^^^^^^^^
  The 6x6 hydrostatic stiffness matrix is calculated for each member using the properties given in the input design yaml.
  
  Hydrodynamics
  ^^^^^^^^^^^^^
  The 6x6 hydrodynamic matrices for each member are calculated in one of two ways: a BEM solver, pyHAMS, or a Morison equation approximation
  
  
  
  Rotor Theory
  ------------
  
  The Rotor uses aerodynamic theory from WISDEM's CCBlade. Check out the `CCBlade documentation <https://wisdem.readthedocs.io/en/latest/wisdem/ccblade/index.html>`_ 
  for more infomation.
  
  Mooring Theory
  --------------
  
  RAFT uses the quasi-static mooring system modeler, MoorPy. Check out `the MoorPy documentation <https://moorpy.readthedocs.io/en/latest/>`_ 
  for more information.