Most of MoorDyn’s theory is described in the following publications. This page gives a very high-level overview, highlights specific theory aspects that may be important to users, and lists the papers where more detail can be found.
MoorDyn is based on a lumped-mass discretization of a mooring line’s dynamics, and adds point-mass and rigid-body objects to enable simulation of a wide variety of mooring and cabling arrangements. Hydrodynamics are included using a version of the Morison equation.
- MoorDyn v2 contains all the features of v1 with the following additional features:
- Simulation of 6 degree of freedom objects
- Non-linear tension
- Wave kinematics
- Bending stiffness
- Bathymetry
- Seabed friction
The main difference between MoorDyn-C and MoorDyn-F is that MoorDyn-C uses quaternions to describe the orientation of 6DOF objects, while F uses traditional Euler angles to handle 6DOF object rotations.
In the following figure the 6DOF object orientation angles convention is depicted:
The roll and yaw angles, ϕ and ψ, follow the right hand criteria, while the pitch angle, θ, follows the left hand criteria. This way the classic rotation matrices can be considered,
The latest MoorDyn-C internally uses quaternions to describe the location and orientation of 6 DOF objects. Externally MoorDyn-C behaves the same as MoorDyn-F, using Euler angles for both inputs and outputs. Quaternions are a common alternative to Euler angles for describing orientations of 3D objects. Further description of quaternions can be found in PR #90 in the MoorDyn repository, put together by Alex Kinley of Kelson Marine: #90 (comment)
The theory behind MoorDyn is available in a collection of papers, listed below by which version they were implemented in.
The v1 lumped-mass formulation of MoorDyn as well as its validation against experiments:
Coupling with WEC-Sim or any Simulink code for wave energy converter simulation:
Version 2 builds upon the capabilities of Version 1. The theory behind the new features is described in the following references.
Early work on seabed friction and independent fairlead points:
Preliminary comparison of seabed friction formulations:
Overview of MoorDyn v2:
Implementation of bending stiffness modeling for power cables:
The Fortran version of MoorDyn is available as a module inside of OpenFAST:
Dynamics of 6DOF objects follows a similar approach to Hydrodyn:
https://www.nrel.gov/wind/nwtc/assets/downloads/HydroDyn/HydroDyn_Manual.pdf
Quaternion references:
- Fossen, Thor I. Handbook of marine craft hydrodynamics and motion control. Page 25 John Wiley & Sons, 2011.
- https://en.wikipedia.org/wiki/Gimbal_lock
- https://www.ashwinnarayan.com/post/how-to-integrate-quaternions/
- https://en.wikipedia.org/wiki/Quaternion#Hamilton_product
- MoorDyn-C Packages used:
- Eigen: https://eigen.tuxfamily.org
- Catch2: https://github.com/catchorg/Catch2
- KISSFFT: https://github.com/mborgerding/kissfft