# Mooring Model

The mooring model technique allows for the simulation of cables, mooring lines etc. considering the dynamic effects of motions and the flow field. Hereby, the approach implemented in *pan*MARE is based on a lumped mass model. Besides simple point to point lines with constant properties, also varying line properties, floaters or weights, and linked lines can be modelled.

In the lumped mass approach, the line is discretized with multiple linear elements represented by a spring damper system. The mass of the original line is lumped to the nodes connecting the elements. In the implemented model, also most of the line properties such as drag and hydrodynamic factors and seabed contact stiffness are cumulated at the nodes. During solving, Newton's second law of motion is solved.

The mooring technique in *pan*MARE utilizes three mooring objects:

- Mooring Nodes
- Connecting elements
- Deformations resulting from the acting forces

In the following a short description of these objects and their properties is given.

##### Mooring Nodes

The mooring nodes lump most properties of the mooring line. These properties are: mass, displaced volume, drag factors, hydrodynamic mass factors, seabed stiffness factor and a seabed damping factor. All nodes with more than one connected mooring element added to a mooring solver, will be deformed by the solver. Hence, open ends with only one attached element or loose nodes will not be deformed. The nodes with only one attached element are used to calculate the resulting tension at a line's end.

##### Connecting Elements

The mooring nodes are connected by the mooring elements. The connecting elements' specific properties are: the element's unsstretched length, stiffness factor (both static and dynamic), damping factor and dynamic mean strain.

##### Acting Forces

Various forces are acting on the lumped mass nodes. These forces are defined based on the node and element properties described above. Thereby both internal as well as external forces are considered in the simulation. The internal forces are: wight forces, spring forces and damping forces, whereas the external forces are the drag force, Froude-Krylov force and the seabed force (e.g. depending on the mud height of the seabed).

##### Mooring Solver

The mooring solver is the core of the mooring technique and integrates the solving procedure into the panMARE simulation. It includes several callbacks, which make it possible to intervene in the simulation. The mooring system can be solved statically or dynamically. Either way, the forces are calculated using the equal position and force vectors definition.