Hydrodynamic Loads |
 
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Hydrodynamic Loads |
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The hydrodynamic loads, denoted FHy (surge), FHz (sway) and MHθ (yaw), are determined according to the theory of manoeuvrability as follows:
(1)
where:
•Mayy is the body added mass in surge
•Mazz is the body added mass in sway
•Maθθ is the body added mass in yaw
•Mazθ is the body added mass in sway-yaw coupling
•θ is the instantaneous body orientation as defined in Local Vessel Axis System
•u' and ν' are the components, in the body axis system, of the relative body/current velocity.
u' and ν' are given by the equations:
(2)
where u and ν are the components in the body axes of the body CoG velocity; νc is the current velocity magnitude (which is a user input); and βc is the current direction as defined in Definition of Wind and Current Directions. Differentiating u' and ν' with respect to time (assuming a constant current velocity) gives:
(3)
Substituting the above expressions into the equations for the hydrodynamic loads gives the following:
(4)
For numerical reasons it is desirable to move any terms consisting of the product of a mass by a structure acceleration term to the left-hand side of the overall matrix equations of motion solved by Flexcom. So Term (1) in FHy, Terms (1) & (4) in FHz, and Terms (1) & (2) in MHθ are moved in this way. This is achieved by adding the relevant body added mass terms to the mass matrix at the location corresponding to the body centre of gravity. The following expressions are then used to calculate the hydrodynamic forces which are applied at the body CoG:
(5)
•*ADDED MASS is used to define added mass for a floating body.
•*CURRENT is used to specify current loading.
If you would like to see an example of how these keywords are used in practice, refer to E02 - CALM Buoy - Complex.