First-Order Wave Loads |
 
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First-Order Wave Loads |
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(1)
where:
•Fi(t) is the instantaneous force or moment in a particular degree of freedom, i (heave force, surge force, sway force, yaw moment, roll moment or pitch moment)
•t is the instantaneous solution time in seconds
•N is the number of regular Airy waves
•RAOi(θ,ω) is the RAO magnitude in degree of freedom i, which is a function of Incident Wave Heading θ and wave frequency ω
•an is the amplitude of the nth regular wave (MWL to crest or trough)
•kn is the wave number of the nth regular wave (k = 2π/λ, where λ is wavelength)
•sn is the horizontal distance from the global X axis to the vessel reference point in the direction of wave propagation for the nth regular wave (sn = y cosθn + z sinθn, where y and z are the coordinates of the vessel reference point in the global Y and Z axes respectively). These coordinates may be original, instantaneous, or computed using an average over a number of preceding time steps. Refer to the Reference Position input for further details.
•ωn is the circular frequency of the nth regular wave
•φn is the phase of the nth regular wave relative to zero datum
•Φi(θ,ω) is the RAO phase angle in degree of freedom i, which is a function of wave heading θ and wave frequency ω. Note that a positive phase angle denotes a phase lag relative to the incident wave harmonic at the vessel reference point.
If there is only a single regular Airy wave present, then the summation from 1 to N in Equation 1 is obviously not required.
All random seas (including Pierson-Moskowitz, Jonswap, Ochi-Hubble, Torsethaugen and User-defined) are simulated using a series of individual component harmonics which are generated using a Spectrum Discretisation technique. Each harmonic is basically a regular Airy wave, so Equation 1 above remains valid.
•*FORCE RAO is used to specify force RAOs for a floating body.
If you would like to see an example of how this keyword is used in practice, refer to E02 - CALM Buoy - Complex.