Derivative Seakeeping Quantities
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The principal seakeeping quantity from a seakeeping analysis of a floating body at zero or forward speed is the Response Amplitude Operator (or RAO)
where [math]L\,[/math] is a characteristic length. The RAO is a complex quantity with phase defined relative to the ambient wave elevation at the origin of the coordinate system
It follows that the only seakeeping quantity with [math]RAO\equiv 1 \,[/math] is [math] \zeta_I(t)\,[/math].
A partial list of derivative seakeeping quantities of interest in practice is:
- Free-surface elevation. Needed to estimate the clearance under the deck of offshore platforms.
- Vessel kinematics at specified points, e.g. needed to estimate the motion properties of containerized cargo.
- Relative wave elevation and velocity near the bow of a ship. Needed to estimate the occurrence and severity of slamming.
- Local and global structural loads needed for the vessel structural design.
According to linear theory, all derivative quantities which are linear superpositions of other quantities, take the form
Example 1 - Acceleration RAO at the bow of a ship
The vertical displacement of point [math]A\,[/math] due to the vessel heave & pitch motions is
So the corresponding RAO in waves of amplitude [math]A\,[/math] is:
So the RAO of the vertical acceleration at the bow is a linear combination of the heave and pitch RAO's.
Example 2 - Hydrodynamic pressure disturbance at a fixed point on a ship hull oscillating in heave & pitch in waves
The linear hydrodynamic pressures at a point [math]A\,[/math] located at [math] \vec{X}_A\,[/math] relative to the ship frame is:
where
Ocean Wave Interaction with Ships and Offshore Energy Systems