MS Thesis R. Hager - Hawaii National Marine Renewable Energy ...

where ijkis the permutation symbol. Force in the surge and heave direction is denoted byi= 1 and 3, respectively. Moment in the pitch direction is denoted by i=5. Motion in thesurge, heave, and pitch directions is denoted by j=1, 3, and 5, respectively. The first terms inEq. (34) and Eq. (35) are the hydrostatic force and moment, respectively, and the latter twoterms are the hydrodynamic forces and moments. The hydrodynamic forces can further bedecoupled in the diffraction and radiation forces, respectively, as shown below: F ( F F ) FDIR(36)The total force and moment with a moment arm, r , are determined by integrating the totalfluid pressure over the wetted surface:Fip n dS (37)T STiMkp r n dST STijkij(38)The total fluid pressure is calculated by applying Eq. (37) to the linearized Euler’s integral.pT t Tit gz gz ie(39)DIjjjfor j=1,3,53.3.1 Hydrostatic Forces and MomentsThe hydrostatic force is:FH g zndS (40)SThe hydrostatic moment is: M g z(r n)dS (41)HSThe hydrostatic force and moment largely describe the buoyancy force and moment, whichis canceled for an unrestrained body by its weight (Newman, 1977). The buoyancy term44