When including the current speed effect, the linearized drag factor on a dynamic cable takes the form

(12–5)

where and are the root mean square of the cable velocity and the current velocity respectively, in either the transverse or axial direction, and:

The linearized drag force due to current velocity may be written as

(12–6)

where is the density of water, is the cross-sectional area of the cable, is the drag coefficient, and is the velocity of a cable section in either the transverse or axial direction.

To estimate the root mean square of the cable velocity in multi-directional waves, the average motion RAOs at the attachment ends of a dynamic cable are used to calculate the harmonic response of that cable.

Denoting as the wave spectral ordinate at the j-th wave component (j = 1, ) of the m-th sub-directional wave spectrum (m = 1, ), and the complex value as the motion RAO of the mooring attachment end at position (x, y, z) due to wave component in the m-th wave direction , the average RAO at the wave frequency is expressed as

(12–7)

where is the random phase of the wave component , and is the total number of sub-directional wave spectra.

The total wave energy at a frequency is assumed to be the summation of all of the wave component energies at that frequency:

(12–8)

Using Equation 12–7 to determine RAOs at the ends of the cable, the average motion RAOs at the nodes of each of the cable elements can be calculated. The root mean square of the nodal motion velocity is then determined by

(12–9)

which will subsequently be used in Equation 12–5 to determine the linearized drag factor by means of an iterative procedure.