where ρw is the water density, *C*c,form is the form drag coefficient = 0.1, *B *is the vessel beam, *T *is the vessel

draft, *V*c is the average current speed, and θc is the angle of the current relative to the longitudinal axis of the

vessel. Skin friction drag is due to the flow of water over the wetted surface area of the vessel and is given

by

1

2

ρw Cc , *fric *S Vc cos θc

(II-7-35)

2

where *C*c,fric is the skin friction coefficient and *S *is the wetter surface area of the vessel. The skin friction

coefficient is a function of the Reynolds number *R*n

0.075

(II-7-36)

( log10 Rn & 2 )2

(II-7-37)

ν

where *L*wl is the waterline length of the vessel and ν is the kinematic viscosity of water. The wetted surface

area is defined as

35 *D*

(II-7-38)

where *D *is the displacement of the vessel.

(j) Finally, the propeller drag is due to the form drag of the propeller with a locked shaft and is given

by

1

2

(II-7-39)

ρw Cc , *prop *Ap Vc cos θc

2

where *C*c,prop is the propeller drag coefficient = 1 and *A*p is the expanded or developed blade area of the

propeller defined as

(II-7-40)

0.838 *A*r

(k) The area ratio *A*r is the ratio of the waterline length times the beam to the total projected propeller

area. Typical values range between 100 for a destroyer and 270 for a tanker.

(l) Thus, to calculate current loads, the following input parameters are needed: the vessel's beam, draft,

waterline length, displacement, and propeller area ratio; and average current speed and direction.

(m) It is difficult to evaluate wave loadings on a moored vessel. Both wind-wave and long-period waves

are oscillatory; so there is a complex interaction with the mooring system dynamics. This interaction depends

on the incident wave frequencies, the vessel added mass and drag characteristics, and the elastic

characteristics of the mooring lines and fender system. The vessel can respond in one or more of the six

modes of oscillation (see above). Rather than an analytical treatment of the problem in which actual wave

loads are determined, scale model testing is often employed. In the latter, the system response in terms of

II-7-72

Harbor Hydrodynamics

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