EM 1110-2-1100 (Part II)
30 Apr 02
where ρw is the water density, Cc,form is the form drag coefficient = 0.1, B is the vessel beam, T is the vessel
draft, Vc 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
Fc , fric ' &
(II-7-35)
2
where Cc,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 Rn
0.075
Cc , friction '
(II-7-36)
( log10 Rn & 2 )2
Vc Lw l cos θc
Rn '
(II-7-37)
ν
where Lwl is the waterline length of the vessel and ν is the kinematic viscosity of water. The wetted surface
area is defined as
35 D
S ' ( 1.7 T Lw l ) %
(II-7-38)
T
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
Fc , prop ' &
(II-7-39)
ρw Cc , prop Ap Vc cos θc
2
where Cc,prop is the propeller drag coefficient = 1 and Ap is the expanded or developed blade area of the
propeller defined as
Lw l B
Ap '
(II-7-40)
0.838 Ar
(k) The area ratio Ar 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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