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Livro do Journee - Offshore Hydromechanics

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.064 -0 .475 0.000 -0 .032
160± -2 .148 0.256 0 .000 0 .081 0 .000 0.127 -0 .027
170± -2 .707 0.397 -0 .175 0 .126 0 .000 0.181 0 .000
180± -2 .529 0.376 -0 .174 0 .128 0 .000 0.155 0 .000
Similar polynomials for the lateral force and the horizontal moment are given in the paper
by [Isherwood, 1973].
4.9 Current Loads
There are several independent phenomena responsible for the occurrence of current: the
ocean circulation system resulting in a steady current, the cyclical change in lunar and
solar gravity causing tidal currents, wind and di¤erences in sea water density. The steady
wind velocity at the water surface is about 3 per cent of the wind velocity at 10 meters
height. Tidal currents are of primary importance in areas of restricted water depth and
can attain values up to 10 knots. However, such extreme velocities are rare; a 2-3 knots
tidal current speed is common in restricted seas. The prediction of tidal currents is left for
the oceanographers.
Although surface currents will be the governing ones for ‡oating structures; the current
distribution as a function of depth below the surface may also be of importance. For the
design of a mooring system of a ‡oating structure, the designer is especially interested in
the probability that a particular extreme current velocity will be exceeded during a certain
period of time. Observations obtained from current speed measurements are indispensable
for this purpose. It may be useful to split up the total measured current in two or more
components, for instance in a tidal and a non-tidal component, since the direction of the
various components will be di¤erent, in general. The variation in velocity and direction of
the current is very slow, and current may therefore be considered as a steady phenomenon.
The forces and moment exerted by a current on a ‡oating object is composed of the
following parts:
² A viscous part, due to friction between the structure and the ‡uid, and due to
pressure drag. For blunt bodies the frictional force may be neglected, since it is small
compared to the viscous pressure drag.
² A potential part, with a component due to a circulation around the object, and one
from the free water surface wave resistance. In most cases, the latter component is
small in comparison with the …rst and will be ignored.
The forces and moments, as given in …gure 4.12, exerted by the current on a ‡oating
structure can be calculated from:¯¯¯¯
Xc =
½ ¢ V 2c ¢ CXc(®c) ¢ ATS
Yc =
½ ¢ V 2c ¢ CY c(®c) ¢ ALS
Nc =
½ ¢ V 2c ¢ CNc(®c) ¢ ALS ¢ L
in which:
Xc = steady longitudinal current force (N)
Yc = steady lateral current force (N)
Nc = steady yaw current moment (Nm)
½ = density of water (kg/m3)
Vc = current velocity (m/s)
®c = current direction, from astern is zero (rad)
ATS ¼ B ¢ T = submerged transverse projected area (m2)
ALS ¼ L ¢ T = submerged lateral projected area (m2)
L = length of the ship (m)
B = breadth of the ship (m)
T = draft of the ship (m)
C¡c(®c) = ®c-depending current load coe¢cient (-)
Results of model tests are given in the literature for various types of structures and vessels.
4.9.1 Current Loads on Moored Tankers
[Remery and van Oortmerssen, 1973] published current loads on several tanker models of
di¤erent sizes, tested at MARIN. The coe¢cients CXc, CY c and CNc were calculated from
these results. A tanker hull is a rather slender body for a ‡ow in the longitudinal direction
and consequently the longitudinal force is mainly frictional. The total longitudinal force
was very small for relatively low current speeds and could not be measured accurately.
Moreover, extrapolation to full scale dimensions is di¢cult, since the longitudinal force is
a¤ected by scale e¤ects.
For mooring problems the longitudinal force will hardly be of importance. An estimate of
its magnitude can be made by calculating the ‡at plate frictional resistance, according to
the ITTC skin friction line as given in equation 4.42:¯¯¯¯
Xc =
(log10 (Rn) ¡ 2)2
¢ 1
2 ¢ cos®c ¢ j cos®cj ¢ S
Rn =
Vc ¢ j cos®cj ¢ L
S ¼ L ¢ (B + 2T) = wetted surface of the ship (m2)
L = length of the ship (m)
B = breadth of the ship (m)
T = draft of the ship (m)
Vc = current velocity (m/s)
®c = current direction (-), from astern is zero
½ = density of water (ton/m3)
Rn = Reynolds number (-)
º = kinematic viscosity of water (m2s)
Extrapolation of the transverse force and yaw moment to prototype values is no problem.
For ‡ow in the transverse direction a tanker is a blunt body and, since the bilge radius is
small, ‡ow separation occurs in the model in the same way as in the prototype. Therefore,
the transverse force coe¢cient and the yaw moment coe¢cient are independent of the
Reynolds number.
The coe¢cients for the transverse force and the yaw moment were expanded by MARIN
in a Fourier series, as was done for the wind load coe¢cients as described in a previous
CY c(®c) =
bn ¢ sin(n ¢ ®c)
CNc(®c) =
cn ¢ sin(n ¢ ®c) (4.59)
The average values of the coe¢cients bn and cn for the …fth order Fourier series, as published
by [Remery and van Oortmerssen, 1973], are given in the table below.
n bn 10 ¢ cn
1 0 .908 -0 .252
2 0 .000 -0 .904
3 -0 .116 0 .032
4 0 .000 0 .109
5 -0 .033 0 .011
These results are valid for deep water. For shallow water, the transverse current force and
moment coe¢cients have to be multiplied by a coe¢cient, which is given in …gure 4.15.
The in‡uence of the free surface is included in the data given on the coe¢cients bn and
cn in the previous table. This in‡uence, however, depends on the water depth and on the
Froude number, and consequently changes if the current velocity or the tanker dimensions
change. For the condition to which these data apply, deep water and a prototype current
speed in the order of 3 knots, the e¤ect of the free surface is very small. For the case of a
small clearance under the keel and a current direction of 90 degrees, damming up of the
water at the weather side and a lowering of the water at the lee side of the ship occurs.
4.9.2 Current Loads on Other Moored Structures
Current loads on other types of ‡oating structures are usually estimated in the same way
as is used for wind loads.
Figure 4.15: In‡uence of Water Depth on Transverse Current Load on a Tanker
4.9.3 Current Loads on Sailing Ships
For sailing ships, generally it is assumed that the ship is moving with the current. So the
forward ship speed is not the ground speed but the speed relative to the water. Then there
is no current load; the current itself is a navigation problem only.
4.10 Thrust and Propulsion
Now that the resistance of a ship or other ‡oating objects moving through still water
has been discussed, it is appropriate to approach this phenomena from the other side by
discussing the propulsion systems needed to overcome the resistance. This section on that
topic is partly based on a text by [Kuiper, 1997] on resistance and propulsion of ships. This
text is a good reference for those who wish to know more than is presented here about
thrust and propulsion.
The basic action of propulsors like propellers is to deliver thrust. In fact, a propulsor is
an energy transformer, because torque and rotation, delivered to the propulsor, will
be transformed into thrust and translation, delivered by the propulsor. A consequence
is that the propulsor also generates water velocities in its wake, which represent a loss of
kinetic energy. It is obvious that this will e¤ect the e¢ciency of the propulsor, de…ned
by: ¯¯¯¯
´ =
T ¢ Ve
Q ¢ 2¼n (4.60)
in which: