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OCR for page 153
APPENDIX D
Description of Mathematical Model
The navigation channel design model is intended to simulate the
reactions of the design vessel ~ s ~ in a given set of conditions. The
model is composed of several modules intended to evaluate squat, bank
suction, vessel attitude, thrust for a ppecif fed stopping distance,
and ship-generated waves ~ Figure D-1 ) . The modular construction
allows f or changes to be made with relative ease as advances are made
in an area of analysis.
As specif fed by the control cards, data are read in and
distributed by the main module to the respective modules. After the
specified modules have completed their evaluation, control is
transferred back to the main module.
The input data consist of eight cards.
is listed below:
The purpose of each card
Card #1 specifies the analysis to be performed and the azimuth of
the inbound vesse 1. In addition, it specif ies whether an
inbound, an outbound, or a combination analysis is to be
performed.
Card # 2 specif ies title inf ormation which would identify the
channel analysis being performed.
Card # 3 specif ies the section geometry f or the channel under
,
· .
consideration.
Card #4 specif ies the magnitude and direction of botch the current
and the wind. In addition, the water density and
temperature are given.
Card #S specifies the navigable channel lion; ts, the thickness of
the channel boundary layer, and the bank elevations .
Card #6 specif ies the primary vessel characteristics , e. g.,
draft, beam, length, minim and maximum speeds, vessel
boundary layer thickness , position from centerline,
maximum rudder angle, wind area, displacement, and
stopping distance.
Card #7 specifies the secondary vessel characteristics, if the
passing condition has been specified.
Card #8 specif ies the entrance length of the primary vessel.
D—1
OCR for page 154
D-2
Vessel
Attitude
1~
Bank
Suction
Neutral
Steering
Line
Boundary
Layer
L
Data
_
.
two_
Main
Control
Squa t
_ l
Sa linity
l
1
;hip -Genera~ced
Waves
Stopping
Dis tance
Power
Required
\
~1 -1
Area
Figure D-1 Channel design evaluation model
OCR for page 155
D-3
Description of Modules
Squat computation module The squat module checks the salinity of the
water to determine if vessel draft needs to be adjusted. Squat is
computed for the primary vessel at various speeds for the
on-centerline or passing case (or both). The basic equation (Garthune
et al., 1948; Tothill, 1966) is
22.6 [ A ]
where
Ad = squat ( in ft)
if = velocity (in Its) 2
A = cross-sectional area of flow in channel, absent vessel (in ft )
A' = cross-sectional area of flow with ship in channel section,
experiencing squat
The computation terminates when the incremental speed reaches one
of the following:
o maximum vessel speed;
o critical velocity; or
o vessel touches bottom.
In the development of the model, calculated values were compared
to field measurements and found to agree satisfactorily (Figure D-2.
Figures D-3(a) through D-31 illustrate results for squat in nine
channels selected by the panel.
Neutral Steering Line and Bank Suction Module If bank suction is
required, then the neutral steering line is calculated. This is the
sailing line of a vessel along which lateral f orces and turning
moments owing to bank suction are balanced. If the channel
cross-section is symmetrical, the neutral steering line is the channel
centerline; if asymmetrical, the module calculates the distance from
centerline to neutral steering line, adding this value algebraically
to the distance from the centerline of the ship's position. These
values are then used in the bank suction computations, which encompass
lateral forces and moments due to bank suction effects for various
speeds, using the method proposed by Schoenherr (1960~. In validation
of the model, computed and measured values (from model tests) were in
satisfactory agreement for symmetric and asymmetric cross-sections of
channels.
Vessel Attitude Module This module computes the additional forces due
to current and wind and adds these values to the forces calculated in
the bank suction module. The rudder and drift angles required to
neutralize the total forces and moments are then calculated for
selected speeds, based on the method described by Bindel (1960), and
the addition of an off-centerline coefficient.
OCR for page 156
D-4
2.0
-
u'
1.0
a)
o
c'
Figure D-2
r It- --
1-.1( 1
1~-1 1
Or I I
0 1..0 2.0
Measured Squat (ft)
Comparison of computed
and measured squat
OCR for page 157
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OCR for page 158
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OCR for page 159
D-7
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OCR for page 160
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OCR for page 161
D-9
Ship-Generated Waves Module The principal purpose of this module is
to determine the effects of ship-generated waves on barge trains, but
it also gives a general indication of other effects that may be
expected in particular channels from ship-generated waves--for
example, bank erosion--and may suggest operational or design changes.
The module computes ~ f or selected speeds ~ the ship wave height at the
vessel, and the wave height at each cusp on lines of propagation. The
methods are based on those suggested by Saunders (1957) and Havelock
(Wigley, 1963~. There are few measurement data for comparison.
Stopping Power Computation Module This module computes the reverse
thrusts needed to bring the vessel (sailing at selected speeds) to a
standstill in a spec' fled distance. The computational procedure
suggested by D' Arcangelo ~ 1957 ~ was adjusted in consultations with
p ilots, ship masters, and other sources of inf ormation about the
behavior of ships in restricted waters.
OCR for page 162
D-10
Ref erences
Bindel, S . ~ 1960 ), "Turning Characteristic Coefficients for a Cargo Ship
and a Destroyer, " Report 1461, David Taylor Model Basin, U.S. Navy.
'Arcangelo, A. M., gent ed. ( 1957 ), "Guide to the Selection of Backing
Power, " Tech . and Res . Bull . No . 3-5, Panel M-9, Society of Natural
Architects and Marine Engineers.
Garthune, R. S., et al. ~ 1948 ), "The Performance of Model Ships in
Relation to the Design of the Ship Canal, " Report 601, David Taylor
Model Basin, U. S. Navy.
Saunders, H. E . ~ 1957 ), Hydrodynamics in Ship Design, Vol. II ~ New York :
Society of Naval Architects and Marine Engineers ~ .
Schoenherr , K. E . ~ 196 0 ), "Data f or Estimating Bank Suction Ef f eats in
Restricted Waters and on Merchant Ship Hulls, " Report 1461, David
Taylor Model Basin, U. S. Navy.
Tothill, J. T. (1966), Ships in Restricted Channels, Report MB-264
~ Ottawa: National Research Council of Canada ~ .
Wigley, C., gent ed. (1963), The Collected Papers of Sir Thomas Havelock
on Hydrodynamics (Washington, D.C.: Office of Naval Research).
Representative terms from entire chapter:
specif ies
