Ship resistance in confined water

 Shallow water, restricted water and confined
water
 Effect on a ship moving in confined water :
 sinkage and trim
 increase in resistance
 other effects : propulsion, manoeuvrability, vibration

 Sinkage and trim :
 Restricted cross-section for displacement flow under
the ship
 Increased relative velocity of water
 Decrease in pressure
 Sinkage
 Effect of boundary layers on ship and ground
 With level ground, pressures are lower towards aft
and hence the ship trims aft
 Forward trim may occur if the ship is heading into
shallower water

 Combined sinkage and trim due to ship
moving in shallow water is called squat
 Change of pressure in shallow water of given
depth is proportional to V 2
 Squat increases sharply with speed
 Excessive speed in shallow water may cause
the bottom of the ship to touch the ground
 Shallow water effects become more
pronounced if the water is also restricted in
width, since more displacement flow has to go
under the ship

 Empirical formulas to estimate squat
 Barrass formula for squat in a canal :
= squat in m, CB = block coefficient
S = midship area / canal cross-section area
V = ship speed in knots
0.81 2.08
20
BC S V
 


 For shallow water of unrestricted breadth, an
equivalent breadth b may be used to calculate
the effective canal cross-section area :
where B is the breadth of the ship.
0.85
7.04
B
b B
C
 

 Barrass has also given simpler formulas :
 In unrestricted shallow water with h/T between 1.1
and 1.4 (h = depth of water, T = draught of the ship)
 In a canal for which S lies between 0.1 and 0.266,
 Ships with CB > 0.7 trim forward, ships with CB < 0.7
trim aft according to Barrass.
2
100
BC V
 
2
50
BC V
 

 Confined water affects ship resistance mainly
in two ways :
 The increased displacement flow velocity increases
the viscous resistance
 The waves generated by the ship are different in
shallow water than in deep water. Waves of a given
speed are longer in shallow water and have sharper
crests than in deep water. This causes a change in
wave resistance

 In water of depth h, wave speed (celerity) and
wave length are related as follows :
 As , , and the
familiar relation between wave speed and wave
length in deep water is obtained :
2 2
tanh
2
g h
c
 
 
 
  
 
2
2 c
g

 
h  tanh(2 / ) 1h  

 As , and the
wave speed is given by :
 This is the limiting speed of a wave in water of
depth h and is called the critical wave speed.
/ 0,h   tanh(2 / ) 2 /h h   
2
c g h

 The waves generated by a moving pressure point
in shallow water give guidance on the effect of
shallow water on the waves generated by a ship :
 At speeds V well below , the waves generated by
the pressure point in water of depth h are the same as
in deep water : diverging waves and transverse waves
of wave length lying between lines
making an angle of 19o
28’ with the direction of motion
(i.e. the Kelvin wave pattern)
g h
2
2 /V g 

 As the speed V increases beyond 0.4 , the wave
length starts being affected by the depth of water h and
the angle between which the wave pattern is contained
starts increasing from 19o
28’
 As V approaches , this angle approaches 90o
, the
wave length increases indefinitely
g h
g h

 As the speed V increases beyond the critical wave
speed, a new wave system forms consisting only of
diverging waves emanating from the pressure point,
convex forward. These diverging waves are contained
within two lines making an angle
with the direction of motion. The angle
decreases as V increases


sinV g h 

 The waves generated by a ship in shallow
water have similar characteristics
 As the ship speed V starts increasing towards the
critical wave speed , the waves start becoming
longer than in deep water, the crests become sharper
and the troughs shallower
g h

 When the wave length starts becoming more than
the length of the ship, sinkage and trim by stern start
increasing and the resistance also increases.
 The maximum values are reached at or just before
the ship speed becomes equal to the critical wave
speed
 As the ship speed becomes supercritical, a new wave
system consisting of only diverging waves is formed.

 These observations are mostly based on model
experiments since ships can rarely be made to
go at speeds approaching or exceeding the
critical wave speed.
 Ships do operate at subcritical speeds in
shallow water, and it is necessary to calculate
the effect of shallow water on their resistance.
 A method due to O. Schlichting is widely used
for this purpose.

 In Schlichting’s method :
 The total resistance is divided into viscous resistance
and wave resistance
 It is assumed that if the wave length in shallow water
of depth h at a speed VI (called Schlichting’s
intermediate speed) is the same as the wave length in
deep water at a speed , the wave resistance at the
speed VI in shallow water will be equal to the wave
resistance at the speed in deep water.
 The wave length in deep water at a speed is given
by
V
V
V
2
2 V
g

 


 The wave length in shallow water of depth h at a
speed VI is given by
 For the wave lengths to be equal
2
2
2
tanh
IV
h
g





 
 
 
11
22
2
2
tanh tanhIV h g h
V V

 
    
             

 The total resistance in deep water at the speed
is expressed as the sum of viscous resistance
and wave resistance :
 The total resistance in shallow water of depth h
at the speed VI is similarly :
T V WR R R   
V
TI VI WI VI WR R R R R    

 The value of RVI for shallow water cannot be
determined. However, RVI can be determined
at the speed VI for deep water by the same
method as used to determine at the
speed in deep water.
 Schlichting experimentally determined a speed
Vh in shallow water at which the measured
total resistance RTh is equal to the sum of RVI at
the speed VI in deep water and .
VR 
V
WR 

 Schlichting found that the ratio Vh /VI is a
function of , where AX is the area of the
immersed maximum cross-section of the ship.
 Landweber extended Schlichting’s method to
the resistance of a ship in a canal by replacing
the depth of water h by the hydraulic radius RH,
which is the ratio of the canal cross-section area
to the perimeter.
XA h

 For a rectangular canal of breadth b and depth of
water h, the hydraulic radius is
where p is the perimeter (girth) of the
maximum immersed section of the ship.
 As , so that in shallow water of
unrestricted breadth, the hydraulic radius
becomes equal to the depth of water.
2
X
H
bh A
R
b h p


 
, Hb R h  

 and are given in the following tables
:
0.0 1.0000 0.6 0.9961
0.1 1.0000 0.7 0.9833
0.2 1.0000 0.8 0.9570
0.3 1.0000 0.9 0.9186
0.4 1.0000 1.0 0.8727
0.5 0.9997
IV V h IV V
V
g h

V
g h
IV
V
IV
V

0.0 1.0000 0.6 0.9712 1.1 0.8923
0.1 1.0000 0.7 0.9584 1.2 0.8726
0.2 0.9995 0.8 0.9430 1.3 0.8536
0.3 0.9964 0.9 0.9274 1.4 0.8329
0.4 0.9911 1.0 0.9087 1.5 0.8132
0.5 0.9825
These are Landweber’s values.
X
H
A
R
X
H
A
R
X
H
A
R
h
I
V
V
h
I
V
V
h
I
V
V

 Long but checkered history
 Reliable results from time of W. Froude
 Model experiments in modern times
 Long, narrow towing tank
 Towing carriage with instrumentation
 Variety of experiments : resistance, propulsion,
manoeuvring, seakeeping
 Other types of facilities
 ITTC

 Materials : wood, wax, fibre-glass,
polyurethane foam
 Model size
 Equipment limitations : speed, resistance
 Accuracy of small models – model propellers
 Accuracy of measurements : small forces
 Turbulent flow : large models for high Reynolds
number, artificial turbulence stimulation

 Upper limit on model size – tank wall
interference or blockage
 Increased displacement flow
 Shallow water effects on waves
 Interference of reflected waves
 Criteria to avoid blockage effects :
 not more than 1/200
 not more than 0.7
 LM not more than 0.5 b
XA bh
MV g h

 Geometrically similar model ballasted to
correct draught and trim
 Attached to towing carriage through resistance
dynamometer :
 Model free to sink and trim
 No trimming moment due to tow force
 Resistance measured at steady model speed by
resistance dynamometer
 Test over range of speeds
 Wave profiles, flow lines

 Basic procedure as discussed earlier
 Additional considerations
 Roughness allowance
 Correlation allowance
 Ship correlation factor
 ITTC’s standard method

 ITTC 1978 Ship Performance Prediction
Method : standardized method for prediction
of ship power from model tests
 Basic procedure (as discussed earlier) :
RTM measured at VM
1 2
2
TM
TM
M M M
R
C
S V

M M
nM
M
V L
R


  2
100.075 log 2FM nMC R

 

 1WM TM FMC C k C   S
S M
M
L
V V
L
 
S S
nS
S
V L
R

   2
100.075 log 2FS nSC R

 
WS WMC C (by the Froude law)
 1TS FS WSC k C C  

 Three corrections to this basic procedure in
ITTC method :
 Roughness allowance added to viscous
resistance coefficient where :
 Bilge keels cannot be reproduced in model.
Resistance of bilge keels allowed for by increasing
hull wetted surface SS by bilge keel surface area SBK
 1 FSk C
FC
3
105 0.64 10S
F
S
L
C
k

  
     
   

 Air and wind resistance calculated by
 After making these corrections, the total
resistance coefficient of the ship is obtained as :
 This gives the total resistance of the ship in
ideal conditions.
1 2
2
0.001AA T
AA
SS S S
R A
C
SS V
 
 1S BK
TS FS F WS AA
S
S S
C k C C C C
S

       

 To allow for the differences between these ideal
conditions and the actual conditions on ship
trials or in service, CTS is multiplied by a load
factor (1+x).
 The overload fraction x corresponds to a trial
allowance or a service allowance, and is based
on experience with previous ships
 Service allowances may range from 10 to 40 per
cent, depending on type of ship and service
route.

Ship resistance in confined water

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Ship resistance in confined water