Shallow water effect on ship resistance October 1, 2009 1 Dr. Adel Banawan Ship Hydrodynamics-1
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Shallow water effect on ship
resistance
October 1, 2009 1Dr. Adel BanawanShip Hydrodynamics-1
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• Restricted waterways are the navigational areas with restrictions in depth
and/or width.
• Restricted waterways include channels, rivers, small lakes, and man-made
canals (Suez Canal, Panama Canal,…. etc), and the restriction can either bein their depths, widths or both together.
October 1, 2009 2Dr. Adel BanawanShip Design-2
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Shallow water has the following effects on ship
performance
i. It causes squat, which is a combination of sinkage and trim.
ii. It increases the total resistance of the ship; it increases the viscousresistance and increases the wave-making resistance particularly of theforward part of the ship.
iii. The ship becomes more sluggish to manouevre i.e less steerable.
iv. There will be a drop in speed in shallow water as a result of increasedresistance and reduced propulsion efficiency.
v. There is a greater tendency towards vibration as a result of propellerinduced vibration.
October 1, 2009 Dr. Adel BanawanShip Design-2
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Froude depth number definition
October 1, 2009 Dr. Adel BanawanShip Hydrodynamics-1
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gh
V Fnh
V
h
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October 1, 2009 Dr. Adel BanawanShip Hydrodynamics-1
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Flowcal Supercriti
Fnh 0.1
Flowl Subcritica
Fnh 0.1
FlowCritical Fnh 0.1
Number Froude Depth
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Shallow water effect on ship resistance
• Shallow water has two distinct effects on ship resistance.
1- There is an appreciable change in potential flow around the ship due to the
proximity of the bottom, where the flow passing below the ship will speed
up more than in deep water, with the consequence of greater reduction inpressure and increased speed, and thus increased resistance. This effect is
named the back flow effect and is usually assumed to affect both viscous
and wave-making resistance.
October 1, 2009 Dr. Adel BanawanShip Design-2
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• This effect leads to squat i.e. sinkage and change in trim. Some
investigations have shown that this effect is negligible for
where Am is the maximum sectional area of the immersed hull and h is the
water depth.
October 1, 2009 Dr. Adel BanawanShip Design-2
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18.0/ h Am
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2- The second effect is concerned with the wave system of the ship. The wave
system is modified due to the difference in the relationship between wave
length and wave speed in deep and in shallow water, where the wave of
given length moves more slowly on shallow water than on deep water.
This phenomenon is known as the wave retardation effect. This effect is
negligible for where is Froude depth number .
October 1, 2009 Dr. Adel BanawanShip Design-2
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45.0nh F nh
F ghv
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• In general, shallow water effects become pronounced when
where T is the draft of the ship. At higher ratios, the effect is reduced and
becomes negligible for .
October 1, 2009 Dr. Adel BanawanShip Design-2
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0.3/ T h
10/ T h
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Shallow water effect on ship resistance components
Effect on viscous resistance
• The viscous resistance will be affected due to the presence of shallow
water.
1- The flow is speeded up under the ship due to the back flow effect, and
2- The wetted surface area increases because of the squat, which would occur
in shallow water.
For the above reasons the skin friction would be increased.
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• Also there is another effect of shallow water on the form factor.
Experiments on this effect were carried out and the results showed that
the form factor is dependent upon the water depth namely, as the depth
of water is reduced the form factor is increased.
(1+r)shallow
=(1+r)deep
+0.644(T/h)1.72
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Effect on wave-making resistance
The wave-making resistance is greatly
affected by shallow water due to the
change which would occur in the wave
pattern.
October 1, 2009 Dr. Adel BanawanShip Design-2
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l Subcritica
Fn
deeph
h 4.00
2819 '0
Critical
Fn
shal lowh
h
oo
99.0
9078
cal Supercriti
Fn
shallowh
h 4.1
450
l Subcritica
Fn
shallowh
h 4.0
2819 '0
2
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• In deep water, the wave pattern consists of transverse and divergent
waves with the Kelvin angle α of 19o28`.
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• For shallow water, and at a speed less than commonly named
the hydrodynamic barrier, the angle α increases with the increase of
and the wave system consists of a double set of waves, transverse and
diverging as in deep water
October 1, 2009 Dr. Adel BanawanShip Design-2
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ghv
ghv /
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• when v exceeds , the angle α decreases with the increase of
and the wave system consists only of diverging waves, there being no
transverse waves
October 1, 2009 Dr. Adel BanawanShip Design-2
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gh ghv /
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• The shallow water effect on the ship’s wave resistance is of little practical
importance for Fnh < 0.7. Above this value, the effect increases rapidly to
reach a very high peak value when the Fnh approaches unity.
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Determination of the ship resistance in shallow water
Schlichting method
Schlichting performed an analysis on the effects of shallow water on ship
resistance. The analysis covered the increase in resistance in shallow
water at subcritical speeds, and was for shallow water of unlimited lateral
extent.
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October 1, 2009 Dr. Adel BanawanShip Hydrodynamics-1
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h
w
wc
L
h gL
V
2
tanh2
2
2
2 wc
gLV
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At any particular speed in deep water the wave pattern generated by
the ship will have a wave length given by:
In water of depth h the same wave length would be generated at some
lower speed where
and the ratio of the two speeds is
V
w L
2/2
w gLV
g V Lw /2 2
w L
I V
ww I Lh gLV /2tanh)2/(2
2/1)/2(tanh/ w I LhV V 2/12 )/(tanh/ V ghV V I
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Typical frictional and total resistance curves for deep water are shown in the
Figure below to a base of speed.
October 1, 2009 Dr. Adel BanawanShip Hydrodynamics-1
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R V (deep)
R Total (deep)
V inf
R W (deep)
V
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At any particular speed in deep water they are and ,
respectively.
At this speed the wave pattern generated by the ship will have a wave
lengthLW given by:
At deep water
October 1, 2009 Dr. Adel BanawanShip Hydrodynamics-1
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V F R T R
2
2 W gLV
deepWl deepVl deeptotal R R R
V V
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Step (1)
In water of depth h the same wave length LW
would be generated at some
lower or intermediate speed V I, where
Where
October 1, 2009 Dr. Adel BanawanShip Hydrodynamics-1
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C V V V I
2
1tanh1
h FnV C
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October 1, 2009 Dr. Adel BanawanShip Hydrodynamics-1
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R V (deep)
R Total (deep)
V inf
R W (deep)
dC V V I
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Step (2)
Schlichting assumed that the wave making resistance in shallow water at
speed V Iwould be the same as the speed in deep water.
The total resistance at speed V Iwould then be found by adding the wave –
making resistance to the appropriate frictional resistance at thisspeed, .
Total resistance at water depth h and speed VI
October 1, 2009 Dr. Adel BanawanShip Hydrodynamics-1
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V
w R Fh R
I I I V hwV hV V htotal R R R
,,,
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October 1, 2009 Dr. Adel BanawanShip Hydrodynamics-1
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R V (deep)
R Total (deep)
V inf
R W (deep)
dC V V I
(R w ) h
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Step (3)
There is further loss in speed ∆Vp because of the increase in potential flow
around the hull due to the restriction of area by the proximity of the
bottom, giving as the final speed
Schlichting found experimentally that
October 1, 2009 Dr. Adel BanawanShip Hydrodynamics-1
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p I h V V V
h A f V
V x
I
h
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October 1, 2009 Dr. Adel BanawanShip Hydrodynamics-1
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0.00 0.20 0.40 0.60 0.80 1.00
0.84
0.88
0.92
0.96
1.00
VI/Vinf
(Ax)^0.5/h
I
h
V
V
h A f V
V x
I
h
h
Ax
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October 1, 2009 Dr. Adel BanawanShip Hydrodynamics-1
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• Point on the Rtotal at shallow water (depth h)
hV
R V (deep)
R Total (deep)
V inf
R W (deep)
dC V V I
V p
(R w ) h
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Step (4)
Repeat the previous procedure to construct R-V curve at water depth h
October 1, 2009 Dr. Adel BanawanShi H d d i 1
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R total (h)
R V (deep)
R Total (deep)
V inf
R W (deep)
dC V V I
V p
(R w ) h
V total
hV