Shallow water effect on ship resistance

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Shallow water effect on ship

resistance

October 1, 2009 1Dr. Adel BanawanShip Hydrodynamics-1



• 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



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

3



Froude depth number definition

October 1, 2009 Dr. Adel BanawanShip Hydrodynamics-1

4

gh

V Fnh

V

h




5

Flowcal Supercriti

Fnh 0.1

Flowl Subcritica

Fnh 0.1

FlowCritical Fnh 0.1

Number Froude Depth



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.


6



• 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.


7

18.0/ h Am



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 .


8

45.0nh F nh

F ghv



• 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 .


9

0.3/ T h

10/ T h



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.


10



• 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


11



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.


12

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



• In deep water, the wave pattern consists of transverse and divergent

waves with the Kelvin angle α of 19o28`.


13



• 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


14

ghv

ghv /



• 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


15

gh ghv /



• 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.


16



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.




18

h

w

wc

L

h gL

V

2

tanh2

2

2

2 wc

gLV



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





Typical frictional and total resistance curves for deep water are shown in the

Figure below to a base of speed.


21

R V (deep)

R Total (deep)

V inf

R W (deep)

V



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


22

V F R T R

2

2 W gLV

deepWl deepVl deeptotal R R R

V V



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


23

C V V V I

2

1tanh1

h FnV C




24

R V (deep)

R Total (deep)

V inf

R W (deep)

dC V V I



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


25

V

w R Fh R

I I I V hwV hV V htotal R R R

,,,




26

R V (deep)

R Total (deep)

V inf

R W (deep)

dC V V I

(R w ) h



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


27

p I h V V V

h A f V

V x

I

h




28

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




29

• 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



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

30

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

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Shallow water effect on ship resistance