3 kotb ship resistance similarities mm545 oct2009

8/8/2019 3 Kotb Ship Resistance Similarities Mm545 Oct2009

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Ship Resistance and PoweringShip Resistance and Powering

Ship SimilaritiesShip Similarities

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RecallRecall

[ ]nF RfC = [ ]nR FfC =

if the parameters on the right hand side have the same values for twogeometrically similar but different sized bodies, the flow pattern will bethe same for each.

[ ]nnT FRfC ,=

These Equations state that


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Ship SimilaritiesShip Similarities

Types of SimilaritiesTypes of Similarities

1. Geometrical Similarities1. Geometrical Similarities

2.2. KinematicKinematic SimilaritiesSimilarities

3. Kinetic Similarities3. Kinetic Similarities

Length, Area, VolumeLength, Area, Volume

Position, Velocity,Position, Velocity,AccelerationAcceleration

Forces, MomentsForces, Moments


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31

====

m

s

m

s

m

s

m

s

m

s

SS

DD

BB

LL

1. Geometrical Similarities1. Geometrical Similarities

Preserved dimension ratios

Preserved Coefficients

..........PmPsBmBs CCCC ==

S

Object

m

Object model


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Object could take any shape

Father and son Mother and daughter

Geometrically Similar but different scale


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GeometricallySimilarb

utdifferents

cale

OtherExa

mples


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Geometrically Similar but different scale

More Examples ..


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Ls

Ship

Lm

Model

31

====

m

s

m

s

m

s

m

s

m

s

SS

DD

BB

LL

..........PmPsBmBs CCCC ==

Geometric SimilaritiesGeometric Similarities


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10 m

1 m

Model

Example (1)Example (1) Ship ParticularsLs = 10.0 mBs = 3.0 mCBs =0.55Ss =27.6 m

2

Vols = 9.9 m3

Find model particulars

Ship

Fire rescue boat


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Ls

Ship

Lm

Model

m

s

m

s

BB

LL =

55.0== BmBs CCShip and boat are geometrically SimilarShip and boat are geometrically Similar

31

=

m

s

m

s

L

L

mB3

110 = mBm 3.0=

Similarly mDm 06.0=

Also,m

s

m

s

S

S

L

L =

mS

6.27

1

10= 2276.0 mSm =

31

9.9

1

10

=

m

33109.9 mxm

=

And,

Solu

tion

Solu

tion


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Ls

Lm

Ship

Model


s

s

ns gL

VF =

m

mnm

gL

VF =

nmns FF =

=

m

m

s

s

gL

V

gL

V

m

s

m

s

L

L

V

V=


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Ls

Lm

Ship

Model


s

sssns LVR

=

m

mmmnm

LVR

=

nmns RR =

m

mmm

s

sss LVLV

=

s

m

m

s

L

L

V

V=


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10 m

Ship

1 m

Model

Example (2)Example (2)Ship Particulars

Ls = 10.0 mBs = 3.0 mDs =0.60 mCBs =0.55

Ss =27.6 m2

Vols = 9.9 m3

Vs = 12 knots

Find model speed if the ship and model are

running at the sameFroudenumbersi.e. kinematically similar

Fire rescue boatVs = 12 knots

Vm


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Ship Particulars

Ls = 10.0 mBs = 3.0 mCBs =0.55Ss =27.6 m

2

Vols = 9.9 m3

Vs = 12 knots10 m

Ship


1 m

ModelVm

nmns FF =

=

m

m

s

s

gL

V

gL

V

=

1*81.910*81.912 mV

knotsVm 79.3=

SolutionSolution


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1 m

Model

Example (2)Example (2)

Find model speed if the ship and model are

running at the sameReynoldsnumberi.e. kinematically similar

10 m

Ship

Ship Particulars

Ls = 10.0 mBs = 3.0 mCBs =0.55Ss =27.6 m

2

Vols = 9.9 m3

Vs = 12 knots


Vm


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SolutionSolutionShip Particulars

Ls = 10.0 mBs = 3.0 mCBs =0.55Ss =27.6 m

2

Vols = 9.9 m3

Vs = 12 knots10 m

Ship

Vs = 12 knots

1 m

Model

Vmnmns RR =m

mmm

s

sss LVLV

=

mmss LVLV = 1*10*12 mV=

knotsVm 120=


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Case 1Case 1

Ls

Lm

Geometrically SimilarGeometrically Similar

nmns FF =

RmRs CC=

Hence,Hence,

Also,Also,

m

s

m

s

L

L

V

V

=2

2

2

2

m

s

m

s

L

L

S

S=

kinematicallykinematically SimilarSimilar

Find the ratioFind the ratio RRRsRs// RRRmRm


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Case 1 (Cont.)Case 1 (Cont.)

Ls

Lm

Rmmmm

Rssss

Rm

Rs

CVS

CVS

R

R2

2

212

1

=

2

2

mmm

sss

Rm

Rs

VS

VS

R

R

=

m

s

m

s

m

s

Rm

Rs

L

L

L

L

R

R2

2

=

3

3

m

s

m

s

Rm

Rs

L

L

R

R

=

m

s

m

s

Rm

Rs

R

R

=

m

s

Rm

Rs

R

R

=


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Case 2Case 2 Geometrically SimilarGeometrically Similar

nmns RR =

FmFs CC=

Hence,Hence,

Also,Also,

s

m

m

s

L

L

V

V

=2

2

m

s

m

s

L

L

S

S=

KinematicallyKinematically SimilarSimilar

Find the ratioFind the ratio RRFsFs// RRFmFm

Ls

Ship

Lm

Model


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Ls

Lm

Fmmmm

Fssss

Fm

Fs

CVS

CVS

R

R2

2

21

21

=

2

2

mmm

sss

Fm

Fs

VS

VS

R

R

=

2

2

2

2

s

m

m

s

m

s

Fm

Fs

L

L

L

L

R

R

=

m

s

Fm

Fs

R

R

= 1=

Fm

Fs

R

R


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Case 3Case 3

Ls

Lm

Geometrically SimilarGeometrically Similar

nmns RR =Hence,Hence,

Also,Also,

s

m

m

s

L

L

V

V=

KinematicallyKinematically SimilarSimilar

nmns FF =

TmTs

CC =

m

s

m

s

L

L

V

V=

ms LL =s

m

m

s

L

L

L

L=

2

=

s

m

m

s

L

L

L

L


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Ls

Ship

Lm

Model

Lm

Ship and Model are identical

Sisters

Practically Impossible


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Tmmmm

Tssss

Tm

Ts

CVS

CVS

R

R2

2

2

12

1

=

2

2

mmm

sss

Tm

Ts

VS

VS

R

R

=

1=Tm

Ts

R

R

Ls

Ship

Lm

Model

Find the ratioFind the ratio RRTsTs// RRTmTm


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Ls

Lm

Ship

Model

3. Kinetic Similarity3. Kinetic Similarity

The ship and the model areThe ship and the model are GeometricallyGeometrically SimilarSimilar

ThenThen

This is calledThis is called KineticKinetic SimilaritySimilarity

nmns FF =

RmRs CC =

The ship and the model areThe ship and the model areKinematicallyKinematically SimilarSimilar

IfIf

andand

where,where,


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Ls

Ship

Lm

Model



ThenThen


nmns RR =

FmFs CC =


IfIf

andand

where,where,


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Ls

Ship

Lm

Model



ThenThen


nmns FF =

TmTs CC =


IfIf

andand

where,where, andand nmns RR =


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Kinetic SimilarityKinetic Similarity

IfIf

Geometrical SimilaritiesGeometrical Similarities

KinematicKinematic SimilaritiesSimilarities

Kinetic SimilaritiesKinetic Similarities

SatisfiedSatisfied

satisfiedsatisfied

Automatically satisfiedAutomatically satisfied

andand

thenthen


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AIR

Air-WaterInterface

Water

Thank You for Your Attention!

3 kotb ship resistance similarities mm545 oct2009

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