Longitudinal Stability Yuvaraj Adithya

8/9/2019 Longitudinal Stability Yuvaraj Adithya

1/22

By

Yuvaraj R

AdithyaManda

LONGITUDINAL STABILITY


2/22

CONTENTSLongitudinal ta!ilityLongitudinal "#ta$#ntr#

MCTC %

Tri"Lot !uoyan$y "#thod

Add#d ight "#thod

'looda!l# l#ngth

'a$tor o( u!diviion


3/22

Longitudinal StabilityLongitudinal Metacenter: Similar to the definition of the

transverse meta center, when a ship is inclined longitudinallyat a small angle, A vertical line through the center of

buoyancy intersects the vertical line through (before the

ship is inclined) at .

1B

0B

LM


4/22

The Location of the LongitudinalMetacenter

For a small angle inclination, volumes of forward wedge immersedin water and bacward wedge emerged out of water are!

10

" 1 "0

0 0

(" ) ( tan ) where is the half breadth.

(" ) ( tan ) , .

#hus, " " , which indicates!

moment of area forward of $ moment of area after .

is the cente

l

L l

l L l

v y x dx y

v y x dx v v v

yxdx yxdx

F F

F

=

= = ==

0 0

0 0

r of (mass) gravity of waterline , %

is called of . #herefore, for e&ual

volume longitudinal inclination the new waterline always

passes through the ('.F

W L

W Lcenter of flotation

center of flotation ).


5/22

Location of the LongitudinalMetacenter

sing the same argument used in obtaining transverse metacenter.0 1 1 "

0

1 "0

0" "

0

0 1 0

,

(" ) ( tan ) " tan

tan " " tan

is the moment of inertia with respect to the

transverse a*is passing the center of flotation.

t

l

L l

l

FCL l

FC

B B vg g

vg g y x xdx yx xdx

yx dx yx dx I

I

B B B M

=

= +

= + =

=

0

0

an , .

.

FC

FC FC

ML B B L B g

IB M

I IH B M Z Z GM Z Z

=

= + = + = +


6/22

Location of the LongitudinalMetacenter

"

0,

0,

sually Floatation 'enter ('.F) of a waterplane is not at the

midship,

,

where is the moment of inertia w.r.t. the transverse a*is

at midship (or station +) and is the distance from F

FC T

T

I I Ax

I

x

=

.'. to

the midship.


7/22

Moment to Change Trim One cm(MCTC 1)

#-! (moment to alter (change) the ships trim per inch) at

each waterline (or draft) is an important &uantity. /e may

use the longitudinal metacenter to predict #-


8/22

MCTC 1 ( a function of draft)ue to the movement of a weight, assume that the ship as 1 trim,

and floats at waterline /.2., also e*pressed as MTIin inches

( )

( )

0 1

0 1

0 1 0

13 1tan , where is in feet.

1"

ue to the movement of the weight, moves to ,,

tan tan

tan tan

1

1"

w

L L G

FCw L G w B G

FCw B G

LL L

G GM w h G G

G G G M HM Z

IM HM Z Z Z

IZ Z

L

= =

= =

= =

= = + = +


9/22

MCTC 1 ( a function of draft)

-f the longitudinal inclination is small, MCTC 1can be used to

find out the longitudinalposition of gravity center ( ).

4

1 ,

1" 1"

56 lbft , 2ong #on $ ""60 lb, #- (ton7ft)6"0

FC FC w FCG B w

FCw

I I IZ Z M

L LI

L

>> = =

= =

1GX

0 1

0 0 0

1 0 1

#rimtan

tan ,

Since is in the same vertical line as . under ,

F A

FC FC FCB G G B

FC

G B B

T T T

L L L

I I ITG G Z Z Z Z L

G C B W L

I TX X G G X

L

= = =

= +

= + +

)


10/22

when a compartment is open to S

0 0

1 1

/.2. before the damage

/.2. after the damage

W L

W L

-f W1L1 is higher at any point than the main deckat which the

bulheads stop (the bulkhead deck) it is usually considered

that the ship will belost (sink)because the pressure of water

in the damaged compartments can force off the hatches and

unrestricted flooding will occur all fore and aft.


11/22

(1) Lost buoyancy method

0

0 0

(

1) 'omputing the( )

7 volume of lost buoyancy up to

7 intact . . area8 7 area of the damage

") Find the (e*cluding damage

aera ) area , '.F.,m y m

vyA a

v W L

A W L a

a A I

=

parallel sinkage

midway !L!

) 0at draft 0.+

( 7 draft before the damage).

cf d y

d

+


12/22

"

"

14) pdate the sinage .

6) Find the trim , #rim (in)6"0

distance between the '.F. of mean .

% centroid of lost buoyancy of .

(0.+ )+) raft aft #

y

y

m

mfc w

d

d

m

vyA

I v x

L

x W L

v

v Ld

A L

+

+

=

= =

= +

MTI MTI

rim

(0.+ ) raft forward #rim

is the distance between '.F. % midship

Aassuming that '.F. is aft of midship % the

damage taes place of forward.

m

v Ld

A L

+= + +


13/22

! update the midway . .

0.+ , then find new , and

repeat the procedures given in the previous

page.

#he iteration may be stopped if the results are

convergent, e.g. the mid

m m

W L

d v A A+"econd iteration

L

way . . of the

previous iteration % present iteration are

different by an amount smaller than aprescribed tolerance error.

W L


14/22

(0) (0), , wv x A a

(())

(0) (0)

w

vy

A a=

(0)

1"

(0) "yd d= +(0)

mA(0)

ma

(1)(0) (0)

m m

vyA a

=


15/22

(0) (1)y y


16/22

(2) dded !eight Method(considering the loss of buoyancyas added weight)

also a #rial 9 error (iterative) method

1) Find added weight vunder /020. #otal weight $ W + v

".) According to hydrostatic curve , determine W1L1 (or T) % trim (moment

caused by the added weight % MCTC 1).

4.) Since we have a largerT, and vwill be larger, go bac to step 1) re7compute

v.

#he iterative computation continues until the difference

between two added weights vobtained from the two

consecuti#e computationis smaller than a prescribed error

tolerance.


17/22

$loodable length and its computation

$loodable Length! #he $!L. at any point within the length ofthe ship is the ma*imum portion of the length, having its center

at the point which can be symmetricallyflooded at the

prescribed permeability, without immersing the margin line.


18/22

%ulkhead deck! #he dec tops the watertight bulhead

Margin line! is a line :+ mm (or 4) below the bulheadat the side of a ship

ithout loss of the ship: /hen the /.2. is tangent to

the margin line.

$loodable length(in short) #he length of (part of) the

ship could be flooded without loss of the ship.

&etermine $loodable length is essential to determine

1. ;ow many watertight compartments (bulheads) needed

'! $actor of subdi#ision(;ow many water compartments

flooded without lost ship)


19/22

0 0 0 0

1 1

1 1 1 1

1 0

Steps for computing the F.2. given , , or

1)


20/22


21/22


22/22

T*AN+

YOU,,,

Longitudinal Stability Yuvaraj Adithya

Documents

Transcript of Longitudinal Stability Yuvaraj Adithya