1.Principle of Stability
Transcript of 1.Principle of Stability
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LESSON O!"#: 4.1 "LE: !$"N#"!LES O% S&'"L"(
#ontact p)r*ods allott)d th*s LESSON O!"#:
#lassroom: +.5 )st: 0.0
ra*n)r: 0.5 otal: ,.0
E"&: #lassroom l)ctr) w*th v*sal m)d*a
%%-2 Sta3*l*ty ra*n)r
E$"N&L O'E#"ES:
6.0 E&L7&E sh*p3oard sta3*l*ty 3y analy8*ng
w)*ght and mom)nt cons*d)rat*ons. 9" ,.+.1 6.0
6.1 6.+
EN&'L"N O'E#"ES:
6.1 ES#$"'E th) r)f)r)nc) po*nts forc)s and
l*n)ar m)asr)m)nts s)d *n sta3*l*ty
calclat*ons.
6.+ ES#$"'E th) mov)m)nt of sta3*l*ty r)f)r)nc)
po*nts as a fnct*on of chang)s *n d*splac)m)nt
and *ncl*nat*on.
6., "%%E$EN"&E 3)tw))n *nd*cators of *n*t*al
sta3*l*ty and m)asr)s of ov)rall sta3*l*ty as a
fnct*on of sh*ps d*splac)m)nt.
6.4 "EN"%( and ES#$"'E th) s)s of var*os
typ)s of );t)rnal hll mar
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FUNDAMENTALS OF STABILITY
Sta3*l*ty *s th) t)nd)ncy of a v)ss)l to rotat) on) way or
th) oth)r wh)n forc*3ly *ncl*n)d. Sta3*l*ty can 3) 3ro
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,. & 3ody *mm)rs)d 9or float*ng *n
wat)r w*ll 3) 3oy)d p 3y a forc) )Aal
to th) w)*ght of th) wat)r d*splac)d.
EXAMPLE OF GRAVITY -VS- BUOYANCY
1 ton of st))l 1 ton of st))l
"f th) c3) of st))l *s plac)d *n wat)r *t s*n
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Force:& psh or pll that t)nds to
prodc) mot*on or a chang) *n mot*on.
7n*ts: tons ponds N)wtons )tc.
!arall)l forc)s may 3) math)mat*cally
smm)d to prodc) on) >N)t %orc)>
cons*d)r)d to act throgh on) po*nt.
Weig!:h) forc) of grav*ty act*ng on a
3ody. h*s forc) acts towards th) c)nt)r
of th) )arth. 7n*ts: tons ponds
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Vo$%"e:w)*ght. 7n*ts: c3*c f))t p)r
ton 9%,/L. h) sp)c*f*c volm) of
l*A*ds 9NS 0D6 a3l) 0D6-1 s)d most
fr)A)ntly *n th*s n*t ar):
Salt =at)r C ,5 %,/L
%r)sh =at)r C ,6 %,/L
*)s)l %)l C 4, %,/L
CALCULATING THE WEIGHT OF FLOODING WATER
& compartm)nt has th) follow*ng d*m)ns*ons:
L)ngth C +0 % %lood)d w*th salt
'r)adth C +0 % wat)r to a d)pth
)*ght C F % of 6 %
1. %*rst calclat) th) volm) of wat)r that has 3))n
add)d to th) compartm)nt.
olm) C L)ngth ; 'r)adth ; )pth of %lood*ng =at)r
C +0 % ; +0 % ; 6 %
C +400 %,
+. S)cond d*v*d) th) volm) of wat)r 3y *tBs sp)c*f*c
volm).
STABILITY REFERENCE POINTS
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- )tac)nt)r
- #)nt)r of rav*ty
' - #)nt)r of 'oyancy
G - G))l
( - (ee$:h) 3as) l*n) r)f)r)nc) po*nt from wh*ch
all oth)r r)f)r)nc) po*nt m)asr)m)nts ar)
compar)d.
B - Ce#!er o' B%o)*#c):
h) g)om)tr*c c)nt)r of
th) sh*p?s nd)rwat)r
hll 3ody. "t *s th)
po*nt at wh*ch all th)
forc)s of 3oyancy may 3)
cons*d)r)d to act *n a
v)rt*cally pward
d*r)ct*on.
h) #)nt)r of 'oyancy w*ll mov) as th) shap) of th)
nd)rwat)r port*on of th) hll 3ody chang)s. =h)n th) sh*p
rolls to star3oard >'> mov)s to star3oard and wh)n th)
sh*p rolls to port >'> mov)s to port.
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=h)n th) sh*p?s hll *s mad) h)av*)r th) drafts *ncr)as) as
th) sh*p s*ts d))p)r *n th) wat)r. >'> w*ll mov) p.
=h)n th) sh*p?s hll *s l*ght)n)d th) drafts d)cr)as) as
th) sh*p s*ts shallow)r *n th) wat)r. >'> w*ll mov) down.
++ Te Ce#!er o' B%o)*#c) "o,e
i# !e *"e .irec!io# * !e
i&/ 0*!er$i#e1 ++
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G - Ce#!er o' Gr*,i!):h)
po*nt at wh*ch all forc)s of
grav*ty act*ng on th) sh*pcan 3) cons*d)r)d to act. >>
*s th) c)nt)r of mass of th)
v)ss)l. h) pos*t*on of >>
*s d)p)nd)nt pon th)
d*str*3t*on of w)*ghts
w*th*n th) sh*p. &s th)
d*str*3t*on of w)*ghts *s
alt)r)d th) pos*t*on of >>
w*ll r)act as follows:
21 "G""o,e !o0*r. * 0eig! *..i!io#
31 "G""o,e *0*) 'ro" * 0eig! re"o,*$
41 "G""o,e i# !e *"e .irec!io# * * 0eig! i'!
M - Me!*ce#!er:&s th) sh*p*s *ncl*n)d throgh small
angl)s of h))l th) l*n)s of
3oyant forc) *nt)rs)ct at a
po*nt call)d th) m)tac)nt)r.
&s th) sh*p *s *ncl*n)d th)
c)nt)r of 3oyancy mov)s *n
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an arc as *t cont*n)s to
s))< th) g)om)tr*c c)nt)r of
th) nd)rwat)r hll 3ody.
h*s arc d)scr*3)s th)
m)tac)ntr*c rad*s.
&s th) sh*p cont*n)s to h))l
*n );c)ss of 2-10 d)gr))s
th) m)tac)nt)r w*ll mov) as
shown.
h) pos*t*on of th) m)tac)nt)r *s a fnct*on of th) pos*t*on
of th) c)nt)r of 3oyancy ths a fnct*on of th)
d*splac)m)nt of th) sh*p. h) pos*t*on of >> mov)s as
follows:
A !e Ce#!er o' B%o)*#c) "o,e %&5 !e
Me!*ce#!er "o,e .o0#1
A !e Ce#!er o' B%o)*#c) "o,e .o0#5 !e
Me!*ce#!er "o,e %&1
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LINEAR MEASUREMENTS IN STABILITY
(G- Heig! o' !e i&/ Ce#!er o' Gr*,i!) !e*6o,e (ee$:h*s m)asr)m)nt *s fond *n s)ct*on
""9a of th) # 'oo< for s)v)ral cond*t*ons of
load*ng. o f*nd >G> for load*ng cond*t*ons oth)r
than thos) *n th) # 'oo
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actally th) rad*s of th) c*rcl) for th)
mov)m)nts of >'> at small angl)s of h))l.
THE STABILITY TRIANGLE
=h)n a sh*p *s *ncl*n)d th) c)nt)r of 3oyancy sh*fts offc)nt)rl*n) wh*l) th) c)nt)r of grav*ty r)ma*ns *n th) sam)
locat*on. S*nc) th) forc)s of 3oyancy and grav*ty ar) )Aal
and act along parall)l l*n)s 3t *n oppos*t) d*r)ct*ons a
rotat*on *s d)v)lop)d. h*s *s call)d a copl) two mom)nts
act*ng s*mltan)osly to prodc) rotat*on. h*s rotat*on
r)trns th) sh*p to wh)r) th) forc)s of 3oyancy and grav*ty
3alanc) ot.
h) d*stanc) 3)tw))n th) forc)s of 3oyancy and grav*ty *s
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7s*ng th) S*n) fnct*on to solv) for th) r*ght*ng arm:
=*th *n*t*al sta3*l*ty 90oto 2o-10o th) m)tac)nt)r do)s not
mov) and th) S*n) fnct*on *s almost l*n)ar 9a stra*ght
l*n). h)r)for) th) s*8) of th) sh*pBs $*ght*ng &rm H
*s d*r)ctly proport*onal to th) s*8) of th) sh*pBs
)tac)ntr*c )*ght . hs GM i * goo. "e*%re o' !e
i&/ i#i!i*$ !*6i$i!).
RIGHTING MOMENT 7RM8
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h) $*ght*ng om)nt *s th) 3)st m)asr) of a sh*p?s ov)rall
sta3*l*ty. "t d)scr*3)s th) sh*p?s tr) t)nd)ncy to r)s*st
*ncl*nat*on and r)trn to )A*l*3r*m. h) $*ght*ng om)nt
*s )Aal to th) sh*pBs $*ght*ng &rm mlt*pl*)d 3y th) sh*pBs
d*splac)m)nt.
E9*"&$e:
& d)stroy)r d*splac)s 6000 L and has a r*ght*ng arm of +.4
% wh)n *ncl*n)d to 40 d)gr))s. =hat *s th) sh*pBs $*ght*ng
om)ntI
RM = 2.4 FT x 6000 LT
RM = 14,400 FT-Tons (pronounced "foot tons")
STABILITY CONDITIONS
h) pos*t*ons of rav*ty and th) )tac)nt)r w*ll *nd*cat)
th) *n*t*al sta3*l*ty of a sh*p. %ollow*ng damag) th) sh*p
w*ll assm) on) of th) follow*ng thr)) sta3*l*ty cond*t*ons:
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POSITIVE STABILITY
h) m)tac)nt)r *s locat)d a3ov)
th) sh*pBs c)nt)r of grav*ty. &s
th) sh*p *s *ncl*n)d $*ght*ng
&rms ar) cr)at)d wh*ch t)nd to
r)trn th) sh*p to *tBs or*g*nal
v)rt*cal pos*t*on.
NEUTRAL STABILITY
h) m)tac)nt)r and th) sh*pBsc)nt)r of grav*ty ar) *n th) sam)
locat*on. &s th) sh*p *s *ncl*n)d
no $*ght*ng &rms ar) cr)at)d.
9nt*l th) m)tac)nt)r starts to
mov) aft)r th) sh*p *s *ncl*n)d
past 2o-10o
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NEGATIVE STABILITY
h) sh*pBs c)nt)r of grav*ty *s
locat)d a3ov) th) m)tac)nt)r. &sth) sh*p *s *ncl*n)d n)gat*v)
$*ght*ng &rms 9call)d ps)tt*ng
arms ar) cr)at)d wh*ch t)nd to
caps*8) th) sh*p.
STATICAL STABILITY CURVE 7RIGHTING ARM
CURVE8
=h)n a sh*p *s *ncl*n)d throgh all angl)s of h))l and th)
r*ght*ng arm for )ach angl) *s m)asr)d th) stat*cal
sta3*l*ty crv) *s prodc)d. h*s crv) *s a >snapshot> of
th) sh*p?s sta3*l*ty at that part*clar load*ng cond*t*on.
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ch *nformat*on can 3) o3ta*n)d from th*s crv) *ncld*ng:
R*#ge o' S!*6i$i!):h*s sh*p w*ll g)n)rat) $*ght*ng &rms
wh)n *ncl*n)d from 0oto appro;*mat)ly 24o. 9h*s crv)
sally assm)s that th) )nt*r) sp)rstrctr) *s
wat)rt*ght.
M*9i"%" Rig!i#g Ar":h) larg)st s)parat*on 3)tw))n th)
forc)s of 3oyancy and grav*ty. h*s *s wh)r) th) sh*p
);)rts th) most )n)rgy to r*ght *ts)lf.
A#g$e o' M*9i"%" Rig!i#g Ar": h) angl) of *ncl*nat*on
wh)r) th) ma;*mm $*ght*ng &rm occrs.
D*#ger A#g$e:On) half th) angl) of th) ma;*mm $*ght*ng
&rm.
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SHIPS HULL MAR(INGS
C*$c%$*!i,e Dr*'! M*r;
7s)d for d)t)rm*n*ng d*splac)m)nt and oth)r prop)rt*)s of
th) sh*p for sta3*l*ty and damag) control. h)s) draft mar...*nstall)d on thos) sh*ps whos) l*m*t*ng d*splac)m)nts
ar)
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P$i"o$$ M*r; 7Lo*. $i#e8
ar
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DRAFT DIAGRAM AND FUNCTIONS OF FORM
h) raft *agram *s a nomogram locat)d *n s)ct*on ""9a of
th) amag) #ontrol 'oo
- ons p)r "nch "mm)rs*on 9!"
- )*ght of )tac)nt)r 9G
- Long*td*nal #)nt)r of %lotat*on 9L#%
- Long*td*nal #)nt)r of 'oyancy 9L#'
I#!r%c!io# 'or %e:
1. raw a stra*ght l*n) 9L"NE J1
3)tw))n th) sh*p?s forward and aft draft
r)ad*ngs 9s) calclat*v) drafts
+. =h)r) L"NE J1 *nt)rs)cts th)
*splac)m)nt #rv) *s th) sh*p?s
d*splac)m)nt at thos) g*v)n drafts.
,. raw a hor*8ontal l*n) 9L"NE J+
throgh th) sh*p?s d*splac)m)nt. 9*nt:
=h)n th) forward and aft drafts ar)
)Aal th) l*n) *s hor*8ontal
4. 1> !" G and L#' ar) d)t)rm*n)d s*ng L"NE J+.
5. raw a v)rt*cal l*n) 9L"NE J,
throgh th) sh*p?s d*splac)m)nt 9h)r)
*s no way to )nsr) th*s l*n) *s
v)rt*cal - @st )y)3all *t.
6. =h)r) L"NE J, *nt)rs)cts th) L#%
#rv) *s th) sh*p?s L#% for th) g*v)n
drafts.
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E9*"&$e:
%%-+1 has th) follow*ng drafts: %orward: 2&ft: 2?@>
Fi#.:1. Sh*p?s *splac)m)nt: 4@== LT
+. G: 3314 FT
,. 1>: ? FT-To# &er I#c
4. !": 4313 LT &er I#c
5. L#': 312 FT A'! o' Mi.i&
6. L#%: 3< FT A'! o' Mi.i&
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CROSS CURVES OF STABILITY
h) #ross #rv)s Of Sta3*l*ty ar) s)d to d)t)rm*n) th)
l)ngth of th) r*ght*ng arm at any angl) of *ncl*nat*on for a
g*v)n d*splac)m)nt. 7s*ng th) sh*p?s d*splac)m)nt 9from th)
raft *agram and %nct*ons of %orm a stat*cal sta3*l*tycrv) for th) sh*p can 3) constrct)d.
I#!r%c!io# 'or %e:
1. Ent)r th) sh*pBs d*splac)m)nt along th)
hor*8ontal a;*s.
+. raw a v)rt*cal l*n) at th) sh*p?s
d*splac)m)nt. 9*nt: >t*c< mar ar)
locat)d along th) top of th) crv) to
ass*st *n draw*ng th*s v)rt*cal l*n)
,. h) d*splac)m)nt l*n) w*ll cross )ach
>angl) of *ncl*nat*on> crv) at var*os
po*nts.
4. h) r*ght*ng arm for )ach angl) of
*ncl*nat*on *s r)ad along th) v)rt*cal
a;*s 9l)ft s*d).
5. Each r*ght*ng arm *s plott)d at th)
corr)spond*ng angl) of *ncl*nat*on onth) >Stat*cal Sta3*l*ty #rv) !lott*ng
Sh))t> or on r)glar graph pap)r.
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