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1. CAUSES OF THE SIX DEGREES OF FREEDOM.

a. Pitching - Swaying along the lateal !-a"i#.- Motion a$o%t the &e##el'# tan#&e#e a"i#.- To ha&e a con#tant ti( )ti( $eing the *i++eence o+ the +owa*

an* a+te *a+t#, #ta$ility in the (otion o+ itch (%#t $e ac/%ie*.- Go&ening #ta$ility 0 1ongit%*inal #ta$ility

$. Hea&ing - The yawing along the &etical 2-a"i#.- The &etical $o*ily (otion o+ the &e##el.- To 3ee the &e##el on the #%+ace at a elati&ely con#tant (ean

*a+t #ta$ility in hea&e i# nece##ay.- Go&ening #ta$ility 0 Po#itional (otion #ta$ility

c. S%ge - Rolling along the longit%*inal X-a"i#.- 1ongit%*inal $o*ily (otion.- Thee i# a *e#ie +o a &e##el to (aintain a con#tant #ee* thi#

wo%l* e/%ie that the &e##el ha&e #ta$ility along the #%ge a"i#.- Go&ening #ta$ility 0 Sta$ility in (otion ahea* 4 a#ten

*. Rolling - Motion a$o%t the &e##el'# longit%*inal a"i#.- One o+ the (o#t %n*e#ia$le chaactei#tic o+ #hi#. Setting %

#te##e# in the #t%ct%e ca%#ing *i#co(+ot to $oth a##enge#an* cew.

- Geneate# i#3 o+ cago #hi+ting an* incea#ing the co#t o+oeation.

- Rolling i# #o(eti(e# a *iect ca%#e o+ #ee* e*%ction $%t (oeo+ten a change in co%#e which in t%n (ay e#%lt in #ee*e*%ction.

- It i# a concen to 3ee the &e##el +o( ca#i5ing #ta$ility in olling(otion (%#t $e #%++icient.

- Go&ening #ta$ility 0 Tan#&e#e #ta$ility

e. !awing- (otion a$o%t the &e##el'# &etical a"i#.- Rotation o+ a #hi a$o%t a &etical a"i# ao"i(ately tho%gh it#

cente o+ ga&ity.- Thi# i# %n*e#ia$le $eca%#e it# coection e/%ie# the %#e o+ a

%**e with incea#e in e#i#tance to o%l#ion an* $eca%#e ito*%ce# yaw-heel.

- It i# *e#ia$le +o a &e##el to $e a$le to #tay on co%#e an* not#wing wil*ly +o( it. Thi# can $e con#t%e* to (ean that the &e##eli# #ta$le in yaw (otion o hea*ing.

- Go&ening #ta$ility 0 Diectional #ta$ility

+. Sway - 6o*ily tan#+e o+ the #hi in a lateal *iection *%e to o$ital(otion o+ the wate in a wa&e.

- 1ateal #i*e to #i*e $o*ily (otion.- It i# i(otant to (ini(i5e a &e##el'# #i*eway# o lateal (otion.

Thi# e/%ie# a high *egee o+ #ta$ility in #way.- Go&ening #ta$ility 0 1ateal (otion #ta$ility

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7. COMPUTATIO8 OF RO11I8G PERIOD.

- Fo #hi# o+ o*inay +o( at (o*eate angle# o+ oll the a"i# i# not +a +o( thecente o+ ga&ity9 an* whee the #i(li+ication a##i#t# in the #ol%tion o+ ao$le( the a"i# o+ oll i# a##%(e* to a## tho%gh G.

- Un*e thi# a##%(tion# the e/%ation o+ (otion o+ the #hi i#:

I * ; < M = > - e/%ation no. ? whee: *t I = (a## (o(ent o+ inetia o+ the #hi

a$o%t a long'l a"i# tho%gh thecente o+ ga&ity

M = i# the ighting (o(ent

; = angle o+ inclination o+ the #hi +o( the &etical

I = @ 3 - e/%ation no. 7 whee: g 3 = a*i%# o+ gyation o+ (a## o+ a #hi

a$o%t a long'l a"i# tho%gh G

- Fo #(all angle# o+ inclination:

M = @G2 = @GM #in; = @GM; - e/%ation no.

- S%$#tit%ting the#e &al%e# we ai&e:

* ; < g GM ; = > - e/%ation no. B*t 3

- E/%ation no. ? i# the e/%ation +o #i(le ha(onic (otion ha&ing the eio*:

T; = 73 - e/%ation no. gGM

- Thee+oe the olling eio* o+ a #hi i#:

T; = ?.?>3 - e/%ation no.

GM

- Fo in*%ce* olling )#allying, olling eio* i#:

Peio* = ?.?>3GM

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7. DRA THE SIX DEGREES OF FREEDOM.

HEAVE

YAW

SWAY

PITCH

SURGE

ROLL