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ACADEMIA NAVALĂ „MIRCEA CEL BĂTRÂN” FACULTATEA DE MARINĂ CIVILĂ CATEDRA DE ARHITECTURA NAVALĂ Numele şi prenumele: Facultatea: MARINĂ CIVILĂ. Specializarea: NAVIGAŢIE . Anul de studii / semestrul: III/I TEMA PROIECTULUI DE CURS Se transversalul planului de forme al navei ................... având următoarele dimensiuni principale: L CWL = m; B= m; T= m; D= m. Se cer: - întocmirea calculului de carene drepte prin metoda trapezelor de integrare aproximativă, trasarea diagramelor de carene drepte; - întocmirea calculului de stabilitate la unghiuri mari de înclinare prin metoda Krylov-Dargnier de trasare a plutirilor şi Cebâşev de integrare şi trasare a diagramelor de stabilitate (diagrama stabilităţii statice, diagrama stabilităţii dinamice);

Proiect TCVN

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Proiect TCVN

ACADEMIA NAVAL MIRCEA CEL BTRN

FACULTATEA DE MARIN CIVIL

CATEDRA DE ARHITECTURA NAVALNumele i prenumele:

Facultatea: MARIN CIVIL.Specializarea: NAVIGAIE .Anul de studii / semestrul: III/I

TEMA PROIECTULUI DE CURS Se d transversalul planului de forme al navei ................... avnd urmtoarele dimensiuni principale: LCWL= m; B= m; T= m; D= m.Se cer:

ntocmirea calculului de carene drepte prin metoda trapezelor de integrare aproximativ, trasarea diagramelor de carene drepte;

ntocmirea calculului de stabilitate la unghiuri mari de nclinare prin metoda Krylov-Dargnier de trasare a plutirilor i Cebev de integrare i trasare a diagramelor de stabilitate (diagrama stabilitii statice, diagrama stabilitii dinamice);

1. Trasarea planului de forme

Etapele trasrii planului de forme prin utilizarea transversalului carenei navei sau modelului de referin sunt:

a) Stabilirea dimensiunilor principale ale navei de proiectat. Cunoscndu-se dimensiunile navei de referin: LCWL0=136m; B0=21,5m; T0=8m; D0=10,5m i coeficientul de micorare kl=0,86, se calculeaz dimensiunile navei de proiectat astfel:

LCWL= klLCWL0= 0,86136 m= 116,96 m

B= klB0= 0,8621,5 m= 18,49 m

T= klT0= 0,868 m= 6,88 m

D= klD0= 0,8610,5 m= 9,03 m

b) Alegerea scrii. innd cont de dimensiunile navei de proiectat, scara aleas pentru trasarea planului de forme este 1:100.

c) Trasarea caroiajului. ntreaga construcie se face pe acelai format astfel: caroiajul longitudinalului n partea stng, caroiajul transversalului n partea dreapt, iar caroiajul orizontalului n partea stng, situat sub cel al longitudinalului.

d) Trasarea cuplelor teoretic pn la CWL. Pentru a simplifica reprezentarea, cuplele teoretice din zona pupa se raporteaz la jumtatea stng, iar cele din zona prova la jumtatea dreapt a caroiajului transversalului. Din motive de simetrie ele se traseaz numai ntr-un bord, mai puin cupla maestr care se traseaz n ntregime.

e) Trasarea liniei punii n bord. Dac nu sunt indicaii precise, se poate utiliza urmtoarea modalitate de trasare a LPB:

se msoar nlimea de construcie D, pe proiecia cuplei maestre n longitudinalul planului de forme, iar prin punctul obinut se traseaz segmentul de dreapt orizontal avnd lungimea LCWL;

se mparte segmentul astfel obinut n 6 intervale de lungimi egale, i se obin 7 puncte numerotate de la pupa spre prova cu 1, 2, , 7;

sgeile LPB corespunztoare celor 7 puncte se calculeaz cu ajutorul relaiilor aproximative:

f1= 8,33LCWL+254= 8,33116,96 m+254= 1228,2768 mm;

f2=3,70LCWL+113= 3,70116,96 m+113= 545,752 mm;

f3=0,93LCWL+28,5= 0,93116,96 m+28,5= 137,2728 mm;

f4=0;

f5=1,85LCWL+56,5= 1,85116,96 m+56,5= 272,876 mm;

f6=7,48LCWL+226= 7,48116,96 m+226= 1100,8608 mm;

f7=16,66LCWL+508= 16,66116,96 m+508= 2456,5536 mm;

n care: LCWL se introduce n metri, iar rezultatele se obin n mm;

valorile sgeilor calculate cu relaiile de mai sus, transformate n m, se msoar pe verticalele ridicate din punctele 1, 2, , 7 i se obin punctele prin care se traseaz LPB.

f) Trasarea liniilor etravei i etamboului.

g) Trasarea cuplelor teoretice pn la nivelul liniei punii n bord i proieciei acestei linii pe transversalul planului de forme.

h) Trasarea liniei punii n planul diametral. n acest scop se utilizeaz sgeile calculate cu relaia:

,cu i= EQ \x \to(0, 20) i k=30..50 (k=50 pentru vrachiere)

CuplaBi,maxfi= EQ \f(Bi,max; k)

098,041,9608

1138,8042,77608

2155,1443,10288

3164,6043,29208

4171,8283,43656

5177,3323,54664

6181,1163,62232

7183,183,6636

8184,93,698

9184,93,698

10184,93,698

11184,93,698

12184,93,698

13184,93,698

14184,93,698

15181,8043,63608

16174,0643,48128

17161,1643,22328

18136,9122,73824

19102,1682,04336

2045,0640,90128

i) Trasarea plutirilor i a proieciei liniei punii n bord pe orizontalul planului de forme.

j) Trasarea longitudinalelor n longitudinalul planului de forme.

k) Trasarea curbei de balansare sub orizontalul planului de forme. n acest scop se folosesc diagonalele de balansare din transversalul planului de forme.

2. Calculul de carene drepteCalculul de carene drepte are ca scop determinarea volumului carenei i a coordonatelor centrului de caren pentru orice plutire dreapt cuprins ntre PB i PL. De asemenea unele date rezultate din urma acestui calcul sunt necesare n studiul stabilitii. Datorit geometriei complexe a corpului navei se utilizeaz metode aproximative de integrare, cum sunt: metoda trapezelor, metoda Cebev i metoda coordonatelor polare. Pentru calculul de carene drepte voi folosi metoda trapezelor de integrare aproximativ. ntruct nava are bulb la prova, calculul elementelor geometrice rezultate din integrarea pe lungime, corespunztoare plutirilor care cuprind bulbul, se face separat pentru corpul navei pn la cupla teoretic 20 i pentru bulb. Cu rezultatele obinute se determin n final valorile acestor elemente pentru ntreg corpul navei. n acest scop lungimea LB=2,709 m a bulbului se mparte n 4 intervale de lungime B=0,67725 m prin intermediul cuplelor transversale i= EQ \x \to(0', 4') (cupla 0 coincide cu cupla teoretic 20). Aceast metod presupune parcurgerea a apte etape.

a) Calculul ariilor suprafeelor plutirilor drepte (AWj), ariilor suprafeelor cuplelor teoretice (Axi) i volumului carenei corespunztor CWL (VCWL).

Pentru corpul navei pn la cupla teoretic 20 se utilizeaz relaiile:

, j= EQ \x \to(0, 5) [m2];

Axi=2tUi, i= EQ \x \to(0, 20) [m2];

, [m3],

n care: = LCWL/20= 116,96/20= 5,848 m; t= T/5= 6,88/5= 1,376 m;

j= y0j+ y1j+ y2j+ + ynj( (y0j +ynj);

Ui= yi0+ yi1+ yi2+ + yim( (yi0 +yim);

U0+ U1+ U2+ + Un( (U0+ Un).

Calculul este prezentat sub form tabelar n tabelul 1.

Pentru bulb se utilizeaz relaiile:

, j= EQ \x \to(0, 4) [m2];

AxBi= 2tUi, i= EQ \x \to(0', 4') [m2];

[m3],

n care B= LB/4= 2,709/4= 0,67725 m;

Bj= yB0j+ yB1j+ yB2j+ yB3j+ yB4j( (yB0j+ yB4j);

Ui= yi0+ yi1+ yi2+ yi3+ yi4( (yi0+ yi4);

U0+ U1+ U2+ U3+ U4( (U0+ U4).

Calculul este prezentat sub form tabelar n tabelul 2.

Semilimile yij, i= EQ \x \to(0, 20), j= EQ \x \to(0, 5) i yBij, i= EQ \x \to(0', 4'), j= EQ \x \to(0, 4) au fost scoase din planul de forme.

Pentru ntregul corp al navei se utilizeaz relaiile:

, j= EQ \x \to(0, 5) [m2]; [m3].

Calculul este prezentat sub form tabelar n tabelul 3.

b) Calculul volumului carenei (Vj) i deplasamentului navei (j) corespunztor plutirilor drepte j= EQ \x \to(0, 5).

Relaiile de calcul sunt:

[m3].

j= Vj , j= EQ \x \to(0, 5) [kN],

unde = 10,055 kN/m3.

Calculul este prezentat sub form tabelar n tabelul 4.

c) Calculul abscisei centrului plutirii (xFj) i abscisei centrului de caren (xBj).

Relaia de calcul a abscisei centrului plutirii j (care nu include bulbul) este:

, j= 0, 5 [m].

Pentru plutirile care includ bulbul, aceast relaie este valabil pn la cupla teoretic 20 i este de forma:

, j=1, 2, 3, 4 [m].

Calculul este prezentat sub form tabelar n tabelele 5-10.

Tabelul 1.

Cupla

PlutireaPupaCMProva

01234567891011

0000,3870,8171,291,8492,6664,3866,4077,8698,6438,643

1000,7311,6772,6663,6984,736,7518,2139,0739,2459,245

2000,9892,1933,5264,8165,9777,8268,9019,2459,2459,245

3001,6343,3114,736,027,0958,4719,1599,2459,2459,245

401,9783,6985,2896,4077,318,0848,9019,2459,2459,2459,245

505,2896,1927,1817,748,2568,6439,1169,2459,2459,2459,245

U'i [m]07,26713,63120,46826,35931,94937,19545,45151,1753,92254,86854,868

Corecia= EQ \f(1;2)(yi0+ yi5) [m]02,64453,28953,9994,5155,05255,65456,7517,8268,5578,9448,944

Ui= U'i- Corecia [m]04,622510,341516,46921,84426,896531,540538,743,34445,36545,92445,924

Axi=2tUi [m2] 012,7211228,45980845,32268860,11468874,01916886,799456106,5024119,282688124,84448126,382848126,382848

Prova 'j [m]Corecia= EQ \f(1;2) (y0j+ ynj) [m]j= 'j- Corecia [m]Aw20j=2j [m2]

121314151617181920

8,6437,8696,4075,6334,6013,2681,5050,731081,614081,614954,557344

9,2459,2458,5577,96367,1815,5474,3432,6231,161111,89460,5805111,31411301,929714

9,2459,2458,8588,3427,6116,3644,8593,1391,72121,3460,86120,4861409,204256

9,2459,2458,9878,6437,8696,7084,9452,9671,505128,2690,7525127,51651491,432984

9,2459,2459,1598,8588,1276,9665,1172,7090,473138,5460,2365138,30951617,667912

9,2459,2459,2028,9878,2997,1815,4612,9670149,9840149,9841754,212864

54,86854,09451,1748,426643,68836,03426,2315,1364,859729,2241

8,9448,5577,80457,316,455,22453,4831,8490115,799

45,92445,53743,365541,116637,23830,809522,74713,2874,859615,85462,4295613,4251

126,382848125,317824119,341856113,1528832102,47897684,78774462,59974436,56582413,371968613,42519872,277078

Tabelul 2.

Cupla

Plutirea0'

1'2'3'4' 'Bj [m]Corecia [m] Bj [m]AwBj=2B Bj [m2]

0000000000

11,1611,0320,8170,51603,5260,58052,94553,86302325

21,721,4191,0750,47304,6870,863,8275,0191105

31,5051,0750002,580,75251,82752,39676625

40,47300000,4730,23650,23650,31016975

U'i' [m]4,8593,5261,8920,98908,8365

Corecia [m]0,236500000,11825

Ui' [m]4,62253,5261,8920,989011,02952,311258,71825

Axi' [m2]12,721129,7035525,2067842,72172808,7182515,73316319

Tabelul 3.

PlutireaAw20j [m2]AwBj [m2]Awj [m2]VCWL20 [m3]VB [m3]VCWL [m3]

IIIIIIIVVVIVII

0954,5573440954,557344

11301,9297143,863023251305,792737

21409,2042565,01911051414,223367

31491,4329842,396766251493,82975

41617,6679120,310169751617,978082

51754,21286401754,2128649872,27707815,733163199888,010241

Tabelul 4.

PlutireaAwj [m2]Suma integral a coloanei II [m2]Vj= EQ \f(t;2) III [m3]j= IV [kN]

IIIIIIIVV

0954,557344000

11305,7927372260,3500811555,12085615636,7402

21414,2233674980,3661843426,49193534453,3764

31493,829757888,4193015427,23247954570,82258

41617,97808211000,227137568,15626776097,81127

51754,21286414372,418089888,22363899426,08868

Tabelul 5.

CoeficientSemilimi yi0 [m] II-III [m] IIV [m]

ProvaPupa

IIIIIIIVV

08,64300

18,6437,8690,7740,774

28,6436,4072,2364,472

37,8694,3863,48310,449

46,4072,6663,74114,964

55,6331,8493,78418,92

64,6011,293,31119,866

73,2680,8172,45117,157

81,5050,3871,1188,944

90,73100,7316,579

100000

'0 [m] 81,614 'V [m] 102,125

Corecia [m] 0Corecia [m] 0

0 [m] 81,614 V [m] 102,125

xF0= EQ \f(; 0) V [m] 7,317702845

Tabelul 6.

CoeficientSemilimi yi1 [m]II-III [m]IIV [m]

ProvaPupa

IIIIIIIVV

09,24500

19,2459,0730,1720,172

29,2458,2131,0322,064

39,2456,7512,4947,482

48,5574,733,82715,308

57,96363,6984,265621,328

67,1812,6664,51527,09

75,5471,6773,8727,09

84,3430,7313,61228,896

92,62302,62323,607

101,16101,16111,61

'1 [m]111,8946 'V [m] 164,647

Corecia [m]0,5805Corecia [m] 5,805

1 [m]111,3141 V [m] 158,842

= EQ \f(; 1) V [m] 8,344926797

xF1= EQ \f(+xFB1AwB1; Aw1) [m] 8,496020501

unde:

xFB1AWB1= 2B{ EQ \f(LCWL;2) y01+ ( EQ \f(LCWL;2) + 1B)y11+ ( EQ \f(LCWL;2) + 2B)y21+ ( EQ \f(LCWL;2) + 3B) y31+ ( EQ \f(LCWL;2) + 4 B ) y41( EQ \f(1;2) [ EQ \f(LCWL;2) y01+ ( EQ \f(LCWL;2) + 4 B ) y41]}= 229,5337076 m3.

Tabelul 7.

CoeficientSemilimi yi2 [m]II-III [m]IIV [m]

ProvaPupa

IIIIIIIVV

09,24500

19,2459,24500

29,2458,9010,3440,688

39,2457,8261,4194,257

48,8585,9772,88111,524

58,3424,8163,52617,63

67,6113,5264,08524,51

76,3642,1934,17129,197

84,8590,9893,8730,96

93,13903,13928,251

101,7201,7217,2

'2 [m]121,346 'V [m] 164,217

Corecia [m]0,86Corecia [m] 8,6

2 [m]120,486 V [m] 155,617

= EQ \f(; 2) V [m] 7,553144897

xF2= EQ \f(+xFB2AwB2; Aw2) [m] 7,736918747

unde:

xFB2AWB2= 2B{ EQ \f(LCWL;2) y02+ ( EQ \f(LCWL;2) + 1B)y12+ ( EQ \f(LCWL;2) + 2B)y22+ ( EQ \f(LCWL;2) + 3B) y32+ ( EQ \f(LCWL;2) + 4 B ) y42( EQ \f(1;2) [ EQ \f(LCWL;2) y02+ ( EQ \f(LCWL;2) + 4 B ) y42]}= 297,8073425 m3.

Tabelul 8.

CoeficientSemilimi yi3 [m]II-III [m]IIV [m]

ProvaPupa

IIIIIIIVV

09,24500

19,2459,24500

29,2459,1590,0860,172

39,2458,4710,7742,322

48,9877,0951,8927,568

58,6436,022,62313,115

67,8694,733,13918,834

76,7083,3113,39723,779

84,9451,6343,31126,488

92,96702,96726,703

101,50501,50515,05

'3 [m]128,269 'V [m] 134,031

Corecia [m]0,7525Corecia [m] 7,525

3 [m]127,5165 V [m] 126,506

= EQ \f(; 3) V [m] 5,801657731

unde:xF3= EQ \f(+xFB3AwB3; Aw3) [m]

xFB3AWB3= 2B{ EQ \f(LCWL;2) y03+ ( EQ \f(LCWL;2) + 1B)y13+ ( EQ \f(LCWL;2) + 2B)y23+ ( EQ \f(LCWL;2) + 3B) y33+ ( EQ \f(LCWL;2) + 4 B ) y43( EQ \f(1;2) [ EQ \f(LCWL;2) y03+ ( EQ \f(LCWL;2) + 4 B ) y43]}= 141,0874076 m3.

Tabelul 9.

CoeficientSemilimi yi4 [m]II-III [m]IIV [m]

ProvaPupa

IIIIIIIVV

09,24500

19,2459,24500

29,2459,24500

39,2458,9010,3441,032

49,1598,0841,0754,3

58,8587,311,5487,74

68,1276,4071,7210,32

76,9665,2891,67711,739

85,1173,6981,41911,352

92,7091,9780,7316,579

100,47300,4734,73

'4 [m]138,546 'V [m]57,792

Corecia [m]0,2365Corecia [m]2,365

4 [m]138,3095 V [m]55,427

= EQ \f(; 4) V [m]2,343563501

unde:xF4= EQ \f(+xFB4AwB4; Aw4) [m]2,354324972

xFB4AWB4= 2B{ EQ \f(LCWL;2) y04+ ( EQ \f(LCWL;2) + 1B)y14+ ( EQ \f(LCWL;2) + 2B)y24+ ( EQ \f(LCWL;2) + 3B) y34+ ( EQ \f(LCWL;2) + 4 B ) y44( EQ \f(1;2) [ EQ \f(LCWL;2) y04+ ( EQ \f(LCWL;2) + 4 B ) y44]}= 18,13872698 m3.

Tabelul 10.

CoeficientSemilimi yi5 [m] II-III [m] IIV [m]

ProvaPupa

IIIIIIIVV

09,24500

19,2459,24500

29,2459,24500

39,2459,1160,1290,387

49,2028,6430,5592,236

58,9878,2560,7313,655

68,2997,740,5593,354

77,1817,18100

85,4616,192-0,731-5,848

92,9675,289-2,322-20,898

100000

'5 [m] 149,984 'V [m] -17,114

Corecia [m] 0Corecia [m] 0

5 [m] 149,984 V [m] -17,114

xF5= EQ \f(; 5) V [m] -0,667288991

Momentul static al suprafeei unei plutiri drepte j, care include i bulbul, este:

My (AWj)= xFj AWj= xFj,20 AWj,20+ xFBj AWBj,

de unde rezult:

xFj= EQ \f(+xFBjAwBj; Awj) , j= 1, 2, 3,4 [m],

n care:

xFBj AWBj= 2B{ EQ \f(LCWL;2) y0j+ ( EQ \f(LCWL;2) + 1B)y1j+ ( EQ \f(LCWL;2) + 2B)y2j+ ( EQ \f(LCWL;2) + 3B) y3j+ ( EQ \f(LCWL;2) + 4 B ) y4j( EQ \f(1;2) [ EQ \f(LCWL;2) y0j+ ( EQ \f(LCWL;2) + 4 B ) y4j]} , j=1, 2, 3, 4 [m3].

Pentru plutirile j= 1, 2, 3, 4, care includ bulbul, aceste calcule sunt efectuate sub tabel.

Relaia de calcul a abscisei centrelor de caren este:

[m].

Calculul este prezentat sub form tabelar n tabelul 11.

Tabelul 11.

PlutireaAwj [m2]XFj [m]IIIII [m3]Suma integral a coloanei IV [m3]Vj [m3]xBj= EQ \f(tV; 2VI ) [m]

IIIIIIIVVVIVII

0954,5573447,3177028456985,166992000

11305,7927378,49602050111094,0418618079,208851555,1208567,998410958

21414,2233677,73691874710941,7312840114,981993426,4919358,054625004

31493,829755,8867960748793,87110959850,584385427,2324797,587145421

41617,9780822,3543249723809,24620272453,701697568,1562676,586564151

51754,212864-0,667288991-1170,56693275092,380969888,2236385,224756234

d) Calculul cotei centrului de caren ( EQ \x \to(KB))j.

Pentru aceasta se utilizeaz relaia:

[m].

Calculul este prezentat sub form tabelar n tabelul 12.

Tabelul 12.

PlutireaAwj [m2]III [m2]Suma integral a coloanei III [m2]Vj [m3]= EQ \f(IV; 2V ) [m]

IIIIIIIVVVI

0954,5573440000

11305,7927371305,7927371305,7927371555,1208560,794908196

21414,2233672828,4467335440,0322073426,4919351,502998784

31493,829754481,48925112749,968195427,2324792,224014161

41617,9780826471,91232723703,369777568,1562672,96501485

51754,2128648771,0643238946,346429888,2236383,728681727

e) Calculul momentelor de inerie ale suprafeei plutirii drepte fa de axele longitudinal (ILj)i transversal de inerie (ITj).

Relaia de calcul a momentului de inerie al suprafeei plutirii drepte j (care nu include bulbul) fa de axa longitudinal de inerie este:

, j= 0, 5 [m4].

Pentru plutirile care includ bulbul se utilizeaz relaiile:

, j= 1, 2, 3, 4 [m4];

, j= 1, 2, 3, 4 [m4];

, j= 1, 2, 3, 4 [m4],

unde .

Calculul este prezentat sub form tabelar n tabelele 13 i 14.

Relaia de calcul a momentului de inerie al suprafeei plutirilor drepte j (care nu includ bulbul) fa de axa Oy este:

, j= 0, 5 [m4].

Pentru plutirile care includ bulbul se utilizeaz relaiile:

, j= 1, 2, 3, 4 [m4];

Tabelul 13.

Cupla

Plutirea PupaCMProva

01234567891011

0yi0000,3870,8171,291,8492,6664,3866,4077,8698,6438,643

000,057960600,545338512,1466896,3213630418,948744384,3734644263,005101487,257615645,644623645,644623

1yi1000,7311,6772,6663,6984,736,7518,2139,0739,2459,245

000,390617894,7162757318,948744350,5709043105,823817307,683582553,994519746,883272790,170381790,170381

2yi2000,9892,1933,5264,8165,9777,8268,9019,2459,2459,245

000,9673616610,546683043,8376155111,701610213,525509479,313356705,206656790,170381790,170381790,170381

3yi3001,6343,3114,736,027,0958,4719,1599,2459,2459,245

004,3627081036,2975692105,823817218,167208357,155382607,860671768,323606790,170381790,170381790,170381

4yi401,9783,6985,2896,4077,318,0848,9019,2459,2459,2459,245

07,7388933550,5709043147,951952263,005101390,617891528,297936705,206656790,170381790,170381790,170381790,170381

5yi505,2896,1927,1817,748,2568,6439,1169,2459,2459,2459,245

0147,951952237,406629370,300910463,684824562,741641645,644623757,552872790,170381790,170381790,170381790,170381

Prova [m3]Corecia [m3][m3] [m]

121314151617181920

8,6437,8696,4075,6334,6013,2681,5050,73103864,6924703864,6924715067,14773

645,6446237487,2576159263,0051011178,738971197,399493834,901664833,4088626250,3906178910

9,2459,2458,5577,96367,1815,5474,3432,6231,1616723,804360,782468146723,0218926210,82136

790,1703811790,1703811626,5627847505,0429508370,3009107170,676802381,9161416118,046578371,564936281

9,2459,2458,8588,3427,6116,3644,8593,1391,727640,865832,5442247638,3216029779,26984

790,1703811790,1703811695,0355647580,5111377440,8848401257,7451565114,720411830,929574625,088448

9,2459,2458,9878,6437,8696,7084,9452,9671,5058359,880151,704431318358,1757232585,74108

790,1703811790,1703811725,8455608645,6446237487,2576159301,8416469120,920208626,118765063,408862625

9,2459,2459,1598,8588,1276,9665,1172,7090,4739326,538420,052911909326,4855136360,85818

790,1703811790,1703811768,3236067695,0355647536,7731444338,0262367133,981936619,880486830,105823817

9,2459,2459,2028,9878,2997,1815,4612,967010562,2080010562,208041178,52853

790,1703811790,1703811779,1959504725,8455608571,5803549370,3009107162,860787226,118765060

IyBj= 2 B {( EQ \f(LCWL;2))2 y0j+ ( EQ \f(LCWL;2) + 1B)2 y1j+ ( EQ \f(LCWL;2) + 2B)2 y2j+ ( EQ \f(LCWL;2) + 3B)2 y3j+ ( EQ \f(LCWL;2) + 4 B )2 y4j( EQ \f(1;2) [( EQ \f(LCWL;2))2 y0j+ ( EQ \f(LCWL;2) + 4 B )2 y4j]}, j=1, 2, 3, 4 [m4].

, j= 1, 2, 3, 4 [m4].

Calculul este prezentat sub form tabelar n tabelele 15-20.

Tabelul 14.

[m4]ILBj [m4] [m4] Vj [m3] EQ \x \to(BMT)j= EQ \f(ILj; Vj) [m]

15067,14773015067,147730

26210,821361,12102627226211,942391555,12085616,85524459

29779,269842,95069477829782,220543426,4919358,691752704

32585,741081,28821133932587,029295427,2324796,004354782

36360,858180,02313132336360,881317568,1562674,804456994

41178,52853041178,528539888,2236384,164401013

Tabelul 15.

CoeficientI2 Semilimi yi0 [m] III+IV [m] IIV [m]

ProvaPupa

IIIIIIIVVVI

008,64300

118,6437,86916,51216,512

248,6436,40715,0560,2

397,8694,38612,255110,295

4166,4072,6669,073145,168

5255,6331,8497,482187,05

6364,6011,295,891212,076

7493,2680,8174,085200,165

8641,5050,3871,892121,088

9810,73100,73159,211

101000000

'VI [m] 1111,765

Corecie [m] 0

VI [m] 1111,765

Iy0= 2 3 VI [m4] 444697,9068

Tabelul 16.

CoeficientI2Semilimi yi1 [m] III+IV [m] IIV [m]

ProvaPupa

IIIIIIIVVVI

009,24500

119,2459,07318,318

249,2458,21317,45869,832

399,2456,75115,996143,964

4168,5574,7313,287212,592

5257,96363,69811,6616291,54

6367,1812,6669,847354,492

7495,5471,6777,224353,976

8644,3430,7315,074324,736

9812,62302,623212,463

101001,16101,161116,1

'VI [m] 2098,013

Corecie [m] 58,05

VI [m] 2039,963

[m4]815970,3499

IyB1 [m4] 13640,11307

[m4] 829610,4629

Tabelul 17.

CoeficientI2Semilimi yi2 [m]III+IV [m]IIV [m]

ProvaPupa

IIIIIIIVVVI

009,24500

119,2459,24518,4918,49

249,2458,90118,14672,584

399,2457,82617,071153,639

4168,8585,97714,835237,36

5258,3424,81613,158328,95

6367,6113,52611,137400,932

7496,3642,1938,557419,293

8644,8590,9895,848374,272

9813,13903,139254,259

101001,7201,72172

'VI [m]2431,779

Corecie [m]86

VI [m]2345,779

[m4]938294,5236

IyB2 [m4]17672,2646

[m4]955966,7882

Tabelul 18.

CoeficientI2Semilimi yi3 [m]III+IV [m]IIV [m]

ProvaPupa

IIIIIIIVVVI

009,24500

119,2459,24518,4918,49

249,2459,15918,40473,616

399,2458,47117,716159,444

4168,9877,09516,082257,312

5258,6436,0214,663366,575

6367,8694,7312,599453,564

7496,7083,31110,019490,931

8644,9451,6346,579421,056

9812,96702,967240,327

101001,50501,505150,5

'VI [m]2631,815

Corecie [m]75,25

VI [m]2556,565

[m4]1022607,389

IyB3 [m4]8305,463624

[m4]1030912,853

Tabelul 19.

CoeficientI2Semilimi yi4 [m]III+IV [m]IIV [m]

ProvaPupa

IIIIIIIVVVI

009,24500

119,2459,24518,4918,49

249,2459,24518,4973,96

399,2458,90118,146163,314

4169,1598,08417,243275,888

5258,8587,3116,168404,2

6368,1276,40714,534523,224

7496,9665,28912,255600,495

8645,1173,6988,815564,16

9812,7091,9784,687379,647

101000,47300,47347,3

'VI [m]3050,678

Corecie [m]23,65

VI [m]3027,028

[m4]1210789,164

IyB4 [m4]1060,752754

[m4]1211849,917

Tabelul 20.

CoeficientI2Semilimi yi5 [m]III+IV [m]IIV [m]

ProvaPupa

IIIIIIIVVVI

009,24500

119,2459,24518,4918,49

249,2459,24518,4973,96

399,2459,11618,361165,249

4169,2028,64317,845285,52

5258,9878,25617,243431,075

6368,2997,7416,039577,404

7497,1817,18114,362703,738

8645,4616,19211,653745,792

9812,9675,2898,256668,736

101000000

'VI [m]3669,964

Corecie [m]0

VI [m]3669,964

Iy5= 2 3 VI [m4]1467958,884

Momentele de inerie IT, j= EQ \x \to(0, 5) se calculeaz cu relaia:

, j= EQ \x \to(0, 5) [m4].

Calculul este prezentat sub form tabelar n tabelul 21.

Cu mrimile elementelor obinute n tabelele 121 se construiete diagrama de carene drepte i graficul funciei Ax= g1(x).

f) Calculul coeficienilor de finee.

Calculul coeficienilor de finee este prezentat sub form tabelar n tabelul 22.

Tabelul 21.

PlutireaIyj [m4]Awj [m2]xFj [m]IV2 [m2]IIIV [m4]ITj= II-VI [m4]Vj [m3] EQ \x \to(BML)j= EQ \f(ITj; Vj) [m]

IIIIIIIVVVIVIIVIIIIX

0444697,9068954,5573447,31770284553,5487749351115,37637393582,53040

1829610,46291305,7927378,49602050172,1823643694255,20711735355,25581555,120856472,8605196

2955966,78821414,2233677,73691874759,859911784655,28584871311,50243426,491935254,2867513

31030912,8531493,829755,88679607434,6543680251767,72592979145,12695427,232479180,4133379

41211849,9171617,9780822,3543249725,5428460738968,2034571202881,7147568,156267158,9398621

51467958,8841754,212864-0,6672889910,445274597781,10642661467177,7789888,223638148,3762738

Tabelul 22.

Dimensiunile naveiCoeficienii de finee

LCWL [m]116,96CW= EQ \f(ACWL; LCWLB)0,811162791

B [m]18,49CM= EQ \f(AM; BT)0,993488372

T [m]6,88CB= EQ \f(V; LCWLBT)0,664578364

ACWL= Aw5 [m2]1754,212864CLP= EQ \f(CB; CM)0,668934215

AM=Ax10 [m2]126,382848CVP= EQ \f(CB; CW)0,819290988

V=VCWL=V5 [m3]9888,010241

g) Calculul elementelor necesare trasrii scrii Bonjean.

Se ia fiecare cupl teoretic i= EQ \x \to(0, 20) din planul de forme i i se traseaz conturul deasupra CWL pn la nivelul selaturii punii n plan transversal. Se traseaz plutirile m=1, m+2, m+3, , m+k, situate la distana t= T/5= 6,88/5= 1,376 m. Plutirea corespunztoare punctului de intersecie a liniei bordului cu selatura punii n plan transversal se noteaz cu (m+k)a, iar cea corespunztoare maximului selaturii cu (m+k)f. Se noteaz cu ai distana dintre plutirile m+k, (m+k)a i cu fi distana dintre plutirile (m+k)a , (m+k)f.

n urma realizrii acestor construcii grafice au rezultat: m+k=6 pentru cuplele teoretice i= EQ \x \to(4, 15), m+k=7 pentru cuplele teoretice i= 0;1;2;3;16;17;18;19 i m+k=8 pentru cupla i= 20.

Pn la plutirea m+k, aria Axij se poate calcula cu relaia:

Axij= 2 t [yi0+ yi1+ yi2+ + yij( (yi0 +yij)], j= EQ \x \to(0, m+k).

Pentru plutirea (m+k)a se utilizeaz relaia:

Axi(m+k)a= Axim+k+ (Axi)a [m2], unde:

(Axi)a= ai [yim+k+ yi(m+k)a] [m2].

Pentru plutirea (m+k)f se utilizeaz relaia:

Axi(m+k)f= Axi(m+k)a+ (Axi)f [m2], unde:

(Axi)f= EQ \f(4;3) yi(m+k)afi [m2]. Calculul este efectuat sub form tabelar n tabelele 23-43.

Tabelul 23.

Tabelul 24.

Plutireay0j [m] Suma integral a coloanei II [m] Ax0j=tIII [m2] Plutireay1j [m] Suma integral a coloanei II [m] Ax1j=tIII [m2]

IIIIIIIVIIIIIIIV

00000000

10001000

20002000

30003000

400041,9781,9782,721728

500055,2899,24512,72112

64,18824,18825,76296366,49321,02728,93315

74,764413,140818,0817476,8834,447,3344

7aAx0,7a=Ax0,7+(Ax0)a24,133687aAx1,7a=Ax1,7+(Ax1)a52,59962

7fAx0,7f=Ax0,7a+(Ax0)f25,415257fAx1,7f=Ax1,7a+(Ax1)f55,16849

y0,7a4,902(Ax0)a=2[ EQ \f(a0;2) (y0,7+y0,7a)]6,051939y1,7a6,9402(Ax1)a=2[ EQ \f(a1;2) (y1,7+y1,7a)]5,265219

a00,62608(Ax0)f=2[ EQ \f(2;3) y0,7af0]1,281578a10,38098(Ax1)f=2[ EQ \f(2;3) y1,7af1]2,568873

f00,19608f10,27760

Tabelul 25.

Tabelul 26.

Plutireay2j [m] Suma integral a coloanei II [m] Ax2j=tIII [m2] Plutireay3j [m] Suma integral a coloanei II [m] Ax3j=tIII [m2]

IIIIIIIVIIIIIIIV

00,3870000,81700

10,7311,1181,53836811,6772,4943,431744

20,9892,8383,90508822,1936,3648,756864

31,6345,4617,51433633,31111,86816,33036

43,69810,79314,8511645,28920,46828,16396

56,19220,68328,4598057,18132,93845,32268

67,43934,31447,2160667,980848,099866,18532

77,7449,49368,102367056,080677,16690

7aAx2,7a=Ax2,7+(Ax2)a70,794547aAx3,7a=Ax3,7+(Ax3)a85,18542

7fAx2,7f=Ax2,7a+(Ax2)f74,003837fAx3,7f=Ax3,7a+(Ax3)f89,65941

y2,7a7,7572(Ax2)a=2[ EQ \f(a2;2) (y2,7+y2,7a)]2,692173y3,7a9,159(Ax3)a=2[ EQ \f(a3;2) (y3,7+y3,7a)]8,018521

a20,17372(Ax2)f=2[ EQ \f(2;3) y2,7af2]3,209288a30,87548(Ax3)f=2[ EQ \f(2;3) y3,7af3]4,473988

f20,31028f30,36636

Tabelul 27.

Tabelul 28.

Plutireay4j [m] Suma integral a coloanei II [m] Ax4j=tIII [m2] Plutireay5j [m] Suma integral a coloanei II [m] Ax5j=tIII [m2]

IIIIIIIVIIIIIIIV

01,290001,84900

12,6663,9565,44345613,6985,5477,632672

23,52610,14813,9636524,81614,06119,34794

34,7318,40425,323936,0224,89734,25827

46,40729,54140,6484247,3138,22752,60035

57,7443,68860,1146958,25653,79374,01917

68,34259,7782,2435268,651670,700697,28403

6aAx4,6a=Ax4,6+(Ax4)a103,72356aAx5,6a=Ax5,6+(Ax5)a117,3213

6fAx4,6f=Ax4,6a+(Ax4)f107,66026fAx5,6f=Ax5,6a+(Ax5)f121,5142

y4,6a8,5914(Ax4)a=2[ EQ \f(a4;2) (y4,6+y4,6a)]21,48002y5,6a8,8666(Ax5)a=2[ EQ \f(a5;2) (y5,6+y5,6a)]20,03732

a41,2685(Ax4)f=2[ EQ \f(2;3) y4,6af4]3,936648a51,1438(Ax5)f=2[ EQ \f(2;3) y5,6af5]4,192885

f40,34365f50,35466

Tabelul 29.

Tabelul 30.

Plutireay6j [m] Suma integral a coloanei II [m] Ax6j=tIII [m2] Plutireay7j [m] Suma integral a coloanei II [m] Ax7j=tIII [m2]

IIIIIIIVIIIIIIIV

02,6660004,38600

14,737,39610,176916,75111,13715,32451

25,97718,10324,9097327,82625,71435,38246

37,09531,17542,896838,47142,01157,80714

48,08446,35463,783148,90159,38381,71101

58,64363,08186,7994659,11677,4106,5024

68,94480,668110,999269,150495,6664131,637

6aAx6,6a=Ax6,6+(Ax6)a128,97126aAx7,6a=Ax7,6+(Ax7)a147,6665

6fAx6,6f=Ax6,6a+(Ax6)f133,3456fAx7,6f=Ax7,6a+(Ax7)f152,1405

y6,6a9,0558(Ax6)a=2[ EQ \f(a6;2) (y6,6+y6,6a)]17,97208y7,6a9,159(Ax7)a=2[ EQ \f(a7;2) (y7,6+y7,6a)]16,02951

a60,99846(Ax6)f=2[ EQ \f(2;3) y6,6af6]4,373734a70,87548(Ax7)f=2[ EQ \f(2;3) y7,6af7]4,473988

f60,36223f70,36636

Tabelul 31.

Tabelul 32.

Plutireay8j [m] Suma integral a coloanei II [m] Ax8j=tIII [m2] Plutireay9j [m] Suma integral a coloanei II [m] Ax9j=tIII [m2]

IIIIIIIVIIIIII

06,4070007,86900

18,21314,6220,1171219,07316,94223,31219

28,90131,73443,6659829,24535,2648,51776

39,15949,79468,5165439,24553,7573,96

49,24568,19893,8404549,24572,2499,40224

59,24586,688119,282759,24590,73124,8445

69,245105,178144,724969,245109,22150,2867

6aAx8,6a=Ax8,6+(Ax8)a159,51326aAx9,6a=Ax9,6+(Ax9)a164,5026

6fAx8,6f=Ax8,6a+(Ax8)f164,07166fAx9,6f=Ax9,6a+(Ax9)f169,061

y8,6a9,245(Ax8)a=2[ EQ \f(a8;2) (y8,6+y8,6a)]14,7883y9,6a9,245(Ax9)a=2[ EQ \f(a9;2) (y9,6+y9,6a)]14,21585

a80,7998(Ax8)f=2[ EQ \f(2;3) y8,6af8]4,558401a90,76884(Ax9)f=2[ EQ \f(2;3) y9,6af9]4,558401

f80,3698f90,3698

Tabelul 33.

Tabelul 34.

Plutireay10j [m] Suma integral a coloanei II [m] Ax10j=tIII [m2] Plutireay11j [m] Suma integral a coloanei II [m] Ax11j=tIII [m2]

IIIIIIIVIIIIIIIV

08,6430008,64300

19,24517,88824,6138919,24517,88824,61389

29,24536,37850,0561329,24536,37850,05613

39,24554,86875,4983739,24554,86875,49837

49,24573,358100,940649,24573,358100,9406

59,24591,848126,382859,24591,848126,3828

69,245110,338151,825169,245110,338151,8251

6aAx10,6a=Ax10,6+(Ax10)a166,13636aAx11,6a=Ax11,6+(Ax11)a166,8519

6fAx10,6f=Ax10,6a+(Ax10)f170,69476fAx11,6f=Ax11,6a+(Ax11)f171,4103

y10,6a9,245(Ax10)a=2[ EQ \f(a10;2) (y10,6+y10,6a)]14,31126y11,6a9,245(Ax11)a=2[ EQ \f(a11;2) (y11,6+y11,6a)]15,02682

a100,774(Ax10)f=2[ EQ \f(2;3) y10,6af10]4,558401a110,812(Ax11)f=2[ EQ \f(2;3) y11,6af11]4,558401

f100,369f110,369

Tabelul 35.

Tabelul 36.

Plutireay12j [m] Suma integral a coloanei II [m] Ax12j=tIII [m2] Plutireay13j [m] Suma integral a coloanei II [m] Ax13j=tIII [m2]

IIIIIIIVIIIIIIIV

08,6430007,86900

19,24517,88824,6138919,24517,11423,54886

29,24536,37850,0561329,24535,60448,9911

39,24554,86875,4983739,24554,09474,43334

49,24573,358100,940649,24572,58499,87558

59,24591,848126,382859,24591,074125,3178

69,245110,338151,825169,245109,564150,7601

6aAx12,6a=Ax12,6+(Ax12)a168,20356aAx13,6a=Ax13,6+(Ax13)a169,2375

6fAx12,6f=Ax12,6a+(Ax12)f172,76196fAx13,6f=Ax13,6a+(Ax13)f173,7959

y12,6a9,245(Ax12)a=2[ EQ \f(a12;2) (y12,6+y12,6a)]16,37844y13,6a9,245(Ax13)a=2[ EQ \f(a13;2) (y13,6+y13,6a)]18,47743

a120,885(Ax12)f=2[ EQ \f(2;3) y12,6af12]4,558401a130,999(Ax13)f=2[ EQ \f(2;3) y13,6af13]4,558401

f120,369f130,369

Tabelul 37.

Tabelul 38.

Plutireay14j [m] Suma integral a coloanei II [m] Ax14j=tIII [m2] Plutireay15j [m] Suma integral a coloanei II [m] Ax15j=tIII [m2]

IIIIIIIVIIIIIIIV

06,4070005,63300

18,55714,96420,5904617,96313,596618,70892

28,85832,37944,553528,34229,902241,14543

38,98750,22469,1082238,64346,887264,51679

49,15968,3794,0771248,85864,388288,59816

59,20286,731119,341958,98782,2332113,1529

69,202105,135144,665869,055100,276137,9798

6aAx14,6a=Ax14,6+(Ax14)a166,01936aAx15,6a=Ax15,6+(Ax15)a162,8238

6fAx14,6f=Ax14,6a+(Ax14)f170,57776fAx15,6f=Ax15,6a+(Ax15)f167,2309

y14,6a9,245(Ax14)a=2[ EQ \f(a14;2) (y14,6+y14,6a)]21,35351y15,6a9,0902(Ax15)a=2[ EQ \f(a15;2) (y15,6+y15,6a)]24,84405

a141,157(Ax14)f=2[ EQ \f(2;3) y14,6af14]4,558401a151,36912(Ax15)f=2[ EQ \f(2;3) y15,6af15]4,407026

f140,369f150,364

Tabelul 39.

Tabelul 40.

Plutireay16j [m] Suma integral a coloanei II [m] Ax16j=tIII [m2] Plutireay17j [m] Suma integral a coloanei II [m] Ax17j=tIII [m2]

IIIIIIIVIIIIIIIV

04,6010003,26800

17,18111,78216,2120315,5478,81512,12944

27,61126,57436,5658226,36420,72628,51898

37,86942,05457,866336,70833,79846,50605

48,12758,0579,876846,96647,47265,32147

58,29974,476102,47957,18161,61984,78774

68,47191,246125,554567,48276,282104,964

78,668108,3858149,138977,877691,6416126,0988

7aAx16,7a=Ax16,7+(Ax16)a153,84497aAx17,7a=Ax17,7+(Ax17)a136,0896

7fAx16,7f=Ax16,7a+(Ax16)f157,88477fAx17,7f=Ax17,7a+(Ax17)f139,5528

y16,7a8,703(Ax16)a=2[ EQ \f(a16;2) (y16,7+y16,7a)]4,706075y17,7a8,0582(Ax17)a=2[ EQ \f(a17;2) (y17,7+y17,7a)]9,99079

a160,270(Ax16)f=2[ EQ \f(2;3) y16,7af16]4,03977a170,6269(Ax17)f=2[ EQ \f(2;3) y17,7af17]3,463178

f160,348f170,3223

Tabelul 41.

Tabelul 42.

Plutireay18j [m] Suma integral a coloanei II [m] Ax18j=tIII [m2] Plutireay19j [m] Suma integral a coloanei II [m] Ax19j=tIII [m2]

IIIIIIIVIIIIIIIV

01,5050000,73100

14,3435,8488,04684812,6233,3544,615104

24,85915,0520,708823,1399,11612,54362

34,94524,85434,199132,96715,22220,94547

45,11734,91648,0444242,70920,89828,75565

55,46145,49462,5997452,96726,57436,56582

65,89156,84678,220163,56933,1145,55936

76,39869,135495,1303174,282840,961856,36344

7aAx18,7a=Ax18,7+(Ax18)a108,98047aAx19,7a=Ax19,7+(Ax19)a70,21452

7fAx18,7f=Ax18,7a+(Ax18)f111,47977fAx19,7f=Ax19,7a+(Ax19)f71,60629

y18,7a6,846(Ax18)a=2[ EQ \f(a18;2) (y18,7+y18,7a)]13,85005y19,7a5,1084(Ax19)a=2[ EQ \f(a19;2) (y19,7+y19,7a)]13,85108

a181,046(Ax18)f=2[ EQ \f(2;3) y18,7af18]2,499319a191,4749(Ax19)f=2[ EQ \f(2;3) y19,7af19]1,391773

f180,274f190,2043

Tabelul 43.

Plutireay20j [m] Suma integral a coloanei II [m] Ax20j=tIII [m2]

IIIIIIIV

0000

11,1611,1611,597536

21,724,0425,561792

31,5057,2679,999392

40,4739,24512,72112

509,71813,37197

60,47310,19114,02282

71,12611,790616,22387

81,95214,869420,46029

8aAx20,8a=Ax20,8+(Ax20)a22,07638

8fAx20,8f=Ax20,8a+(Ax20)f22,34715

y20,8a2,253(Ax20)a=2[ EQ \f(a20;2) (y20,8+y20,8a)]1,616085

a200,478(Ax20)f=2[ EQ \f(2;3) y20,7af20]0,270769

f200,090

3. Calculul stabilitii la unghiuri mari de nclinare Calculul stabilitii la unghiuri mari de nclinare are drept scop determinarea ls, MS, ld, MD, = EQ \x \to(0, 90), necesare trasrii diagramelor stabilitii statice i dinamice.

Iniial se traseaz transversalul Cebev. n acest scop se calculeaz abscisele cuplelor Cebev cu relaia:

xi= EQ \f(LCWL;2) ii,

n care coeficienii ii, i= EQ \x \to(3', 3) rezult din tabelul 44.

Tabelul 44.

Cuplaikxi

3'-0,883862-51,68824976

2'-0,529657-30,97434136

1'-0,323919-18,94278312

000

10,32391918,94278312

20,52965730,97434136

30,88386251,68824976

Se traseaz proieciile cuplelor Cebev pe longitudinalul i orizontalul planului de forme i se determin elementele necesare construirii transversalului Cebev. Datele sunt prezentate n tabelul 45. Se traseaz transversalul Cebev. Tabelul 45.

Cupla

Cebev

Plutirea3'2'1'0123

0016,718439,078486,4375,241453,73287,6282

1034,064662,590892,4590,94578,664229,1884

2044,582474,00392,4591,908282,628833,6604

38,264656,58881,682892,4592,303885,234632,0608

421,620470,623287,315892,4592,4586,885829,928

555,34181,132490,592492,4592,4588,339234,1334

Linia punii70,812487,969491,297692,4592,4589,981854,5412

DPD101,4897,618695,262293,99896,578100,9296111,327

DPB97,498294,410891,564290,392,888696,9994110,3896

1) Calculul razei metacentrice transversale ( EQ \x \to(BMT)), = EQ \x \to(0, 90). Acest calcul se face dup urmtorul algoritm: a) Calculul ariei suprafeei plutirii. Se utilizeaz relaia:

, = EQ \x \to(0, 90) [m2].

b) Calculul distanei dintre centrul plutirii ajuttoare i centrul plutirii reale anterioare. Se utilizeaz relaia:

,= EQ \x \to(0, 90) [m];

c) Calculul momentului de inerie al suprafeei plutirii nclinate ajuttoare n raport cu axa longitudinal ce trece prin centrul plutirii reale anterioare. Se utilizeaz relaia:

,= EQ \x \to(0, 90) [m4]. d) Calculul momentului de inerie al suprafeei plutirii nclinate n raport cu axa longitudinal central de inerie proprie. Se utilizeaz relaia:

,= EQ \x \to(0, 90) [m4].

e) Calculul razei metacentrice transversale. Se utilizeaz relaia:

( EQ \x \to(BMT))= EQ \f(IL;V) ; = EQ \x \to(0, 90) [m].

Calculul este prezentat sub form tabelar n tabelele 46-55.

Tabelul 46. Cupla Cebevai0bi0

3'5,53415,534130,6262630,62626169,4888169,4888

2'8,113248,1132465,8246665,82466534,0513534,0513

1'9,059249,0592482,0698382,06983743,4903743,4903

09,2459,24585,4700385,47003790,1704790,1704

19,2459,24585,4700385,47003790,1704790,1704

28,833928,8339278,0381478,03814689,3827689,3827

33,413343,4133411,6508911,6508939,7684539,76845

53,4438453,44384439,1498439,14983756,5223756,522

I

106,88768m

II

0m2

III

7513,044585m3

IVAW0=CI1785,940436m2

V0= EQ \f(1;2) EQ \f(II;I)0m

VIIL0,0= EQ \f(1;3) C III41844,0807m4

VIIIL0=VI-IVV241844,0807m4

VIII( EQ \x \to(BMT))0 = EQ \f(VII;V)4,231708569m

Tabelul 47. Cupla Cebevai10bi10

3'6,526543,835642,5957214,71183278,002756,42869

2'8,755667,2790476,6615852,98442671,2227385,6757

1'9,28378,8132886,1870977,6739800,135684,5619

09,387769,3877688,1300488,13004827,3436827,3436

19,387769,3877688,1300488,13004827,3436827,3436

29,080748,8055482,4598477,53753748,7964682,7599

33,747883,2327414,046610,4506152,6449933,7841

56,1700450,74172478,2109409,61844205,4893497,898

I

106,91176m

II

68,5925379m2

III

7703,386666m3

IVAW10=CI1786,342779m2

V10= EQ \f(1;2) EQ \f(II;I)0,320790425m

VIIL10,0= EQ \f(1;3) C III42904,19545m4

VIIIL10=VI-IVV242720,36917m4

VIII( EQ \x \to(BMT))10 = EQ \f(VII;V)4,320327972m

Tabelul 48. Cupla Cebevai20bi20

3'6,993523,1759848,9093210,08685342,048332,03563

2'7,494046,841356,1606446,80339420,87320,196

1'6,977188,8958448,6810479,13597339,6564703,9809

06,6581210,1798244,33056103,6287295,15821054,922

17,3134410,1368253,4864102,7551391,16961041,61

28,399629,335370,5536287,14783592,6236813,5511

33,91733,5483615,3452412,5908660,1119144,6769

47,7532252,11342337,4668442,14872441,6384010,973

I

99,86664m

II

-104,6819234m2

III

6452,610616m3

IVAW20=CI1668,628888m2

V20= EQ \f(1;2) EQ \f(II;I)-0,524108568m

VIIL20,0= EQ \f(1;3) C III35937,96846m4

VIIIL20=VI-IVV235479,61314m4

VIII( EQ \x \to(BMT))20 = EQ \f(VII;V)3,588067426m

Tabelul 49.

Cupla Cebevai30bi30

3'6,534282,3890842,696825,707703278,992913,63616

2'5,705245,9494832,5497635,39631185,7042210,5897

1'5,295888,2491228,0463468,04798148,5301561,336

05,0619610,4593225,62344109,3974129,70481144,222

15,5418410,3354830,71199106,8221170,20091104,058

26,341649,1942640,216484,53442255,0379777,2314

35,55563,2490830,8646910,55652171,471934,29898

40,0364449,82582230,7094420,46251339,6433845,372

I

89,86226m

II

-189,7530134m2

III

5185,015266m3

IVAW30=CI1501,46999m2

V30= EQ \f(1;2) EQ \f(II;I)-1,05579925m

VIIL30,0= EQ \f(1;3) C III28878,06598m4

VIIIL30=VI-IVV227204,35928m4

VIII( EQ \x \to(BMT))30 = EQ \f(VII;V)2,751187703m

Tabelul 50.

Cupla Cebevai40bi40

3'5,87811,2994634,552061,688596203,10052,194263

2'5,264064,8151427,7103323,18557145,8688111,6418

1'4,91927,1448824,1985351,04931119,0374364,7412

04,739,834122,372996,70952105,8238951,0511

15,117869,214926,1924984,91438134,0495782,4775

25,768028,3359833,2700569,48856191,9023579,2553

37,237762,5103452,385176,301807379,151315,81968

38,91543,1548220,6815333,33781278,9342807,181

I

82,0698m

II

-112,6562226m2

III

4086,114481m3

IVAW40=CI1371,269115m2

V40= EQ \f(1;2) EQ \f(II;I)-0,686343957m

VIIL40,0= EQ \f(1;3) C III22757,71189m4

VIIIL40=VI-IVV222111,75085m4

VIII( EQ \x \to(BMT))40 = EQ \f(VII;V)2,236170182m

Tabelul 51.

Cupla Cebevai50bi50

3'5,490240,6140430,142740,377045165,49090,231521

2'4,984564,2131424,8458417,75055123,845674,78555

1'4,683566,3932421,9357340,87352102,7373261,3142

04,521027,7382820,4396259,8809892,40794463,3758

14,852987,7382823,5514159,88098114,2945463,3758

25,411987,3048429,2895353,36069158,5143389,7913

36,71232,3159845,054975,363763302,422512,42237

36,6566436,3178195,2598237,48751059,7131665,296

I

72,97444m

II

-42,22767353m2

III

2725,009523m3

IVAW50=CI1219,298643m2

V50= EQ \f(1;2) EQ \f(II;I)-0,289331946m

VIIL50,0= EQ \f(1;3) C III15177,00542m4

VIIIL50=VI-IVV215074,9343m4

VIII( EQ \x \to(BMT))50 = EQ \f(VII;V)1,524534118m

Tabelul 52.

Cupla Cebevai60bi60

3'5,10840,331126,095750,109627133,30750,036298

2'4,662924,162421,7428217,32557101,38572,11597

1'4,392026,0337619,2898436,4062684,72136219,6666

04,245826,6073818,0269943,6574776,53934288,4615

14,543386,6073820,642343,6574793,78582288,4615

25,044766,6073825,449643,65747128,3871288,4615

36,23072,8870238,821628,334884241,885924,06298

34,22833,23642170,0689193,1488860,01211181,266

I

67,46442m

II

-23,07982817m2

III

2041,278497m3

IVAW60=CI1127,23408m2

V60= EQ \f(1;2) EQ \f(II;I)-0,171051853m

VIIL60,0= EQ \f(1;3) C III11368,94919m4

VIIIL60=VI-IVV211335,96775m4

VIII( EQ \x \to(BMT))60 = EQ \f(VII;V)1,146410939m

Tabelul 53.

Cupla Cebevai70bi70

3'4,8590,1651223,609880,027265114,72040,004502

2'4,447064,3576219,7763418,9888587,9465882,7462

1'4,195085,8806817,598734,582473,82794203,368

04,060925,9400216,4910735,2838466,96892209,5867

14,335265,9400218,7944835,2838481,47895209,5867

24,800525,9400223,0449935,28384110,6279209,5867

35,907343,6575834,8966713,37789206,146548,93071

32,6051831,88106154,2121172,8279741,7172963,8095

I

64,48624m

II

-18,61578969m2

III

1705,526751m3

IVAW70=CI1077,472947m2

V70= EQ \f(1;2) EQ \f(II;I)-0,14433924m

VIIL70,0= EQ \f(1;3) C III9498,971847m4

VIIIL70=VI-IVV29476,523974m4

VIII( EQ \x \to(BMT))70 = EQ \f(VII;V)0,958364649m

Tabelul 54.

Cupla Cebevai80bi80

3'4,763540,017222,691310,000296108,0915,09E-06

2'4,366224,639719,0638821,5268283,2370899,87797

1'4,127145,534117,0332830,6262670,29875169,4888

03,9995,534115,99230,6262663,95201169,4888

14,26135,534118,1586830,6262677,37957169,4888

24,70425,534122,129530,62626104,1016169,4888

35,75774,2733433,1511118,26143190,874178,03732

31,979131,06664148,2198162,2936697,9341855,8705

I

63,04574m

II

-14,07383731m2

III

1553,804618m3

IVAW80=CI1053,40425m2

V80= EQ \f(1;2) EQ \f(II;I)-0,111616085m

VIIL80,0= EQ \f(1;3) C III8653,951813m4

VIIIL80=VI-IVV28640,828345m4

VIII( EQ \x \to(BMT))80 = EQ \f(VII;V)0,873850416m

Tabelul 55.

Cupla Cebevai90bi90

3'4,78676-0,1139522,913070,012985109,6794-0,00148

2'4,389445,0456219,2671825,4582884,57215128,4528

1'4,157245,3423217,2826428,5403871,8481152,4719

04,031685,3423216,2544428,5403865,53272152,4719

14,288825,3423218,3939828,5403878,88846152,4719

24,723985,3423222,3159928,54038105,4203152,4719

35,748244,7076433,0422622,16187189,9349104,3301

32,1261631,00859149,4696161,7947705,8759842,6689

I

63,13475m

II

-12,3251021m2

III

1548,544821m3

IVAW90=CI1054,89148m2

V90= EQ \f(1;2) EQ \f(II;I)-0,097609495m

VIIL90,0= EQ \f(1;3) C III8624,657251m4

VIIIL90=VI-IVV28614,606653m4

VIII( EQ \x \to(BMT))90 = EQ \f(VII;V)0,871198606m

2) Calculul ls, ld, MS, MD, = EQ \x \to(0, 90). Se utilizeaz relaiile:

[m];

[m]; ls=yBcos+[( EQ \x \to(KB))- EQ \x \to(KB)]sin-asin; = EQ \x \to(0, 90) [m];

[m]; MS=ls; = EQ \x \to(0, 90) [KNm];

MD=ld; = EQ \x \to(0, 90) [KNm].

Calculul este prezentat sub form tabelar n tabelul 56. Cu datele din acest tabel se traseaz diagramele stabilitii statice i dinamice. Se cunosc: =99426,08868 kN; EQ \x \to(KG) = kD=0,79,03=6,321 m; EQ \x \to(KB)=3,72868 m;

a= EQ \x \to(KG)- EQ \x \to(KB)=6,321-3,72868=2,5923m;

EQ \f(; 2)=0,0872 rad; EQ \x \to(GMT)= EQ \x \to(BMT)-a= 4,1644-2,5923=1,5721 m. Tabelul 56. []sincos( EQ \x \to(BMT)) [m]IIIIV [m]Suma integral a coloanei V [m]IIIV [m]Suma integral a coloanei VII [m]Coordonatele centrului de caren

yB= EQ \f(; 2) VI [m]( EQ \x \to(KB)) - EQ \x \to(KB)= EQ \f(; 2) VIII [m]

IIIIIIIVVVIVIIVIIIIXX

0014,23170864,23170856900000

100,1736481780,9848077534,3203284,2546924828,4864010510,75021710,7502170790,7400141720,065418929

200,3420201430,9396926213,58806743,37168048316,112774021,22719132,7276254941,4050338940,237848943

300,50,8660254042,75118772,38259844121,867052941,37559395,3304106811,9068070160,464811811

400,642787610,7660444432,23617021,71300574225,962657121,43738258,1433870182,2639437010,710103348

500,7660444430,642787611,52453410,97995164228,655614511,167860910,748630392,4987695850,93728057

600,8660254040,51,14641090,5732054730,208771620,99282112,909312282,6342048851,125692031

700,9396926210,3420201430,95836460,32778001531,10975710,900568214,802701462,7127708191,290795568

800,9848077530,1736481780,87385040,15174253231,589279650,860574716,563844322,7545851851,444367225

90100,8711986031,741022180,871198618,295617592,7678171341,595377854

IIIIXIIXlsf=XI+XII [m]ls=XIII-asin [m]Suma integral a coloanei XIV [m]ld= EQ \f(; 2) XV [m]MS=XIV [kNm]MD=XVI [kNm]

XIXIIXIIIXIVXVXVIXVIIXVIII

00000000

0,7287716940,011360,7401315710,2899802270,2899802270,02528627628831,599812514,115503

1,3202999820,0813491,4016491120,5150240451,09498450,09548264851206,826359493,466264

1,6513433160,2324061,8837492220,5875900862,197598630,19163060158421,7839719053,08108

1,7342814920,4564462,1907271260,5244170593,3096057750,28859762452140,7370628694,13292

1,6061781290,7179992,3241767010,3383456944,1723685280,36383053633640,3889536174,24711

1,3171024430,9748782,2919803380,0469668594,5576810810,397429794669,7311139514,88957

0,9278222641,2129512,140773334-0,2952090174,3094389230,375783074-29351,4779337362,64125

0,4783286981,4224241,900752739-0,6521823953,3620475120,293170543-64843,944629148,80041

01,5953781,595377854-0,9969404191,7129246980,149367034-99121,886514850,97994

M=3030

Scri: ls: 1um=0,1 mV=6130

ld: 1um=0,05 mMext.adm=39074,4528 kNm

MS: 1um=9942,60886 kNm

MD: 1um=4971,30443 kNm4. Verificarea stabilitii navei sub aciunea vntului.Aciunea vntului constituie sursa principal a forelor i momentelor ce se exercit asupra navei i se apreciaz dup scara Beaufort.

Verificarea stabilitii navei se face pentru cazul cel mai nefavorabil, adic la aciunea vntului dup o direcie normal pe PD.

a) Calculul AV i zV.

Iniial se va calcula aria Av a suprafeei velice (proiecia suprafeei emerse pe PD) i cota zV a centrului velic fa de PB. Pentru aceasta, se reprezint la scar proiecia navei n PD i se mparte suprafaa velic n mai multe suprafee geometrice regulate i= EQ \x \to(1, n), avnd ariile Ai, i= EQ \x \to(1, n) i cotele centrelor geometrice zi, i= EQ \x \to(1, n). Aria AV este dat de relaia:

[m2].

Din relaia momentului static al suprafeei velice calculat n raport cu PB, rezult:

[m].

Calculul AV, zV se face sub form tabelar i este prezentat n tabelul 57.

Tabelul 57.

SuprafaaDenumirea suprafeeiAi[m2]zi[m]IIIIV

[m3]

IIIIIIIVV

1Bordaj ntre T=6,88m i puntea principal359,81548,3853017,052129

2Teug20,8012512,04250,44705

3Etrav1,3867512,4717,2927725

4Bordaj suprastructur59,16812,04712,38272

5Suprastructur etaje superioare31,617915,48489,445092

6Coul de fum10,8166518,92204,651018

7Anten radio1,84919,7836,57322

8Guri de magazie (5 buci)58,243510,32601,07292

9Macarale de punte (5 buci)27,73512,04333,9294

10Catarg prova4,437614,1962,969544

11Catarg pupa5,54718,92104,94924

12Dunet7,39610,7579,507

13Parapet punte etalon0,554717,639,779361

III589,36875 V5920,051467

AV= III =589,3688 m2 ; zV= EQ \f( V ; III ) =10,0447 m. b) Calculul MVD.

MVD este momentul de nclinare produs la aciunea dinamic a vntului i se calculeaz cu formula:

MVD=0,001pDAV(zV-T) [kNm],

unde pD este presiunea dinamic a vntului n N/m2, i depinde de zV-T.

MVD=0,0011002,8589,3688(10,0447-6,88)=1870,3979 kNm,

n care valoarea lui pD=1002,8 a rezultat pentru (zV-T)=3,16 m. c) Verificarea stabilitii.

Stabilitatea navelor pentru zonele de navigaie limitate ct i pentru zona de navigaie nelimitat se consider suficient dup criteriul de vnt K, dac la varianta de ncrcare cea mai defavorabil n ceea ce privete stabilitatea, este adevrat expresia:

K= EQ \f(Mext. adm. ; MVD ) 1,00,

unde Mext. adm. se determin din diagrama stabilitii statice, iar MVD este momentul de nclinare produs la aciunea dinamic a vntului, i a fost calculat mai sus.

K= EQ \f(Mext. adm. ; MVD ) = EQ \f(39074,4528 ; 1870,3979) = 20,89 >> 1, deci stabilitatea navei este foarte bun.

5. Calculele de inundare pentru compartimentul mainii, considerat de categoria a III-a.

Compartimentele inundate de categoria a III-a sunt neumplute complet i comunic cu exteriorul. Astfel de compartimente sunt cele dispuse n zona liniei de plutire.

Se consider un compartiment inundat de categoria a III-a definit de: doi perei transversali etani, un perete longitudinal dispus n PD, bordajul navei i puntea principal. Se reprezint compartimentul pe seciunile navei n PD, PL i planul transversal median al acestuia. Plutirea navei nainte de inundare este W-L. n vederea efecturii studiului teoretic a consecinelor inundrii, se exclude compartimentul din configuraia corpului navei. Aceasta presupune urmtoarele ipoteze:

se exclude volumul v de ap dizlocuit de compartiment pn la W-L, deci dispare mpingerea Arhimedic dat de acesta;

se exclude volumul v de ap care ptrunde n compartiment pn la W-L, deci nu se ia n consideraie greutatea acesteia ca ambarcat la bord.

Din ipoteze rezult c pentru corpul navei rmas dupa excluderea compartimentului apare o variaie de pescaj T creia i corespunde V=v. Plutirea intermediar rezultat este W'-L'.

a. Calculul variaiei pescajului mediu:

[m]; b. Calculul coordontelor centrului plutirii:

[m];

[m]; c. Calculul momentelor de inerie ale suprafeei plutirii fa de axele centrale de inerie:

[m4];

[m4];

d. Calculul deplasrilor centrului de caren:

[m];

[m];

[m]. e. Calculul variaiei razelor metacentrice:

[m];

[m]. f. Calculul modificrii nlimilor metacentrice:

[m];

[m]. g. Calculul modificrii asietei:

[rad]; Tpv = T + T + ( EQ \f(LCWL ; 2) xF) [m];

Tpp = T + T ( EQ \f(LCWL ; 2) + xF) [m];

h. Calculul modificrii poziiei transversale:

[rad]. Cu datele obinute se traseaz plutirea WL rezultat n urma inundrii compartimentului. Pentru compartimentul maini,cuprins ntre cuplele teoretice 25 i considerat de categoria a III-a se vor efectua calculele de inundare. Se cunosc:

Pentru nava nainte de inundare: V= 9888,223638 m3; xB= 5,224756234 m;

yB= 0;

EQ \x \to(KB)= 3,72868 m;

= 99426,08868 kN;

AW= 1754,212864 m2;

xF= -0,667288991 m;

yF= 0;

IL= 41178,52853 m4;

IT= 1467177,778 m4;

EQ \x \to(GMT)= 1,5721 m;

EQ \x \to(GML)= 145,78396 m.

Pentru compartimentul inundat:

aW= 259,01 m2; xA= -38,012 m; yA= 0; xC= -38,012 m; yC= 0; zC= 3,44 m; l= 17,544 m; b= 18,49 m; iL= 9241,832778 m4;

iT= 8320,348575 m4; =10,055 KN/m3;

v= 1781,97449 m3; q= 17917,75349 kN. Pentru nava dup inundare i excluderea compartimentului inundat:

V=9888,223638 m3;

xB= xB+xB= 13,12051502 m;

yB= yB+yB= 0 ;

EQ \x \to(KB')= EQ \x \to(KB)+( EQ \x \to(KB))= 4,455997845 m;

= 99426,08868 kN;

AW= AWaW= 1495,204944 m2;

xF= xF+xF= 5,801774638 m;

yF= yF+yF= 0;

IL= 31936,69575 m4;

IT= 1035065,367 m4. a. Calculul :

= 1,191792802 m;b. Calculul :

= 5,801774638 m;ntruct rezult c i ; c. Calculul :

= 31936,69575 m4;

= 1035065,367 m4; d. Calculul :

= 7,895758789 m; = 0;

= 0,727316118 m; e. Calculul :

= -0,93463023 m;

= -43,6997004 m; f. Calculul :

= -0,20731412 m;

= -42,9723843 m;

= 1,364768623 m;

= 102,8115712 m; g. Calculul :

= -0,07679835 rad -4,40022119 ;

Tpv = T + T + ( EQ \f(LCWL ; 2) xF) = 3,430295737 m;

Tpp = T + T ( EQ \f(LCWL ; 2) + xF) = 13,00852688 m; h. Calculul : ntruct yC=0 i yF=0, rezult .

BMT: 1cm(4m

BML: 1cm(100m

IL :

IT :

xB

xF

:

Scri:

z :1um-1,376m

Scri:

x :1um-5,848m

4

3

2

1um-8000m4

M

V

I

M

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