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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