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Vrachier 8000 TDW
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Vrachier 8000 TDW
MAXIM CRISTIAN CONSTANTIN
CUPRINS1CUPRINS
CAPITOLUL 1 3DOCUMENTARE
CAPITOLUL 2 6DESCRIEREA GENERALA A NAVEI
72.1 CARACTERISTICILE NAVEI
72.2 DIMENSIUNI PRINCIPALE
72. 3 CLASA NAVEI
82.4 DEADWEIGHT
82.5 VITEZA
82.6 MOTOR PRINCIPAL
82.7 AUTONOMIE
92.8 STRUCTURA ECHIPAJULUI
92.9 STABILITATE I ASIET
92.10 COMPARTIMENTAREA NAVEI
92.11 MATERIALE
92.12 INSTALAIILE NAVEI
CAPITOLUL 3 11DETERMINAREA DIMENSIUNILOR PRINCIPALE SI A COEFICIENTILOR DE FINETE
123.1 CALCULUL DEPLASAMENTULUI NAVEI CUNOASCND DEADWEIGHT-UL
123.2 LUNGIMEA NAVEI
143.3 LIMEA NAVEI
143.4 PESCAJUL NAVEI
153.5 INLIMEA DE CONSTRUCIE
163.6 COEFICIENI DE FINEE
CAPITOLUL 4 19FORMELE NAVEI
204.1 GENERAREA PLANULUI DE FORME UTILIZND PROGRAMUL MULTISURF
214.2 TABELUL DE TRASAJ PE CUPLE
CAPITOLUL 5 28CALCULE HIDROSTATICE PE PLUTIRI DREPTE
295.1 CALCULUL HIDROSTATIC PE PLUTIRI
615.2 CARACTERISTICI DE VOLUM
635.3 COEFICIENTI DE FINEE
645.4 TRASAREA DIAGRAMEI DE CARENE DREPTE
CAPITOLUL 6 65DETERMINAREA DEPLASAMENTULUI NAVEI GOALE, DEADWEIGHT-ULUI SI A REZERVELOR
666.1 CLASIFICAREA GRUPELOR DE MASE
666.2 DETERMINAREA GRUPELOR DE MASE PRIN METODA PARSONS
CAPITOLUL 7 70CALCULUL REZISTENTEI LA INAINTARE SI A PROPULSIEI
717.1 .CALCULUL REZISTENEI LA NAINTARE
757.2 ESTIMAREA PRELIMINAR A PROPULSIEI I ALEGEREA MOTORULUI
777.3 PROIECTAREA ELICEI
CAPITOLUL 8 82ESANTIONAJUL NAVEI IN ZONA CENTRALA
838.1 EANTIONAJUL NAVEI N ZONA CENTRAL
838.2 GROSIMI MINIME
898.3 ELEMENTE DE OSATUR N AFARA TANCURILOR DE GURN I DE ANTIRULIU
928.4 TANCUL DE GURN [PARAGRAF 23, B.4.4] + [PARAGRAF 8, B.4]
978.5 TANCURI ANTIRULIU [PARAGRAF 23, B.6]
CAPITOLUL 9 104EVALUAREA STABILITATII INITIALE IN CAZURI TIPICE DE INCARCARE
1059.1 CALCULAREA GRUPELOR DE MASE
1059.2 CALCULUL DIFERITELOR SITUAII DE NCRCARE ALE NAVEI
CAPITOLUL 10 106PROIECTAREA INSTALATIEI DE SANTINA
10710.1 INSTALAIA DE SANTIN
10710.2 ELEMENTE COMPONENTE ALE INSTALATIEI DE SANTINA
10810.3 SCHEME FUNCTIONALE ALE INSTALATIILOR DE SANTINA
10910.4 CALCULUL INSTALATIEI
11210.5 SCHEMA FUNCIONAL A INSTALAIEI DE SANTIN (VEDERE DEASUPRA DUBLULUI FUND)
CAPITOLUL 11 TEMA SPECIALA 113DIMENSIONAREA OPTIMA A PLANSEULUI DE DUBLU FUND
11411.1 FUNDAMENTE TEORETICE
12011.2 MODEL DE CALCUL
12111.3 UTILIZAREA ADD-IN-ULUI SOLVER DIN EXCEL PENTRU REZOLVAREA PROBLEMEI DE OPTIM
12411.4 VERIFICAREA STRUCTURII REZULTATE PRIN METODA ELEMENTULUI FINIT
13411.5 CONCLUZII
Bibliografie135
CAPITOLUL 1
DOCUMENTARE
n urma unei documentri am ales un numr de 17 de nave construite n ultimii 25 de ani, cu dimensiuni i caracteristici apropiate de cele ale navei de proiectat. Pe baze statistice putem determina dimensiunile principale, deadwight-ul, puterea instalat, turatia motorului etc. Toate rezultatele obinute sunt consultative urmnd s trecem la proiectarea propriu-zis.
Caracteristicile acestor nave sunt prezentate n tabelele de mai jos.
Nr. navaNumeSteagDwtLOALPPBDTViteza
01234567810
1SumatraItalia7800.00107.00102.8816.309.757.5010.00
2Sider SunMalta7376.00119.60115.4416.808.206.3012.00
3Marine KobePanama6485.00109.05105.8716.448.766.7411.00
4Coreea de sud6036.00108.45105.2916.409.156.6014.00
5SecaPanama8746.00100.3393.5019.6013.008.2613.80
6Sider TideItalia6280.00111.30108.0618.007.555.8111.00
7TbnPanama6500.00100.8097.8617.209.006.8313.00
8Bulk9000.00108.00104.8518.009.507.6012.00
9Badger IIFilipine7353.00100.7097.7718.309.357.4312.00
10Turcia7051.0097.8089.0117.019.207.4614.00
11Hai MenSt. Vincent8036.00109.58102.0018.309.357.2513.00
12WygosSpania9062.00120.00116.5018.5510.008.3713.00
13Timber StonePolonia7850.00131.60122.0017.008.807.0013.00
14Permai IISingapore7652.00120.53111.9917.848.826.5013.00
15B-HartPanama9413.00115.30105.7019.0010.508.1313.00
16Atasoylar IITurcia8379.00115.95106.8017.209.807.5812.00
17Dim9062.00120.00110.0018.5510.008.3713.00
Nr. navaNumeAn fabricatieMotor principalPutereaRPMClasa
01911121316
1Sumatra1987PIELSTICK2200 KWRINA 100 A1
2Sider Sun2005DAIHATSU 8DKM-282500 KW750 RPMNK NS* MNS*
3Marine Kobe1982MITSUBISHI 6UEC37/88H3900 CPKR CLASS
41996FUJI DIESEL2600 KW330 RPMKR CLASS
5Seca1997KAWASAKI MAN B&W 6L35MC5280 CP1200 RPMNK NS* MNS*
6Sider Tide1992HANSIN DIESEL WORKS3500 CPBV CLASS
7Tbn1998AKASAKA MHI 6UEC3800 CPNK NS* MNS*
8Bulk2006WARTSILA 6L322740KW750 RPMCCS CLASS
9Badger II1997AKASAKA4400 CPNK NS* MNS*
101983MAK 8M452AK 32641 CPABS CLASS
11Hai Men1991HITACHI 6L35MC4101 CPCCS CLASS
12Wygos1984MAN8L40/54A3680 KW450 RPMKR CLASS
13Timber Stone1989B&W 7L45GBE6376 CPRS-ICE STRENGTHENED-1A
14Permai II1980MITSUBISHI 6UET45/80D2941 KWGL 1C
15B-Hart1985MAKITA-MITSUI-B&W 6L35MC4080 CP200 RPMKR CLASS
16Atasoylar II1991WARTSILA, 9R32D4585 CP750 RPMBV CLASS
17Dim1984MAN 8L40/54A5000 CP450 RPMGL 1C
CAPITOLUL 2
DESCRIEREA GENERALA A NAVEI
Prezenta descriere are ca scop s prezinte ct mai complet construcia corpului, suprastructura, mainile, accesoriile i performanele vrachierului de 8000 tdw.
2.1 CARACTERISTICILE NAVEI
Nava este de tip vrachier destinat s transporte mrfuri generale, crbune, minereu de fier, fosfai, grne i cherestea.
Nava care este propulsat de un motor principal lent, are o singur punte continu, suprastructur, bulb la prova.
Nava are 3 magazii, amenajate s transporte mrfuri uscate, minereu, crbune, fosfai i gru. Dublu fund este extins ntre pereii picurilor, C.M. amplasat n pupa navei i sub toate magaziile.
Nava nu este prevzut cu perei longitudinali, are tancuri superioare amplasate n borduri, sub puntea principal, ntre compartimentul maini i picul prova.
Tancurile de combustibil sunt amplasate n zona magaziilor n dublul fund precum i n zona compartimentului de maini.
Tancurile de balast sunt amplasate n picurile pupa i prova, n tancurile superioare i n dublul fund ( n zona magaziilor).
2.2 DIMENSIUNI PRINCIPALE
LWL - lungimea la linia de plutire
122 m
LPP - lungimea ntre perpendiculare
119 m
B - limea navei
16,8 m
T - pescajul navei
6,8 m
D - nlimea de construcie
9,52 m
Deadweight
8000 tdw
2. 3 CLASA NAVEI
n conformitate cu Regulile pentru Clasificarea i Construcia Navelor Maritime ale Registrului Germanisher Lloyd clasa navei va fi:
100 A5 BULK CARRIER (single side skin)
MC - 100A5 Corpul navei corespunde cerinelor Regulilor de Constructie ale Germanisher Lloyd
- BULK CARRIER - Tipul navei - MC Instalaiile inclusiv instalaiile electrice corespund cerinelor Regulilor de Constructie ale Germanisher Lloyd
Nava va trebui s respecte urmtoarele Reguli i Regulamente inclusiv protocoalele i amendamentele n vigoare.
1. Cargo stowage and securing;2. International Load Line Convention;
3. International Convention on Tonnage Measurement of Ships;
4. MARPOL 73/78 2002 Consolidated edition;
5. SOLAS 2001 Consolidated edition;
6. International Telecommunications and Radio Regulations, including
GMDSS 1989 / 1990;
7. Suez Canal Rules including Tonnage Measurements;
8. Safe loading and unloading of bulk carriers;
9. GL Rules regarding marine pollution as applicable to foreign flag vessels;
10. IMO resolution as applicable at this type of ship, request by Class.
2.4 DEADWEIGHT
Deadweight-ul navei complet dotat, gata de exploatare i cu marf , n ap de mare (greutatea specific 1,025 t/m3) la pescajul de eantionaj de 6,8 m, pe chil plat este de aproximativ 8000 tdw.
Deadweight-ul cuprinde :
marf i balast ;
combustibil, ulei, ap tehnic i ap potabil n tancuri;
rezerve, echipaj, bagaje;
2.5 VITEZA
Viteza navei pe chil dreapt, cu corpul proaspt vopsit i carena curat, n ap adnc, la o intensitate a vntului nu mai mare de 30 pe scara Beaufort i starea mrii maxim 20, la pescajul de plin ncrcare, i 85% din puterea maxim continu a motorului principal va fi de cel puin 14 Nd.
Aceast vitez se va deduce din rezultatele probelor de mar cu nava n balast.
2.6 MOTOR PRINCIPAL
Propulsia navei este asigurat de un motor principal avnd urmtoarele caracteristici:
Producator:
MITSUBISHI
Tipul motorului:
UEC45LAP1
Putere:
3530 kW
Turaie:
158 RPM
Masa motorului:
111 t.
2.7 AUTONOMIE
Rezervele de combustibil, ulei, ap, hran, asigur navei o autonomie de 5.000 Mm la o vitez de exploatare de 14 Nd la 85% din puterea maxim continu a motorului principal i un consum specific de 170g/kW(h.
2.8 STRUCTURA ECHIPAJULUI
Echipajul navei este compus din 23 persoane dup cum urmeaz: cpitan de curs lung, ef mecanic, ef electrician, cpitan secund, 2 ofieri de cart punte, 2 ofieri de cart maini, ofier ef staie RTG, ofier RTG, 1 ofieri electricieni, ef mecanic secund, ajutor ofier mecanic, ef echipaj, ef timonier, 2 timonieri, 2 marinari, 2 motoriti, un buctar, un sanitar: TOTAL: 23 persoane.
2.9 STABILITATE I ASIET
Stabilitatea navei va satisface criteriile de stabilitate ale Germanischer Lloyd ediia 2004.La navigaia n balast, pescajul pupa asigur funcionare normal a elicei, iar pescajul prova este mai mare de 2,5% din lungimea navei.2.10 COMPARTIMENTAREA NAVEI
Nava are o construcie metalic, realizat din table i profile, mbinate prin sudur.
Nava este mprit n urmtoarele compartimente, delimitate de 5 perei transversali etani:
- pic pupa
- compartimentul de maini
- magazii de mrfuri nr.1: 3
- pic prova.
Dublul fund este extins ntre pereii picurilor. Structura dublului fund a fost calculat n acord cu destinaia magaziilor i pentru utilizarea graifrelor la descrcarea mrfii. 2.11 MATERIALE
Corpul rezistent al navei proiectate: tablele nveliului, osatura format din platband, profile cu bulb, platbenzi confecionate din table va fi executat din oel cu o limit de curgere cu ReH = 235N / mm2 .
Toate elementele ce compun structura corpului navei se execut din oel laminat sub form de table i sub form de profile.
Ca profile se folosesc: profile simple cu bulb i profile compuse cum ar fi profilul T format din inim i platband.
2.12 INSTALAIILE NAVEI
Nava proiectat este dotat cu instalaii de bord care asigur securitatea de navigaie, integritatea mrfii transportate, condiiile necesare pentru locuit i pentru desfurarea activitii echipajului.
Instalaiile navale existente pe nav sunt: instalaii cu tubulaturi; instalaii mecanice de punte; instalaii mecanice de bord, instalaii electrice; instalaii de navigaie,
radiocomunicaii, comunicri i semnalizri.
Instalaiile cu tubulaturi sunt utilizate pentru:
ambarcarea i asigurarea cu combustibil, ulei i ap potabil i tehnic,
evacuarea apelor uzate i de santin,
balastarea navei,
acionarea hidraulic a mecanismelor de bord,
sistemul de control i msurare a pescajului navei,
sistemul de control al ncrcrii magaziilor,
stingerea incendiilor de la bordul navei cu CO2,
sistemul de aer condiionat i ventilaie n magazii, spaii sociale i cabine,
nclzirea spaiilor sociale i cabinelor,
sistemul de pstrare (refrigerare) al proviziilor,
sistemului de preparare al apei de but,
incinerarea resturilor menajere.
Instalaiile mecanice de punte deservesc diferite echipamente de punte sunt:
instalaia de ancorare i manevr,
instalaia de lumini,
instalaia de crm,
instalaia de salvare,
instalaia de ncrcare a proviziilor,
instalaia de acces la bordul navei (scri de bord i pilot).Instalaiile aferente compartimentului de maini
instalaii de rcire a M.P. i D.G -urilor cu ap de mare i ap dulce,
instalaii de ungere a M.P. i D.G -urilor,
instalaia de transfer i alimentare cu combustibil a M.P. i D.G-urilor,
instalaia de aer comprimat,
instalaia de abur,
instalaia de evacuare gaze arse de la instalaia de la M.P. i D.G.,
instalaia de ventilaie a compartimentului maini,
Instalaii de navigaie, radiocomunicaii, comunicri i semnalizri
n conformitate cu cerinele societii de clasificare precum i cu ultimele tendine n domeniu nava este dotat cu urmtoarele echipamente de navigaie :
- sistem integrat de comunicri interioare,
- receptor de navigaie prin satelit,
- calculator de ncrcare,
- radare,
- sonda ultrason.CAPITOLUL 3
DETERMINAREA DIMENSIUNILOR PRINCIPALE SI A COEFICIENTILOR DE FINETE3.1 CALCULUL DEPLASAMENTULUI NAVEI CUNOASCND DEADWEIGHT-UL
Legtura dintre deplasamentul navei ( si deadweight Dw a fost stabilit pe baze statistice sub forma:
Unde:(Dw- coeficent de utilizare al deplasamentului
Valorile informative sunt date n tabelul de mai jos:
Tipul navei(Dw(u
Vrachiere0,67 0,790,60 0,69
Vom alege
[ t ]
O estimare brut a raportului ( Dw/( ), pentru nave de constructie si amenajri normale este oferit de Sch(nemann.
* Se va intra n diagrama dup Sch(nemann (fig. 4.1 pag. 57Proiectarea Navei) cu viteza navei v=14 Nd si deadweight-ul, si se va scoate raportul Dw/(= 0,72.
De aici rezult:
[ t ]
Vom adopta un deplasament al navei:
3.2 LUNGIMEA NAVEI
Suprafaa udat a navei este influenat de lungimea navei. n acelai timp, mrimea suprafeei udate influeneaz rezistena de frecare, cea mai nsemnat component a rezistenei la naintare pentru navele cu vitez mic. Proiectantul va trebui s in cont de limitarea lungimii navei. Pentru meninerea deadweight-ului, vor rezulta forme mai pline la extremiti, fapt ce va genera o cretere a rezistenei de form.
Micorarea rezistenei de val, la aceeai vitez, se realizeaz prin mrirea lungimii navei.
Rezult c lungimea navei este un parametru foarte important, cu implicaii majore asupra rezistenei la naintare a navei i implicit asupra puterii instalaiei de propulsie, precum i asupra volumului necesar ncrcturii utile.
n mod uzual, se utilizeaz n calcule lungimea ntre perpendicularele planului de forme Lpp i lungimea la plutirea de plin ncrcare LWL, ntre care exist relaia:
De asemenea, se definete i lungimea relativ, l, cu relaia:
Dup Galin lungimea ntre perpendiculare poate fi determinat cu relaia:
Unde:
- v este viteza de serviciu [Nd]
- coeficientul c are valorea c = 7,17 pentru nave cu o elice i v = 11 16,5 Nd - deplasamentul volumetric
Jager propune pentru lungimea ntre perpendiculare urmtoarea relaie de calcul:
Unde:
- v este viteza de serviciu a navei [Nd] - coeficientul b are valorea b = 5/6 pentru nave obinuite (vrachiere, petroliere)
O relaie de calcul foate simpl aparine lui Noghid:
Unele expresii sunt utilizate pentru determinarea lungimii relative.
Astfel, cu relaia lui Pozdiunin:
Literatura de specialitate recomand i utilizarea urmtoarelor relaie pentru nave de transportat mrfuri uscate:
De asemenea pentru navele care circul prin Canalul Panama (limea este limitat la 32,3 m):
Vom adopta lungimea navei :
Calculare numrului Froude:
3.3 LIMEA NAVEI
ntr-o prim aproximaie, calculul limii navei se poate realiza cu ajutorul unor relaii statistice.
Dup Arkenbout i Schokker, limea navei B, msurat n metri, nu trebuie s fie mai mic dect valoarea calculat cu formula:
De asemenea, Watson recomand urmtoarea relaie pentru nave de transport mrfuri uscate:
Sanderson propune urmatoarea relaie:
Van Manen indic urmtoarea relaie de calcul ale raportului L/B pentru nave de transport mrfuri uscate:
Vom adopta limea navei :
3.4 PESCAJUL NAVEIPescajul navei se determin n funcie de raportul B/T, astfel:Valorile uzuale ale raportului B/T propuse de Galin pentru vrachiere i petroliere sunt:
Van Manen recomand utilizarea urmtoarei relaii pentru calculul raportului B/T n cazul navelor de transport mrfuri uscate:
Vom adopta pescajul navei :
3.5 INLIMEA DE CONSTRUCIEConform conveniei LoadLines 66, navele sunt mprite n dou tipuri:Tipul A nave proiectate pentru a transporta numai ncrcturi lichide n vrac, deschiderile n tancurile de marf fiind de mici dimensiuni, nchise cu capace rezistente i prevzute cu garnituri etane.
Tipul B orice nav ce nu satsiface condiiile pentru tipul A
Astfel n funcie de aceasta mprire rezult o valoare a bordului liber de baz n funcie de lungimea navei si pentru nava de proiectat avem un bord liber de baz:
Acest bord va fi corectat n funcie de particularitile navei, astfel:
La navele cu , bordul liber de baz trebuie s fie multiplicat prin factorul
Dac raportul , bordul liber de baz va fi majorat cu valoarea
Rezult astfel un bord liber corectat:
Pentru vrachiere i petroliere raportul L/D se poate calcula n funcie de deadweight (Dw), cu expresia:
Vom adopta nlimea de construcie navei :
3.6 COEFICIENI DE FINEE
3.6.1 Coeficientul bloc
n general, exist o dependen liniar ntre coeficientul de finee bloc CB i numrul Froude, exprimat sub forma:
Unde a i b sunt constante.
Aik propune urmtoarea expresie general pentru :
Pentru petroliere i vrachiere sunt recomandate urmtoarele expresii:
Ayre recomand pentru nave de transportat mrfuri uscate cu :
Coeficientul bloc se determin cu relaia general:
Unde:
- este volumul real al carenei navei - L este lungimea navei - B este limea navei - T este pescajul considerat
Adoptm coeficientul bloc:
3.6.2 Coeficientul suprafeei plutirii
n stadiul preliminar de proiectare se pot folosi unele relaii empirice care furnizeaz valorile coeficientului de finee al suprafeei plutirii Cw, n funcie de coeficientul bloc.Coeficientul suprafeei plutirii se determin cu expresia:
Unde:
AWL este aria suprafeei plutirii de plin ncrcare
Pentru navele cu forme clasice se recomand:
formula lui Galin:
formula lui Lyndbladom:
formula de calcul:
pentru navele cu bulb:
pentru navele de transport, formula lui Bronikov:
Adoptm un coeficient al plutirii:
Din relaia putem determina
3.6.3 Coeficientul seciunii maestre
Coeficientul de finee al seciunii maestre, CM, se calculeaz n funcie de aria seciunii maestre, AM, cu expresia:
Literatura de specialitate recomand urmtoarele relaii generale:
pe baze statistice:
formula lui Noghid pentru :
dup Jeleazkov:
Adoptm un coeficient al seciunii maestre:
Din relaia putem determina
3.6.4 Coeficientul prismatic longitudinal
Coeficientul de finee prismatic longitudinal are o mare influen asupra rezistenei la naintare i se determin cu relaia general:
n funcie de valorile numrului Froude, Fn, literatura de specialitate furnizeaz urmtoarele expresii pentru calculul coeficientului prismatic longitudinal:pentru pe baza unor prelucrri statistice:
pentru dup Aik:
pentru dup Noghid:
Adoptm un coeficient prismatic longitudinal:
CAPITOLUL 4FORMELE NAVEI
4.1 Generarea planului de forme utiliznd programul MultiSurf Pentru generarea suprafeelor navei s-au construit urmatoarele curbe :
curba ce delimiteaz poriunea cilindric a navei
cubele punilor
curba fundului navei
curbele de profil pupa respectiv prova
Cu ajutorul acestor curbe s-au generat suprafeele definitorii ale navei pe care s-au generat contururile corespunzatoare plutirilor,longitudinalelor si cuplelor navei.
n urma construciei contururilor navei s-au extras cu ajutorul programului Multisurf tabelul cu semilaimile navei si caracteristicile contururilor navei :
Dimensiuni principale:
DimensiuneaSimbolValoarea [m]
LungimeLpp119
LimeB16,8
nlime de construcieD9,52
Pescaj de calculd6,8
Distana ntre cuple ntregiL5,95
Distana ntre plutiri ntregid0,68
4.2 TABELUL DE TRASAJ PE CUPLE
Tabelul cu abscisele cuplelor
CuplaX
[m]
- 1/2-60.988
0-59.5
1/4-58.013
1/2-56.525
3/4-55.038
1-53.55
1 1/4-52.063
1 1/2-50.575
1 3/4-49.088
2-47.6
3-41.65
4-35.7
5-29.75
6-23.8
7-17.85
8-11.9
9-5.95
100
115.95
1211.9
1317.85
1423.8
1529.75
1635.7
1741.65
1847.6
18 1/449.0875
18 1/250.575
18 3/452.0625
1953.55
19 1/455.0375
19 1/256.525
19 3/458.0125
2059.5
20 1/460.9875
20 1/262.475
Tabelul cu cotele plutirilor
WLz
[m]
00.00
10.68
21.36
32.04
42.72
53.40
64.08
74.76
85.44
96.12
106.80
117.48
128.16
138.84
149.52
Tabelul cu ordonatele longitudinalelor
Longitudinalay
[m]
0 (PD)0
I2.10
II4.20
III6.30
IV (Bord plat)8.40
Semilimile naveiC\WL01234567891011121314
--------1.2333.6464.6455.245.6325.8796.052
0--------1.9354.1135.015.5445.916.1536.323
1/4--------2.6834.5935.3715.846.1676.46.563
1/2--------3.4975.0555.7126.126.4096.6236.777
3/4---0.245----4.2755.4726.0236.3776.6336.8266.969
1-0.4140.6960.8550.8620.619-1.4234.9275.8386.3036.6126.8387.0117.143
1 1/4-0.7831.0411.2141.2891.3191.5593.0015.4486.166.5566.8267.0267.1817.301
1 1/20.2931.0721.3581.5611.6941.882.4354.1945.8776.4466.7847.027.1977.3357.443
1 3/40.5621.3711.6981.9352.1292.4593.2965.0966.2386.7026.997.1977.3537.4757.572
20.821.7092.0832.3572.6213.1054.1965.7476.556.937.1777.3577.4947.6027.688
32.1693.5814.1344.5585.176.0186.7177.1927.4617.6377.7647.8617.9377.9988.048
43.6495.756.3846.9017.3067.5817.7827.9258.0238.0948.1488.198.2248.2518.273
54.6527.3487.8978.088.1588.2158.268.2938.3178.3358.3488.3598.3678.3748.379
65.0037.9088.3358.388.3868.3918.3948.3968.3978.3988.3998.3998.48.48.4
75.0467.9558.3668.48.48.48.48.48.48.48.48.48.48.48.4
85.0467.9558.3668.48.48.48.48.48.48.48.48.48.48.48.4
95.0467.9558.3668.48.48.48.48.48.48.48.48.48.48.48.4
105.0467.9558.3668.48.48.48.48.48.48.48.48.48.48.48.4
C\WL01234567891011121314
115.0467.9558.3668.48.48.48.48.48.48.48.48.48.48.48.4
125.0467.9558.3668.48.48.48.48.48.48.48.48.48.48.48.4
135.0467.9558.3668.48.48.48.48.48.48.48.48.48.48.48.4
144.9997.9248.3428.3838.3888.3928.3958.3978.3988.3998.3998.48.48.48.4
154.5397.5248.0048.1038.1578.2038.2418.2738.2998.3218.3388.3528.3638.3728.379
162.7046.0786.7476.9987.1927.3667.5197.6537.7697.8717.9588.0338.0978.1528.198
171.2864.0374.7985.1525.4315.7175.9986.2676.5196.7516.9637.1567.337.4867.625
180.6822.6153.1963.523.6923.8774.1334.4434.7755.1095.4365.756.0446.3186.573
18 1/40.5612.3832.9143.2163.3773.4963.6893.9714.34.6474.9955.3335.6535.9556.238
18 1/20.4352.1782.6642.9483.1053.1733.2843.5113.8214.1714.5354.8955.2385.5645.872
18 3/40.3081.9882.4372.7042.8542.9022.9313.0663.3363.6814.0584.4364.7975.1445.476
19-1.8042.2222.4742.6172.6692.6432.6472.8393.1663.5563.9514.3284.6915.043
19 1/4-1.6132.012.2492.3862.4452.3992.2812.332.6113.0163.4263.8184.1984.569
19 1/2-1.4031.7882.0192.1522.2122.1752.0071.8161.9812.4072.8353.2463.6464.037
19 3/4-1.1441.5411.7691.8991.961.941.7761.3411.1771.6512.1222.573.0033.423
20-0.7521.2311.4721.6061.6671.6571.5130.98-0.131.0991.6822.1952.674
20 1/4--0.7361.061.2191.2881.2821.1460.608----0.9191.638
20 1/2----0.4570.6070.60.315-------
Tabel de nlimi pe longitudinale
Long0IIIIIIIV
Cupla(PD)(bord plat)
- 1/25.3515.5956.44511.039
05.2625.4696.179.413
1/45.1745.3445.9028.516
1/25.0715.2175.6497.88
3/41.7285.0715.4177.31
10.3674.8715.1996.794
1 1/40.0204.47856.327
1 1/203.7734.7615.9
1 3/402.6344.4595.509
201.3964.0825.147
3001.4613.648
4000.0361.252
50000.184
60000.087.051
70000.0741.623
80000.0741.623
90000.0741.623
100000.0741.623
110000.0741.623
120000.0741.623
130000.0741.623
140000.0796.27
150000.157
16000.0890.84
1700.0520.7874.846
1800.3194.2358.794
18 1/400.4395.2399.676
18 1/200.5996.17410.531
18 3/400.827.05211.371
1901.1257.92712.204
19 1/40.0201.5788.84313.041
19 1/20.0832.4039.80713.892
19 3/40.2077.44710.822
200.4348.7111.89
20 1/40.91310.05613.012
20 1/22.28111.46214.184
Extremitile plutirilor
WLzPupaProva
XppYXpvY
00.00-51.520.0053.460.00
10.68-54.140.0059.510.00
21.36-54.790.0061.670.00
32.04-55.150.0062.320.00
42.72-54.940.0062.680.00
53.40-53.390.0062.830.00
64.08-54.140.0062.830.00
74.76-62.240.0062.580.00
85.44-62.370.4661.620.00
96.12-62.493.2558.970.00
106.80-62.614.2959.510.00
117.48-62.734.9160.120.00
128.16-62.7315.2660.420.00
138.84-62.8535.4860.730.00
149.52-62.9755.6261.34
Linia punii i a parapetului
CuplaPuntea in bord Puntea in P.D.SageataParapetDunetaTeuga
XYZXYZFXYZXYZXYZ
Extr. pp-63.135.74610.36063.8830.00010.6990.339-63.7395.89013.780-63.5235.88412.57250.5007.17012.932
- 1/2-60.98756.19710.298-60.98750.00010.6250.327-60.9886.47713.695-60.9886.41112.494---
0 -59.506.42510.26-59.50000.00010.5880.328-59.5006.71913.644-59.5006.65112.444---
1/4-58.016.64510.233-58.01250.00010.5510.318-58.0136.95613.604-58.0136.87912.402---
1/2-56.536.86410.206-56.52500.00010.5130.307-56.5257.17813.572-56.5257.10212.372---
3/4-55.047.05610.171-55.03750.00010.4380.267-55.0387.33613.526-55.0387.26812.333---
1 -53.557.20310.124-53.55000.00010.4050.281-53.5507.48713.484-53.5507.41512.290---
1 1/4-52.067.34910.077-52.06250.00010.4060.329-52.0637.63513.454-52.0637.56312.253---
1 1/2-50.587.48210.032-50.57500.00010.4000.368-50.5757.74513.419-50.5757.68912.223---
1 3/4-49.097.5949.992-49.08750.00010.3640.372-49.0887.83913.381-49.0887.78412.181---
2 -47.607.7069.951-47.60000.00010.3280.377-47.6007.93313.345-47.6007.87812.143---
3 -41.658.0539.814-41.65000.00010.2920.478-41.6508.19313.211-41.6508.15912.012---
4 -35.708.2639.699-35.70000.00010.1590.460-35.7008.32412.224------
5 -29.758.3749.605-29.75000.00010.0420.437-29.7508.38210.806------
6 -23.808.3989.546-23.80000.0009.9490.403-23.8008.39910.745------
7 -17.858.4009.523-17.85000.0009.8980.375-17.8508.40010.723------
8 -11.908.4009.52-11.90000.0009.8870.367-11.9008.40010.720------
9 -5.958.4009.52-5.95000.0009.8870.367-5.9508.40010.720------
10 0.008.4009.520.00000.0009.8870.3670.0008.40010.720------
CuplaPuntea in bord Puntea in P.D.SageataParapetDunetaTeuga
XYZXYZFXYZXYZXYZ
11 5.958.4009.525.95000.0009.8870.3675.9508.40010.720------
12 11.908.4009.5211.90000.0009.8870.36711.9008.40010.723------
13 17.858.4009.54717.85000.0009.8870.34017.8508.40010.747------
14 23.808.3989.63423.80000.0009.8770.24323.8008.40010.833------
15 29.758.3739.79229.75000.00010.0260.23429.7508.38610.992------
16 35.708.20710.01435.70000.00010.1390.12535.7008.27111.215------
17 41.657.74310.28141.65000.00010.243-0.03841.6507.92611.480------
18 47.606.91210.58447.60000.00010.6240.04047.6007.41812.358------
18 1/449.096.64210.66349.08750.00010.9280.26549.0887.45813.267------
18 1/250.586.35510.74250.57500.00010.9880.24650.5757.51414.180---50.5757.15712.937
18 3/452.066.02210.81952.06250.00011.0640.24552.0637.29014.219---52.0636.90213.018
19 53.555.68110.89753.55000.00011.2140.31753.5507.08314.303---53.5506.65513.102
19 1/455.045.26710.9855.03750.00011.2880.30855.0386.83214.387---55.0386.32013.183
19 1/256.534.84511.06256.52500.00011.3600.29856.5256.50914.472---56.5255.99113.272
19 3/458.014.30511.14758.01250.00011.4290.28258.0136.18114.562---58.0135.55313.348
20 59.503.71811.23359.50000.00011.4930.26059.5005.71814.647---59.5005.06413.439
20 1/460.992.96911.32860.98750.00011.5470.21960.9885.21814.740---60.9884.49113.536
20 1/262.4751.90411.42362.47500.00011.5800.15762.4754.56914.831---62.4753.74513.626
Extr. Pv63.736011.50863.73600.00011.5080.00066.9770.00015.120-37.2508.29111.92165.8320.00013.844
CAPITOLUL 5CALCULE HIDROSTATICE PE PLUTIRI DREPTE
5.1 CALCULUL HIDROSTATIC PE PLUTIRI
Relaii de baz
Aria plutirii
Abscisa centrului de plutire
Momentul de inerie n raport cu axa x
Momentul de inerie n raport cu axa y
Momentul de inerie n raport cu axa yF
Metoda numeric de integrare: metoda trapezelor
unde:
f
funcia de integrat, respectiv f=y, f=xy, f=y3 sau f=x2y, dup caz.
i = 0 .. nindicele punctelor de calcul
xi,
abscisele n punctele de calcul
fi,
valoarea funciei la abscisele n punctele de calcul
n tabele se calculeaz sumele care reprezint:
Aw=2S1
MYW = 2S2
XF = MYW /Aw
Ix = 2/3 S3
Iy = 2S4
IyF = Iy - (XF)2Aw
WL=0.00z=0.000
Cuplaxdxys(y)xys(xy)y3s(y3)x2ys(x2y)
Extr. pp-51.52-0.000-0.000-0.00-0.00-
- 1/4----------
0----------
1/4----------
1/2----------
3/4----------
1----------
1 1/4----------
1 1/2-50.580.9440.2930.138-14.818-6.990.030.01749.44353.59
1 3/4-49.091.4880.5620.636-27.587-31.540.180.151354.191564.57
2-47.601.4880.8201.028-39.032-49.550.550.541857.922389.01
3-41.655.9502.1698.892-90.339-384.8810.2032.003762.6116721.10
4-35.705.9503.64917.309-130.269-656.3148.59174.904650.6125029.35
5-29.755.9504.65224.695-138.397-799.28100.67444.054117.3126084.58
6-23.805.9505.00328.724-119.071-765.97125.23672.052833.9020679.85
7-17.855.9505.04629.896-90.071-622.20128.48754.781607.7713213.96
8-11.905.9505.04630.024-60.047-446.60128.48764.47714.566908.94
9-5.955.9505.04630.024-30.024-267.96128.48764.47178.642657.29
100.005.9505.04630.0240.000-89.32128.48764.470.00531.46
115.955.9505.04630.02430.02489.32128.48764.47178.64531.46
1211.905.9505.04630.02460.047267.96128.48764.47714.562657.29
1317.855.9505.04630.02490.071446.60128.48764.471607.776908.94
1423.805.9504.99929.884118.976621.92124.93753.892831.6313207.22
1529.755.9504.53928.376135.035755.6893.51649.864017.3020375.57
1635.705.9502.70421.54896.533688.9119.77337.023446.2222203.97
1741.655.9501.28611.87053.562446.532.1365.142230.8516889.30
1847.605.9500.6825.85532.463255.920.327.271545.2511233.90
18 1/449.091.4880.5610.92427.53844.630.180.371351.782154.66
18 1/250.581.4880.4350.74122.00036.840.080.191112.661832.92
18 3/452.061.4880.3080.55316.03528.290.030.08834.841448.45
19----------
19 1/4----------
19 1/2----------
19 3/4----------
20----------
20 1/4----------
20 1/2----------
Extr. Pv53.460.0000.0000.0000.0000.000.000.000.000.00
Sume391.210-437.998479.12215577.37
WL=1z=0.68
Cuplaxdxys(y)xys(xy)y3s(y3)x2ys(x2y)
Extr. pp-54.140-0.000-0.000-0.000-0.000-
- 1/4----------
0----------
1/4----------
1/2----------
3/4----------
1-53.5500.5900.4140.122-22.170-6.5390.0710.0211187.187350.161
1 1/4-52.0632.0770.7830.813-40.765-42.3430.4800.4992122.3252204.459
1 1/2-50.5753.5651.0721.911-54.216-96.6381.2322.1962741.9944887.468
1 3/4-49.0881.4881.3711.817-67.299-90.3772.5772.8333303.5384496.365
2-47.6001.4881.7092.291-81.348-110.5564.9915.6293872.1845336.943
3-41.6505.9503.58115.738-149.149-685.72945.921151.4656212.04130000.570
4-35.7005.9505.75027.760-205.275-1054.410190.109702.1917328.31840282.567
5-29.7505.9507.34838.967-218.603-1261.037396.7411745.8816503.43941149.476
6-23.8005.9507.90845.387-188.210-1210.270494.5382651.5574479.40832673.969
7-17.8505.9507.95547.192-141.997-982.366503.4092968.8922534.64220866.797
8-11.9005.9507.95547.332-94.665-704.067503.4092995.2811126.50810891.920
9-5.9505.9507.95547.332-47.332-422.440503.4092995.281281.6274189.200
100.0005.9507.95547.3320.000-140.813503.4092995.2810.000837.840
115.9505.9507.95547.33247.332140.813503.4092995.281281.627837.840
1211.9005.9507.95547.33294.665422.440503.4092995.2811126.5084189.200
1317.8505.9507.95547.332141.997704.067503.4092995.2812534.64210891.920
1423.8005.9507.92447.240188.591983.499497.5462977.8404488.47120893.760
1529.7505.9507.52445.958223.8391226.980425.9382747.3656659.21033164.350
1635.7005.9506.07840.466216.9851311.450224.5341935.1547746.35042856.542
1741.6505.9504.03730.092168.1411145.74965.792863.7217003.07543879.539
1847.6005.9502.61519.790124.474870.53017.882248.9315924.96238460.910
18 1/449.0881.4882.3833.717116.976179.57813.53223.3645742.0358677.330
18 1/250.5751.4882.1783.392110.152168.92610.33217.7495570.9558414.037
18 3/452.0631.4881.9883.098103.500158.9047.85713.5285388.4828151.081
1953.5501.4881.8042.82096.604148.8285.87110.2105173.1557855.217
19 1/455.0381.4881.6132.54188.775137.8764.1977.4884885.9817481.482
19 1/256.5251.4881.4032.24379.305125.0102.7625.1754482.6916967.950
19 3/458.0131.4881.1441.89466.366108.3431.4973.1683850.0756197.495
2059.5001.4880.7521.41044.74482.6380.4251.4302662.2684843.555
20 1/4----------
20 1/2----------
Extr. Pv59.5130.0130.0000.0050.0000.2910.0000.0030.00017.290
Sume670.6581108.33635057.973451947.234
WL=2z=1.36
Cuplaxdxys(y)xys(xy)y3s(y3)x2ys(x2y)
Extr. pp-54.785-0.000-0.000-0.000-0.000-
- 1/4----------
0----------
1/4----------
1/2----------
3/4----------
1-53.5501.2350.6960.430-37.271-23.0220.3370.2081995.8511232.837
1 1/4-52.0631.4881.0411.292-54.197-68.0291.1281.0902821.6353583.005
1 1/2-50.5751.4881.3581.784-68.681-91.3902.5042.7023473.5344682.032
1 3/4-49.0881.4881.6982.273-83.351-113.0734.8965.5044091.4715626.473
2-47.6001.4882.0832.812-99.151-135.7359.03810.3634719.5786553.218
3-41.6505.9504.13418.496-172.181-807.21270.650237.0717171.34335375.490
4-35.7005.9506.38431.291-227.909-1190.267260.183984.2278136.34445540.369
5-29.7505.9507.89742.486-234.936-1376.963492.4782239.1656989.33944998.906
6-23.8005.9508.33548.290-198.373-1289.094579.0513187.7974721.27734839.082
7-17.8505.9508.36649.685-149.333-1034.426585.5363464.6462665.59621975.948
8-11.9005.9508.36649.778-99.555-740.443585.5363483.9391184.70911454.658
9-5.9505.9508.36649.778-49.778-444.266585.5363483.939296.1774405.638
100.0005.9508.36649.7780.000-148.089585.5363483.9390.000881.128
115.9505.9508.36649.77849.778148.089585.5363483.939296.177881.128
1211.9005.9508.36649.77899.555444.266585.5363483.9391184.7094405.638
1317.8505.9508.36649.778149.333740.443585.5363483.9392665.59611454.658
1423.8005.9508.34249.706198.5401034.921580.5113468.9904725.24221987.744
1529.7505.9508.00448.629238.1191299.059512.7683252.5077084.04035132.616
1635.7005.9506.74743.884240.8681424.986307.1372439.2198598.98446656.997
1741.6505.9504.79834.346199.8371311.096110.4541242.3338323.19950343.493
1847.6005.9503.19623.782152.1301047.10032.645425.7207241.36946304.588
18 1/449.0881.4882.9144.544143.041219.53324.74442.6837021.52410608.027
18 1/250.5751.4882.6644.149134.732206.59418.90632.4656814.06110290.216
18 3/452.0631.4882.4373.794126.876194.57114.47324.8266605.4989980.797
1953.5501.4882.2223.465118.988182.86210.97118.9246371.8139651.875
19 1/455.0381.4882.0103.148110.625170.7758.12114.1996088.5449267.390
19 1/256.5251.4881.7882.825101.067157.4465.71610.2915712.7958777.246
19 3/458.0131.4881.5412.47689.397141.6583.6596.9735186.1598106.097
2059.5001.4881.2312.06273.245120.9651.8654.1094358.0487098.504
20 1/460.9881.4880.7361.46344.88787.8600.3991.6842737.5345277.339
20 1/2----------
Extr. Pv61.6680.6800.0000.2500.00015.2700.0000.1360.000931.309
Sume726.0291485.48442021.465518304.443
WL=3.00z=2.04
Cuplaxdxys(y)xys(xy)y3s(y3)x2ys(x2y)
Extr. pp-55.154-0.000-0.000-0.000-0.000-
- 1/4----------
0----------
1/4----------
1/2----------
3/4-55.0380.1160.2450.014-13.484-0.7820.0150.001742.13643.044
1-53.5501.4880.8550.818-45.785-44.0820.6250.4762451.8002375.490
1 1/4-52.0631.4881.2141.539-63.204-81.0611.7891.7963290.5524270.874
1 1/2-50.5751.4881.5612.064-78.948-105.7253.8044.1603992.7745416.973
1 3/4-49.0881.4881.9352.600-94.984-129.3627.2458.2184662.5426437.391
2-47.6001.4882.3573.192-112.193-154.08813.09415.1275340.3967439.686
3-41.6505.9504.55820.572-189.841-898.55194.694320.6707906.86539410.603
4-35.7005.9506.90134.091-246.366-1297.714328.6521259.4548795.25549688.809
5-29.7505.9508.08044.568-240.380-1448.068527.5142547.0947151.30547441.017
6-23.8005.9508.38048.969-199.444-1308.476588.4803320.0844746.76735396.765
7-17.8505.9508.40049.921-149.940-1039.417592.7043514.0242676.42922084.009
8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210
9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542
100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708
115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708
1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542
1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210
1423.8005.9508.38349.929199.5151039.630589.1133515.9054748.46722089.064
1529.7505.9508.10349.046241.0641310.724532.0323335.4057171.66135462.381
1635.7005.9506.99844.925249.8291460.406342.7062602.3458918.88147869.364
1741.6505.9505.15236.146214.5811381.618136.7501426.3828937.29053122.110
1847.6005.9503.52025.799167.5521136.84543.614536.5847975.47550315.477
18 1/449.0881.4883.2165.010157.865242.02933.26257.1777749.21811695.240
18 1/250.5751.4882.9484.584149.095228.30225.62043.7947540.48511371.716
18 3/452.0631.4882.7044.204140.777215.59219.77133.7597329.20311059.330
1953.5501.4882.4743.851132.483203.23715.14325.9677094.44910727.591
19 1/455.0381.4882.2493.513123.779190.59511.37519.7236812.50510343.297
19 1/256.5251.4882.0193.174114.124176.9418.23014.5826450.8589864.626
19 3/458.0131.4881.7692.817102.624161.2065.53610.2385953.4819225.727
2059.5001.4881.4722.41087.584141.4673.1906.4895211.2488303.767
20 1/460.9881.4881.0601.88364.647113.2221.1913.2583942.6446808.207
20 1/2----------
Extr. Pv62.3201.3330.0000.7060.00043.0770.0000.7940.0002627.181
Sume746.2271537.56543783.036554508.661
WL=4.00z=2.72
Cuplaxdxys(y)xys(xy)y3s(y3)x2ys(x2y)
Extr. pp-54.938-0.000-0.000-0.000-0.000-
- 1/4----------
0----------
1/4----------
1/2----------
3/4----------
1-53.5501.3880.8620.598-46.160-32.0400.6410.4452471.8731715.727
1 1/4-52.0631.4881.2891.600-67.109-84.2442.1422.0693493.8404436.999
1 1/2-50.5751.4881.6942.219-85.674-113.6324.8615.2084332.9655821.186
1 3/4-49.0881.4882.1292.843-104.507-141.4479.65010.7935130.0017038.081
2-47.6001.4882.6213.533-124.760-170.51718.00520.5695938.5578232.240
3-41.6505.9505.17023.178-215.331-1011.768138.188464.6768968.51544348.540
4-35.7005.9507.30637.116-260.824-1416.560389.9771571.2929311.42454382.819
5-29.7505.9508.15846.005-242.701-1497.986542.9392775.4257220.34049181.997
6-23.8005.9508.38649.218-199.587-1315.805589.7453369.7364750.16635612.255
7-17.8505.9508.40049.938-149.940-1039.842592.7043517.7872676.42922094.120
8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210
9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542
100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708
115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708
1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542
1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210
1423.8005.9508.38849.944199.6341039.984590.1673519.0434751.29922097.490
1529.7505.9508.15749.221242.6711315.858542.7393370.3987219.45535612.992
1635.7005.9507.19245.663256.7541485.790372.0052721.3659166.13248747.121
1741.6505.9505.43137.553226.2011436.793160.1911583.2859421.27855297.545
1847.6005.9503.69227.141175.7391195.77350.325626.2878365.18652914.730
18 1/449.0881.4883.3775.258165.768253.99638.51266.0728137.16112273.620
18 1/250.5751.4883.1054.821157.035240.08529.93550.9087942.06411958.923
18 3/452.0631.4882.8544.432148.586227.30623.24739.5547735.77811660.395
1953.5501.4882.6174.069140.140214.74117.92330.6207504.51611334.969
19 1/455.0381.4882.3863.721131.319201.89813.58323.4337227.49610956.933
19 1/256.5251.4882.1523.375121.642188.1409.96617.5156875.80310489.328
19 3/458.0131.4881.8993.013110.166172.4076.84812.5066390.9909867.177
2059.5001.4881.6062.60795.557153.0064.1428.1745685.6428981.995
20 1/460.9881.4881.2192.10174.344126.3641.8114.4284534.0407600.888
20 1/262.4751.4880.4571.24728.55176.5280.0951.4181783.7284698.840
Extr. Pv62.6790.2040.0000.0460.0002.9050.0000.0100.000181.494
Sume760.3421507.73244972.550581157.328
WL=5.00z=3.40
Cuplaxdxys(y)xys(xy)y3s(y3)x2ys(x2y)
Extr. pp-53.394-0.000-0.000-0.000-0.000-
- 1/4----------
0----------
1/4----------
1/2----------
3/4----------
1-53.550-0.1560.619-0.048-33.1472.5850.237-0.0181775.046-138.453
1 1/4-52.0631.4881.3191.441-68.670-75.7272.2951.8833575.1553979.212
1 1/2-50.5751.4881.8802.379-95.081-121.7906.6456.6494808.7226235.508
1 3/4-49.0881.4882.4593.227-120.706-160.49214.86916.0015925.1647983.327
2-47.6001.4883.1054.138-147.798-199.70029.93533.3237035.1859639.259
3-41.6505.9506.01827.141-250.650-1185.382217.950737.45910439.56051987.366
4-35.7005.9507.58140.457-270.642-1550.842435.6921944.5849661.90959801.869
5-29.7505.9508.21546.993-244.396-1532.238554.3992945.5217270.78850374.774
6-23.8005.9508.39149.403-199.706-1321.204590.8013406.9714752.99835770.765
7-17.8505.9508.40049.953-149.940-1040.196592.7043520.9272676.42922102.545
8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210
9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542
100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708
115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708
1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542
1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210
1423.8005.9508.39249.956199.7301040.267591.0123521.5564753.56422104.231
1529.7505.9508.20349.370244.0391320.212551.9733400.3827260.16835740.853
1635.7005.9507.36646.318262.9661508.341399.6642831.1229387.89349527.982
1741.6505.9505.71738.922238.1131490.711186.8551744.8949917.40957433.273
1847.6005.9503.87728.542184.5451257.40858.276729.2648784.35255637.736
18 1/449.0881.4883.4965.484171.610264.89042.72875.1228423.90112798.638
18 1/250.5751.4883.1734.960160.474246.98831.94655.5398115.99712301.549
18 3/452.0631.4882.9024.518151.085231.72324.43941.9367865.88211886.522
1953.5501.4882.6694.143142.925218.67019.01332.3187653.63111542.638
19 1/455.0381.4882.4453.804134.567206.38414.61625.0127406.21411200.760
19 1/256.5251.4882.2123.464125.033193.07710.82318.9217067.50710764.830
19 3/458.0131.4881.9603.103113.705177.5617.53013.6506596.28210162.444
2059.5001.4881.6672.69899.187158.3384.6329.0455901.5979295.298
20 1/460.9881.4881.2882.19878.552132.1932.1375.0354790.6847952.384
20 1/262.4751.4880.6071.40937.92286.6280.2241.7562369.1975325.162
Extr. Pv62.8330.3580.0000.1090.0006.7800.0000.0400.000423.576
Sume773.9621355.18746278.421605452.969
WL=6z=4.08
Cuplaxdxys(y)xys(xy)y3s(y3)x2ys(x2y)
Extr. pp-54.140-0.000-0.000-0.000-0.000-
- 1/4----------
0----------
1/4----------
1/2----------
3/4----------
1----------
1 1/4-52.0632.0771.5591.619-81.165-84.3073.7893.9364225.6764389.209
1 1/2-50.5751.4882.4352.971-123.150-151.96014.43813.5566228.3187775.157
1 3/4-49.0881.4883.2964.262-161.792-211.92635.80637.3697941.98410539.162
2-47.6001.4884.1965.572-199.730-268.88273.87781.5779507.12912977.778
3-41.6505.9506.71732.466-279.763-1426.491303.0581121.38111652.13162948.798
4-35.7005.9507.78243.135-277.817-1658.802471.2742303.6399918.08164171.381
5-29.7505.9508.26047.725-245.735-1557.568563.5603078.6327310.61651255.375
6-23.8005.9508.39449.546-199.777-1325.399591.4353436.1104754.69735894.308
7-17.8505.9508.40049.962-149.940-1040.409592.7043522.8132676.42922107.601
8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210
9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542
100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708
115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708
1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542
1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210
1423.8005.9508.39549.965199.8011040.479591.6463523.4424755.26422109.286
1529.7505.9508.24149.492245.1701323.788559.6803425.1957293.80035845.965
1635.7005.9507.51946.886268.4281527.954425.0892929.6899582.89050208.154
1741.6505.9505.99840.213249.8171541.779215.7841906.59910404.86659463.574
1847.6005.9504.13330.140196.7311328.47970.599851.9899364.38658813.524
18 1/449.0881.4883.6895.818181.084281.00050.20389.8468888.95013575.919
18 1/250.5751.4883.2845.186166.088258.20935.41763.6798399.91612858.594
18 3/452.0631.4882.9314.622152.595237.02125.18045.0697944.48712156.150
1953.5501.4882.6434.146141.533218.75818.46332.4597579.07311545.648
19 1/455.0381.4882.3993.750132.035203.46613.80724.0007266.87411041.674
19 1/256.5251.4882.1753.402122.942189.63910.28917.9216949.28910573.272
19 3/458.0131.4881.9403.061112.544175.1437.30113.0836528.97310024.458
2059.5001.4881.6572.67598.592157.0324.5508.8145866.1949218.906
20 1/460.9881.4881.2822.18678.186131.4782.1074.9514768.3677909.455
20 1/262.4751.4880.6001.40037.48586.0300.2161.7282341.8755288.243
Extr. Pv62.8270.3520.0000.1050.0006.5880.0000.0380.000411.597
Sume790.185981.10147697.045636722.109
WL=7.00z=4.76
Cuplaxdxys(y)xys(xy)y3s(y3)x2ys(x2y)
Extr. pp-62.243-0.000-0.000-0.000-0.000-
- 1/4----------
0----------
1/4----------
1/2----------
3/4----------
1-53.5508.6931.4236.185-76.202-331.2042.88112.5244080.59817735.978
1 1/4-52.0631.4883.0013.290-156.240-172.87827.02722.2448134.2229084.773
1 1/2-50.5751.4884.1945.351-212.112-273.96173.77174.96810727.54214028.437
1 3/4-49.0881.4885.0966.909-250.150-343.807132.339153.29412279.23317111.289
2-47.6001.4885.7478.064-273.557-389.507189.812239.60013021.32318817.288
3-41.6505.9507.19238.494-299.547-1704.984372.0051671.40612476.12475854.905
4-35.7005.9507.92544.973-282.923-1732.846497.7352587.47610100.33367164.961
5-29.7505.9508.29348.249-246.717-1575.677570.3423177.5267339.82351884.466
6-23.8005.9508.39649.650-199.825-1328.461591.8583457.5434755.83035984.569
7-17.8505.9508.40049.968-149.940-1040.550592.7043524.0712676.42922110.971
8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210
9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542
100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708
115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708
1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542
1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210
1423.8005.9508.39749.971199.8491040.621592.0693524.7004756.39722112.656
1529.7505.9508.27349.593246.1221326.762566.2253445.9257322.12235933.593
1635.7005.9507.65347.380273.2121545.018448.2243017.9869753.67250800.487
1741.6505.9506.26741.412261.0211589.342246.1382065.72810871.50661359.904
1847.6005.9504.44331.862211.4871405.70987.706993.18610066.77262291.376
18 1/449.0881.4883.9716.258194.926302.27062.618111.8039568.45314603.698
18 1/250.5751.4883.5115.565177.569277.04343.28178.7628980.54313795.816
18 3/452.0631.4883.0664.892159.624250.78728.82153.6268310.40512860.143
1953.5501.4882.6474.249141.747224.14418.54635.2307590.54411826.331
19 1/455.0381.4882.2813.665125.541198.79511.86822.6216909.43710784.361
19 1/256.5251.4882.0073.189113.446177.7468.08414.8396412.5179908.203
19 3/458.0131.4881.7762.814103.030161.0045.60210.1795977.0399214.732
2059.5001.4881.5132.44690.024143.5843.4646.7425356.3988429.244
20 1/460.9881.4881.1461.97869.892118.9371.5053.6954262.5197154.069
20 1/262.4751.4880.3151.08719.68066.6190.0311.1431229.4854084.677
Extr. Pv62.5780.1030.0000.0160.0001.0160.0000.0020.00063.462
Sume817.390-64.47949466.354698619.312
WL=8.00z=5.44
Cuplaxdxys(y)xys(xy)y3s(y3)x2ys(x2y)
Extr. pp-62.365-0.458--28.532-0.096-1779.397-
- 1/4-60.9881.3781.2331.164-75.198-71.4441.8751.3574586.1134384.245
0-59.5001.4881.9352.356-115.133-141.5587.2456.7836850.3848505.894
1/4-58.0131.4882.6833.435-155.648-201.39319.31419.7539029.50311810.666
1/2-56.5251.4883.4974.596-197.668-262.77842.76546.17111173.17915025.745
3/4-55.0381.4884.2755.780-235.285-322.00978.12889.91412949.51517941.254
1-53.5501.4884.9276.844-263.841-371.225119.605147.06414128.67820139.406
1 1/4-52.0631.4885.4487.716-283.637-407.186161.700209.22114766.82521491.030
1 1/2-50.5751.4885.8778.423-297.229-432.019202.986271.23615032.37122163.152
1 3/4-49.0881.4886.2389.011-306.208-448.806242.737331.50715030.97722359.614
2-47.6001.4886.5509.511-311.780-459.628281.011389.53814840.72822217.080
3-41.6505.9507.46141.683-310.751-1852.029415.3282071.60912942.76582655.890
4-35.7005.9508.02346.065-286.421-1776.586516.4292771.97610225.23368924.794
5-29.7505.9508.31748.612-247.431-1588.209575.3083247.9157361.06552319.237
6-23.8005.9508.39749.724-199.849-1330.656592.0693472.9464756.39736049.448
7-17.8505.9508.40049.971-149.940-1040.621592.7043524.7002676.42922112.656
8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210
9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542
100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708
115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708
1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542
1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210
1423.8005.9508.39849.974199.8721040.692592.2813525.3304756.96322114.342
1529.7505.9508.29949.674246.8951329.134571.5803462.4877345.13436003.738
1635.7005.9507.76947.802277.3531559.639468.9163095.4789901.51351308.773
1741.6505.9506.51942.507271.5161632.887277.0402219.22111308.65663100.252
1847.6005.9504.77533.600227.2901483.949108.8731148.09210819.00465829.788
18 1/449.0881.4884.3006.750211.076326.03579.507140.10810361.20515752.781
18 1/250.5751.4883.8216.040193.247300.71555.787100.6259773.47114975.165
18 3/452.0631.4883.3365.323173.681272.90237.12669.1049042.24113994.186
1953.5501.4882.8394.593152.028242.24622.88244.6318141.12312780.127
19 1/455.0381.4882.3303.844128.237208.44812.64926.4277057.86511304.247
19 1/256.5251.4881.8163.084102.649171.7225.98913.8625802.2579564.716
19 3/458.0131.4881.3412.34877.795134.2052.4116.2484513.0697672.024
2059.5001.4880.9801.72658.310101.2280.9412.4943469.4455936.995
20 1/460.9881.4880.6081.18137.08070.9470.2250.8672261.4414262.346
20 1/2----------
Extr. Pv61.6220.6350.0000.1930.00011.7710.0000.0710.000717.894
Sume853.409-1819.62751616.265797036.409
WL=9.00z=6.12
Cuplaxdxys(y)xys(xy)y3s(y3)x2ys(x2y)
Extr. pp-62.487-3.251--203.158-34.366-12694.757-
- 1/4-60.9881.5003.6465.171-222.360-319.03348.46762.10513561.20619685.409
0-59.5001.4884.1135.771-244.724-347.39469.57987.79714561.04820915.927
1/4-58.0131.4884.5936.475-266.451-380.18696.892123.81315457.51322326.305
1/2-56.5251.4885.0557.176-285.734-410.688129.171168.13416151.10723508.911
3/4-55.0381.4885.4727.829-301.165-436.506163.847217.93216575.38024340.325
1-53.5501.4885.8388.412-312.625-456.506198.972269.84716741.06324779.105
1 1/4-52.0631.4886.1608.924-320.705-471.039233.745321.83316696.70424869.340
1 1/2-50.5751.4886.4469.376-326.006-480.992267.837373.05216487.77624680.957
1 3/4-49.0881.4886.7029.779-328.984-487.149301.032423.09716149.02324273.619
2-47.6001.4886.93010.139-329.868-490.021332.813471.42215701.71723688.988
3-41.6505.9507.63743.337-318.081-1927.648445.4192315.23813248.07686125.633
4-35.7005.9508.09446.800-288.956-1805.935530.2612902.64710315.72270102.298
5-29.7505.9508.33548.876-247.966-1597.343579.0513300.2037376.99652635.836
6-23.8005.9508.39849.781-199.872-1332.320592.2813484.7124756.96336098.528
7-17.8505.9508.40049.974-149.940-1040.692592.7043525.3302676.42922114.342
8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210
9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542
100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708
115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708
1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542
1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210
1423.8005.9508.39949.977199.8961040.763592.4923525.9594757.53022116.027
1529.7505.9508.32149.742247.5501331.152576.1383476.6757364.60536063.351
1635.7005.9507.87148.171280.9951572.420487.6293164.70810031.51151753.445
1741.6505.9506.75143.500281.1791672.467307.6842366.05611711.11264684.302
1847.6005.9505.10935.284243.1881559.993133.3551312.08811575.76869278.466
18 1/449.0881.4884.6477.256228.110350.528100.350173.81811197.33116937.492
18 1/250.5751.4884.1716.558210.948326.54972.564128.60510668.71216262.869
18 3/452.0631.4883.6815.840191.642299.42749.87791.0659977.36515355.519
1953.5501.4883.1665.092169.539268.62931.73560.6989078.83014173.045
19 1/455.0381.4882.6114.297143.703232.97417.80036.8417909.04912634.735
19 1/256.5251.4881.9813.415111.976190.1617.77419.0216329.44510589.880
19 3/458.0131.4881.1772.34968.281134.0661.6316.9953961.1357653.619
20----------
20 1/4----------
20 1/2----------
Extr. Pv58.9750.9620.0000.5660.00032.8460.0000.7840.0001905.504
Sume879.746-2971.47853570.006873172.695
WL=10.00z=6.80
Cuplaxdxys(y)xys(xy)y3s(y3)x2ys(x2y)
Extr. pp-62.609-4.291--268.680-79.030-16821.763-
- 1/4-60.9881.6224.6457.245-283.287-447.507100.221145.32817276.96227645.542
0-59.5001.4885.0107.181-298.095-432.403125.752168.06717736.65326041.376
1/4-58.0131.4885.3717.721-311.585-453.450154.941208.76518075.83326635.536
1/2-56.5251.4885.7128.243-322.871-471.877186.365253.84618250.27227017.540
3/4-55.0381.4886.0238.728-331.491-486.681218.494301.11418244.42827142.933
1-53.5501.4886.3039.167-337.526-497.581250.404348.74318074.49927012.202
1 1/4-52.0631.4886.5569.564-341.322-504.893281.784395.81517770.06426659.393
1 1/2-50.5751.4886.7849.922-343.101-509.039312.218441.78917352.32326122.275
1 3/4-49.0881.4886.99010.244-343.122-510.378341.532486.22616842.98325432.759
2-47.6001.4887.17710.537-341.625-509.280369.682528.96616261.36024621.355
3-41.6505.9507.76444.449-323.371-1978.363468.0122492.14013468.38588445.991
4-35.7005.9508.14847.338-290.884-1827.406540.9453001.64610384.54570962.467
5-29.7505.9508.34849.076-248.353-1604.229581.7653340.0617388.50252874.813
6-23.8005.9508.39949.822-199.896-1333.541592.4923493.4154757.53036134.443
7-17.8505.9508.40049.977-149.940-1040.763592.7043525.9592676.42922116.027
8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210
9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542
100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708
115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708
1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542
1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210
1423.8005.9508.39949.977199.8961040.763592.4923525.9594757.53022116.027
1529.7505.9508.33849.793248.0561332.656579.6763487.2027379.65136108.113
1635.7005.9507.95848.481284.1011583.164503.9783223.87310142.39152128.077
1741.6505.9506.96344.390290.0091707.976337.5902503.66512078.87366108.261
1847.6005.9505.43636.887258.7541632.569160.6341482.21612316.67172576.744
18 1/449.0881.4884.9957.758245.192374.810124.625212.16212035.86518112.199
18 1/250.5751.4884.5357.088229.358352.94693.268162.05811599.76217578.998
18 3/452.0631.4884.0586.391211.270327.71766.825119.06910999.22516807.996
1953.5501.4883.5565.663190.424298.75944.96683.14410197.19415764.837
19 1/455.0381.4883.0164.888165.993265.08527.43453.8489135.84514378.948
19 1/256.5251.4882.4074.033136.056224.64913.94530.7767690.54712514.629
19 3/458.0131.4881.6513.01895.779172.4274.50013.7195556.3589852.386
2059.5001.4880.1301.3257.73576.9880.0023.349460.2334474.839
20 1/4----------
20 1/2----------
Extr. Pv59.5130.0130.0000.0010.0000.0500.0000.0000.0002.989
Sume898.787-3216.83255192.451927008.616
WL=11.00z=7.48
Cuplaxdxys(y)xys(xy)y3s(y3)x2ys(x2y)
Extr. pp-62.731-4.912--308.141-118.523-19330.021-
- 1/4-60.9881.7445.2408.850-319.575-547.211143.878228.74819490.05033841.396
0-59.5001.4885.5448.021-329.868-483.023170.400233.74419627.14629093.414
1/4-58.0131.4885.8408.467-338.793-497.317199.177274.87319654.22929215.523
1/2-56.5251.4886.1208.895-345.933-509.265229.221318.62119553.86329161.018
3/4-55.0381.4886.3779.295-350.974-518.325259.328363.35819316.73928910.010
1-53.5501.4886.6129.661-354.073-524.379289.067407.86918960.58828468.762
1 1/4-52.0631.4886.8269.995-355.379-527.654318.053451.54518501.90027862.725
1 1/2-50.5751.4887.02010.298-355.037-528.371345.948493.85117955.97127115.541
1 3/4-49.0881.4887.19710.574-353.283-526.812372.782534.55517341.76626252.692
2-47.6001.4887.35710.825-350.193-523.210398.201573.41816669.19625295.654
3-41.6505.9507.86145.274-327.411-2015.871485.7732629.82213636.65490159.903
4-35.7005.9508.19047.752-292.383-1843.886549.3533079.50110438.07371622.312
5-29.7505.9508.35949.233-248.680-1609.663584.0673371.9267398.23753063.024
6-23.8005.9508.39949.855-199.896-1334.515592.4923500.2654757.53036163.407
7-17.8505.9508.40049.977-149.940-1040.763592.7043525.9592676.42922116.027
8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210
9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542
100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708
115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708
1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542
1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210
1423.8005.9508.40049.980199.9201040.834592.7043526.5894758.09622117.712
1529.7505.9508.35249.837248.4721333.966582.6013496.5337392.04236146.661
1635.7005.9508.03348.745286.7781592.369518.3623275.36610237.97852449.310
1741.6505.9507.15645.187298.0471739.856366.4472632.30712413.67467388.666
1847.6005.9505.75038.395273.7001700.949190.1091655.75513028.12075689.338
18 1/449.0881.4885.3338.243261.784398.266151.675254.20212850.30419247.078
18 1/250.5751.4884.8957.607247.565378.828117.289200.04212520.58118869.596
18 3/452.0631.4884.4366.940230.949355.89587.292152.15712023.79518254.880
1953.5501.4883.9516.238211.576329.12861.677110.79511329.89717369.309
19 1/455.0381.4883.4265.487188.558297.60040.21375.78010377.78716145.090
19 1/256.5251.4882.8354.657160.248259.42522.78646.8559058.03914455.396
19 3/458.0131.4882.1223.687123.103210.7429.55524.0537141.48512048.396
2059.5001.4881.0992.39665.391140.1921.3278.0943890.7358205.214
20 1/4----------
20 1/2----------
Extr. Pv60.1230.6230.0000.3420.00020.3710.0000.4140.0001212.054
Sume914.591-3231.84656606.532971559.029
WL=12.00z=8.16
Cuplaxdxys(y)xys(xy)y3s(y3)x2ys(x2y)
Extr. pp-62.731-5.264--330.218-145.867-20714.936-
- 1/4-60.9881.7445.6329.499-343.482-587.298178.644282.89220948.08436319.738
0-59.5001.4885.9108.584-351.645-517.000206.425286.39520922.87831141.528
1/4-58.0131.4886.1678.982-357.763-527.622234.543327.97020754.73130997.721
1/2-56.5251.4886.4099.353-362.269-535.524263.251370.23420477.24030666.278
3/4-55.0381.4886.6339.700-365.064-540.954291.830412.84220092.19530173.517
1-53.5501.4886.83810.019-366.175-543.859319.733454.85019608.66629527.516
1 1/4-52.0631.4887.02610.311-365.791-544.400346.836495.76119044.00028747.921
1 1/2-50.5751.4887.19710.578-363.988-542.773372.782535.21618408.70727855.451
1 3/4-49.0881.4887.35310.822-360.940-539.166397.552572.93517717.66126868.986
2-47.6001.4887.49411.042-356.714-533.756420.863608.69616979.60525806.092
3-41.6505.9507.93745.907-330.576-2044.689499.9992739.56513768.49291475.591
4-35.7005.9508.22448.079-293.597-1856.914556.2233142.26210481.40672143.447
5-29.7505.9508.36749.358-248.918-1613.982585.7463397.3597405.31853213.003
6-23.8005.9508.40049.882-199.920-1335.294592.7043505.8894758.09636186.156
7-17.8505.9508.40049.980-149.940-1040.834592.7043526.5892676.42922117.712
8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210
9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542
100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708
115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708
1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542
1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210
1423.8005.9508.40049.980199.9201040.834592.7043526.5894758.09622117.712
1529.7505.9508.36349.870248.7991334.940584.9063503.3917401.77836175.624
1635.7005.9508.09748.969289.0631600.140530.8513319.37710319.54652720.937
1741.6505.9507.33045.895305.2951768.213393.8332750.93412715.51668529.308
1847.6005.9506.04439.788287.6941764.142220.7871828.49413694.25378569.064
18 1/449.0881.4885.6538.700277.492420.357180.650298.56813621.37120315.995
18 1/250.5751.4885.2388.100264.912403.413143.713241.24513397.91720095.595
18 3/452.0631.4884.7977.464249.744382.775110.385188.98513002.28719635.152
1953.5501.4884.3286.787231.764358.12281.070142.39512410.98418901.120
19 1/455.0381.4883.8186.059210.133328.66155.655101.69011565.20517832.290
19 1/256.5251.4883.2465.254183.480292.75034.20266.83110371.21516315.212
19 3/458.0131.4882.5704.326149.092247.35116.97538.0628649.20714146.439
2059.5001.4881.6823.162100.079185.3214.75916.1645954.70110861.656
20 1/4----------
20 1/2----------
Extr. Pv60.4200.9200.0000.7730.00046.0150.0002.1880.0002737.903
Sume927.103-3131.03157843.9001005813.589
WL=13.00z=8.84
Cuplaxdxys(y)xys(xy)y3s(y3)x2ys(x2y)
Extr. pp-62.853-5.479--344.377-164.485-21645.143-
- 1/4-60.9881.8665.87910.594-358.546-655.651203.194342.95221866.79440585.760
0-59.5001.4886.1538.949-366.104-538.958232.949324.38121783.15832464.652
1/4-58.0131.4886.4009.336-371.280-548.429262.144368.22521538.88132220.767
1/2-56.5251.4886.6239.686-374.365-554.574290.512411.03821160.98631758.026
3/4-55.0381.4886.82610.003-375.686-557.850318.053452.62020676.81731116.866
1-53.5501.4887.01110.291-375.439-558.649344.620492.86220104.76130331.299
1 1/4-52.0631.4887.18110.555-373.861-557.292370.301531.72219464.12929429.362
1 1/2-50.5751.4887.33510.796-370.968-553.966394.639568.92418761.68828430.451
1 3/4-49.0881.4887.47511.015-366.929-548.811417.670604.15518011.63027350.155
2-47.6001.4887.60211.214-361.855-542.033439.323637.38917224.30826206.729
3-41.6505.9507.99846.410-333.117-2067.541511.6162829.04313874.31192518.389
4-35.7005.9508.25148.341-294.561-1867.340561.7203193.17410515.81772560.629
5-29.7505.9508.37449.459-249.127-1617.469587.2173418.0887411.51353333.808
6-23.8005.9508.40049.903-199.920-1335.913592.7043510.2664758.09636204.588
7-17.8505.9508.40049.980-149.940-1040.834592.7043526.5892676.42922117.712
8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210
9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542
100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708
115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708
1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542
1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210
1423.8005.9508.40049.980199.9201040.834592.7043526.5894758.09622117.712
1529.7505.9508.37249.897249.0671335.736586.7973509.0157409.74336199.322
1635.7005.9508.15249.159291.0261606.778541.7423357.40310389.64252953.173
1741.6505.9507.48646.523311.7921793.384419.5172859.74512986.13369542.931
1847.6005.9506.31841.067300.7371822.273252.1961998.34714315.07281221.083
18 1/449.0881.4885.9559.128292.316441.083211.176344.63314349.06521318.951
18 1/250.5751.4885.5648.567281.399426.701172.251285.17414231.77021256.996
18 3/452.0631.4885.1447.964267.810408.474136.114229.34613942.83220954.860
1953.5501.4884.6917.315251.203386.016103.228178.01013451.92320374.849
19 1/455.0381.4884.1986.611231.047358.67473.982131.80012716.27319462.596
19 1/256.5251.4883.6465.834206.090325.12148.46791.07211649.24618121.854
19 3/458.0131.4883.0034.945174.212282.84927.08156.18910106.44716180.796
2059.5001.4882.1953.866130.603226.70510.57628.0077770.84913296.239
20 1/460.9881.4880.9192.31656.048138.8210.7768.4433418.1988321.853
20 1/2----------
Extr. Pv60.733-0.2550.000-0.1170.000-7.1330.000-0.0990.000-435.005
Sume939.467-2958.99458974.6371041136.322
WL=14.00z=9.52
Cuplaxdxys(y)xys(xy)y3s(y3)x2ys(x2y)
Extr. pp-62.975-5.624--354.195-177.919-22305.436-
- 1/4-60.9881.9886.05211.603-369.096-718.771221.665397.08722510.26444535.602
0-59.5001.4886.3239.204-376.219-554.328252.796352.88022385.00133390.853
1/4-58.0131.4886.5639.584-380.736-562.985282.688398.26622087.44933076.385
1/2-56.5251.4886.7779.922-383.070-568.081311.252441.74321653.02832531.980
3/4-55.0381.4886.96910.224-383.556-570.178338.463483.22621109.98231804.988
1-53.5501.4887.14310.496-382.508-569.760364.453522.79420483.28530934.992
1 1/4-52.0631.4887.30110.743-380.108-567.196389.177560.51219789.38929952.801
1 1/2-50.5751.4887.44310.966-376.430-562.675412.329596.12019037.93328877.821
1 3/4-49.0881.4887.57211.167-371.691-556.414434.142629.56318245.36027729.449
2-47.6001.4887.68811.350-365.949-548.619454.402660.85517419.16326525.489
3-41.6505.9508.04846.815-335.199-2085.915521.2712902.62813961.04793356.123
4-35.7005.9508.27348.555-295.346-1875.872566.2253235.30210543.85672902.085
5-29.7505.9508.37949.540-249.275-1620.249588.2703434.6227415.93953430.389
6-23.8005.9508.40049.918-199.920-1336.356592.7043513.3974758.09636217.753
7-17.8505.9508.40049.980-149.940-1040.834592.7043526.5892676.42922117.712
8-11.9005.9508.40049.980-99.960-743.453592.7043526.5891189.52411501.210
9-5.9505.9508.40049.980-49.980-446.072592.7043526.589297.3814423.542
100.0005.9508.40049.9800.000-148.691592.7043526.5890.000884.708
115.9505.9508.40049.98049.980148.691592.7043526.589297.381884.708
1211.9005.9508.40049.98099.960446.072592.7043526.5891189.5244423.542
1317.8505.9508.40049.980149.940743.453592.7043526.5892676.42911501.210
1423.8005.9508.40049.980199.9201040.834592.7043526.5894758.09622117.712
1529.7505.9508.37949.918249.2751336.356588.2703513.3977415.93936217.753
1635.7005.9508.19849.317292.6691612.283550.9653389.22310448.26953146.018
1741.6505.9507.62547.073317.5811815.493443.3222958.00413227.25970434.696
1847.6005.9506.57342.239312.8751875.607283.9822163.73014892.84083657.296
18 1/449.0881.4886.2389.528306.208460.443242.737391.74715030.97722255.839
18 1/250.5751.4885.8729.007296.976448.618202.469331.12215019.58122350.103
18 3/452.0631.4885.4768.440285.094432.915164.206272.71514842.71922210.086
1953.5501.4885.0437.824270.053412.891128.253217.51714461.31921794.879
19 1/455.0381.4884.5697.149251.466387.88095.381166.32813840.07921049.165
19 1/256.5251.4884.0376.401228.191356.74565.792119.87312898.52019886.833
19 3/458.0131.4883.4235.548198.577317.40940.10778.76311519.93618161.227
2059.5001.4882.6744.535159.103266.02419.12044.0509466.62915608.757
20 1/460.9881.4881.6383.20799.898192.6324.39517.4896092.50011572.102
20 1/2----------
Extr. Pv61.3430.3560.0000.2910.00017.7570.0000.7810.0001082.957
Sume950.401-2764.34760006.4431072548.765
Centralizatorul de carene drepte
Coeficient de nveli i apendici(1+k)=1,006
Densitate ap1,025 t/m3WLzAWxFVxBzBIxIyFrR
00782.42-1.120.000.00-1.120.005652.75430174.02--
10.681341.321.65722.07744.560.630.4323371.98900231.1832.371246.74
21.361452.062.051671.821723.901.330.7728014.311030530.1716.76616.41
32.041492.452.062672.952756.211.601.1229188.691102681.1610.92412.53
42.721520.681.983697.423812.591.721.4729981.701156335.108.11312.74
53.41547.921.754740.754888.421.751.8230852.281206160.146.51254.42
64.081580.371.245804.375985.171.702.1731798.031271007.935.48218.97
74.761634.78-0.086897.527112.371.522.5332977.571397228.454.78202.57
85.441706.82-2.138033.668283.911.152.9034410.841586313.254.28197.46
96.121759.49-3.389212.219499.170.653.2635713.341726272.143.88187.39
106.81797.57-3.5810421.6110746.240.173.6436794.971830990.623.53175.69
117.481829.18-3.5311654.7012017.75-0.234.0137737.691920277.613.24164.76
128.161854.21-3.3812907.0613309.11-0.544.3838562.601990478.812.99154.22
138.841878.93-3.1514176.3214617.92-0.784.7539316.422063633.042.77145.57
149.521900.80-2.9115461.4315943.06-0.975.1240004.302129016.712.59137.70
unde:
Deplasamentul n ap srat
= (1+k)V
Abscisa centrului de volum
xB = MyOz / V
Cota centrului de volum
zB = MxOy / V
Raza metacentric transversal r=Ix/V
Raza metacentric longitudinal R = IyF/V5.2 CARACTERISTICI DE VOLUM
Relaii de baz
Volumul
Momentul static n raport cu planul yOz
Momentul static n raport cu planul xOy
Metoda numeric de integrare: metoda trapezelor.
unde:
f
funcia de integrat, respectiv f=Aw, f=xFAw sau f= zAw dup caz.
i = 1 .. nindicele plutirilor pn la care se face calculul
j = 0 .. iindicele plutirilor de calcul
zj,
cotele plutirilor de calcul
fj,
valoarea funciei la cotele de calcul
Centralizatorul calculului de volum
WLzdzAWs(AW)VxFs(xFAW)MyOzs(zAW)MxOy
00-782.42-0.00-1.12-0.00-0.00
10.70.681341.321061.87722.071.65670.35455.84456.05310.11
21.40.681452.061396.691671.822.052593.822219.641443.451291.66
320.681492.451472.262672.952.063023.054275.312509.702998.25
42.70.681520.681506.573697.421.983045.306346.113590.435439.75
53.40.681547.921534.304740.751.752862.928292.904699.608635.48
64.10.681580.371564.155804.371.242336.299881.575855.4212617.17
74.80.681634.781607.576897.52-0.08916.6210504.877114.7317455.18
85.40.681706.821670.808033.66-2.13-1884.119223.688533.3223257.84
96.10.681759.491733.169212.21-3.38-4791.115965.7310026.5930075.93
106.80.681797.571778.5310421.61-3.58-6188.311757.6811495.8037893.07
117.50.681829.181813.3811654.70-3.53-6448.68-2627.4212952.8946701.03
128.20.681854.211841.6912907.06-3.38-6362.88-6954.1814406.3056497.31
138.80.681878.931866.5714176.32-3.15-6090.03-11095.3915870.0567288.95
149.50.681900.801889.8715461.43-2.91-5723.34-14987.2717352.7079088.79
unde:
dzi = zi - zi-1
sumele pariale si(f) = 1/2(fi+fi-1)
Vi = Vi-1+si(Aw)dzi
(MyOz)i = (MyOz)i-1 + si(xFAw)dzi
(MxOy)i = (MxOy)i-1 + si(zAw)dzi5.3 COEFICIENTI DE FINEE
WLzAWVCWCBCPV
00782.420.000.39--
10.71341.32722.070.670.530.792
21.41452.061671.820.730.610.847
321492.452672.950.750.660.878
42.71520.683697.420.760.680.894
53.41547.924740.750.770.700.901
64.11580.375804.370.790.710.900
74.81634.786897.520.820.720.886
85.41706.828033.660.850.740.865
96.11759.499212.210.880.750.856
106.81797.5710421.610.8990.7670.853
117.51829.1811654.700.910.780.852
128.21854.2112907.060.930.790.853
138.81878.9314176.320.940.800.853
149.51900.8015461.430.950.810.854
unde:
CW = Aw/LB
CB = V/LBz
CPV = CB/CW
5.4 TRASAREA DIAGRAMEI DE CARENE DREPTEStabilirea formatului de hrtie i a scrilor de reprezentare
Se va face conform urmtoarelor considerente:
- claritatea curbelor;
- evitarea aglomerrii curbelor;
- scrile s fie rotunde.
Am ales formatul A3 landscape pentru reprezentarea diagramelor de carene drepte.
Exprimarea scrilor se poate face n dou moduri:
- prin axe multiple fiecare ax la scara ei
- prin explicitare:
z,zB1cm
0.5 m
Aw1cm
100 m2xF,xB1cm
5 m
V,
1cm
500 m3Ix1cm
1500 m4IyF1cm
50000 m4r1cm
1 m
R1cm
30 m
Am ales a doua variant.
Pe diagram se traseaz explicit linia de plutire i cuplul maestru corespunztor graficelor pentru XB i XF.Trasarea propriu-zis a curbelor de carene drepte
Se face conform urmtoarelor observaii:
- curbele trec prin punctele de definiie
- curbele sunt aviate
- curbele se inscripioneaz.
Pentru trasarea diagramelor de carene drepte am utilizat programul AUTOCAD. Aa cum am artat la capitolul 5.2, pentru calculul de carene drepte am utilizat, programul EXCEL. Tabelul final coninnd valorile pe plutiri ale variabilelor ce formeaz diagrama de carene l-am completat cu scrile de reprezentare. Apoi am obinut reprezentarea grafica a curbelor de carene drepte.
CAPITOLUL 6
DETERMINAREA DEPLASAMENTULUI NAVEI GOALE, DEADWEIGHT-ULUI SI A REZERVELOR6.1 Clasificarea grupelor de mase
n conformitate cu ecuaia flotabilitii, deplasamentul navei () reprezint masa volumului de fluid dezlocuit de carena navei:
Cu s-a notat densitatea apei, iar este deplasamentul volumetric (volumul real al carenei, incluznd volumul nveliului tablelor i al apendicilor).
Deplasamentul navei se calculeaz prin nsumarea urmtoarelor grupe principale de mase:
S-au utilizat notaiile:
- masa corpului navei;
- masa instalaiei de propulsie;
- masa amenajrilor i instalaiilor de corp i punte, cu mecanismele i echipamentele aferente;
- masa combustibilului, uleiului i apei aferente instalaiei de propulsie;
- masa ncrcturii utile;
- masa echipajului i a bagajelor;
- masa rezervelor echipajului;
- masa balastului lichid;
- rezerva de deplasament.
Un parametru caracteristic pentru navele de transportat mrfuri este deadweight-ul (Dw) care cuprinde urmtoarele grupe de mase:
Celelalte grupe de mase care nu intr n componena deadweight-ului alctuiesc deplasamentul navei goale ().
6.2 Determinarea grupelor de mase prin metoda Parsons
Coeficientul bloc calculat la 80% din nlimea de construcie:
- coeficientul bloc al navei
Masa corpului navei
Numrul Lloyd
Unde: B laimea navei
T pescajul navei
D nlimea de construcie
Coeficientul conform TABEL 11. VII
Masa motorului
- puterea motorului in kW
- turaia motorului
Masa amenajrilor i instalaiilor de corp i punte cu mecanismele i echipamentele aferente:
Deplasamentul navei goale complet dotat, cu rezervDenumirea componenteiValoare [t]
Mc masa corpului metallic1920,93
Mm masa instalaiei de propulsie367,04
Mai - masa amenajrilor i instalaiilor de corp i punte368,928
g0 nava goala complet dotat net2656,9
RD rezerva de deplasament106,28
g nava goala complet dotat cu rezerv2763,18
Componentele deadweight-ului masa util, masa combustibilului, uleiului i apei aferente instalaiei de propulsie
Masa util
Masa combustibilului, uleiului i a apei aferente instalaiei de propulsie
Unde - coeficient de siguran
- consumul specific de combustibil
- autonomie
- puterea motorului in kW
- viteza de serviciu a navei
Unde - masa apei, - masa uleiului
Masa echipajului i a bagajelor
Masa rezervelor echipajului
Masa de balast lichid
CAPITOLUL 7
CALCULUL REZISTENTEI LA INAINTARE SI A PROPULSIEI
7.1 .CALCULUL REZISTENEI LA NAINTARE
n faza iniial de proiectare a unei nave, determinarea rezistenei la naintare ocup un loc important prin necesitatea unei estimri ct mai exacte a acesteia, tiut fiind faptul c rezistena la naintare condiioneaz puterea instalaiei de propulsie, caracteristicile propulsorului i ale liniei de arbori, i prin acestea, estimarea corect a maselor de la bordul navei i asigurarea performanelor nautice.
Pentru determinarea rezistenei la naintare a unei nave exist mai multe ci, plecnd de la determinri pe nave n mrime natural pn la formule aproximative menite s ofere doar o idee asupra ordinului de mrime.
Metoda se bazeaz pe diagramele obinute n cadrul testelor experimentale pe serii de modele, care prezint variaia coeficientului rezistenei rezidue pentru nave cu forme standard (form normal a seciunilor, pup moderat de crucitor, raport B/T = 2,5 i poziie normal a centrului de caren).
Conform acestei metode, rezistena total la naintare a navei se determin cu relaia :
- unde CT este coeficientul rezistenei totale la naintare a navei, care se calculeaz nsumnd coeficientul rezistenei de frecare a plcii plane echivalente CF0, coeficientul de corelare de la model la nav CA, coeficientul total al rezistenei rezidue , coeficientul rezistenei aerului CAA i coeficientul coreciei de rezisten la manevrabilitate CAS :
Coeficientul rezistenei de frecare se calculeaz cu formula ITTC-1957
Coeficientul de corelare model-nav ine cont de rugozitatea carenei reale i include i efectul de scar n trecerea de la model la nav. Se recomand alegerea coeficientului CA n funcie de lungimea navei, n conformitate cu datele prezentate n tabelul de mai jos. Pentru valori intermediare ale lungimii, mrimea CA se va stabili prin interpolare.Lungimea naveiCA
501500,000350,0004
1502100,0002
2102600,0001
2603000
300350-0,0001
350400-0,00025
Coeficientul rezistenei rezidue, CR, se determin din diagramele specifice metodei Harvald, n funcie de valorile numrului Froude, coeficientului prismatic longitudinal CP i raportului LWL/(1/3. Numrul Froude i coeficientul prismatic se calculeaz n funcie de lungimea la plutire, LWL.
Coeficientul total al rezistenei rezidue include urmtoarele corecii :
Corecia este datorat raportului B/T diferit de cel standard i se determin cu expresia :
Corecia ine cont de poziia longitudinal a centrului de caren, LCB.
Poziia standard este definit n diagrame, prin intermediul unei funcii liniare de numrul Froude. Abscisa centrului de caren este exprimat n procente din lungimea la plutire. Dac abscisa se afl n prova seciunii maestre, ea este considerat pozitiv.
Dac centrul de caren al navei proiectate se afl n prova centrului de caren standard, atunci corecia coeficientului rezistenei rezidue se determin cu relaia :
n care (LCB este diferena dintre abscisa centrului de caren al navei proiectate i valoarea standard a abscisei centrului de caren, calculate n procente din lungimea la plutire.
n continuare prezint mersul de calcul al metodei Guldhammer Harvald cu ajutorul cruia am calculat rezistena la naintare pentru nava tip vrachier 8000 tdw.
Pentru efectuarea calcului respectiv este necesara cunoasterea vitezei de mars a navei pe care trebuie s-o asigure elicea. De aceea calculele trebuie efectuate tabelar pentru mai multe viteze, trei sau cinci, gama ce va contine si viteza de serviciu a navei preconizata.
v1213141516Nd
v6.1736.6887.202227.7178.231m/s
Fr0.180.190.210.220.24
Re6.324E+086.851E+087.378E+089.238E+089.854E+08
103*Cf01.621510751.605060771.590051.545779701.53341428
103*CA0.3240.3240.3240.3240.324
CM =0.9830.9830.9830.9830.983
CB =0.750.750.750.750.75
CP =0.7620.7620.7620.7620.762
103*CR0.790.821.051.211.7l =
103*C1-0.005-0.005-0.005-0.005-0.005
LCB1.50.80.1-0.5-1.1
Abaterea dLCB0.020.080.180.250.32
103*C20.030.0640.018-0.125-0.352
103*C3-0.080.3947-0.1057-0.1477-0.1753
103*C40.03160.03280.0420.04840.068
103*CRT0.7671.3071.0000.9811.236
103*CF1.945510751.929060771.914051.869779701.85741428
103*CAA0.070.070.070.070.07
103*CAS0.040.040.040.040.04
103*CT2.822404863.345854893.023652.960773823.20340840
CBpp0.73260.73260.73260.73260.7326
Sudata2946.9162946.9162946.9162946.9162946.916
RT162.4502255226.012428236.87850266.2724687327.786294kN
RF194.940271.215284.254319.527393.344kN
PE1203.4311813.8252047.2622465.6833237.654kW
PD1784.6812689.8913036.0763656.5924801.420kW
Numrul Froude pentru viteza de calcul:
Suprafaa udat pentru viteza preconizata:
- unde CB este calculat la LWLCoeficientul lui Poisson:
Numrul Reynolds pentru viteza de proiectare:
Coeficientul de rezisten la frecare pentru viteza preconizata:
Coeficientul de influen a rugozitii:
pentru Lpp = 119
EMBED Equation.DSMT4 Coeficientul rezistenei rezidue funcie de :
Coeficientul coreciei datorit raportului
Abaterea LCB (xB) fa de valoarea standard
Coeficient de corecie pentru abaterea centrului de caren:
Corecii pentru bulb n funcie de Fr:
Corecii pentru forma corpului la extremiti:
Coeficientul total al rezistenei rezidue:
Coeficientul total al rezistenei de frecare pentru viteza preconizata:
Corecie datorat rezistenei aerului:
Corecie datorat manevrabilitii:
Coeficientul rezistentei totale:
Rezistena total la naintare a navei pentru viteza de proiectare:
Rezistena i puterea efectiv calculate folosind diagramele, corespund unei nave n condiii de prob, adic pentru condiii ideale privind valurile i vntul, adncimea apei i rugozitatea corpului. Pentru condiii de exploatare se fac o serie de majorari.
Creterile pentru condiii de exploatare se fac asupra rezistenei calculate sau a puterii calculate in funcie de zonele de navigaie a navei. Astfel majorm rezistena la naintare cu 20%. Deci rezistenta la inaintare finala a navei pentru viteza de proiectare va fi:
Rezistena final la naintare a navei
7.2 ESTIMAREA PRELIMINAR A PROPULSIEI I ALEGEREA MOTORULUI
Determinarea preliminar a puterii de propulsie folosind diagramele KT-J :
Din diagrama KT-J n funcie de se extrage valoarea corespunzatoare lui J - obinem J = 0,46
Turaia optim se calculeaz cu relaia :
Se intr n diagrama KT - J cu valoarea obinut pentru kn i se extrage J=0,42Diametrul optim devine :
Din diagrama KT -J se extrage randamentul efectiv .
Vom alege un motor MITSUBISHI tip UEC45LAP1 din catalog cu urmatoarele caracteristici:
putere la flan de 3530 kW
n=158 RPMnumr cilindri 4consum specific 170g/kWh
Lungime 4625 mm
Lime 2560 mm
nlime 7720 mm
Masa 111 t
7.3 PROIECTAREA ELICEI
Tabelul rezistenei la naintare pe o gam de 5 vitezev [Nd]1314151617
v [m/s]6.6887.2027.7178.2318.746
R [kN]194.940271.215284.254319.527393.344
PE1303.7160841953.3482193.4932630.063440.005
w0.3530.3530.3530.3530.353
t0.2610.2610.2610.2610.261
Pentru navele cu o singura elice coeficientul de siaj se calculeaz :
Puterea disponibil la elice este:
Determinarea turaiei optime / diametrului elicei:
turaie motor mic
turaie motor mare se adopt
Ne ncadrm n primul caz n=158 rot/min = 2,63 rot/s. Aadar se calculeaz:
cu acesta intrm n grafice i scoatem un Jopt = 0,46
Tipul de diagram folosit :
KQ-J ; B4-40; z = 4; AE/A0 = 0,4
Calculul se va face tabelar pentru o gam de viteze apropiate de viteza de proiectare.Nr.DenumireSimbolUMViteze
m/s6.697.207.728.238.75
Nd1314151617
1Viteza avans n eliceva=v(1-w)m/s4.3244.6574.9905.3225.655
2Avans relativJ=va/nD-0.370.400.430.460.49
3Raport pasH/D din diagr kQ-J-0.590.610.620.650.68
4Randament elice0 din diagr kQ-J-0.530.550.580.60.62
5Coeficient mpingerekT din diagr KT-J-0.130.1250.120.1250.13
6mpingerea eliceiT=kT*ro*D^4*n^2KN352.670339.105325.541339.105352.670
7Coeficient de influen al corpuluih =(1-t)/(1-w)-1.1431.1431.1431.1431.143
8Randament relativ de rotaier =1,7-CB-0.930.930.930.930.93
9Randament cvasipropulsivD =0*h*r-0.560.590.620.640.66
10Puterea efectiv de remorcarePE=R*v-1086.431627.791827.912191.722866.67
11Puterea disponibilPD=R/D-1924.432778.502958.713429.324340.72
Se vor face dou grafice, unul PD = f(v), si unul H/D = f(v), din care se va extrage o vitez optim pentur puterea disponibil la elice, iar n funcie de aceast vitez un raport de pas corespunztor.
Verificarea la cavitaie
Din diagrama Schonner .
, unde l-am extras din tabele pentru .t0510152030
pd [ N/m2 ]8341226170723354248
Deci elicea nu caviteaz
Geometria elicei, geometria unui profil.
r/Rrx1br=Dx1/zx2bri=brx2bre=br-brix3cr=brx3x4er=Dx4bri-crbre-cr
0.20.3851.6620.6400.6170.3950.2450.350.2240.03660.1410.171-0.030
0.30.57751.8820.7250.6130.4440.2800.350.2540.03240.1250.191-0.066
0.40.772.050.7890.6010.4740.3150.350.2760.02820.1090.198-0.090
0.50.96252.1520.8290.5860.4860.3430.350.2900.0240.0920.196-0.103
0.61.1552.1870.8420.5610.4720.3700.3890.3280.01980.0760.145-0.069
0.71.34752.1440.8250.5240.4330.3930.4430.3660.01560.0600.067-0.007
0.81.541.980.7620.4630.3530.4090.4790.3650.01140.044-0.0120.056
0.91.73251.5820.6090.3510.2140.3950.50.3050.00720.028-0.0910.118
11.925--0----0.0030.012-0.1700.170
Pozititia ordonatei masurata in procenteDiametrul de racordare la muchia de intrare si iesire, in % din grosimea maxima
r/RDe la grosimea maxima la muchia de iesireDe la grosimea maxima la muchia de intrare
10080604020204060809095100r/RMuchia de iesireMuchia de intrare
Ordonatele dosului palei0.255.3572.6586.9096.4598.6094.5087.0074.4064.3556.950.26.4
0.350.9571.6086.8096.8098.4094.0085.8072.5062.6554.900.36.5
0.447.7070.2586.5597.0098.2093.2584.3070.4060.1552.200.46.6
0.543.4068.4086.1096.9598.1092.4082.3067.7056.8048.600.56.7
0.640.2067.1585.4096.8098.1091.2579.3563.6052.2043.350.66.8
0.739.4066.9084.9096.6597.6088.8074.9057.0044.2035.000.76.9
0.840.9567.8085.3096.7097.0085.3068.7048.2534.5525.450.87
0.945.1570.0087.0097.0097.0087.0070.0045.1530.1022.000.911.111.1
Ordonatele fetei palei0.230.0018.2010.905.451.550.452.305.9013.4520.3026.2040.000.9515.715.7
0.325.3512.205.801.700.051.304.6010.8516.5522.2037.55vrf26.7
0.417.856.201.500.302.657.8012.5017.9034.50
0.59.701.750.704.308.4513.3030.40
0.65.100.804.458.4024.50
0.70.402.4516.05
0.80.70