ΝΑΥΠΗΓΙΚΟ ΣΧΕΔΙΟ 2010 ναυπηγικο σχεδιο 3

Click here to load reader

  • date post

    21-Jan-2016
  • Category

    Documents

  • view

    1.374
  • download

    2

Embed Size (px)

Transcript of ΝΑΥΠΗΓΙΚΟ ΣΧΕΔΙΟ 2010 ναυπηγικο σχεδιο 3

  • . / /

    1

    , 2010

  • . / /

    2

    , . , () , , . , , . , , , :

    - - - - -

    , , . . , , . , , , ( ) . . . , . , I.T.T.C. (International Towing Tank Conference) . , .

  • . / /

    3

    , , . . . (offsets) . (, , , .) , (, , ). , . .

  • . / /

    4

    1 1. 1.1 ( ) . ( ) , (....) (....), .

    , , , .

    . (), ( , ), , , (, , , ), , ).

    , : - , , , , , .. , . - , , ( , , , , ), , . , . , / , . , , ....

  • . / /

    5

    , ...., 10 , . : - , - (... = ) 10,00

    ( ( )31 2,83 m = ). - , (), ... ( ) . - ,

    , , , .

    , , , , .

    .... < 10,00. , ...., , , . ...., , . , , , , ( , , ). , , . , , , . (= ) (, ) , , , , , . (, ). , , . , , .

  • . / /

    6

    1.2. : . : , , . . , . , . . . . . . . : , ..., , . . : , . : 1. ,

    ( , , , ). .

    2. , , .

    . :

    : - - . , , , :

    2. : , , , , ,

    3. : , , ,

    . 4. : , , , ,

    , 5. : (hydrofoils), (hovercrafts).

  • . / /

    7

    6. :

    , , , , ..

    7. : , , , , () ..

    , . :

    - = , , , , , , , ,

    - = .. , ,

    , .. , ..

    , , : - (tramps), , . , , , . - (liners), . , , , , .

  • . / /

    8

    (general cargo) , / , , .

    -30 0C 12 0C . , . , . (), .

  • . / /

    9

    (CONTAINER SHIPS) () . , . - . .

    (BULKCARRIER SHIPS) () , , , , , , . , .

  • . / /

    10

    , , , . - , , , . - .

    , 0 0C.

  • . / /

    11

    Ro Ro (Roll on / Roll off) , . () .

    / . (), (, , ), . , , .

  • . / /

    12

    Passenger / : 2006 / x : 289 m X 50 m / (DWT): 8900 t

    ( / ): 15.9 / 12.6 knots /: Bermuda [BM]

    : High Speed Craft / : 1981 / x : 35 m X 6 m

    ( / ): 33.2 / 27.4 knots / : Greece [GR]

  • . / /

    13

    (CONTAINER SHIP)

    : Cargo / : 2003 / x : 352 m X 43 m / : 7 m

    (DWT): 109000 t / ( / ): 20.3 / 17.2 knots / : Denmark [DK]

    Tanker / : 2009 / x : 274 m X 46 m / (DWT): 159400 t

    ( / ): 15.2 / 13.4 knots / : Greece [GR]

  • . / /

    14

    : Tug : 1971 / x : 49 m X 12 m / (DWT): 814 t

    ( / ): 8.2 / 6 knots : Panama [PA]

  • . / /

    15

    . 19 , . 1915. "Barque" .

    . , .

    , . "" , - . , .

    , , , , , , ,

  • . / /

    16

    . 250 . , .

    , , "" "". ("") "-". - . , "".

    - . , .

    ( naftotopos.gr)

    -

    ( naftotopos.gr)

    , , , () .

  • . / /

    17

    , .

    .

    .

    , .

    .

    , , .

    , .

    , .

    , .

    , 1,5 .

    , , , , , ..

    T ' .

    ( naftotopos.gr)

    (trabaccolo) .

  • . / /

    18

    T . H . A 17 s.

    T , ( : 3:1), , , E .

    . T . X , , , . H .

    , , , ( ) .

    H . () ( - - ). T . T , 3 . A 30-40 .

    , . 100 , () . E : . E 3 .

    H , , .

    E 1920. . H

    : , , .

    ,

    , 5 9 , .

  • . / /

    19

    . 1/3 .

    , , ( ) .

    1.3. , , . : 1. / : ,

    (= ) 2. 3. : , . 4. : 5. : ,

    . 6. : (

    ), ( ), ( )

    7. : .

  • . / /

    20

    2. 2.1. :

    - , , - , - ,

    - , - ,

    - .

    , , . , , . , , . , () ( , .) . , (, , , ). , , , , . , .

  • . / /

    21

    . . . () , , . , , 18 . . . , . , . , . :

    1 : , .

    () 6 ( 1). , , . . , .

    2 : . , . .

    3 : . , . . , .

    , .

  • . / /

    22

    , . () . : : () . : . , , .

    1.1

  • . / /

    23

    , ( ) . , . , . (DWL = Design Water Line) . 2.2 (, hull) = . (shell plating) (framing). , , , , . () . = (molded hull surface) , . (outer shell surface) = , . : ( ). , . , ( ) . .

  • . / /

    24

    , , ( ) , . , , . , . . , : , . , , , . , . , . , , .

  • . / /

    25

    , ( ), , , (, ). , , . ,

    1.2. . , .

    , , ( / ) . .

  • . / /

    26

    , , , , (, ) , . .... ( ) 1966, , ( ) / 4. , . , , . . . , , , . : : . (, keel) = ( ) . . (molded surface) = . , . , ( ). , , .

  • . / /

    27

    1.3 , . (). (longitudinal plan centre line) C.L. (center line). , . (lines drawing plan lines plan). , ( ) , ( ) . ( ), , , ,

    ( 1.3) , . ( ). .

  • . / /

    28

    , : ( ) . , . : 1 , . longitudinal lines vertical lines buttok lines buttoks. , , profile.

    ( 1.4 )

    2 , .

  • . / /

    29

    water lines.

    ( 1.4 )

    , . , , . , , , .

    1.5

  • . / /

    30

    3 , .

    ( 1.5) , , frames. , : , , . , :

    ( 1.5 )

  • . / /

    31

    , :

    ( 1.5 )

    , : - ()

    (). - ()

    . - ()

    . - ,

    . - ,

    .

    (longitudinals)

    ( ) (frames)

    ( ) (water lines)

  • . / /

    32

    - ,

    . .

    .. , , :

    - : , , .

    - : .

    - : , .

    , :

    - = , . - = - =

    :

    1.6

  • . / /

    33

    - : - : - :

    . . , .

    1.7

  • . / /

    34

    3. : - = - = - = : , , , . , , , . (-2-) , . , , . , .

    2.1

  • . / /

    35

    , , , . , , , , . , (L) , . , , :

    2.2 - . .( )B PL =

    . - . .( )W LL =

    . . , ( ).

    - ( ). .O AL =

    , .

  • . / /

    36

    - ( )OSL =

    ( ), , .

    - ( ).L =

    :

    0,96 0,97

    0,96 0,960,97 0,97

    BP WL BP WL

    WL BP WL

    WL BP WL

    L L L L LL L L LL L L L

    = = < = >

    , . - ( ) ( ). . . . F BL L =

    . 85 % .

    , : - - 0,96 WLL , . , , BPL > 24,00 . 24,00 24,00 98 / 18, , .. 399 / 1980, , : SL = . AL = .

  • . / /

    37

    2.3.

    PL = . , . EL = . RL = . , EL RL . , :

    , E F R AL L L L .

  • . / /

    38

    , :

    2.4

    . .O AB = . . .W LB = XB = . MB = , . , , .

  • . / /

    39

    D , , . ( ) , .

    D ( ). . . , . , F , . , . , . :

    F D T=

  • . / /

    40

    , . , :

    2.5 ( , , , F FT d T d , d ,T ) = . ( ). ( , , , A AT d T d , d ,T ) = . ( ). MT == . XT = . , . , , . , .

  • . / /

    41

    , , , . - ( ) , :

    FT = AT = MT

    = = - ( ) , T , , :

    AT - FT = T 1

    2A M M FT T T T T = =

    : 2

    T TFATM+=

    . ( ).

  • . / /

    42

    , ( = = ) . ( )

    2.6 , , , ( ), . . , . , . , ( ), . , ,

    1 2 3, c c c+ + .

  • . / /

    43

    ' ' ' , , T T TM FA , :

    (m)

    ' ' ' TA ' ' '

    MT ' ' '

    FT ' ' TA

    ' ' MT

    ' ' FT

    ( )' ' ' ' ' ' 2A AA T TT += ( )' ' ' ' '

    ' 2M M

    M

    T TT

    += ( )' ' ' ' ' ' 2F FF T TT += , , T T TM FA , : ( )' '

    ' ' ' ' ' '' ' '

    1 2 3

    , ,

    F

    A F A F A FA A M M F F

    m m m

    T T T T T TT T c T T c T T cL L L

    > = + = = i i i

    ( )' '

    ' ' ' ' ' '' ' '

    1 2 3

    , + ,

    F

    F A F A F AA A M M F F

    m m m

    T T T T T TT T c T T c T T cL L L

    < = = = +i i i

  • . / /

    44

    , , . ( ) . . , . , . , : = = ( ), , . ( ), , . . , :

    D V= = . : ( )3 1,000 t m = ( )3 (1,025 1,026) t m = , , , .

  • . / /

    45

    :

    ( ) ( )i i iD V S t V = + : iS =

    it =

    iV =

    , ( ) .

    ( )3 1,028 t m ( )3 1,035 t m ( )3 1,032 t m . , .

    - - ()

    : . : , ,

    , , , . . : , ,

    , . .

    . : , , , , , , .

    . , ( )

    . : , , . . . . , ,

    , , , .

    , .

  • . / /

    46

    , . light ship. () : . , . , , . , , , , , . : ,

    , . , , , . , , , . , . , , . , . deadweight (DWT). : , , . . : = = + Displacement = ship weight = light ship + dead weight

  • . / /

    47

    . , , , , , , . , : ( )3100 ft ( )32,832 m . :

    1. : ( , ), , , . .

    , ( ) : , ( , ), : ( , , , , , , , , , , . , 50 . ( , ). , . , ( ) , , ( ).

  • . / /

    48

    2. :

    , . . : , ( , , , , .), , , , , , , , ( ), .

    . , , , , (engine casing). .. 973 / 71 , 14, 15 . , , George Moorsom (, 1849) , . , , : - ( ) - ( , . 23% )

    () , : - ( ) - (dead weight) ( , dead weight , )

    - . ( ) (dead weight) , , .

  • . / /

    49

    , , . : - :

    . , , . , . , , .

    - : , , , , (, , ).

    - : . ( )10 15 % .

    - : . , , . , , . , .

    - : . (). .

    - : . .

    , , . ( ( )23 ).

  • . / /

    50

    : - :

    , ( )18 .

    - : ( ) . .

  • . / /

    51

    - , () , ( ), , . , , , , . , . , ( ) . (, ) . . , , . . , , , . . . . :

    ( ) ( )( ) ( ) ( )

    3

    2 2

    ( )

    m WL

    V m L m d m

    m A m A m

    = = = = = =

  • . / /

    52

    :

    - -

    . : 1.

    WPWP

    WL WL

    C L B

    = =

    . 1 , . WPC 0,70 0,80. 2.

    X X

    C d

    = =

  • . / /

    53

    3.

    LLA

    DWL

    C

    L d

    = =

    ( 2BPL )

    2

    BP

    M

    L C

    d

    = =

    MC . , : , . 0,80 0,95.

  • . / /

    54

    . 1.

    B X x

    VC L B d

    = =

    X xL B d ( ) , , . BC . BC = 0,70 70 % . BC = 1. BC ,

    , , ( ) , B L BC B d= ( ), L BB d . BC :

    - ( ) : BC = (0,50 0,65) - : BC = (0,65 0,75) - , : BC = (0,75 0,85) - ( ), ( ) : BC 0,90

  • . / /

    55

    , . , , , .

    2.

    P X

    VC L A

    = = , : X X X xA C B d= ,

    : BPX

    CCC

    =

    , . 1, . 0,60 0,75. ,

    2BPL .

  • . / /

    56

    3.

    DWL

    VP

    VCA d

    = =

    , .

    ( ) ( )( ) ( )

    ,

    ,

    FW AFTP PFW AFT

    X FW X AFT

    UEP PE U

    X E X U

    V VC CA L A L

    VVC CA L A L

    = = = =

    ( )PC . .

  • . / /

    57

    . : . :

    , , , , L L L B d d D D

    = = = = = . ( ) :

    3VVCL

    = . :

    :

    S = . :

    - , :

    ( )12SCSL

    =

    - - iE = ,

  • . / /

    58

    - - iR = , .

    3.1 - , I TC I LC ,

    ( ) , , . :

    12

    3ITCI T L BWL WL

    = ii

    , 12

    3ILCI L L BWL WL

    = ii

    . Bonjean (Bonjean curves) .

  • . / /

    59

    , , . , , . . ,

    3.2 , . , , , . . , (, ) ( knuckle line). , , ( ) .

  • . / /

    60

    () (dead rise)

    3.3 , . , , . , , ( 2.6, 29). :

    3.4

  • . / /

    61

    - U : .

    - V : , .

    - : , , .

    - . - :

    , .

    ( ) . . , ( ) ( ) . , ( ), ( )

    3.5

  • . / /

    62

    , .

    3.6 . , 3.1 (, ) . 0,57cB < . . . . 75 R mm= ( )8% 2BRD = . , 020 .

  • . / /

    63

    , . . . ( ) . . , . . . . ( ), ( ) . . ( 3.7) ( 3.7 ( 3.7 ) :

    3.7

  • . / /

    64

    3.7

    1. ( ) :

    ( ) .

    , , , . -. , , . . , .

  • . / /

    65

    2. :

    . . , , .

    3. ( , ) :

    , .

    , , .

    , :

    3.8

  • . / /

    66

    1. :

    . U . () .

    2. -

    ( ) : . ( )0 015 30 , . , . , . , .

    3. CLIPPER : .

    , . V . . , ( ). , .

    4. : , , .

    ( ), . , ( ) .

  • . / /

    67

    T

    ( ) ( )0,15 0, 20L L . (bow wave crest). : - - (sonar domes)

    - .

    ,

    : - ,

    - - -

    .

  • . / /

    68

    5. :

    . ,

    , .

    6. : .

    . ( ), .

  • . / /

    69

    .

    3.9.

    , .

    (2BPL ),

    (2BPL ) .

    (2BPL ) .

    . . , .

  • . / /

    70

    2 1. , ( ) . , , , , . , , , . , () , ( ) (). . , (body plan) 900. , , () . (body plan) , (sheer plan) . , , ( ) (). , , .

  • . / /

    71

    , 1 (, ), . , , , , (table of offsets) ( / / ) / / , , , , . , (, .), . , , . , . , BODY PLAN, , C.L. C.L. (= ) ( ) , C.L. (= ) ( ) . C.L. . . () . . 21 1 / 20 , . 0 ( ) 1,2,3,

  • . / /

    72

    , , , , , 1 , 2 , .. , 20 , 21 , . . , , C, D - , -1 , -2 , .. : - 0 1,2 3, . - . :

    - = , 10 20.

    - = .

    () , , C.L. , . , . , , poop deck), (forecastle deck) , . : - 0 WL., WL 1, WL 2, ., WL .

  • . / /

    73

    - (0, 1,

    2 ..). - 0, 5, 10, 20, ( , 0, 0,05, 0,10, 0,20, ).

    () , . . , . , . 0 VL. (, , , .) VL. ( ) , . , , .

    ( )

    ( ) , .

    ( ) .

    , C.L., ( ) .

  • . / /

    74

    . .

    . . , , , 90. , . , , , , (.) . ( ) , , , a,b,c,, . , . , () ().

    , , , , . .

  • . / /

    75

    (offsets) . ( ) , ().

  • . / /

    76

    3 .

    1 , . , , . , ( 1) ( ) . , .

    , .

  • . / /

    77

    2

    , , ( 3).

    3

  • . / /

    78

    , OB (1) . . . , . () , ( ) . , , . , , , .

    4

    5

  • . / /

    79

    : , , .

    6 , . ( ). , , .

    7 1.5. -4- , , C, D , C , C D C D 1.

  • . / /

    80

    , C D . 1.0 1.5 1.5. , 1.0 1.5. , . , . ( 1.0) ( 1.5) , . , , 1.0 1.5 . , , . ( 8)

    8

  • . / /

    81

    F 1.5 2.0. F . . , , ( 9)

    9

    ( 10) .

    10

  • . / /

    82

    . ( 11).

    11 , J. J 18 . 0 0.5 . - . , - 1. 0 () , , 12, .

  • . / /

    83

    12

    13, .

    13

    J, .

  • . / /

    84

    ( 1).

    1

    . , ( 2) .

    2

    - , (Body plan) .

  • . / /

    85

    , . , , -1-. , , - , 3.

    3

    , ( 4).

    4 , .

  • . / /

    86

    4 , , , . -5 : 1. 2. 3. 4. 5. . 4.1. , . , . , , . , , , , , . - , , , ( LCB) . , , .. , , . - , , , . ,

  • . / /

    87

    . , , ( ) . , , , . , , , .

    3.1

  • . / /

    88

    , , , , . , , . , . , . , . , , . ( ). , . , , . 4.2. , :

    - ( ).

    - ,, , , :

    ( )' ' ' , ,X p X Y q Y Z r Z X Y Z = = =i i i [ ], , p q r ( ).

  • . / /

    89

    , :

    p q r = = = = :

    ' ' ' L p L B q B d r d= = =i i i , , D r D i , . :

    ' ' '

    V dV V dVV V

    = =

    : dV dX dY dZ= , : 2 2 2

    1 2 1

    X Y Z

    X Y Z

    V dX dY dZ= : ' ' ' ' dV dX dY dZ= , :

    ' ' '2 2 2

    ' ' '1 2 1

    ' ' ' 'X Y Z

    X Y Z

    V dX dY dZ= , :

    ' ' '1 1 2 2

    ' ' '1 1 2 2

    ' ' '1 1 2 2

    dX p dX X p X X p X

    dY q dY Y q Y Y q Y

    dZ r dZ Z r Z Z r Z

    = = =

    = = =

    = = =

    i

    ( ), :

    2 2 2'

    1 2 1

    X Y ZV p q r dX dY dZ

    X Y Z= : 'V p q r V=

    :

    ' ' ' A p q A A q r A A q r AW W X XS S= = =

  • . / /

    90

    . :

    ( ) ( ) ( )'' ' ' '

    V p q r V VC CB Bp L q B r d L B dL B d = = = = i i

    :

    ' ' ', , ' ' '

    '2

    B q B L p L L p Lr d q B r dd B d

    q rC CV Vp

    = = =

    =

    i i i

    i

    ( ) .

    4.1

    :

    ( ) ( )'' '' ( )

    dY q dY q dY qtg i tg iE Ep dX p dX pdX

    qi arctg tg iE Ep

    = = = =

    =

  • . / /

    91

    : ' ( )Rqi arctg tg iR p

    = . .

    . , , . , , . , , :

    ' '' ' 'X p X Xx x

    LL p L= = = =

    , :

    '' '

    A q r A AS S Sa aS Sq r A AA X XX

    = = = =

    .., :

    - p - q - r

    . , ( ) ( , , ) , , . . . p , q , r , .

  • . / /

    92

    , , . p ,q , r :

    ' ' '2, , V V

    q rV p q r V C C d r Tp= = = =

    , :

    1 11 2'3 3' ' '3 3

    ' ' , , V V

    V V

    C CV d V dp q VV C d V C d

    = = = i i i

    , , , .

    4.3 . ( ) . . , . . LX. :

    ' ' ', ,

    '

    L L L B B d dX

    V V V V C L B dX X X

    = + = =

    = + = +

  • . / /

    93

    , CX , :

    - : ( )'' ,VCB L L B dX

    = +

    ' V V V V C L B d C L B d C L B dX X X B X X= + = + = + :

    ( ) ( )' B X XC L B d C L B dCB L L B d L L B dX X = ++ +

    : XXLlL

    = , :

    ( ) ( )1

    ' 1

    CX lXCLL BXC C C CB B X B lL L L L XX X

    + = + = ++ +

    XB

    CC

    > 1 ,

    ' C CB B> Xl > 0 (= ). , CB ,

    ( Xl < 0). - :

    ' '

    '' 'B B B

    P P P PX X B

    C C CC C C CC C C

    = = = - :

    ( )'

    ' '( ), WWP W W W X WP X

    X

    AC A A A C L B L BL L B

    = = + = + +

    : ( ) ( )' WP XWP X XC L B L BCL L B L L B

    = ++ +

  • . / /

    94

    : ( ) ( )'11

    1

    XWPX

    WP WP WPX X X

    lCLLC C C

    L L L L l

    + = + = + + +

    :

    '

    '

    0

    0

    WP WP X

    WP WP X

    C C l

    C C l

    > >

    < <

    - :

    ( )'

    '3V

    X

    VCL L

    = + , ' X X X

    P

    VV V A L AL C

    = + = , :

    ( ) ( ) ( )'

    3 3 3 1X X

    VPX P X X

    V L LV VCL CL L L C L L L L

    = + = + + + + i ,

    ( )3L , :

    ( )'

    31 1

    1X

    V VPX

    lC CCl

    = + + i

    ( Xl < 0) ( Xl > 0). - : :

    : Xl > 0 Xl < 0

    , ,

  • . / /

    95

    5.1

    ( ) ( )'' 1 2B E X X E XBV X V X V L V L L L = + + + , :

    BV X =

    E XV L =

    12X E X

    V L L L + = ( ) .

    , :

    ' 1 2

    EB B X E X

    X X X

    VV VX X L L L LV V V V V V

    = + + + + + + . . . , .

  • . / /

    96

    4.4 ( ), CB LCB. CB LCB L, C LCB. ( D.W Taylor). C LCB / L. . , C. , , C, , . LCB , LCB . 6.1, C LCB. , , . , . , , , - . , . , .

  • . / /

    97

    6.1 4.5 , . , . . () . (PARENT FORM) .

  • . / /

    98

    CB , B LD B ,

    . , , (, ) . . . . , . , , - . , . , . ( ). ( = ) ( ) . - - - ( ) . , :

    - -

    (, ) .

  • . / /

    99

    ( 7.1). / L, , ( 7.2) - . - . , -, , , 2X

    BA d

    .

  • . / /

    100

    7.2 . : . TAYLOR:A , Cp, / A/(L / 100)3 . ' 1900. TAYLOR (1933) GERTLER(1954).

  • . / /

    101

    . 60 (SERIES 60) : S.N.A.M.E. TODD (1963). CB , . (LCB),to LBp / /. U. . B.S.R.A. (BRITISH SHIP RESEARCH ASSOCIATION) : . LCB /. V. . S.S.P.A. ( SWEDISH SHIPBUILDING EXPERIMENTAL TANK ) : , , . . (NATIONAL PHYSICAL LABORATORY N.P.L.): Cb L/B /. . : , . WEBB INSTITUTE OF TECNOLOGY S.N.A.M.E. (1963, 1966). . FORMDATA: GULDHAMMER HARVALD ( 1974 ). . - L/V1/3 Cp. / = 2,5 , /. FORMDATA FORMDATA 60 . FORMDATA , . . : - - CM - - . . II ( 0 ) ( 10 ).

  • . / /

    102

    .. U2F, B43F, T1A, CB2A ... ' . U , V . U, V (.2) (.3) . ( BULBOUS BOW ). To (.4). (TRANSOM STERN) (.5). C (CRUISER STERN) . (.2). Cm . (. 6) :

    6 F ( AFTER D) ( FORE BODY) . 0,4,5,8,10 % . A, B,C, D C . ( D).

  • . / /

    103

    - ( - ) , II III. - C () % (L ). LBP , , , D LCB (=B ). FORMDATA . C CBF , ). LCB L :

    C = CB [0,997 + 3,5 (LCB/LBP)]

    CBF= CB [1,003 - 3,5 (LCB/LBP)]

  • . / /

    104

    FORMDATA CBA CBF [ (. 7) (. 12)]. . , . ( 5), (4 6) . FORMDATA ( -). .

  • . / /

    105

  • . / /

    106

    2 :

  • . / /

    107

    3 :

  • . / /

    108

    1. CB , , LCB 1, 2 3 .

    2. FORMDATA . , . , .

    3. ( BASE LINE)

    ( 1.0) . . , CL ( 0) ( 1.0). , . , 1/10 , .

    4.

    3.

    5.

    .

    6.

    . .

    7. . . 8. /2 ( ).

    9. .

    10.

    -4-, (BODY PLAN). 11. , (HALF

    BRREATH PLAN) (SHEER P[LAN). .

  • . / /

    109

    - , . . , . , . . . , FORMDATA. . (SMOOTHING). () . . (BILGE DIAGONAL) . , , . , ( ) , ( ) . , , , .

  • . / /

    110

    . : , , , Froude, :

    VFrg L

    = : V = (m / sec) g = (m / sec2) L = (m) : , : Fr < 0,20 , : 0,20 < Fr < 0,35 ,.. : Fr > 0,35 : 300 16 ( 8,23 m / sec, 1 = 1 / = 1852 m / h = 0,5144 m / sec) Fr = 0,152, 20 12 Fr = 0,441. , , ( ). BC XC WLC L / B B / d 1000 C D / d 0,78 -0,85 0,99 0,85 0,95 5,5 7,0 2,2 3,0 7,0 8,5 1,2 1,4 &

    0,72 0,78 0,98 0,99 0,75 0,85 5,5 7,0 2,2 3,0 6,0 7,0 1,4 1,6

    &

    0,65 0,72 0,96 0,98 0,70 0,80 6,0 7,5 2,4 3,5 5,0 6,5 1,4 1,7

    0,57 0,65 0,94 0,97 0,70 0,75 6,0 7,5 2,4 3,5 4,5 6,0 1,5 1,9 0,68 0,75 0,98 0,99 0,75 0,82 5,0 7,0 2,2 3,0 6,0 7,5 1,2 1,4 0,55 0,65 0,93 0,97 0,65 0,80 6,0 8,0 2,5 3,5 2,5 5,0 1,6 2,0 0,55 0,62 0,92 0,97 0,70 0,80 5,5 7,5 3,0 4,0 3,5 5,5 1,1 1,5 0,50 0,62 0,70 0,90 0,65 0,80 4,5 6,0 2,0 3,0 7,0 10,0 1,2 1,5 0,40 0,55 0,65 0,85 0,65 0,80 3,0 5,0 2,0 3,0 9,0 14,0 1,2 1,5

    0,50 0,60 0,84 0,95 0,65 0,78 7,0 9,5 3,0 4,5 1,5 2,5 1,5 2,0

    0,40 0,52 0,70 0,85 0,60 0,75 5,0 8,0 3,5 4,5 2,0 3,5 1,7 2,2

    0,35 0,55 0,60 0,75 0,60 0,80 3,0 7,0 3,0 4,5 3,0 8,0 1,8 2,2

  • . / /

    111

    5

    :

    (, .. ). , , , , . ... - . :

    1. BEZOUT :

    , . .1

    (1) , , , 1 , 2 , 3 , 4 n-3 , n-2 , n-1 .

    n . 0,1,2,3,4n-3, n-2, n-1 n , 0,1,2,3,4n-3, Yn-2 , n-1,Yn .

    1 , 1 2 n-1B 1, 12 n-1 B, , :

  • . / /

    112

    1=(0+1)/2 ,2=(1+2)/2 ,3=(2+3)/2 ,4=(3+4)/2 , , F3=(Yn-3+Yn-2)/2 F2=(Yn-2 +Y n-1)/2 ,F1=(Y n-1 +Y n)/2

    :

    ()=1+2+3+4++F3+F2+F1= = (0+1)/2 + (Y1+Y2)/2 + (2+Y3)/2+ (3+4)/2 +(4+)/2+

    +(+n-3)/2+(Yn-3+Yn-2)/2+(Yn-2+Yn-1)/2+(Yn-1+Yn)/2 =>()=/2[0+1+1+2+2+3+3+4+4+..+n-3+Yn-3+Yn-2+Yn-2+Yn-1+Yn-1+Yn] =>()= [1/2(0+21+23+24+2 n-3 +2Y n-2 +2Y n-1 +Yn)]

    =>(A)= [0/2+21/2+22/2+23/2+24/2+2n-3/2+2Yn-2/2+2Yn-1/2+Yn/2]

    =>(A)=[0/2+1+2+3+4+n-3+Yn-2+ Yn-1+Yn/2]

    =>()= [1/2(0+n) +Y1+Y2+Y3+Y4+Yn-3+Yn-2+n-1]

    , ,

    .

    1.

    15m, 2,5m 5,81m , 5,55 m , 5,25m , 4,75m , 4,06m , 3m , 0,62m . ;

  • . / /

    113

    CENTER LINE :

    =2 [6/2 +5+4+3+2+1+0/2] =>

    =2*2,5[5,81/2+5,55+5,25+4,75+4,06+3+0,62/2] =>

    =5*25,825=>

    =129,125m 2

    . . , .

    , () () .

    1. , , 2/3 ..2

  • . / /

    114

    2.

    F1= F2 =.

    F1 :

    f1=2 [(Y1+Y3)/2] 2/3 f2 h=, h= Y2-[(Y1+Y3)/2] (1).

    1

    2 :

    (1) h=-Y1

    (2) h=-Y2

    (3) h=-Y3

    (1),(2),(3)h=-Y1=-Y2=-Y3 (1),(2) -Y1=-Y2=h Y2-Y1=-=h (4) (2),(3) -Y2=-Y3=h =>Y2-Y3 =-=h (5) (4),(5) Y2- Y1 =h (i) , Y2-Y3=h (ii)

    (i)+(ii)=>Y2+Y2-Y1-Y3=2h =>2Y2-Y1-Y3=2h => h=(2Y2/2)-[(Y1-Y3)/2]=>h=Y2-[(Y1 Y3)/2]

    To f2 :

    f2=2/3*2 h=4/3 [Y2-(Y1+Y3)/2]

    F1=f1+f2

    F1 = f1+f2 = 2 [(Y1+Y3)/2] + 4/3 [2-(1+3)/2] =

    = 2 [(Y1+Y3)/2] + [4/3(Y2)]-[4/3 (Y1+Y3)/2]=

    = [(Y1+Y3)/2] [2-4/3] +4/3 (Y2) =

    = [(Y1+Y3)/2] [(6 - 4)/3] + 4/3(Y2)=

    = [(Y1+Y3)/2] (2/3) + 4/3(Y2) = [(Y1+Y3)/2] (2/3) + (2/3) (Y2) + (2/3) (Y2)=

    = /3[[2(Y1+Y3)/2] + 2Y2 +2Y2]= /3[Y1+Y3+4Y2]= /3[Y1+4Y2+Y3]

  • . / /

    115

    F2==/3 [Y3+4Y4+Y5]

    F : F=F1+F2= [/3 (Y1+4Y2+Y3)]+[/3(Y3+4Y4+Y5)]=

    =/3[Y1+4Y2+Y3+Y3+4Y4+Y5]=/3[Y1+4Y2+2Y3+4Y4+Y5]

    1 .

    1 ( ) ( ) .

    , , . .

    2

    y=x2

    ) 20

    X

    X

    y(x) dx = 20

    X

    X

    x 2 dx = [x3/3] 20xx = [(x 2)

    3/3] [03/3] = (x2)3/3 (1)

    ) x1/3 (Y0+4Y1+Y2) = 1/3 x1 [4(x1)2 + (x2)2]

    x1 = x2/2

    1/3 x2/2 [ 4(x2/2)2 +x22]=x2/6 [4 (x22/4) + x22] = x2 /6 (x22 +x22 ) = x2/6 2x22 =x23/3 (2)

    (1) (2) :

  • . / /

    116

    20

    X

    X

    y(x) dx = 1/3 x 1(Y0 + 4Y1 Y2 )

    2. 1 , 1 .

    / . . 1 0,62 1 0,62 2 3 4 12,00 3 4,06 2 8,12 4 4,75 4 19,00 5 5,25 2 10,50 6 5,55 4 22,20 7 5,81 1 5,81

    (1) 78,25

    = 2,5m :=1/3 x 2,5 x 78,25 = 65,21 m2

    = 2 x 65,21=130,42 m2

    3

    4 , , . :

    (=0m , = 6,1824m, =9,0804m , A=11,109m).

    ( 1= 12,529m , 2= 14,555m , 3= 14,49m , 4= 14,149m 5=14,49m , 6=14,49m , 7=14,49m , 8= 14,388m , 9= 11,553 m ).

    (=8,887m , =5,119m , =0m).

    =3,64m

    . (h) = 10 m .

    =3,57m.

  • . / /

    117

    FR. FR .1 , FR.1 FR.9 FR.9 FR.

    :

    E1=1/3 h1 [() +4() + 2() + 4 () + (1)]

    2 = 1/3 h[(1)+ 4 (2) + 2(3) ++ 4(8) + (9) ] (1)

    3=3/8 h2 [ (9)+ 3()+3() +()]

    h1 = 3, 29 x 1,105 = 3,64m

    h = 9, 05 x 1,105 = 10m

    h2 = 3, 23 x 1,105 = 3,57m

    h1/h = 3,64 / 10 h1 = 0,364h h2/h = 3,57 /10h2 = 0,357h

    9,05 .

    1,105 :

    /= [ . ] / [ . ] = 10/9,05 = 1,105.

    (1) :

    1= 1/3 x 0,364 h x [() + 4 () + 2 () + 4() + 1 ]

    2= 1/3x h x [(1) + 4(2) + 2(3) + +4(8) + (9)] (2)

    3 =3/8 x 0,357 h x [(9) + 3() + 3() + ()]

  • . / /

    118

    : 3/8 x 0,357 h = 9/8 x 0,357 x h/3= 0,402 h/3

    (2) :

    1 =1/3 x h x [0,364 ( ) +1,456 () + 0,728() + 1,456() +0,364(1)]

    2 = 1/3 x h x [ (1) + 4(2) +2(3) ++4(8) +(9)]

    3 = 1/3 x h x [0,402(9) +1,206() + 1,206() + 0,402()]

    .

    ) (, , ) ( , ), 4 , FR FR1 , FR 1 FR 9 FR 9 FR.

    ) .

  • . / /

    119

  • . / /

    120

    / .

    .

    .

    0 0,966 0 0,364 0 6,4 0,966 6,1824 1,456 9,002 9,4 0,966 9,0804 0,728 6,611 11,5 0,966 11,109 1,456 16,175 1 12,97 0,966 12,529 1,364 17,09 2 14964 0,966 14,455 4 57,821 3 15 0,966 14,49 2 28,98 4 15 0,966 14,49 4 57,96 5 15 0,966 14,49 2 28,98 6 15 0,966 14,49 4 57,96 7 15 0,966 14,49 2 28,98 8 14,894 0,966 14,388 4 57,55 9 11960 0,966 11,553 1,402 16,1977 91997 0,966 8,887 1,206 10,718 52991 0,966 5,119 1,206 6,1745 0 0,966 0 0,402 0 1= 400,198

    h=10m

    E = 31 x h x 1 =

    31 x 10 x 400,198 =>

    E =1333,9927m2

  • . / /

    121

    3/8

    3 ( 3). , , , 3 : 3/8 (0+ 31 + 32+ 3) . : 4

    3

    / (m) .

    1 4 1 4 2 3,5 3 10,5 3 3 3 9 4 2,5 1 2,5

    1= 26 =3 (1+32+33+4) => 3 . 1,5 . 26 => =14,625 m2 8 8

  • . / /

    122

    3 .. 9

    : 1 3 3 1 1 3 3 1 1 3 3 1 = 3 . . (1+32+33+24+35+36+27+38+39+10) 8

    , (.4)

    , . (5 0 +81-2) 12

    4

  • . / /

    123

    : 5 . 4 4,5 m 0=2,00m 1=2,5m 2=2,4m. ,

    1 (A)

    / .

    .

    1 2 5 10 2 2,5 8 20 3 2,4 -1 -2,4

    1= 27,6

    = . 121 (50 +81-2) => = 12

    5.4 . 27,6=10,35 m2

    2 =()

    / .

    .

    1 2,4 5 12 2 2,5 8 20 3 2 -1 -2

    1= 30 2= 1= 4,5 .30 =11,25 m2 12 12 ()= 1+2=10,35+11,25=21,6 m2 1

    / .

    .

    1 2 1 2 2 2,5 4 10 3 2,4 1 2,4

    1= 14,4

    =31 *h*1=

    31 *4,5*14,4=21,6m 2

  • . / /

    124

    (center of Flotation) () (F).

    , , , , .

    5

    .5 f y1 x .x . Lcf :

    = = x = (m)

    F

    = F. (m3)

    Y1-Y7 n .

  • . / /

    125

    ( ), , n .

    () .

    . 1.

    , , , ..., , .

    6

    .. 6 ( . . ) /2 /2 . : , . . /2 = 2 .

  • . / /

    126

    . . /2 =1/2 2 . ( ) , ( ) . 6 : X = 2 = . = 2 = .

    , , . . , 5, (1 7 ...) , , .

  • . / /

    127

    : 6

    WL 4 , . , :

    ( = 0 M , = 6,1824 , = 9,0804 , = 11,109 ) . (1= 12,529 , 2=14,455 , 3=14,49 , 4=14,49 , 5= 14,49 , 6=14,49 , 7=14,49 , 8=14,388 , 9=11,553 ) ( =8,887 , =5,119 , =0 ) =3,64 . (h) =10 = 3,57

    .

    / .

    0 0,364 0 -5,456 0 6,1824 1,456 9,002 -5,092 45,836 9,0804 0,728 6,611 -4,728 31,255 11,109 1,456 16,175 -4,364 70,586 1 12,529 1,364 17,09 -4 68,359 2 14,555 4 57,821 -3 173,462 3 14,49 2 28,98 -2 57,96 4 14,49 4 57,96 -1 57,96 5 14,49 2 28,98 0 -505419 6 14,49 4 57,96 1 57,96 7 14,49 2 28,98 2 57,96 8 14,388 4 57,55 3 172,6512 9 11,553 1,402 16,1977 4 64,771 8,887 1,206 10,718 4,357 46,698 5,119 1206 6,1745 4,714 29,107 0 0,402 0 5,071 0 1= 400,198 429,1468 2= -76,2718

  • . / /

    128

    : = 1 . h 1 = 1 . 10 . 400,198 = 1333,9927 2 3 3 = h . 1 . h . 2 => = h2 . 2 => = 102 . (-76,2718) => = - 2542,3933 m3 3 3 3 Lcf = M= -2542, 3933 m3 = -1,90 m E 1333, 9927 m2 :

    ( Lcf ) : = = h2 . 2 : h . 1 = h . 2 , 3 3 1 2 ( , ) .

    Lcf = -1,90 m 1,9 m 5.

    Lcf : Lcf = h . 2 1

  • . / /

    129

    , , . 5 , - , . X2 (m4 cm4 ). , , , , , , , . . , . ( J ) ( J1 ) . .

    , . , , , , : JL = J0 + A2 J0 = JL A2 : JL = . J0 = . = . = .

  • . / /

    130

    7 .

    ( WL4 ) WL4 6 : 1. () 2. ( Lcf ) 3. () 4. ( JL ) . 5. (J0) . 6. (J) 7. (Cw ) 8. T.P.C. 9. ( BML ) 10. ( BMT )

  • . / /

    131

    (WL4)

    1 2 3 4 5 6 7 8 9

    A/A

    JL

    JT

    WL 4 WL 4 (2x3) 5 (4x5) (5x6) (3x8)

    0 0,364 0 -5,456 0 0 0 0

    6,1824 1,456 9,002 -5,092 45,836 233,397 236,304 344,059

    9,0804 0,728 6,611 -4,728 31,255 147,772 748,712 545,062

    11,109 1,456 16,175 -4,364 70,586 308,039 1370,96 1996,1178

    1 12,529 1,364 17,09 -4 68,359 273,433 1966,75 2682,647

    2 14,555 4 57,821 -3 173,462 520,387 3020,455 12081,82

    3 14,49 2 28,98 -2 57,96 115,92 3042,322 6084,644

    4 14,49 4 57,96 -1 57,96 57,96 3042,322 12169,288

    5 14,49 2 28,98 0 -505,419 0 3042,322 6084,644

    6 14,49 4 57,96 1 57,96 57,96 3042,322 12169,288

    7 14,49 2 28,98 2 57,96 115,92 3042,322 6084,644

    8 14,388 4 57,55 3 172,6512 317,954 2978,277 11913,108

    9 11,553 1,402 16,1977 4 64,771 259,164 1542,12 2162,052

    8,887 1,206 10,718 4,357 46,698 203,464 701,932 846,529

    5,119 1,206 6,174 4,714 29,107 137,208 134,202 161,8476

    0 0,402 0 5,071 0 0 0 0

    1=400,198 429,1468 3=2948,58 4=75325,75

    2=-76,2718

    1. A = 1/3h x 1 = 1/3 x 10 x 400,198 = 1333, 9927 m2 2 .= h 2= 10(-76,2718) = -1,905 m = = - 2542,39 = -1,905m 1 400,198 1333,9927

    3. JL=h3/3 x 3 = 103/3 x 2948,577 = 982,859 m4

    4. J0= JL-A2 = 982,859-(1333, 9927x (-1, 9) 2 ) =978043, 29 m2

    5. JT =h/9 x 4 = 10/9 x 75325, 75 = 83695, 2778 m4

    6. Cw = A = 1333, 9927 = 0, 87 L x B 105, 27 x 14, 49

    7. T.P.C = A x 1, 025 = 1333,9927 x 1, 025 = 13,67 t/cm 100 100

    8. BML= J0 = 978043,29 (m4) =93,52m V 10457,686 (m3)

  • . / /

    132

    9. BMT =JT = 83695, 2778m4 =8,003m

    V 10457,686m3

    10.M= h2/3 2 = 102/3(-76,2718) = - 2542,39m3

    BML , BMT V WL4 .

  • . / /

    133

    . :

    ) .

    ) , .

    ) ,

    ) .

    1 , . . .

    , .

    , ( ) . .

    .

    ( ).

    , , , , .

    (center line) ( ).

  • . / /

    134

    .

    8.

    WL3(7, 05 m) .

    WL3

    / / /

    C1 0 2 1/2 87 6 1/2 96 B1 1 3 93 7 95 A1 2 3 1/2 95 7 1/2 93 0 3 4 96 8 87

    1/2 20 4 1/2 96 8 1/2 76 1 43 5 96 9 55

    1 1/2 65 5 1/2 96 D1 37 2 80 6 96 E1 19 F1 0

    C1 0 =1,2m 0, , 18, 8 , 9=5m 9 F1 =3,3m WL 3 7, 05m . FR. C1 FR.0, FR.0 FR.9 FR.9 F .

    : V1=3 x h1 x [(C1) +3 (B1) +3 (A1) + (0)]

    8 V2 = 1 x h [(0) + 4() + 2(1) ++4(8 ) + (9)] [1] 3 V3 = 3 x h2 x [(9) + 3(D1) + 3(E1) + (F)]

    8 h1 M = 1,2 m h1= 1,2 =0,24 h1=0,24h h=5m h 5

  • . / /

    135

    h2 R = 3,33m

    h2 = 3,3 = 0,66 h2 =0,66h h 5 [1] : V1=3 x 0,24h x [(C1) +3 (B1) +3 (A1) + (0)] 8 V2=1 x h x [(0) +4() +2(1) ++4(8 ) + (9) [2] 3

    V3=3 x 0,66h x [(9) +3(D1) +3(E1) + (F)] 8 3 x 0,24 x h = 9 x 0,24 x h = 0,27 x h 8 8 3 3

    3 x 0, 66 x h = 9 x 0, 66 x h = 0,742 x h 8 8 3 3

    [2] :

    V1=1 x h x [0, 27 (C1) + 0, 81(B1) + 0, 81(A1) + 0, 27(0)] 3 V2=1 x h x [(0) +4() + 2(1) ++4 (8 ) + (9)] 3 V3=1 x h x [0,742(9) + 2,226(D1) +2,226(E1) +0,742(F)]

    3

    = 5m.

  • . / /

    136

    1 2 3=1+2 4 5=3x4

    A/A

    .

    C1 0 0,27 0 -0,72 0 B1 1 0,81 0,81 -0,48 -0,3888 A1 2 0,81 1,62 -0,24 -0,3888 0 3 1,27 3,81 0 0 20 4 80 1 80 1 43 2 86 2 172

    1 65 4 260 3 780 2 80 2 160 4 640

    2 87 4 348 5 1740 3 93 2 186 6 1116

    3 95 4 380 7 2660 4 96 2 192 8 1536

    4 96 4 384 9 3456 5 96 2 192 10 1920

    5 96 4 384 11 4224 6 96 2 192 12 2304

    6 96 4 384 13 4992 7 95 2 190 14 2660

    7 93 4 372 15 2580 8 87 2 174 16 2784

    8 76 4 304 17 5168 9 55 1,742 95,81 18 1724,58

    D1 37 2,226 82,362 18,66 1536,87 E1 19 2,226 42,294 18,132 766,87 F1 0 0,742 0 18,192 0.00 1= 4.494,71 2= 42.839,54

    WL3(7,05m) V=1/3 x 5 x 4.494, 706=7.491, 176m3 0 WL3 = h x 2 = 5x 42.839,5424 =47,66 1 4.494,706 50 47,66=2,34m ( FR.5)

  • . / /

    137

    : 9 , WL 4 = 9,4 . : WL 0 = 102,6187 M2 WL 1 = 1084,5317 M2 WL 2 = 1168,724 M2 WL 3 = 1264,1683 M2 WL 4 = 1333,9927 M2 h = 2,35 WL 4 .

    /

    .

    WL .

    . 0 102,6187 1 102,6187 0 0 1 1084,5317 4 4338,1268 1 4338,1268 2 1168,724 2 2337,448 2 4647,896 3 1264,1683 4 5056,6732 3 15170,02 4 1333,9927 1 1333,9927 4 5335,9708 1= 13168,859 2= 29519,014

    V= 1/3 x h x 1 => V= 1/3 x 2,35 x 13168,859 => V= 10315,607 M3

    n= h . 2 => n = 2,35 . 29519,014 => n = 5,27 M

    1 13168,859

  • . / /

    138

    ( HYDROSTATIC CURVES)

    ( Hydrostatic curves ) . .

    . . .

    1 . (V) ,

    2 . Lcb

    . ( WL ) , :

    1. ( Lcf =Longitudinal centre of Floatation ).

    B2. ().

    3. (JL) )( .

    4. (J) Lcf .

    5. (JT) .

    B6. (Cw) .

    7. ..C. .

    8. (L ) .

    9. (t) .

    10. .

    11. (n) .

    12. .

    V. = V x 1,005 3

    13. .

    ) D = V x 1 t .

    ) D = V x 1,025 t .

  • . / /

    139

    . :

    1 . : Cw = A .

    L x b

    2 . : Cb = V .

    L x b x i

    3 . : C = A .

    B x i

    4 . : Cp = V .

    AM x L

    5. : Cpv = V .

    i x A

    . . : T.P.C. = A (M2) x 1,025 (MT/ CM)

    100

    . P.I. = A (ft2) (LT/ in)

    420

    T.P.C : TONS PER CM = .

    . P.I : TONS PER inch = .

    .

    . (WL). :

    1 . : BML = Jo (M)

    V

    2 . : BMT = JT (M)

    V

  • . / /

    140

    . WL . :

    P. = Jo

    L

    . (2) (WL).

    1. Olsen :

    = L x B x ( 1,22 x d + 0,46) x (Cb + 0,765) M2

    B

    2. Normand :

    = L x [1,52 x d +(0,374 + 0,85(Cb)2) x B] M2

    :

    1. (V) .

    2. (WL) Olsen Normand .

    ( Hydrostatic curves ) .

    1.

    .

    i) .

  • . / /

    141

    .. FR.M = 10,1 = 0,8080

    HFR.B 12, 5

    :

    HFR.M=0, 8080 HFR.M = 0, 8080 HFR.B

    HFR.B

    ii)

    HFR.B = 12,5 =1,2376

    HFR.M 10,1

    HFR.M 1,2376 = HFR.B

    HFR.M = HFR.B

    1, 2376

    . .

    i) .

    . = 14,42 =0,87926

    16,4

    :

    = 0,87926 =0,87926

    . 8m

    =0,87,926x 8=7,034m

  • . / /

    142

    ii) , = 16, 4 = 1, 1373

    . 14,42

    :

    . = 1,14

    .

    =

    1,14

    (8m) . ii :

    = 1373.18 = 7,034

    )

    i) .

    . = 14,95 = 1,64285

    9,1

    :

    = 1,64285 =1,64285 x

    ii) = 9, 1 = 0, 60869

    14,95

    :

    = 0,60869 =

    0,60869

  • . / /

    143

    i) . :

    D

    (D)

    (D)

    ii) ( BL =D) . :

    HWL

    HWL

  • . / /

    144

    2. .

    () WL4 ( 18,19)

    1 2 3 4 5 6

    .

    / .

    WL 4

    WL 4 ( 2 x 3 ) ( 4 x 5 ) 0 0,364 0 0 0 6,1824 1,456 9,002 0,364 3,278 9,0804 0,728 6,611 0,728 4,813 11,109 1,456 16,175 1,092 17,663 1 12,529 1,364 17,09 1,456 24,883 2 14,555 4 57,821 2,456 142,008 3 14,49 2 28,98 3,456 100,155 4 14,49 4 57,96 4,456 258,2698 5 14,49 2 28,98 5,456 158,115 6 14,49 4 57,96 6,456 374,189 7 14,49 2 28,98 7,456 216,075 8 14,388 4 57,55 8,456 486,643 9 11,553 1,402 16,1977 9,456 153,165 8,887 1,206 10,718 9,813 105,176 5,119 1,206 6,1745 10,17 62,795 0 0,402 0 10,527 0 1= 400,198 2= 2107,2278

  • . / /

    145

    1) 5 h=10 m. 2) . = h 2 = 10 x 2107,2278 = 52,655 m 1 400,198 L WL 5 . =54,56m =54,56-52,655=1,905m )0(. 1. 5 WL4

    ,,..6,7,8,9,,,. h.

    2. ( ) 5

    , h 10. 5 10 =2/1 =h 2/1 1,905 (0).

    3. 3 6 WL4 :

    ) . 5. ) (WL4). ) . 1 , =1,905 )0( . 6 .

  • . / /

    146

    () WL4 . 1 ( 18.19).

    1 2 3 4 5 6

    .

    / .

    WL 4

    -

    WL 4 ( 2 x 3 )

    1 ( 4 x 5 ) 0 0,364 0 -1,456 0 6,1824 1,456 9,002 -1,092 -9,8302 9,0804 0,728 6,611 -0,728 -4,813 11,109 1,456 16,175 -0,364 -5,888 1 12,529 1,364 17,09 0 0 2 14,555 4 57,821 1 57,821 3 14,49 2 28,98 2 57,96 4 14,49 4 57,96 3 173,88 5 14,49 2 28,98 4 115,92 6 14,49 4 57,96 5 289,8 7 14,49 2 28,98 6 173,88 8 14,388 4 57,55 7 402,85 9 11,553 1,402 16,1977 8 129,5816 8,887 1,206 10,718 8,357 89,57 5,119 1,206 6,1745 8,714 53,805 0 0,402 0 9,071 0

    1= 400,198 1545,067 -20,5312 2= 1524,5358

    = h 2 =10 x 1524,5358 = 38,0945382m 1 400,198 .1 =40 m. =40-38,0945 = 1,905 . , .

  • . / /

    147

    . , : 1 : 2 : 3 : () 4 : (L.C.B.) 5 : 6 : (L.C.F.) 7 : (T.P.I.)(t/in.) (T.P.C.)(t/cm) 8 : ()

    9 : (M.C.I.) ( t ft in ) (M.C.T) ( t m cm

    (L.C.B.) (L.C.F.) .