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    UNIVERSITATEA POLITEHNICA DIN TIMI OARAFACULTATEA DE CONSTRUC IIDEPARTAMENTUL DE MSURTORI TERESTRE I CADASTRU

    RECUCEREA OBSERVAIILOR GEODEZICE PESUPRAFAA ELIPSOIDULUI DE REFERIN

    Prof. Coordonator, Student:Conf. Dr. Ing. Grecea Carmen andr M!"ae#a

    E$%e foar%e !m&or%an% de re'!n% c( )na!n%e de a f! fo#o$!%e )n ca#c#e* o+$er,a'!!#e geode-!ce $e redc

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    #a $&rafa'a e#!&$o!d#! de refer!n'.Acea$% o&era'!e e$%e nece$ar )n%rc/% o+$er,a'!!#e de %eren $n% ra&or%a%e #a ,er%!ca#a &e

    geo!d* da%( de &o-!'!a f!r#! c m+* )n %!m& ce ca#c#e#e $e efec%ea-( &e e#!&$o!d d&( ceo+$er,a'!!#e !n$%rmen%a#e a fo$% &ro!ec%a%e &e e#!&$o!d# de refer!n'* d&( norma#a #a ace$%a.

    Pen%r ca#c## corec'!!#or de redcere &e e#!&$o!d a o+$er,a'!!#or geode-!ce e$%e nece$ar

    de%erm!narea &rea#a+!# a ond#a'!!#or geo!d#! 0N1 2! a com&onen%e#or de,!a'!e! ,er%!ca#e! 3*4.Adcerea re'e#e#or geode-!ce de $&r!5!n* e6!$%en%e &e $&rafa'a f!-!c a Pm/n%#!* &e

    $&rafa'a e#!&$o!d#! de refer!n' $e &oa%e rea#!-a d& ma! m#%e me%ode* d!n%re care $e ,ormen'!ona ce#e ma! !m&or%an%e.

    Metoda desfurrii. E#emen%e#e m$ra%e &e $&rafa'a f!-!c a Pm/n%#! $e redc #a$&rafa'a geo!d#! 7#a n!,e## mr!!8 rm/nd $ f!e $&$e ne! com&en$r!* )n fnc'!e de geome%r!are'e#e! de %r!ang#a'!e.

    Pen%r ca#c#e $e a#ege npunct fundamental, )n care $e con$!der c e#!&$o!d# de refer!n'e$%e %angen% #a geo!d. De a$emenea* $e acce&% !den%!%a%ea d!n%re coordona%e#e a$%ronom!ce 2! ce#egeode-!ce* &recm 2! co!nc!den'a norma#e! #a e#!&$o!d c ,er%!ca#a #a geo!d.

    Re-#% a$%fe# datele iniiale ale triangulaiei9 coordona%e#e geode-!ce a#e &nc%#!

    fndamen%a#* #ng!mea 2! a-!m%# ne! #a%r! care ne2%e ace$% &nc% c n &nc% oarecare a# re'e#e!de %r!ang#a'!e. Ca#c#e#e $e efec%ea- )n con%!nare &r!n de$f2rare: &orn!nd d!n &nc%#fndamen%a# $e de%erm!n coordona%e#e %%ror &nc%e#or re'e#e!* fo#o$!nd;$e e#emen%e#e red$e #a$&rafa'a geo!d#!* fr a $e ma! rea#!-a %recerea #or #a $&rafa'a e#!&$o!d#! de refer!n'.

    Me%oda de$f2rr!! !n%rodce eror! $!$%ema%!ce de ca#c#* care $e mre$c &e m$ra)nde&r%r!! de &nc%# fndamen%a# 2!* ca rmare* &oa%e f! %!#!-a% nma! &en%r %er!%or!! re#a%!,m!c!* &en%r care $e &oa%e adm!%e c e#!&$o!d# de refer!n' )nf2oar o&%!m $&rafa'a geo!d#!. Inace$% mod $;a ca#c#a% %r!ang#a'!a &r!mord!a#( de ord!n# I d!n 'ara noa$%r* d!na!n%ea ce#! de;a#do!#ea r-+o! mond!a#* &e e#!&$o!d# !n%erna'!ona#Hayford. Pnc%# fndamen%a# $;a con$!dera% )no+$er,a%or# a$%ronom!c m!#!%ar d!nDealul Piscului c ,!-( de or!en%arespre Foiorul de foc.

    Metoda proiectrii

    Metoda PizzettiMetoda Bruns- Helmert

    Reducerea observaiilor zenitale la normala la elipsoid

    E$%e cno$c% fa&%# c( )n re'e#e#e geode-!ce de $&r!5!n*

    e#emen%e#e de an!me%r!e 7X, Y $a B, L) a ca $&rafa'( de refer!n' an# de &ro!ec'!e $ae#!&$o!d# de refer!n'* !ar e#emen%e#e de a#%!me%r!e a ca $&rafa'( de refer!n'( geo!d# $ac,a$!geo!d#. A$%fe#* redcerea o+$er,a'!!#or -en!%a#e #a norma#a #a e#!&$o!d n ma! are $en$.

    Redcerea o+$er,'!!#or -en!%a#e #a norma#a #a e#!&$o!d e$%e nece$ar nma! )n ca-#o&era'!!#or efec%a%e )n geode-!a %r!d!men$!ona#* nde %oa%e ce#e %re! coordona%e (X, Y, H$aB, L,

    H) $e e6&r!m )n ra&or% de $&rafa'a e#!&$o!d#! de refer!n'.In f!gra

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    F!g.

    = =

    < < > >: ! ! u ! ! u = + = +

    Ung"!r!#e 0u"# 2! 0u $# re&re-!n% co%ponentele de&iaiei &erticalei pe direcia "'$, dea-!m% 01* de%erm!na%e )n &nc%e#e < 2! >.

    E6&r!m/nd de,!a'!a ,er%!ca#e! )n fnc'!e de com&onen%e#e B31* B41 2! a-!m%# d!rec'!e! $eo+'!ne9

    co$ $!nu = +

    =

    < < < > > >

    co$ $!n :

    co$ $!n

    ! !

    ! !

    = + +

    = + +

    Ung"!r!#e -en!%a#e red$e #a norma#a #a e#!&$o!d $e %!#!-ea-( #a ca#c## n!,e#men%#!geode-!c $!m#%an 2! rec!&roc* a$%fe#9

    > < < > > < > < < > > >

    %

    (

    H ! ! ) ) * *

    H H H D tg+

    = = + + +

    )n care9

    < >

    >%

    H HH

    +=

    H ;a#%!%d!n!#e a&ro6!ma%!,e a#e &nc%e#or < 2! > care $e &o% e6%rage de &e "ar%(:RA;ra-a $ec'!n!! norma#e de a-!m% BA1*&en%r #a%!%d!nea med!e Bm a ce#or do( &nc%e:I!2! S! )n(#'!mea !n$%rmen%#! 2! $emna##! )n &nc%# B!1.In ca-# n!,e#men%#! %r!gonome%r!c n!#a%era# n $e 5$%!f!c( redcerea ng"!r!#or -en!%a#e

    #a norma#a #a e#!&$o!d )n%rc/% eror!#e de refrac'!e $n% m#% ma! mar! fa'( de corec'!!#e de redcere

    #a norma#a #a e#!&$o!d.

    Reducerea distanelor pe elipsoid

    In fnc'!e de ca%egor!a a&ara%e#or %!#!-a%e* m($rarea #a%r!#or 7+a-e#or8 nece$are )n&re#crarea re'e#e#or geode-!ce $e rea#!-ea-( )n mod d!fer!% 9

    c a5%or# f!r#! de !n,ar: c a5%or# a&ara%e#or e#ec%ron!ce.

    In fnc'!e de ace$%ea 2! redcerea d!$%an'e#or &e $&rafa'a de refer!n'( *$e ,a face )n modd!fer!%.

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    Reducerea bazelor geodezice msurate cu firul de invar

    Lng!mea +a-e! geode-!ce d, m$ra% c f!r# de !n,ar 2! &re#cra% )n &rea#a+!# d&me%odo#og!a cno$c%* $e redce #a o $&rafa' de n!,e# med!e* $!%a% #a a#%!%d!nea 0Hm19

    < >

    >%

    H HH +=

    nde 9H"2!H$$)n% a#%!%d!n!#e ca&e%e#or +a-e!.

    Pen%r redcerea* )n con%!nare* a +a-e! #a e#!&$o!d $e &oa%e &roceda a$%fe# 9

    >

    %

    H HH

    +

    =

    F!g.> Redcerea +a-e#or #a e#!&$o!d

    In #!m!%a a&ro6!ma'!!#or adm!$!+!#e $e &oa%e )n#oc! $&rafa'a e#!&$o!d#! c $&rafa'a$fer!c( de ra-( BRA1* #a #a%!%d!nea med!e a ca&e%e#or +a-e!.

    =G co$d d u=

    nde9co$ $!n

    % %u = +

    < > < >:> >

    % % + += =

    >8 Se ca#c#ea-( +a-a red$( #a n!,e## e#!&$o!d#! d!n re#a'!a9

    G

    ( ( %

    s d

    + + H=

    +

    de nde9

    G G G7< 8

    ( % % %(

    ( % ( % (

    + H H H+

    s d d d+ H + H +

    +

    = = + +

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    Pr!n de-,o#%area )n $er!e a re#a'!e! de ma! $$ re-#%(9

    G7< ...8

    % %

    ( (

    H Hs d

    + +

    = +

    A#%!%d!n!#e e#!&$o!d!ce a#e ca&e%e#or +a-e! $e ca#c#ea-( )n fnc'!e de co%e#e or%ome%r!ce 2!ond#a'!!#e geo!d#! .

    Pen%r redcerea r!groa$( a +a-e#or m($ra%e c f!r# de !n,ar* #a $&rafa'a e#!&$o!d#! derefer!n'(* $n% nece$are com&onen%e#e de,!a'!e! ,er%!ca#e! 2! ond#a'!!#e geo!d#! )n &nc%e#e deca&(% a#e +a-e!.

    Reducerea laturilor msurate cu aparate electronice

    La%r!#e m$ra%e c a5%or# a&ara%e#or e#ec%ron!ce de %! $%a'!!#or %o%a#e* %e#rome%re#or

    e%c* $n% &re#cra%e de a$emenea )n &rea#a+!#* &r!n a!carea a2a nm!%e#or corecii fi!ice. D!$%an'a Dre-#%a% d& acea$% o&era'!e e$%e $!%a% #a n!,e## ce#or do &nc%e* )n%re care $;a efec%a%

    m$r%oarea. Re-#% c e$%e nece$ar cnoa2%erea a#%!%d!n!#or e#!&$o!d!ce < < H si H * 2! &r!n

    rmare* a ond#a'!!#or geo!d#! )n ace$%e &nc%e.Se o+$er,( c( n e$%e nece$ar( cnoa2%erea de,!a'!!#or ,er%!ca#e#or )n &nc%e#e < 2! >* a2a

    cm a fo$% )n ca-# redcer!! +a-e#or m($ra%e c f!r# de !n,ar* dar &en%r de%erm!narea co%e#ore#!&$o!da#e $n% nece$are ond#a'!!#e geo!d#! )n ace$%e &nc%e.

    ILIOGRAFIE

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    Conf.n!,.dr.!ng.M!rcea ORTELECAN* GEODEIE* EDITURA ACADEMICPRES* CLU;NAPOCA* >==?