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Reducerea observatiilor la suprafata de referinta
Se considera reteaua din figura de mai jos:
In aceasta retea se cunosc :
coordonatele preliminarii ale punctelor retelei;
azimutul de la A la B ;
latitudinile geodezice ale punctelor retelei;
cotele;
precum si directiile observate si compensate in statie.
Se cere:
Sa se reduca directiile unghiulare orizontale in planul proiectie stereografic 1970 considerand ca elipsoidul de
referinta este Krasovski.
Nr pct |
Denumire |
Latitudine |
Coordonate[m] |
||
X |
Y |
H |
|||
|
Albu (A) |
|
|
|
|
|
Bran (B) |
|
|
|
|
|
Capra(C) |
|
|
|
|
|
Dealu(D) |
|
|
|
|
|
Unu (1) |
|
|
|
|
|
Doi (2) |
|
|
|
|
Directii masurate si compensatate in statii:
Statia Albu(A):
Statia Albu S'o=±1.7 | ||
Punct vizat |
Directie comp.[g c cc] | |
Brad |
| |
Doi |
| |
Capra |
| |
Unu |
| |
Dealul |
|
Statia Brad(B) :
Statia Brad S'0=±4 | ||
Punct vizat |
Directie comp.[g c cc] | |
Capra |
| |
Doi |
| |
Dealul |
| |
Unu |
| |
Albu |
|
Statia Capra (C) :
Statia Capra S'0=±4.2 | ||
Punct vizat |
Directie comp.[g c cc] | |
Dealul |
| |
Unu |
| |
Albu |
| |
Doi |
| |
Brad |
|
Statia Dealu(D) :
Statia Dealul S'0=±4.3 | ||
Punct vizat |
Directie comp.[g c cc] | |
Albu |
| |
Unu |
| |
Brad |
| |
Doi |
| |
Capra |
|
Statia unu (1) :
Statia Unu S'0=±2.6 | ||
Punct vizat |
Directie comp.[g c cc] | |
Albu |
| |
Brad |
| |
Doi |
| |
Capra |
| |
Dealul |
|
Statia doi(2) :
Statia Doi S'0=±3.3 | ||
Punct vizat |
Directie comp.[g c cc] | |
Albu |
| |
Brad |
| |
Capra |
| |
|
| |
Dealul |
| |
Unu |
|
Schita foii de centrare
a) Denumire punct statie ALBU(A):
Ordinal punctului (IV)
Data intocmirii: 02.09.1997
Inceput ora 17:00 - Terminat ora 18:00
Starea timpului : senin,vant din est
Vizibilitate : buna
Numar serii:6
Se dau urmatoarele valori:
l=6.5(cm)
θ=130.7100(g c cc)
l1=6.3(cm)
θ1=87.6500(g c cc)
b) Denumire punct statie Brad(B):
Ordinal punctului (IV)
Data intocmirii: 03.09.1997
Inceput ora 6:00 - Terminat ora 08:00
Starea timpului : senin,fara vant
Vizibilitate : buna
Numar serii:6
Se dau : l=11.5(cm)
Θ=32.2600(gc cc)
Memoriu tehnic
.Corectia de reducere de la sectiunea normala directa la linia geodezica :
(corectia de linie geodezica )
=-ρ[Km] sin2A
ρ=636691.772369
e-prima excentricitate numerica. ;
f -turirea geometrica ;
e= f=
a=semiaxa mare a=6378245(m)
b=semiaxa mica
1/f=298,3
e=2f-f2=0,006693421623
Bm- latitudinea medie intre cele 2 puncte
Rm-raza medie de curbura R=
M= M-raza de curbura a elipsei meridiane
N= N-raza de curbura a primului vertical
W=
s-lungimea liniei geodezice s=√∆x2+∆y2
2.Corectia datorata altitudinii punctului vizat:
C2= ρHsin2A
A- azimutul dintre cele doua puncte
H-altitudinea punctuli vizat
3.Corectia datorata deviatiei verticalei :
C3=(ηcosA-ζsinA)ctgζ
η=componenta in sectiunea primului vertical
ζ=componenta in planul meridian
η=6.513(cc)
ζ=2.881(cc)
ctg ζ=∆H/D
Primele 3 corectii le aplicam masuratorilor pentru a le reduce la elipsoidul de referinta.
4.Corectia de reducere
C4= ρ
l-.distanta dintre proiectia punctului si proiectia instrumentului
Θ-orientarea fata de directia de referinta.
α'-Directii masurate.
5.Corectia de centrare
C5= ρ
l1= distanta dintre proiectia semnalului si a punctului matematic
θ1=orientarea fata de directia de referinta
M1=-Directii masurate.
6.Corectia de reducere la planul de proiectie stereografic 1970
C6=-(C6)= ρ
Xi,Xj,Yi,Yj=coordonatele punctelor vechi.
R0=raza medie Gauss pt. punctul de referinta de coordonate geodezice (B=46 L=26)
Tabel corectia 1
PS |
PV |
|
B |
Bm |
M |
N |
Rm |
s |
Azimut=Θ |
c1 |
[g c cc] |
[s,] |
[s,] |
|
|
[m] |
[km] |
[g c cc] |
[cc] |
||
ALBU A |
BRAD B |
|
|
|
|
|
|
|
|
1.202E-12 |
DOI 2 |
|
|
|
|
|
|
|
9.562E-13 |
||
CAPRA C |
|
|
|
|
|
|
|
1.609E-12 |
||
UNU 1 |
|
|
|
|
|
|
|
-3.724E-13 |
||
DEALUL D |
|
|
|
|
|
|
|
-1.492E-12 |
||
BRAD B |
CAPRA C |
|
|
|
|
|
|
|
|
-1.338E-12 |
DOI 2 |
|
|
|
|
|
|
|
-4.865E-13 |
||
DEALUL D |
|
|
|
|
|
|
|
-1.388E-12 |
||
UNU 1 |
|
|
|
|
|
|
|
-3.549E-13 |
||
ALBU A |
|
|
|
|
|
|
|
1.202E-12 |
||
CAPRA C |
DEALUL D |
|
|
|
|
|
|
|
|
1.929E-12 |
UNU 1 |
|
|
|
|
|
|
|
1.481E-12 |
||
ALBU A |
|
|
|
|
|
|
|
1.609E-12 |
||
DOI 2 |
|
|
|
|
|
|
|
-1.632E-14 |
||
BRAD B |
|
|
|
|
|
|
|
-1.338E-12 |
||
DEALUL D |
ALBU A |
|
|
|
|
|
|
|
|
-1.492E-12 |
UNU 1 |
|
|
|
|
|
|
|
-2.535E-13 |
||
BRAD B |
|
|
|
|
|
|
|
-1.388E-12 |
||
DOI 2 |
|
|
|
|
|
|
|
1.205E-13 |
||
CAPRA C |
|
|
|
|
|
|
|
1.929E-12 |
||
UNU 1 |
ALBU A |
|
|
|
|
|
|
|
|
-3.724E-13 |
BRAD B |
|
|
|
|
|
|
|
-3.549E-13 |
||
DOI 2 |
|
|
|
|
|
|
|
4.315E-13 |
||
CAPRA C |
|
|
|
|
|
|
|
1.481E-12 |
||
DEALUL D |
|
|
|
|
|
|
|
-2.535E-13 |
||
DOI 2 |
ALBU A |
|
|
|
|
|
|
|
|
9.562E-13 |
BRAD B |
|
|
|
|
|
|
|
-4.865E-13 |
||
CAPRA C |
|
|
|
|
|
|
|
-1.632E-14 |
||
DEALUL D |
|
|
|
|
|
|
|
1.205E-13 |
||
UNU 1 |
|
|
|
|
|
|
|
4.315E-13 |
Tabel corectia 2:
PS |
PV |
|
M |
H |
Azimut=Θ |
c2 |
[g c cc] |
|
[m] |
[g c cc] |
[cc] |
||
ALBU A |
BRAD B |
|
|
|
|
|
DOI 2 |
|
|
|
|
|
|
CAPRA C |
|
|
|
|
|
|
UNU 1 |
|
|
|
|
|
|
DEALUL D |
|
|
|
|
|
|
BRAD B |
CAPRA C |
|
|
|
|
|
DOI 2 |
|
|
|
|
|
|
DEALUL D |
|
|
|
|
|
|
UNU 1 |
|
|
|
|
|
|
ALBU A |
|
|
|
|
|
|
CAPRA C |
DEALUL D |
|
|
|
|
|
UNU 1 |
|
|
|
|
|
|
ALBU A |
|
|
|
|
|
|
DOI 2 |
|
|
|
|
1.63E-05 |
|
BRAD B |
|
|
|
|
|
|
DEALUL D |
ALBU A |
|
|
|
|
|
UNU 1 |
|
|
|
|
|
|
BRAD B |
|
|
|
|
|
|
DOI 2 |
|
|
|
|
-4.8E-05 |
|
CAPRA C |
|
|
|
|
|
|
UNU 1 |
ALBU A |
|
|
|
|
|
BRAD B |
|
|
|
|
|
|
DOI 2 |
|
|
|
|
|
|
CAPRA C |
|
|
|
|
|
|
DEALUL D |
|
|
|
|
|
|
DOI 2 |
ALBU A |
|
|
|
|
|
BRAD B |
|
|
|
|
|
|
CAPRA C |
|
|
|
|
2.54E-05 |
|
DEALUL D |
|
|
|
|
-5.6E-05 |
|
UNU 1 |
|
|
|
|
|
Tabel 3:
PS |
PV |
|
H |
∆ H |
D |
ctg ζ |
Azimut=Θ |
c3 |
[g c cc] |
[m] |
[m] |
[m] |
[cc] |
[g c cc] |
[cc] |
||
ALBU A |
BRAD B |
|
|
|
|
|
|
|
DOI 2 |
|
|
|
|
|
|
|
|
CAPRA C |
|
|
|
|
|
|
|
|
UNU 1 |
|
|
|
|
|
|
|
|
DEALUL D |
|
|
|
|
|
|
|
|
BRAD B |
CAPRA C |
|
|
|
|
|
|
|
DOI 2 |
|
|
|
|
|
|
|
|
DEALUL D |
|
|
|
|
|
|
|
|
UNU 1 |
|
|
|
|
|
|
|
|
ALBU A |
|
|
|
|
|
|
|
|
CAPRA C |
DEALUL D |
|
|
|
|
|
|
|
UNU 1 |
|
|
|
|
|
|
|
|
ALBU A |
|
|
|
|
|
|
|
|
DOI 2 |
|
|
|
|
|
|
|
|
BRAD B |
|
|
|
|
|
|
|
|
DEALUL D |
ALBU A |
|
|
|
|
|
|
|
UNU 1 |
|
|
|
|
|
|
|
|
BRAD B |
|
|
|
|
|
|
|
|
DOI 2 |
|
|
|
|
|
|
|
|
CAPRA C |
|
|
|
|
|
|
|
|
UNU 1 |
ALBU A |
|
|
|
|
|
|
|
BRAD B |
|
|
|
|
|
|
|
|
DOI 2 |
|
|
|
|
|
|
|
|
CAPRA C |
|
|
|
|
|
|
|
|
DEALUL D |
|
|
|
|
|
|
|
|
DOI 2 |
ALBU A |
|
|
|
|
|
|
|
BRAD B |
|
|
|
|
|
|
|
|
CAPRA C |
|
|
|
|
|
|
|
|
DEALUL D |
|
|
|
|
|
|
|
|
UNU 1 |
|
|
|
|
|
|
|
Tabel corectia 4:
PS |
PV |
|
|
l |
D |
c4 |
[g c cc] |
[g] |
[m] |
[m] |
[cc] |
||
ALBU A |
BRAD B |
|
|
|
|
|
DOI 2 |
|
|
|
|
||
CAPRA C |
|
|
|
|
||
UNU 1 |
|
|
|
|
||
DEALUL D |
|
|
|
|
||
BRAD B |
CAPRA C |
|
|
|
|
|
DOI 2 |
|
|
|
|
||
DEALUL D |
|
|
|
|
||
UNU 1 |
|
|
|
|
||
ALBU A |
|
|
|
|
Tabel corectia 5:
PS |
PV |
|
|
l1 |
D |
c5 |
[g c cc] |
[g] |
[m] |
[m] |
[cc] |
||
BRAD B |
Albu A |
|
|
|
|
|
DOI 2 |
|
|
|
|
||
CAPRA C |
|
|
|
|
||
UNU 1 |
|
|
|
|
||
DEALUL D |
|
|
|
|
Tabel corectia 6:
PS |
PV |
Ni |
Ei |
Nj |
Ej |
C6 | |
ALBU A |
BRAD B |
|
|
|
|
| |
DOI 2 |
|
|
|
|
| ||
CAPRA C |
|
|
|
|
| ||
UNU 1 |
|
|
|
|
| ||
DEALUL D |
|
|
|
|
| ||
BRAD B |
CAPRA C |
|
|
|
|
| |
DOI 2 |
|
|
|
|
| ||
DEALUL D |
|
|
|
|
| ||
UNU 1 |
|
|
|
|
| ||
ALBU A |
|
|
|
|
| ||
CAPRA C |
DEALUL D |
|
|
|
|
| |
UNU 1 |
|
|
|
|
| ||
ALBU A |
|
|
|
|
| ||
DOI 2 |
|
|
|
|
| ||
BRAD B |
|
|
|
|
| ||
DEALUL D |
ALBU A |
|
|
|
|
| |
UNU 1 |
|
|
|
|
| ||
BRAD B |
|
|
|
|
| ||
DOI 2 |
|
|
|
|
| ||
CAPRA C |
|
|
|
|
| ||
UNU 1 |
ALBU A |
|
|
|
|
| |
BRAD B |
|
|
|
|
| ||
DOI 2 |
|
|
|
|
| ||
CAPRA C |
|
|
|
|
| ||
DEALUL D |
|
|
|
|
| ||
DOI 2 |
ALBU A |
|
|
|
|
| |
BRAD B |
|
|
|
|
| ||
CAPRA C |
|
|
|
|
| ||
DEALUL D |
|
|
|
|
| ||
UNU 1 |
|
|
|
|
|
Tabel centralizator:
PS |
PV |
α |
c1 |
c2 |
c3 |
c1+c2+c3 |
Dir reduse la elipsoid |
c4 |
c5 |
c6 |
Dir
reduse |
ALBU A |
BRAD B |
|
|
|
|
|
|
|
|
|
|
DOI 2 |
|
|
|
|
|
|
|
|
|
|
|
CAPRA C |
|
|
|
|
|
|
|
|
|
|
|
UNU 1 |
|
|
|
|
|
|
|
|
|
|
|
DEALUL D |
|
|
|
|
|
|
|
|
|
|
|
BRAD B |
CAPRA C |
|
|
|
|
|
|
|
|
|
|
DOI 2 |
|
|
|
|
|
|
|
|
|
|
|
DEALUL D |
|
|
|
|
|
|
|
|
|
|
|
UNU 1 |
|
|
|
|
|
|
|
|
|
|
|
ALBU A |
|
|
|
|
|
|
|
|
|
|
|
CAPRA C |
DEALUL D |
|
|
|
|
|
|
|
|
|
|
UNU 1 |
|
|
|
|
|
|
|
|
|
|
|
ALBU A |
|
|
|
|
|
|
|
|
|
|
|
DOI 2 |
|
|
|
|
|
|
|
|
|
|
|
BRAD B |
|
|
|
|
|
|
|
|
|
|
|
DEALUL D |
ALBU A |
|
|
|
|
|
|
|
|
|
|
UNU 1 |
|
|
|
|
|
|
|
|
|
|
|
BRAD B |
|
|
|
|
|
|
|
|
|
|
|
DOI 2 |
|
|
|
|
|
|
|
|
|
|
|
CAPRA C |
|
|
|
|
|
|
|
|
|
|
|
UNU 1 |
ALBU A |
|
|
|
|
|
|
|
|
|
|
BRAD B |
|
|
|
|
|
|
|
|
|
|
|
DOI 2 |
|
|
|
|
|
|
|
|
|
|
|
CAPRA C |
|
|
|
|
|
|
|
|
|
|
|
DEALUL D |
|
|
|
|
|
|
|
|
|
|
|
DOI 2 |
ALBU A |
|
|
|
|
|
|
|
|
|
|
BRAD B |
|
|
|
|
|
|
|
|
|
|
|
CAPRA C |
|
|
|
|
|
|
|
|
|
|
|
DEALUL D |
|
|
|
|
|
|
|
|
|
|
|
UNU 1 |
|
|
|
|
|
|
|
|
|
|
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