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1. #$ ................................. 5

1.1. #% & # ...................................... 5

1.2. .......................................................................................8

1.2.1. "!'( ) (()"*...........................................................................8

1.2.2. #+,! ) (()"* ............................................................................9

1.2.3. # ) (()"* ............................................................................... 9

1.3. ................................................................................................... 91.3.1. ),* .......................................................................................................9

1.3.2. - ),* .................................................................................................... 10

1.3.3. " .................................................................................................................... 11

1.3.4. ( "(. )*")/(. +( ................................................... 11

1.4. #% ............................................................................... 13

1.4.1. + ) (()"* )" , + /"/" ...................... 14

1.4.2. ,(" "*,(" )" ........................................................... 16

1.4.3. "()+" ")+ "0 (()"* – UTM.............................................. 17

2. #................................................................................................................... 18

2.1. # – CONTROL SURVEY ............................................ 19

2.2. # # – TOPOGRAPHIC SURVEY.............................................. 20

2.3. # 12 % – ROUTE SURVEYING.................. 202.4. # # 3 2 –

CONSTRUCTION SURVEY............................................................................................ 21

2.5. # &$ – LAND SURVEY.................................................................... 22

2.6. # – PHOTOGRAMMETRIC SURVEY...................... 23

2.7. 2 # .......................................................................................... 23

2.8. # # ........................................................................................ 24

3. #4 5 # ................................................................................. 25

3.1. , # # ............................25

3.1.1. "")0 3 (()"* ..................................................................................... 25

3.1.2. ")0 3 (()"*................................................................................... 25

3.1.3. ")0 2 (()"*................................................................................... 26

3.1.4. ")0 ) (()"* ................................................... 30

3.1.5. "6 +,!. . )............................................................31

3.2. 4, % 5 ........................ 32

3.2.1. , 6*"7, +" )0" ......................................................................................... 32

3.2.2. " ,! !- +" 6*"7, +" )0" .................................................. 32

3.3. 5 3 4........................................... 34

3.4. %# 3...........................................................................................37

4. 3 #4 5 # ................................................... 39

4.1. 3 #4 5 2 ................. 39

4.1.1. #!( *" ............................................................................................... 39

(),*") "* 6 *""8" , ,!+ , !(* +, ................... 40

#!(" )0" ............................................................................................................ 40()" !(. ++ ............................................................................................44

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6+8" !(! + ........................................................................................ 54

#- *") 6+8 !(! +......................................................... 55

26) )0() ("'/" *""8 , !(* *"* .................. 56



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#()8" !"9 , !(* +* ............................................................... 61

#!( + , )*"6* (), ........................................................ 66

9) "!() "!() !(! + .............................................................67

4.1.2. ()" *")" .6)! 68 ........................................................ 69

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4.1.5. "*")/ +,!. ) ....................................................................... 79

4.2. 3 #4 5 ...................... 824.2.1. "*")/( +"* - !"" +"*................................................... 82

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4.2.2. "7+8" +( )0 *")* )!*")/(! +"* ...................... 91

#"9"8" !"9 , )!*")/(* +"*, ................................................. 93

4.2.3. "7+8" +( )0 "): - "): +"* ......................................... 93

+"* +9 (,). )0 .................................................................................. 94

+"* +9 "'(" +*.................................................................. 95

+"* +9 "'(" +* '!,* ................................................... 96

+"* ,6,! '.......................................................................................... 97+"* "0. '........................................................................................ 99

0,8 +( "):. )0 ............................................................................... 101

4.3. 3 # (3) #4 5............... 103

4.3.1. # *") "7+8 ()! / ...................................................... 103

#/* *" #...................................................................................................... 103

*")" GPS............................................................................................................ 103

4.3.2. #68" )0 GPS )".!/*.......................................................... 106

(,) GPS 68" ................................................................................... 106

'""/" ")+" )"." GPS 68 ................................... 107

4.3.3. GPS "'"") (()"*...................................................................................... 108

"")( ) (()"*................................................................................... 108

WGS84 "'"") "( ....................................................................................... 109

4.3.4. GPS *""8 .......................................................................................................... 109

4.3.5. GPS *" ........................................................................................................ 110

5. # # # # ......................................... 112

5.1. # # .................................................................................. 112

5.1.1. ),* )8.............................................................................................. 112

5.1.2. "'"") ) (()"* )8" ............................................... 113

5.1.3. !'(" )" + ............................................................................ 113

5.1.4. #"()+:8" ":"' )"" ........................................................................... 114



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5.1.5. #() '* ()"* .................................................................... 117

5.1.6. 6" 6" )!'(. ) +.................................................... 118

5.1.7. "*") (/ ) + ................................................................ 118

5.1.8. ) )0() )!'(. ) ) 8* ...................... 119

5.1.9. ) 6*"" !). ) ......................................................... 121

5.1.10. #" ()+" (" "): +...................................................... 121

5.2. # # ....................................................................................... 126

5.2.1. #8" "*" ........................................................................................... 1265.2.2. (()+:8" *)"*)0" (+" "*".................................................... 127

5.2.3. / 0 (*8 )0 "): ......................................................... 129

5.2.4. "." (*8 ("*") .............................................................................. 132

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6. # &$ (LAND SURVEYING), # # #

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6.1. # &$ ............................................................................................. 142

6.1.1. ()" "*" 6"*:9) .................................................................................. 142

6.1.2. "* *")" "*" 6"*:9) ................................................................ 1436.2. # #................................................................................... 147

6.3. # .................................................................................................... 147

6.3.1. #/*, (/ )+() 6 )() ++ ................................. 147

6.3.2. #"* +, )+8", -""+8" (*8" ++ ................... 148

6.3.3. 6 + "!() ++ .................................................................... 152

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:................................................................................................................. 158

.................................................................................................................. 164



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⋅⋅⋅++=ω . (1.4.1-2)

"'*/ , (0,) 66, 1.4.1-1 ( (" /", ,". ,"

*8" 10 km () (" (* + 0 66 1.4.1-2. "'*/" (" +"+/,

,:+8"* ("8"! *"/. ()/8, 90 km, "'*/ 6( 1 dm/km

, )* (,0/, 9 6" 6( 2°15′.

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 50 100 150 200

Y

D e f o r m a c i j a

1.4.1-2: % $ m/ km –

- (" - +" 9 6", ,*"() ! () (" (", /

"(" "( ()/8, 90,18 km, ( -" ()" ("8"! *"/ 6".

*" (" ()" (""":

"'*/ ("8"* *"/, 6" 6(: - 1 dm/km;

"'*/ ()/8, 90,18 km ("8"! *"/ /" ,;

"'*/ /, 6" ( 120 – 130 km ")! *"/) 6( 1

dm/km.

+/ 0 ()!,) /" 9 6" -," 3°.



1

–

16

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 20 40 60 80 100 120 140 160

Y

D e f o r m a

c i j a

1.4.1-3: % $ m/ km – * (ω - 0.0001)

1.4.2. !"& &(!"& $!&' )" )0 /" (" (" 6+/, ("

60+/, (" ( X,Y ( Y*" -) 6)+ "!)+, 6+(

/ )0" "* X (. )" /" (" (" 6+/, ("

60+/, (" ( X,Y . "6 6*"7, + (()"* )

6!"

MXX

MYY

⋅⋅⋅⋅====

⋅⋅⋅⋅====, (1.4.2-1)

!" /" - " *, / 6( = 0,9999.

# 1.4.2-1: ) (, "*,(" )": 48,36222Y −−−−==== 68,2198374X ==== , , ("*/ 6. 0,) *,(" )".

$3:

96,73583649999,068,4837219X

76,6394777)9999,0()48,22362(00,7500000Y

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# 1.4.2-2: )" (, *,(" )":41,6302460X

11,4115327Y

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====. 0,) "*,("

)":

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09,76360649999,0 / 41,4606302X

35,414329999,0 / )00,750000011,7532411(Y

========

====−−−−====

",/ ," ( "( (, 9"* "*", - ,)" +(" +9) d +

/"/" d ( (","* ,) 0, (" "* 66,



1

–

17

d)0001,0R2

Y(dd

2

2

⋅⋅⋅⋅−−−−++++==== . (1.4.2-2)

1.4.3. !&')& $'$) $1& '( – UTM

!- 6 )")/" "*:" /0"9" (" () &

(Universal Transverse Mercator – UTM) / /" "'( *")*

)"! "(.

6, 9", /" ,(+/"" +" /"/", &

(UTM (()"*) " "*:, 60 6. #0") *"/ +" 6" 6(

°°°°==== 180λ , 9 6" 6( 6, (+ 6 (" )"" 84

("+"" !"!'(" 9"

80 /," !"!'(" 9". +""" +9, ("- (, 6+/"" +" "

6". ")/, -/" + 34. 6 / (" ()" 18. 24. *"/ ()0"

!"!'(" ,". UTM *" "'( /" , *")*. + 6 (" /"),/"

/ /" /")( . )" )0

( "'"")! "( , !+/,/ 6 /"),/, (" UTM *",. ,(-

!"+" /"/", "(" ")! *"/ 6" "+) "'9" )

0") +,!! )! (()"*. +" /"/" )" (" (, (,)

"'(" , (, 9 + ) (()"* (X ( /" ,(*"" , +, (), Y ( , +, ("+"). ("+"/ ."*('", )" )! 0")

6(" X0 = 500 000 m, Y0 = 0 m. ) 6*"" /" *":+ "" (" 0.9996 ,

")! *"/ UTM 6" 1.00 ()/8, 180 km ()0 6

")! *"/ 6" (*(* "'*/ 6( 1:2500 4 dm/km).

(+" )"()" UTM /"/" (,:

$ 6": 6 ;

"'"") "(: GRS80;

X ( (" 6 , + "+);

Y ( (" ( ")* *"/* 6";

)" (" 6+/, , *")*;

"8 *"/ 6" * +"() )" =500 000.00 m; ) 6*"" ("8"* *"/, 6( 0.9996;

#+ 6" (" (" 6 6*"7, 180

W 174

W *"/, ("8 – 60. 6

6*"7, 174

E 180 *"/.



1

–

18

2.

: * #" "

$

.

#" )! 9) /" +"9), "*" * (+ ,0 -""/.

#"*" /" /" (:,0+ !"")( (),08 (",/" ". 68 )".* "*" (+, 0"! ,0,/" 6-, /"'(/. *") /" *

"9+8 /6+(/. -"* "*" +" )*. "6,)).

,0 -""/ "*" ()0, 6 *"" ()!. *)"*)0. )". /" (" ()" , - 6 ) )""(. *""8.

6+(() )")* 6"*:" 6+:"(), "*" (" ,(+ *" ") :

#"*" , + (plane surveying),

"")( "*" (geodetic surveying).

$($ " $)&, +9 "*:" (* ( +*"6* + ("'9" X,Y/"). ( (Z H /) (" "'9" , (, ("8 / "*:"

(("8 + *). +" (,0/"+, , "8"(* )()(-)!'(*

"*", *"8,/, (" "*" , +. ("'0* /")*, ,)

,!0. /(. "8"/(. -/") (,)"+ ""6"), 0, (" ,6* , -6

6"*: 6+:"().

!' $($ * "'(8 / )0, "*:, )") , 8"*

* 6+:"* -,. "*: (" -0 (* *)"*)0 "'(*

+9 -)! "(. , "*", , +, +(" (" "'9, , (,

("8, 6"*:, +9 (("8 + *). , !"")( "*" /" ,+"

(*) "*" +(" "6() +". ,0/* (+ !,

)" *"" .) 98" +"*", (+"*" "*" ()" !-" )".!/"

68 (#, , .) /" (" 6(+/, !"*")/(*

-, "*:". + (), 6.)"+ :+ *)"*)0 *"+8" ) "*"

8.+ !7+8" 6.)"+* +((. (()"* "*" (+"*,) /")*

! "*".

6+(() *"", "*" (" *" ") :

#"*" 6 )"-" "6/" *)"*)0" (!"")(") (+" (control survey);

#"*" 6 )"-" "'(8 ! +(9)+ 6"*:9. " (land,

boundary, property survey – "*" 6"*:9));

#"*" *"8" 6, '!,/" )"" / . +"9)0.

-/") (topographic survey – )!'( "*"); #"*" *"8" 6, / +". +9 6 )"-" +!/",

+(-"+8 6!8" -/") + (hydrographic survey- .!'(

"*");

#"*" *"8" )"-* 6!8" "()/" , / ()

" " " +"". - "*" (control, land, topographic) (

:"* )" 6 + +"6. 6 "()/, , (mine surveying –

"*" ,);

#"*" *"8" -""+8,, 8, "8, 6!8" -/") (construction

survey – "8"( "*");



1

–

19

#"*" *"8" 6!8 *,/ (,)"+, ,!", , )()" /",

-/") *,/" .) / () " )!, "8"(!,

"*" 6"*:9) )!'(! "*" (route surveying - "*" *,/);

#"*" / () " " )""()0" ')!*")/" 0"*, ("

*""8 ')!'/* ()" 6 )"-" "7+8 / ')!'(.

-/") (photogrammetric survey).

2.1. – CONTROL SURVEY

"'(8" !"")(" (*)"*)0" (+", , :"* )"(), "*" ). )0)

(+" 6,*"+ "7+8" .6). +"). ( ().) /

-. )0 6"*:/ +9. ")" *""8 -" , "*", ).

)0 "*") (, 6,0+8 !"")(. (, "* 8. -" +9" "0 ,

"* !+:* (!*")/, )!,/, ))"/, # .).

, "7+8" .6). +"). / ). )0 -

/" +/" )" /+* # )".!/" 6 -/"8"8 ). +"/, "/ ,

/",, 0*" (" ! !,-. 9) /" " *",), !"")( "*"

). )0 ,6* , -6 6"*:, 6+:"() !"" (" ()

,(()+:8 *. !"")(. *" +". *"6/ +(. 6.)"+ )0() ()"). +.). 98" +"*", , +" (,0/"+ 6 )"-" !"")(!

"*" ). )0 (!"")(. *") () (" # )".!/ 0"*, ("

:" )0" +(( "7,/, )".* +"*, ) '""/ # ,)*)(

/" )" .6)* /, )0.

#"*" ). )0 , +, "8"(! "*" -"6-"7,/" ".,

.6), +"), (+, -+8 6!8" "8"(. – !7"+(.

-/"). 6+(() +"0" -/"), "*" ). )0 *" -)" !"")(!

)" 6"*,/" 6+:"(), )" * (+ -""/ "*" , +. /0"9 /"

,! (,0/, 0"*, (, +/"" "/" .6)! +")! 68." - - (" "*" ). )0 6 )"-" "8"(! "*" (8

)" )0" (.6) +")) " (+") *"".

",- -/ "!6()/, +" 60)" /" !"")(" (+":

.

) / *" -,.+):

"" )!*")/(. )0 (+!, ,!!, )""! 0")+)! ");

#!(" *"" ((+ ,( ( +* +!, ,!!, )""! 0")+)!

");

"" /(. )0 (+ +!, ,!! )""! ").

+ / *" -,.+):

(+, "'""), *",; +, "'""), *",;

()+ "")( "'"") +) *",;

, "'""), *",;

#!(, *",;

/(, *",.

(+ "'"") *", + "'"") *" *" "6+" (,

*"* # )".!/" "'(" (, , +, !"

– ITRF (International Terestrial Reference Frame; !"")0 ()



1

–

20

+,! ) (()"* ( "6 ,)+7"* /"* 0")! *"/

/ (" 6"*:" )/") */, (+ -""/ (). -3 "'""). (()"*.

+((* !",, 6+0 (()"* +( (8" /" ("8 / (!

* / /" "7" (*)8"* +"" +9 *"!', () "" 1875.

!". (, +(" )0, (+, *""8 6 70. ! 9! +", (0,)" ,

(, "6/" "'( ("8 / (! *, (), " (" :"

" ()". ", , 6+0/ *" /9 ,+" (" ()" +(" (8"" *""8 ,

+, # – I. " )0 "7". +(,"* ()!,)/ "6(), 0, ()-6/" )0, +"0 !, ()/8,

6*"7, )0 0, "7+8 +((. 6 ":" /" 0") )"!/",

):

", +"* +(" )0();

", "6! +"*;

", )".0! +"* +"" )0();

", )".0! +"*.

2.2. – TOPOGRAPHIC SURVEY

!'(* "*"* "'9, (" / +(" -. )0 6"*:/ +9 ".. 6 "()+:8" ":"' *")/(. / /".

""*") () )!'(* +* )*. !'( "*" -,.+):

(()+:8" *"" ). )0 ,0/ "*" (*""8"* +""

"6());

#68" )0 "):, ,:,0,/, )0" )!'(" +9 (*""8"*

*8" "6() (88"* )" )0" /" "'9, *)"*)0,

(+,).

!'( "*" , 6+(() 6*"" *" -):

,6*" (1:1000 ,/");

"8"6*" ( 1:2000 1:10 000),

)6*" (()/" 1:20 000).

6+(() *"" )!'(. + ) " +9 "*",)!'( "*" "* )", *" 60/ +). 6+(() *"8""

)".!/" )!'( "*" (" *" "6+):

)!*")/(* *")*,

""()0* *")*;

())""()0* *")* (()")(" *")" - #, , );

*-+.

" " ()6*"! ("8"6*"! )!'(! "*" 6+ (" *"*

')!*")/(. *"). (0" )""()0" ()")(" *")" ()" (" ,!+* ,

,6*"* )!'(* "*", , ')!*")/(* *")* /"

*/, "7" !0"8 , "+* !,()" +"!")/" (":*. +, "*"),

-" (" )""()0" ()")(" *")" (# *") "*").

2.3. 23 – ROUTE SURVEYING

#"*" (-/. *,/ /"()" 9 /*. # 8* (" /0"9" 6,*"+

"*" / -"6-"7,/" ,(()+:8" .6). +"). 6.)"+ )0()

6!8" (-/. -/"). /0"9", -/") 6 )() '*/, *", -/")

/ ,:,0,/" )() :, - 60)* )()* (()"**. #"*"

(-/. *,/ (()"* 6+ (" , (+* '6* 6+7"8 /") (



1

–

21

8 "8 "()/"). "8" /") /" )/ / "*"

,: (+" "." )" "." 6 ,(()+:8" - -""+8" -/").

/ "( ,:,0,/" ,:8" '*/ )"", ) ,)"- 6"*:9) ,

/(, -/"), 0"*, (" "*" 6+ - (" ,)+ )!'/ )""

,(()+" )" )0" (!"")( *" -/")) 6 )"-" 8"!+! -""+8.

- !"")( "8" - , ()8, !+ (+* )* 6.)"+* ". /":

6/" !"*")/, .6). +"). + (" ()" ,

(),, -""+8 /")+! -/"); 6/" *")" ,:8 )""(. ) / (, ". , (),,

-""+8 /")+! -/");

6/" )"." "," -" "6,)) *""8 - (0,

0" (6"*") 6"*:. +;

6/" "( ()-,/" 6"*:. *(.

"):/" "*", (-/. *,/ -" +9" "0 , +, "*") +"6.

6 -() "8"(" !""6/".

2.4. 4 53 –

CONSTRUCTION SURVEY

#"*" 6 )"-" 6!8" !7"+(. -/") -,.+):

(()+:8" "7". 6 (*") )"", (+, /. (" *""8"*

/ +(( "'9, 6"*: +;

(()+:8" /" !- +9 0*" (" "*9" )"- ()+:8

*"" )""(. *";

6+7"8" *""8 ".. +"'+8 /" *"). "+

(),)," "7+8 0" 6+"". + ," "'(*

+"*"(* "* ( *"(" (.), 9) /" (()+ " )".!/" )"

6+"". +."(" " -""+8 (),/" 6+ (" )!'( "*" )"" 67,/,

(" !+/," !"")(" !" (+ )") /" "()+:/, (+, 6 /")+8" -/"). 5* (" /") ,(+/ 608" "( "(//" /* ("

"9+ )8" *+(-+. ( , /(, -/"). )" )"-" ". /" 6+) *", ). )0 / " (" ()) , ), -""+8 !7"8

-/"). "")( "8" * -+"6, )* +* ) 6/ *", ). )0 (, )"-* "*" 6"*:9), "*" *"" ). )0

6!8" -/"). )/ '6, 6/8" (()"* "*" )"- /" ,(*""

)"!/ (+. ) "*" , . +/

/" ("- + " (* *8. (+ +" 60//. /") ,)

6!8" "*, *()+, -, (()"* 6 +8+8", , ()6+. *"!/")).

, /* (,0/"+*, (+ "* 6 !"")(! (),08 /"(, (()"* )). (), # ,"7/, ("( ,"7/, +" (., " (+ (),*")

(()"* 0/" (" " *"" *")" -" -7,/, , +, "*") +"6. 6

)"." *""8 "*".

"):/" "*", (-/. *,/ -" +9" "0 , +, "*") +"6.

6 -() "8"(" !""6/".



1

–

22

2.5. – LAND SURVEY

#"*" 6"*:9) -+ (" 60+8"* *""8"* , + / (!) /"

'*/, !" +(9) 6"*:9. ". #"*" 6"*:9) (" 6+ 6 ("""

)"-":

-"6-"7+8 ".. ) 6 6, +! (, "8 ( 0,8)

+9 " ! +(9)+ "'(. +:+* -/")*;

#+ ,(()+:8" ! " 0/ /" "*" /" 6+9" 0/ /" ( ,7" ").* "*"*;

#"" " +" +9" *8. /" , (, ( * "/" /*

(, "'( +9, - / +. ".

*"), 6"*:9), * "( 6"*:9) ( /"! ,!! +(, + /" + 6+) ()8" / ! +(9)+, !)+, , ", "("/,

" ,! -/"). ,/ !"")(! (),08 6 ), +(), "*" (land surveyor) /"()" 6+9 )""( *""8, (0, *"6/" +9,, "* / 6,/"

," +" !0. / +9 6"*:9. " 9" ", )

/, /" *!," /"60 + "'(). "")( (),08 6 ), +(), "*" (land

surveyor) * 6+) " (* )".0" "," +" +" (")" ,( +

"")()*. +" 6"*:, !"")( (),08 * -) (")') (",)/* (" )+7,/" 8"!+ +'+() 6 +, +(), ")().

(, ( " +""* )"-*, "*" 6"*:9) (" " :

! "*" 6"*:9);

-+, "*" 6"*:9),

#"*" 6 )"-" " ("8) ".

#"*" 6"*:9) 6+ (": ))* ()*, # )".!/*, )")* (

,"7/*, )* )")* *"* )* – ):*. (* +""*

(),*")*, , +" 6"*:, ( 9/) "*" 6"*:9) *" (" 6+) *"*

')!*")/(. *"). ! /" *!,", )""( ", (" - ) ,"

,!+ 6*"7, "*. )0 +(9)+ -,, ") *"". (+, )! (" *"

6:,0) (" 6 )" *"" 0"() ()" !*")/", 0"*, "*"

)0" */, )" !(. )0, !" " (, ()" !. (,

!0" /" "+! -, ) (" !( + 6+//, "6+(.

(" () # )".!/, ". /" (+, "*, )0, ") ("(),

, (" )* *"(), 6 "", (" # )" * 9) -" ()+).

"", "6() "*" 6"*:9) 6+( +"() 6"*:9). 0!" /" /"

!( 6"*:9)" +"/" ,!. /" ! *!,", ": - - "*"

)0" ! +(9)+ +"6) ( )0* +" *"" ). )0.

9"8"* ) +" /"/", (+ "*" (" )"!9, , /" 6/"0

(()"* (+, /"! (" 9" *!, ,(()+) 9)"" !0 (),-+ 6+9)

")'/ " (8/, (" /"()+", ,)*)6+, */,)"( , -6, ).

"):/" "*", 6"*:9) -" +9" "0 , +, "*") +"6. 6 -()

)() '*. (()"*.



1

–

23

2.6. – PHOTOGRAMMETRIC SURVEY

)!*")/( *") 6,*"+ ()++8" '*/ -/")* ")*

,)"*, *""8"* ')!'(! (* -/"). " 6 6, (0. *"),

')!*")/(" + ')!'9, -/"), 6)* (" , -, +9 - (".

)!*")/(, *"), )"9, (""" "/":

#8" ')!*")/( (*8" -/");

- "* ')!'/ (" 6 :, ,)"-, , +, ')!*")/(. (()"* 6 "()),/,;

)!*")/( "()),/ ( (+, 0"! (" 0,/, )" )0

"/, ,!" (" !) 6+.

"):/" ')!*")/(* "*", -" +9" "0 , +, "*") +"6. 6 ')!*")/" :(" ")"/".

2.7. 3

2!'( "*" -,.+) ,:8" 6+8" (+. ""+). )

+"6. 6 () *, /"6", 6+, " ,. 2!'(* "*"*:

"'9, (" ,-" + 8, / +". "" , +.

,)"+;

"'9, (" / *(. )'* 6 , +. ,)"+;

6/, (" ("*")" "6+" +9" , -. /;

# (" 67,/, *" -/") 6 ""/,;

"7,/, (" / +. -+ ,!. ++;

"'9, (" ,)/ 6/", ("- (* +*,

).

#* 6.)"+ .!'(! "*" /"()" 6 )!'(" '!,/"

+. . +"9)0. -/"). ", 0 6+ (0 /"

)!'(/ ). "7,)*, *")" ,:8 ) 60/ (" 6,/,.

.6)/ +, / +! -/") ( /"! (" +9 "*" (0* - 6

"*") , ), 6+7"8 "*" * -) "'( ( "+)* )09,. )0()

/ + (0*, - (.) ,)0, +"*"( ,(+, ("- +"), )(

*!. "'(8" ,-" ( 0* ((8") 6+( +(" )( *.

+//. 6 )! 6!, *""8 ,- (" */, ",+). (* )!, 6-!

("'0() "*" )"- *) , +, (, )9+ .!'(! "*" 60/

+9 )!'(!. "")(* (),08, / 6+ )!'( "*" 60/ /"

9" ,0 -/")" (*8. ) (" 0"() "9+ (" " + .!'(

(/ /"()+ 6()+".

*""8" ,- () (" "a (echo-sounder). .(," " , *""8 +"*"(! " ".! ,()0 (! "7" ,) +"!

6 ("0/ -6 1500 m/s. " )( (" 9:, , 9"() ("/ ,

(",, 0"*, 9 ( 6( 30°. -/ ".(," +9 ("

"7"8"* "). *""8 ," "*:"* )"() !* /* ("

()+:/, .6)" *(" 60)* ," 6)* +")* ()/8*-

,-*.

"'(8" .6)! / + , .6)/ + * 6+7"8

*""8 /"()" ',*") 6.)"+ .!'(! "*". ) + ")8



1

–

24

+ , ), "*" /"()" + 08" / (" * -"6-") - "*" -

(+((.. )* !",, /+9" (" ()" (""" ) )".":

,";

")(;

GPS.

&"& 6,*"+ *", (0. (),*") 9) (, )"), ("())

(.

'$& )"." 6,*"+/, *", ('(). ,"7/ (

,)*)6+* ",* *8* )""(* (*.

GPS )". ,:,0,/" *", '""/! GPS (DGPS) /* (" ()" )0()

1 m RTK GPS / -"6-"7,/" ")*")(, )0(). ("8" +"*", GPS )".!/

-/ *), ,!, , 68, +. !" +" "" (, (()+""

DGPS (()"*" / (",/, (" "" 9:0" " /. ),

"*),/, '""/" GPS " "/" "!0"* -/, ( , "0,

100 km 400 km. "")( (),08 / " +, *!, ()) (!"

, ()* RTCM '*), ,)"* GPS /"* ) (+/ / ( )09,

-:* 1 m ") ")+, -6, ")8 0.1 0+. )".0

*(/ #*(" ,-" SAD 6+ /" 6 )"-" DGPS "*(/" )6+. RTCM SC104'*) RTK ,". "7,)*, /9 ,+" *"" RTK ()" (" ()

6+70 GPS "*". , '* TRIMBLE () 6 RTK )"-" )6+. CMR 6(.

",) RTK 9:0 */, *")" 10 km 20 km. "+" )")/

6+ DGPS *"), 6+70 GPS "*" 0"() 6+//, )6+. -6" ()" /" (, ,

()8, 12 ), 6+" '6 *""8 "6,/ 0.5 s, (

)09, 10 cm ( *""8), ( 0.005 m ('6 *""8). 6" ()" (, ,

()8, "*),/, '""/" +" ()" RTCM ()" (6 *""8)

GPS /"** , +,. #" ,"7/ 6 68", + ,-*",

+ ""*") /"()" !* 6 -, )"!/, (+. +"". ("6 (+" ,!"

("'0" /" /" (, (()+ " '*. (()"* 6 +!/,.

2.8.

#"* 9* !"")(* (*, "*" "")() -,.+):

#()+:8" "7+8" ) )0 !"")(" (+" 6 (*8" "):;

)+7+8" )()(" )")/" /"";

""8", ,:8" ,)+7+8" (). (. )

"")()*:

#,:8" ) (, + "")(), ( ,

"")();

#",6*8" ) )9/ +"() "")();

)()( (8" -)8" 6"*:9); 6, )()( +;

")9 -"6-"7"8" !"")(. + 8.+, ()6/,.

9/" "*", "")() -" "0 , +, !," "*") 6 -()

)().



1

–

25

3. 6 7

3.1. ,

3.1.1. ,&'$1& 3 '(

+ )0 6"*:/ +9, ( 6 8", *" (" "'() :

/, (, .6)/ +),

+( (, +")/ +).

-! ()" " "*:" ()*"6()), /" /" )0

6"*:/ +9 "'() ,

(( 3.1-1) )* X’,Y’,Z’. (* +,!*, / )0

(" *!, 6) () )* – (ϕ), $ (λ)

(ρ + h - , +, *" "(. +"" ) (()"* (" ,!+*

() , !"")(* "*", ( /"! (" 6+:"() "*:" * ,6") , -6).

3.1.1-1: $

3.1.2. ,&'$1& 3 '(

"'"") (+ "*" , + /" )" "'9" (" X,Y,Z

)* +,!! "( /")(! )! (()"* (( 3.1.2-1).

(.9)" (()"* () (" ("9 )0 +9 "*". XY1 + /" )!")

"'"") "( , (.9/ )0, ( Y /" ,(*"" (!"") , +, ("+".

#/ )0" P , 3 (()"*, "'9" (":

X,Y,Z )*,

,!+* α β ,* d. ! X,Y,Z (()"* Z ( ( +"* +")".

1XY (" , (/* !+:* "'9" NE +, !" ( X !+ ( E (Easting), ( Y !+

( N (Northing). 60+8" ). ( 6* NE ,+"" /" 6-! ',6/" /, *" 66+)

/ XY ( )! (()"* 9". , !""6/, *)"*), /"/ (.



1

–

26

3.1.2-1: +

3.1.3. ,&'$1& 2 '(

"*", , +, / )0 P (" ," d d’ /"),/, (" , 2 (XY)

.6), + ()0" P' ') . .6)/ + / )0" P’ "'9" (":

,* +"* ( 6)" )0" - hd α ;

#+* α α’ ( 6). )0 ;

,* d d’ ( 6). )0 .

"", ,!+ *""8 (" +9" , +" + – .6)/ +")/.

.6)/ +, ,!+ (" *"" , (, :

6+: +,

) (6), "'"")) +.

+")/ +, ,!+ (" *"" , (, :

6") – 6") ,!+ – ZOP,

.6), + – +") ,!+ - β β’.



1

–

27

3.1.3-1: $ 2 %

#)"- 6 + /+: (" * 0,8 ) "6).

)0 , +* )* (()"*,. /")/ + 6,*"+ #

*"". + / /" ( (")

$ X (N) .

" (, )" )0" , %. )0" ". /" (*) +:+" -/")" 6+9)

/")/, *""8 + ( )0" (( 3.1.3-2). #", /" ("":

")(8 .6)8 (),*") /, (" )" )0" 0,/, ,!+ 6 /")/,, ()" (""" 66"

nnn

222

111

O

...

O

O

ν α

ν α

ν α

−=

−=

−=

, (3.1.3-1)

!" (,: αi – *"" +, νi – " ,!+. / ,!+ 6 /")/, /" /" -/, ). )0 /" /" ( 6)" )0" . "8 +"()

0, (" )*")0 (" (+. *""8, ()" 66

-

n

O

O

n

1i

i== . (3.1.3-2)

0,8 ,! 6 /")/, ( /")! ,!) 0,/, ("

/")( + (+, 66 -,

k,1 j,O j j ====−−−−==== α ϕ . (3.1.3-3)



1

–

28

0,8 /")(. + , "):. )0, 0,/, ("

)" / "6). )0 "):

"*", , + /0"9" (" ()" +,! ) (()"*. (" +,!!

(()"* (" ," "'9,. 6 )0. 6!, -0 (" 6 + ( +,!!

)! (()"* ()" + (N- North, X ( +""! +!

)! (()"* , ",- -/, ( Y ( "()+"! (()"* +,!"

")+" "0" /"/" – 6)/" UTM) (E – East, Y ( +""!

+! )! (()"* , ",- -/, ( X ( UTM /"/".

(.9)" +,!! (()"*, 6 )0. 6!, - (" ) )" ,+" -,,

6)+". (" *" () + 0:

6-* /8" /,!-6" )0" +9 "*" (.9",

(-* "'(8"* ) / (.9).

3.1.3-3:

3.1.3-2:

0°00′00″ X

%

α1

α2

ν1

ν2

O

A

1

2

X

Y

PYp

Xp



1

–

29

+,!* )* (()"*,, / )0" "'( /" +,!* )*

Xp (, +, ("+") Yp (, +, ()).

# 1.2.2-1: P(Xp Yp) = P(1100,00 1200,00) 60 /" Xp = 1100,00 m, Yp = 1200,00 m.

$0)& $)"# $!&'& '( )")/" ",-" -/" ":" /" , +"

6" – 9"(), ("*,. ) 0") )! (()"* 6. 6 (" ,

"(", ")! *"/ 6" (*"/ 18°) "+), 7. , , "(",

")! *"/ 6" (*"/ 21°) "+). -6* ") *"/ 6 ("* )")/" 6", - (" 6-"!" "!)+" )", ")*

*"/, 6" ":" /" +"() )" Y = 500 000.00. - (" 6 // 6 /" "0, (" +"() Y )" /" (" -/ 6" ( *", Y =7 523 000.00

60+ (" )0 6 , ("*/ 6, 23 km ()0 o ("8"! *"/).

3.1.3-4: %$ - 7.

Y

X

ekvator



1

–

30

3.1.4. ,&'$1& $& $!&'& '(

"'( /" ( (.9)")

)! (()"* . 0 P1 "7" /" !"0&( d1

)0" P1 "#( αααα1 ! -6,/" 0") + + )0 P1. /,( d1 /" ,+"

6)+ +"0, ,! α *" -) 0° 360° ()" , (*", ")8 6:" (),, 0,/, 0")! +. 0") +, /0"9" (" - )0 ()/""

*"" ( +, 6 0"), /")/, */, (" ,6") /*8" +" 6)" )0").

/" /" 6) (" ,!+ *"" , ()""* , *. #, ,! ( 360

()"". )"" (" " 60 ,0. *,), (+ *,) (" " 60 ,0. (",.

/" -"6*"6 +"0. " (1 rad) /"()" ,! 0/ /" , /"

8"!+* /,(,. "() π () "'9" (" ( -* ,! () 8"!+!

"0 d, (,

d

O====π , (3.1.4-1)

, π π ⋅⋅⋅⋅====⋅⋅⋅⋅==== r2dO , !" /" r – ,"0 ,!.

#, ,! ( 2π ( ∼6.28 /).

rad2r

Oπ = . (3.1.4-2)

(,

.rad180

,rad2360

π

π

=°

=°

:" /",

rad0175.0180

1 =°

=°π

,

.8.2642068.44715729578.57180

rad1 ′′′′′′′′====′′′′′′′′′′′′°°°°========°°°°

====π

"() 206264.8″ 60+ (" ( ρ () 6 ")+8" ,!+ 6 , (","

-,). #* ")+8 6 , (",", ,! (" * ( ρ , *

+"6/" 6 (", , ", ,! (" " ( ρ * ( .00000485.0 / 1 = ρ

)0* *"* " )" (" 0"() ()" * 0,8

)8 "):. )0 * -""+8 /")+. -/") *,

)). (). )-" 3.1.4-1, 6" (, +"() ,!+ +)* 6

)" , 6+(() +).

3.1.4-1:

ν1

d1

d2

ν2

P1

P2O

"

"

" )

R



1

–

31

3.1.4-1: ,

+) 6 6 N ( +"()

,! , ()""*

#+ + + 0 90

,! + - 90 180

" - - 180 270

5")+) - + 270 360

3.1.5. + $)"#/ $&/ $!&'

( 3.1.5-1 ,()+ (, + (, ) – " ),d( ν 3 +,!"

)X,Y( PP )" )0" P . (, )" " )" ),d( ν , +"() +,!.

) 0,/, (" *, 66

3.1.5-1:

ν

ν

cosdX

sindY

P

P

⋅=

⋅=, (3.1.5-1)

, , (, 6)" +,!" )", " )" (" 0,/, *, 66

P

P

2

P

2

P

X

Y

tan

XYr

=

+=

ν

, (3.1.5-2)

,

P

P1

P

P

X

Ytan

X

Yarctan −==ν . (3.1.5-3)

3 (" "'"") + ( 6)+* (*"* X (" / /" " ("8"* *"/,

6" /"/", ) (" ,! α 60+ ( ν 6+ (" !$,&( "#(.



1

–

32

ν

/" +" /" (),), d /" ,+" 6)+, +) ,! (" "7,/" (+,

6 YP XP.

3.1.5-2: " "

3.2. 6, 5 7

3.2.1. "0& +(8" !) '1

(" +" 0,(. "/ "6,/" ()" +,!" )", (0" "/" *!, (" 6+"() ( * )*. " 6! 6 ,)"-, +,!.

) /"()" 8.+ 0"9 )0a *".

( 3.2.1-1 )" (, +" )0" P1 P2, ( )* Y1,X1 Y2,X2, "(")+.

()" #)!, )""*, , ),!, P1P2P, , 6*"7, ). )0 0, ("

(+, 66 -,

( ) ( )2

12

2

12

2

12 XXYYd −+−= , (3.2.1-1)

)/.

( ) ( )2

12

2

1212 XXYYd −+−= . (3.2.1-2)

3.2.1-1: %

3.2.2. $,& "# &# $) +(8" !) '1

$,& "# +" /"()" ,! ! '* + ( 6)+* (*"* X (N) ("

*" (" , (*", ")8 6:" (),, 0"+ 6)+! (*" X (". " *)

+"() 0° 360°. ( 3.2.1-1, " ,! +" P1P2 , 6 ν12 *8 /"

90°. ,!" ()" " ,! +" P2P1 , 6 ν21 +" /" 180°. "6 6*"7,

+ " ,! ()" +" !(:

ν

P

X

Y

d

YP

XP



1

–

33

°+= 1801221 ν ν . (3.2.2-1)

" ,! ν12 +" P1P2 0, (" (+, 66 -

12

1212

XX

YYtana

−

−=ν , (3.2.2-2)

-,), " ,! +" P2P1 6(

21

2121

XX

YYtana

−

−=ν . (3.2.3-3)

# $) /" /" )!"(, ,! θ / + '* ( 6)+* (*"* Y (E) ("

-""+ (" ( m (( 3.2.1-1). !- m12 +" P1P2 0, (" (+, 66 -

12

121212

YY

XXtanm

−

−== θ , (3.2.2-4)

, !- m21 +" P2P1,6(

21

212121

YY

XXtanm

−

−== θ . (3.2.2-5)

# 3.2.2-1: 0,) +"() "! ,! 6*"7, )0 A C, (, )" 8.+" )": YA= 1023.25 m, XA= 2134.32 m YC = 1141.71 m, XC = 2012.89 m.

627144XX

YYtan

AC

AC1 ′′′°−=−

−= −α

( "6,)) , ,),)

#"* )-" 3.2.2-1 ,! (" 6 , ,!* +),, 0 +"() "!

,! -/ (" 4324135180C

A′′′°=−°= α ν .

:

C

AACAC

C

AACAC

cosdXX

sindYY

ν

ν

⋅=−

⋅=−

3.2.2-1: -



1

–

34

# 3.2.2-2: ) (, , " ,! 6*"7, )0 F: dAF = 91.88 m

5452295F

A′′′°=ν . 0,) )" )0" F (, )" )0" (Y,X) = (1932.76 m

, 770 m). 0,) ,, 6*"7, )0 F G (dFG) (, )" )0" G /""

G(Y,X) = (2016.29 m, 952.18 m).

$3:

m45.395452295cos88.91X

m93.825452295sin88.91Y

AF

AF

+=′′′°⋅=

−=′′′°⋅=

∆

∆

)" )0" F 6("

m92.80945.3947.770X

m78.184998.8276.1932Y

F

F

=+=

=−=

)" 6" , FG 6("

m26.14292.80918.952X

m51.16678.184929.2016Y

FG

FG

=−=

=−=

∆

∆

, dFG 6(

m01.21926.14251.166XYd 222

FG

2

FGFG =+=+= ∆∆

3.3. 7 4 6

"9" *""8 + , ,)0, )0() " / )0. " ()

(),8 *""" ," d + α 6(" d α σ , "(")+. )"+

"(!,() "" / "" )0" *" (" 66) "(* 0/ /" ") "7" *""* ,* +"* )", )0,. +)") "" / "6)" )0"

+",/" (" +"0* ,( "(, ( ")+* (* (),8 *")

"(" , +, ( -! )! (()"*. *", "(!,() *""8 ," *" (" 66) ")+ "6(), )/. ( $

$. *", /" =dσ 0,1 m, =d 100 m, 6( 1:1000. 0

)*", 66+ !"9* + α σ = 20″ , 100

m 6( 0,01 m, )/. 6( 1:10 000. +"" *" ,6,/"

*""8 + , , )/. ")+ "6()

+ * -) (!( ")+/ "6() , d d σ (( 3.3-1).

)0/ *", " (() (" ()!/ /"() ")+. "6() *""8

+ ,, +" (" 0",/" 6 " -," 60/. )-" 3.3-1 6 60) () (),8 ,!+. *""8 )" (, +"() ")+" "6()

" (),8 6 ," 100, 300 500 m.

#"* * 6 )-"" 3.3-1, ,6 ")()+, ," )"- *") ( ")+*

"69, 1:10 000, "(") "6() *""8 + 6( α σ = 20″. /"

, "6)" )0" =d 400 m 6*"" ( d σ = 0.15 m, 6-! 6.)"+ .*!"()

*""8, "6() *""8 + )"- 6( 1′≈α σ ( 12,087267,0)300 / 400( ====⋅⋅⋅⋅ m).



1

–

35

3.3-1 : " "

α σ 100 m 300 m 500 m d d

10′ 0,29087 0,87267 1,45433 1/344

5′ 0,14543 0,43630 0,72717 1/688

1′ 0,02909 0,08726 0,14543 1/3440

30″ 0,01454 0,04363 0,07272 1/6880

20″ 0,00970 0,02291 0,04485 1/1030010″ 0,00485 0,01454 0,02424 1/20600

5″ 0,00242 0,00727 0,01212 1/41200

1″ 0,00048 0,00145 0,00242 1/206300

#/+ "")(. ,"7/ 6 *""8" , ( Electronic Distance Measurement)

60/ /" ,) )0() "*". *", -"6 +". , ( ," (" *"" +"* "6. *", *""8" ," 3000 m ( ()* (),8"*

0.015 m "(") /" ")+/ "6() 1:200 000, ( "6() *""8

,!+ 1″. /" "0 )!'(* "*",, 0!" )+ + "6() /" ,. "*", + /" )!'( )()(, ,)(* *""8"* ):*

*" (" () ")+ "6() 1:1000, 9) /" "(") ,!+/ "6() 3′.

#* ",/" ,, 0"() (" ()" 66 / , ("- (" )!*")/("

',/", /" (, 0"() +"* ("):+" , -6 "7". +"() ,!+. *",

)0() 0,8 *"8" (" ( *"* ,!. "7,)*, (, -6" *"" (,(

*. ,!+ (,( ,!+ -(. 90° )!"( )!"( *. +" ,!+ 60/", ()"" "6() *""8 ,!+ 6+(" +"0" ,!

',/" / (" () * 0,8. /" )0 (+ ,! *") ( ()* "69,, !)+, " ( *(**. "")( (),08 * 6+) *",

"*" (-" )!*")/(. ',/ - -"6-" "+), "6() *""8 ,!+. (* 3.3-2 3.3-3 6 /" ")+ "6() "(")

()* (),8* *""8 ,!+ 5″ 1′, 6 ',/" (,(, (,(, )!"( )!"(.

(+, 6. !' *!," /":

") ")+, "6() , 6+(() )! ,! 8"!+" !"9";

") *(* ** ,! / - , /" !"9 *""8 6)

-"6-" 6.)"+, ")+, "6();

") "6() ( /* ,! "7"" +"0" )"- 6*") -

6.)"+ ")+ "6() * 0,8 - 0,+;

3.3-1: ( ( d=100m, α =60° , σ d =0.5 m, σ α =30′ )



1

–

36

3.3-2: ( ) ( )

3.3-3:

" *" ,()+" (" 0 9"8 !' ((" 3.3-2 3.3-3):

,)* )")* 6*"" /" ,! 32° 00′. /" "(!,() *""8

,! 30″ (0,) ")+, "(!,() 0,8 , (" ()

',/ ,!. ( 3.3-3 ")+ "6() / !+ "(", +"

03 ′′=α σ /" "(")" ,!, 32° 6( 1:3000.

)!*")/(/ *" ,!+ (, *"" ( 5 ′′′′′′′′

≤≤≤≤α . #* 0,8 () (" ',/ 0"*, (" 6.)"+ ")+ "6()

1:20000 * -) (0,+. - (" 0,+ ". "6() )"- /"

") ** ,!. ( 3.3-2 6 ")+, "6() 1:20 000

5 ′′=α σ ** ,! 6( °= 26 α .

") ( /* "69, )"- *") ,! (" 6.)"+ ")+

"6() 1:10 000 (" , 0,8* () ',/ ,!.

( 3.3-2 ")+/ "6() 1:10 000 ,!, 76°, !"9 *""8

,!+ " (*" -) +" 5″, 6 ,! 64° !"9 *""8 ,!+ " (*" -)

+" 10 ″, ).



1

–

37

3.4. 4

"*",, *""8 (, 0 :. "", (+, "6,)) *""8 0,/, ("

,!" +"0" 9) (, ,!+, ,", ")+ (, +9", 6"*" (.

"6" /" (" ,(()+:/, * ,(()+:8 ( 6*"7, *""8 "6).

*") (+(, ) (.) "()+:/, *)"*)0 - "" /+". +,

/", *)"*)0, '*,/, 6+* . ""8 (" 0"() "

,+" , *" "), +" (" "). +!+/, "7"* 6* (" +:/, 6 6) (()"*)( ,)/, ( (+" (" "'""), (+, 6 /, *" +". *", /" ) +( )0" " )"- ") +(" )0 B

C. -6* (" +(" " "7,/, "), *""8"* (" "7,/, +((" 6" ;h1,;h2 ;h3 (( 3.4-1).

3.4-1:

" /" /"()+ – )"- ") +(" HB HC )0 B C , (, +(,

+9 "'(, +(* )" )0" . - *" - 6()"), ". /"

6*") +" +((" 6". -6* (, *""8 )""" (,0/* !"9*,

-/ *""8 /" +" ".! (, 9"* *", ** ) *""8). ) +( (HA),

) "6,)) *""8 (;h1, ;h2 ;h3) 8.+ () (),8 + "6)

*") (+(" HB HC) ()),9, . - (0, *")"

(+(" HA HC) ". /" () +"6, 6*"7, ""*") *)"*)0! *", )/.

C3A

C2B

B1A

HhH

HhH

HhH

====++++

====++++

====++++

∆

∆

∆

. (3.4-1)

-6* (, +" +"0" "6)", 6 (+8" ',! *" (,

"." (+" ) /"0" (+:" (, - /" +"). "7,)*, ,(" !"9 *""8,

(+ /"0 - ,!0/ "6,)). *", 6- "+)! /"0 /"

/"()+ /" " ()/" 6)": / - 6+/ " "9"8. )+*

(,0/"+*, , (" (" +9* *""8 ( ",)()) ". /"

)+ !)* / - -"6-" "6). *"), 6()"),

*)"*)0* *",. + (), 6+ (" (data adjustment). 66 6+8" () (" - ,6 (), *"88 +"() 8 - -

6()") ( *"* / + /"()+". " "6). *").

(),, 6+8 ",). *""8 () (" " )".. /()/

8. / (" /0"9" () /"()" " (least squares method). "

)". 6+8 / (" , ( 0"() (), 6 (6)+8

'!,"). (+, (" 3.4-1, *" (" () 66 -

h321 f hhh =++ ,

B

C

;h1

;h2 ;h3



1

–

38

!" /" hf - !"9 6)+8 '!,". (, (+ *""8 /"! +)") (()"

)"") (+ 8" )"- +) 6 +"() )3

f ( h− . /",

0h ˆh ˆh ˆ)3

f h()

3

f h()

3

f h()vh()vh()vh( 321

h3

h2

h1332211 =++=−+−+−=+++++ , (3.4-2)

!" (,: 321 v,v,v ( , , 9/ )"), (" () 66 ),

(, 321 h ˆ,h ˆ,h ˆ 6+)" +"() 8 ("" "6,)) *""8). (, ih ˆ 6()")" ( *"*, 6- - /" +" 6+)" +"() 8 " ()"

+"() *") (+(" HB HC).



1

–

39

4. 54 6 7

4.1. 54 6 7 3

#/ )0 , .6)/ + *" (" ") +9" 0, ):

!(/ *";

#"("8"* +; ,0* "("*;

+, ,+/;

# )".!/*;

!,/*;

)"/*, .

( (, 0"() ()" 8.+" *-/". #* "6/" "*", 6+//,

(" +" (+" '6":

#+ - ,(()+:8" !"")(" (+" "*" (*" ). )0,

*)"*)0 (+ "*");

,! - "*" ((*8) )0 "):. +* !+:, "):/" " -) -/98" + '6, , ")* 9"()* -/(" ("

"*" )0 "):.

4.1.1. #& ($0

#!*")/ /"()" "'( /"()+ *") ,(()+:8 *"" ).

)0 , .6)/ + / /" +"* ( , !,() (":"* ("* 6(*

)""* !" (, )" +6," "*+" !" *" )!,/"

))"/" /" "(, ( ,(" +"9)0. . "" # /"

*":+a.

#!( *" /" *"8":

*8, ! ("; (()+:8, *)"*)0" (+" 6 6+7"8" )!'(! "*";

8, -""+8, /")+. "): "8"(. -/");

8, ). )0 6 "6/, ')!*")/(! "*".

#!(, *", 0" !( +. #!( + "()+: (, 6*9:".

+. / – !(. () /" !"")(* *""8* , ,!+ +"6,/,

)/ ()-6+" !"")(" )0" )")/ 6+7"8 "*". 0" +"6"

!(* ()* 6+/, (" #&( '1(.

," !(. () *"" (":

") ("")(* :*"*, *"* )* – ):*);

") (*"* ).*")/(. *")).

#" !"0&, (+/ !(/ )0 6*"7, +" (,("" ()" )")* (" *"

"#.

#!( + *" -) "'( ,:

+*"6/ + (.6) +);

*"6/ + (()).



1

–

40

&'$"(&' $( + ($- !"0& "#) " #&( )"

(),*")" "*, 6 *""8" , ,!+ 0:

()"* ))" ()" ( )") ( *"* )*);

6," *";

"'") 6*" ( *-/ *" "'"));

"!()) ) ( )""( 6();

#* "* (())+, +(, ):, "* 6 *""8" *")

)*('"",...).

(" ()" ).*")/( (),*"), ,*"() () (" ).*") (

/,* .6)* +")* ")+*.

#& '1

0a !(" *"" // (" ")9" (),*") 0/" )" /" ".

") *""8"* , ,!+ 6+ (" #& '1 (()). #/

!(. )0 ,)+7,/" (" "* (""* 6.)"+*:

". /" *"7,(- +:+() 6*"7, !(. )0;

!(. )0 ". /" (*) -"") 9) +9" "):;

"() 6 !(, )0, (" - ) -"6-"7,/" )/() -""!" !() 6

*""8" ,, ,!+ )0 "):.

#"* )/(), !(" )0" *!, -):

)/" () C D),

+"*"".

#"* *)"/, /" (, +:"", !(" )0" *!, -):

+"", "*0", ()0", *")",

*"", -")(".

-6* 0 ()-6/" !(" )0" *!, -):

-"6 6"*! "),

( 6"** ")*.

""!* ) C -"6 6"*! ") ()-6,/, (" !(" )0" , ('), -"),.

)")+, *!, (" ,)"-) ," *")" 0" "0 10 cm ( ('"*

)* , (" ,* "0 2 mm 6* – + "*" (( 4.1.1-4).

""!* ) D ( 6"** ")* ()-6,/, (" !(" )0" ()-/

0+()/ 6"*:/ 6. )-6/ !(. )0 *" (" +9) *"* -""!* ( -7"* !+* ,!7"* -* (( 4.1.1-1).

""!" /" (" ()-6,/, , -+* 6"*:9), ,+/, (" /*8" 50 cm ( +9

)"" 6"*" -")(" *"" -""!", ( 6"** ")* (( 4.1.1-2).

()"+)* )""* !(" )0" (" *!, ()-6+) +") ,!7"

"" ( !+6"* -* )+* "0 2 mm.



1

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4.1.1-1: -

4.1.1-2: ) –

4.1.1-3: – . C D



1

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42

4.1.1-4: $ – .27

"(" ()-6/" (" ( / !(. )0 ,

)!*")/(* -(, -. 27- 27 (( 4.1.1-4).

#"* +"* (* ( $ , - 1997 ) !"")( (+ 6 (*8" "): (*" ). )0 6 )"-" (*8 "): – $ , $ , $ $

" ) 67,/" (":

6+/8"* *"",

"(),/* *"".

) !( *" (" " :

!(, *", 1. ",

!(, *", 2. ".

'*9 !( *" (" " :

(+,,

,(,.

(+, *", 0" + I ", ,(, II, III IV ".

4.1.1-5: * $

"

"(



1

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6 !"")(" (+" 6 (*8" "): +9 (" , (+"*, "* "9"8* 6 "/!

!+! /"), -"6 -6 (" +/ *" "(),/ ()".

#/") !(" *"" 67,/" (" +* 6*" 1:2500, 1:5000 1:10 000

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+/")+" )0" !(" *"" 1. 2. " ,$&( ),9"*. #/")+" ()"

!(" *"" 1. " ()+/, (" ,$&( ),9"* "-:* /" 0.6 mm, ()"

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(+, )()(, 9), 67,/" (" , !(" *"" , 6*" 1:5000

1:10000, / (:

), *", ( ((* )* 6+ + ();

")" ()/"" )0" +"* +"7"" )0" * ),9"*;

, )()(" 9)" "), 6""* ),9"* "-:" 0.8 mm;

, !7"+(! " "), ,)* ),9"* "-:" 0.5 mm;

#", ()+" ("), ""* /* :,-0()* ),9"* "-:" 0.5

mm) (" "): ("), ""* /* :,-0()* ),9"* "-:" 0.2

mm) (0! (*8, (* ", ()+" ')!*")/(" *")"

(*8;

") *""" ()" ()" ""* /*, 0,(" ("* /* (* ),9"* "-:" 0.2 mm).

(": ( +" +9" )()(. 9) , /* (" ,*"/ !(. )0

+9 "", 67,/" (" /"()+" ( *"" 6 " (":". ,*"/

!(. )0 *"" 1. 2. " +9 (" )()(* 9)*, -/ 1

:". !+" !( (":, ,*"/ !(. )0 +9 (" "" -"6

-6 !" )()(. 9).

!(" *"" 67,/" (" /"* +9" ()+ '*) 100 cm ( 70 cm

70 cm ( 50 cm, 6+( +"0" )()(" 9)" 6-" 6*"".

) #!' &) 67,/" (": (" ").* ()+8* ,)+ /" ,0/, )()(" 9)"

,9)" () "', +: -/ )0 -"6 /. /" *!,

6 +8" )() 6"*:9) 6 )() "")();

)"-" +8 "*" ,0/* !" /" "*" 6+9"

"')!*")/(* *")*.

(" !(. )0 "7,/, (":

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# *""8*.

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&'$",* ()/"" !"")(" (+" +9 (" , (""* (,0/"+*:

6-! 9)""8 ,9)"8 )0 , +""* -*,,

6-! 8"" "',(),

6-! 9"8 !7"+(! " (":,

6-! ".*!"() *"" 60). *")!/ *""8 -" ,

()/"/ *",



1

–

44

()/" *" /" , ,(-!"+/ /"/ *")(* (()"*,.

"(),/ ()/"" *"" +9 (" ,0/, /"* /" 6+"" (0 "*".

# "(),/* (" 6,*"+:

+ 6+8" ()/"" *"",

, 9"8" ()/"" *"" (,(" .*!"6/" )0 ", !"

(" " () ,(-!"+ /"/ *")( (()"*).

+ ,( *""8 * "(),/" ()/". *" 6+" (" ("'/* /" +" 6 6+/8" *""8 , &)* #&* ($0 1. 2. $!.

!$0)- !"")(" (+" +9 (" , (+., +8 "*". 6,/"* +8"

'*9 !"")(" (+" &) !"")(" (+". +8" !"")(" (+" -,.+):

"8" ,)+7+8" *" )0*,

-+, ()-6/" 9)"". ,9)". )0,

,8+8" ()/"" !"")(" (+" +* )0*,

)88" !"9 +7"8" (). *" , "-)* *".

$' #&/ ))

+ (, (+ ) !(. ++ (!):

)+" ((") 6)+".

')$& ! ((" +, opened traverse)) 6 6)" )0" 6+9+

"6)/. )+". ! /" *!, 0,( ) *""8 ,!+ ,

, +, !. " 0 )" *""8 /"()" +:8"* *""8 ().

+"0. 6 )! 6! + +() ! (" ") *"8,/", 0"*, (" 6+:+

*(* +" ("" ()". "7,)*, , "* (+*, *" , "*", ,.

-(", +/ - ! /" /" *!,.

')$& !( + (closed traverse) 6 6)" )0" 6+9+ (" 6)/ )0. 26) / )" )0" *" -) "'( !"!'(*

+,!* )*. ( 4.1.1-6 ,()+ /" *" !(! +

PQ1234RS / 08" )" )0" Q ( 6)* 6*,)* ()" QP, 6+9+ ("

)0 R 6*,)* ()" RS. +/ ) ! (" , ( /0"9" /+: *!,,/" ), 0,8 )+8" (()"*)(. !"9 *""8 , ,!+.

6, ! / 08" /"/ 6+9+ ,!/ 6)/ )0, !

/ 08" 6+9+ ()/ – )/ )0, 6+ (" +')$& #& (closed loop

traverse). ( 4.1.1-7 ,()+ /" *" 6)+"! !(! + / 08"

6+9+ ()/ )0.

4.1.1-6:

P

Q

1

2

34

R

S



1

–

45

)+" ! *!,,/" ), ,,)98, ), ,!+, " )+8"

(()"*)(. !"9 *""8 , !"9 /")/" !. )+"

! " )"- ()) /") +". *"6/. - (" 6)+".

! /+ !"9 **6+, "*, 6 *""8" , )"- :+ ())

-().

4.1.1-7:

1"&- " #&( )"

!(* +, (" )"", *"" . (+, *""8 +

0,/, (" 6*"7, !(. () +9 $

!. )!, 0,/, (" +" -. +"() ". ,!+

"')+" +"() (). "6,)) *""8 , ("

+:/, 6 (()"*)(" ,)/" (+" , + /"/" -! )!

(()"* (! +!). #*, , () "')+. ".

,!+ 0,/, (" )0. /,,

$ $ ,

. *"* " !(. ++, ,()+" (" (), "9+8 !(! +.

#& ) "('&"' +(8" !) !' '1

( 4.1.1-8 6 /" !( + ,*"),) 6*"7, ). )0 B. ""8

,!+ , ) (, , )-" 4.1.1-1. )-" 4.1.1-2 6 (, 0,8

". ,!+ !(. ().

4.1.1-8:

3

P

Q

1

2

4

νP

A

2

3

4

B

α1

α2

α3

α4

α5

νz

P

Q



1

–

46

#* 0,8 ". ,!+ !(. () *"8,/, (" ("" +:

1. ""* ,!, () /" (" " ,! ")." !("

()";

2. /" 6- *8 180° /" (" 180°, , /" 6- +" 180°,

,6* (" 180°.

4.1.1-9: - "

)" 6" 6*"7, )0 !(. () 0,/, (" (+, 66 -,

ijijij

ijijij

cosdX

sindY

ν

ν

⋅=

⋅=. (4.1.1-1)

4.1.1-10: ) "

4.1.1-11:

X

3

A

2

2

Aν

2

Aν

3

2ν 2α

Xij

Yij

ν jk

νij

Y j

X j

j

i

k

dijd jk

X

Y

Yi

Xi Xk

Yk

I

sin +cos +

II

sin +

cos -

III

sin -

cos -

IV

sin -cos +

X

Y



1

–

47

!"-( 6 ). 6 !(. () 6+( (,( (,(

". ,!+ (). ( 4.1.1-11 6 (, !"-( 6 ',/

(,( (,( , (+* +).

# 4.1.1-1: (+, ). ) "6,)) *""8 ,!+ , ,

!(* +,, (0,) +"() ". ,!+ !(. ()

+"() ,!+! (),8 ("6)+8) !.

$3:

4.1.1-1: % (Anderson and Mikhail, 1998)

#!(

()

""8

, !

)

A2 305.41 α1=104° 00′30″ νP = 43°31′30″

23 359.61 α2= 63°2

0′00″

νZ = 106°17′30″

34 612.15 α3= 258°11′00″ σd = 0.01 m

4B 485.12 α4= 120°45′00″ σα = 30″

α5= 236°30′30″

4.1.1-2: - " "

#!( ()

"6+) " ,!+

#+" 6+) "

,!+

AP ': 43°°°°31′′′′30″″″″

α1 104° 00′ 30″ 12 147°°°°32′′′′00″″″″

α2 63° 20′ 00″

-10″ 147°°°°31′′′′50″″″″

32

23210°52′00″

-180° = 30°°°°52′′′′00″″″″

α3 258 ° 11′ 00″

-20″ 30°°°°51′′′′40″″″″

43

34289°03′00″

-180° = 109°°°°03′′′′00″″″″

α4 120° 45′ 00″

-30″ 109°°°°02′′′′30″″″″

B4

4B229°48′00″

-180° = 49°°°°48′′′′00″″″″

α5 236 ° 30′ 30″

- 45″ 49°°°°47′′′′15″″″″

286°18′30″

- 180°00′00″

BQ 106°°°°18′′′′30″″″″

': 106°°°°17′′′′30″″″″

- 01′ 00″ 106°°°°17′′′′30″″″″

!+

"6)+8"

– α f

- 01′00″



1

–

48

4.1.1-2: " (, 6*,) () ij ik νij = 43°30′00″ ν jk = 153°25′40″ ,"

() dij = 432.182 m d jk = 385.151 m. 0,) )" 6" "6). !(. () ij ik.

$3:

) ij: m494.313000343cos182.432X;m494.297000343sin182.432Y ijij =′′′°⋅==′′′°⋅= .

) ik:

m468.3440452153cos151.385X;m288.1720452153sin151.385Y ikik −=′′′°⋅==′′′°⋅= .

(, 6)" )" )0" i, (Xi,Yi) )" "6)" )0" j 0,/, ("

*, 66

iji j

iji j

XXX

YYY

+=

+=. (4.1.1-2)

4.1.1-3: (, )" )" 0")" )0" i, Yi = 7 470450.100 m;

Xi = 4 850 340.400 m, (+, ) 6 ").! *", (0,) )"

"6). )0 j k.

$3:

m426.4850309468.344894.4850653X

m882.7470919288.172594.7470747Y

m894.4850653494.313400.4850340X

m594.7470747494.297100.7470450Y

k

k

j

j

====−−−−====

====++++====

====++++====

====++++====

0,8 (+. ). 6 , +, +9 (" +" )0() 8,

( " +)") !. +, ,*"),)* 6*"7, +" 6)" )0", %

% % $

. /" ! 6)+", % . + / ( i=1,2,…,n () / 08" ()" i = 1 6+9+ (" i = n,

,(+ (" '*,9, ("" 0:

−

=+

−

=+

=−

=−

1n

1i

1i,i1n

1n

1i

1i,i1n

XXX

YYY

. (4.1.1-3)

#* 8, ,(" /+" (,0/. !"9, "*"+. (()"*)(. ,)/ "(!,() 6+8 ) ). )0, ,(+ (4.1.1-3) /" ") , (

()+). "() 6 /" ,(+ (4.1.1-3) (, 6+:", 6+/, ("

$ $ . #/ (),8 Y X (* XY f ,f ,

0,/, (" (+, 66

−

=+

−

=+

−−=

−−=

1n

1i

1i,i1nX

1n

1i

1i,i1nY

X)XX(f

Y)YY(f

, (4.1.1-4)

, $ Y,Xf , 0, ("

2

Y

2

Xy,x f f f += . (4.1.1-5)

0,8 +"" +"() "6)+8 !, +9 (" 6+8" +.



1

–

49

(" ,!+! "6)+8 + 6+9" /" +*" ") (), 9) 6( –

12″ ,!,. -6* /" () *""8 ,! 30″, +" (, 6,"" -10″ (6

) ,! – ()" 1, 2 3) -15″ (6 + ,! – ()" 4 B).

4.1.1-3: - "

'&, "0& $,&

"#

$!&'& $+

Yij Xij

$!&' '1

Y X

A 64 321.404 66 240.562305.41 147°31′50″ 163.959 - 257.668

2 64 485.363 65 982.894

359.61 30°51′40″ 184.465 308.694

3 64 669.828 66 291.588

612.15 109°02′30″ 578.654 - 199.717

4 65 248.482 66 091.871

485.12 49°47′15″ 370.464 313.205

B 65 618.946 66 405.076

S=1762.29 S=1297.542 S=164.514 [65 619.243] [66 405.272]

Y5 – Y1 = 1297.839 X5 – X1 = 164.710

f Y = + 0.297 f X = + 0.196 ∆Y = 0.297 ∆X = 0.196

m36.0196.0297.0f f (f 222

X

2

YX,Y=+=+=

,", 6+) " ,!+, '(" )" 0")" 6+9" )0" +

/ (),8 + 6 (, , )-" 4.1.1-3.

#+" "6)+8 ! (,*"),)! +) ()" B 6(" ∆Y = 0.297 m

∆X = 0.196 m. +""" +"() (0,)" (, (+, 66 4.1.1-4. ( 4.1.1-126" (, "" *")" /! (),8 !. (+, 66 4.1.1-5

*" (" (0,) $ ( m36.0f X,Y = ). ,*"),)! !(!

+, ,, " (),8" (" /": ,0/. !"9 *""8;

"*"+. (()"*)(. ,)/ * ",/" ,.

( ,,! "! (),8 X,Yf ,," ," + 6+ ("

$ "()+: ($" )'' ! , ( –

. #"* ")+* "* (),8, 0"() (" (',/" (

"6() ! (1:1000, 1:5000 (.) , (, 8 60/ )"""

"*"+* (()"*)(* ,)/* , ("- (" !,-" !"9", +"()

")+! (),8 /" 60/. ")+ "6() + ( /" *"7,(-!

"7"8 +9" 60). ++, " )"- /" ()) /, (,)"

)0() / )0 !. 9"* *", ")+ "6() + 6(

4894 / 11762 / 36.0 = (( 1/4800 /" (" 6,,/" , ()),).



1

–

50

4.1.1-12: +

')$& #& * 1- +)$.) & '* '1,

+ 608" 6+9+ , ()/ )0, !"-( 6- ). 6

* -) /" ,. ( 4.1.1-13 6 /" 6)+" !( +,

*""8 ) (, , )-" 4.1.1-4.

# 4.1.1-3: #"* )* * *""8, (0,) )" !(. )0.

4.1.1-13: )+" !

4.1.1-5: - " , " "

'$& "0& αααα αααα′′′′ ν νν ν Yij

+ -

Xij

+

-

12 103.40 94°10′00″ 94°09′57″ 187°°°°22′′′′20″″″″ 13.27 102.55

23 157.25 178°19′00″ 178°18′57″ 185°41′17″ 15.59 156.48

34 143.36 118°21′45″ 118°21′41″ 124°02′58″ 118.78 80.27

45 169.08 94°42′25″ 94°42′21″ 38°45′20″ 105.85 131.85

56 176.74 158°07′30″ 158°07′26″ 16°52′46″ 51.32 169.1367 110.60 89°03′55″ 89°03′52″ 285°56′38″ 106.35 30.37

140.83 167°15′50″ 167°15′46″ 273°12′24″ 140.61 7.88

1001.26 900°°°°00′′′′25″″″″ 900°°°°00′′′′00″″″″ 275.95 275.82 339.23 339.30

275.82 339.23

+0.13 -0.07

, 6- ,,)98. ,!+ , 6)+"* !, 6(

000090090)272(90)4n2( ′′′°=°⋅−⋅=°⋅− . "7,)*, ( -6* , 9"* *",, ,("

α1

α5

α6

1

2

4

3

5

6

7

α2

α3 α4

α7

4.1.1-4: $ #. ) ! ,

12 α1 = 94°10′00″ 103.40

23 α2 = 178°19′00″ 157.25

34 α3 = 118°21′45″ 143.36

45 α4 = 94°42′25″ 169.08

56 α5 = 158°07′30″ 176.74

56 α6 = 89°03′55″ 110.60

67 α7 = 167°15′50″ 140.83

" ,! ()" 12 6( ν νν ν12 = 187°°°°22′′′′20″″″″

f Y

f Xf x,y

5 – )" )"

5' – (0,)" )"

4



1

–

51

!"9 *""8, 6- 6( 5200900 ′′′° , 60 /" ,!+ "6)+8" ! /"

52f ′′=α )"- ! (") -/, *"". ,!+ (3 ,) 3″ 4 ,)

4″, )-" 4.1.1-5).

, , +, (,)* + ")8 6:" 0(+ 9),/, +""

+, , )-" 4.1.1-6 (0,) (, " ,!+ ().

4.1.1-6: - "

=2

1ν 0222187 ′′′°

=2α 7581178 ′′′°

6- 7114365 ′′′′° - "6 °180

- °180

=3

2ν 7114185 ′′′°

=3α 1412118 ′′′°

6- 8520304 ′′′° - "6 °180

- °180

=4

3ν 8520124 ′′′°

=4α 222494 ′′′°

6- 0254218 ′′′° - "6 °180

- °180

=5

4ν 025438 ′′′°

=5α 6270158 ′′′°

6- 6425196 ′′′° - "6 °180

- °180

=6

5ν 642516 ′′′°

=6α 253089 ′′′°

6- 8365105 ′′′° - *8" °180 + °180

=7

6ν 8365285 ′′′°

=7α 6451167 ′′′°

6- 4221453 ′′′° - "6 °180

- °180

=1

7ν 4221273 ′′′°

=1α 659094 ′′′°

0222367 ′′′° - "6 °180

- °180

=2

1ν 0222187 ′′′°

)" 6" !(. )0 (0,)" (, (" (+, 66 4.1.1-1.

). 6 (" (, 6 )!*")/(. ',/ (,( (,(

". ,!+ (), /" (, ," () ,+" 6)+". 0,)" +"()

). 6 6" (, , )-" 4.1.1-5. -6* (" 6)+"*

!,, !"-( 6- (+. ). 6 )"- -) /" ,. ("

!"9 *""8 )" 6" (, )7" )"""" !"9*, ) "

(),8 )* (* 6(" f Y = + 0.13 m, f X = - 0.07 m. -

!+/," )" 6" (+" !(" ()" !'0 "()+, )0 ’



1

–

52

- - -( )0 , 6 0.07 m /, 0.13 m ()0 8". " ()/8"

A’A "()+: " "6)+8" ! /" 6( m15.007.013.0f 22

Y,X =+=

,(*"" /" , +, 0/ " ,! 6( 8111807.0

13.0arctan

Y,Xf ′°≈

−+

=ν .

")+ " (),8 + 6( 6700

1

26.1001

15.0

d

f Y,X ≈=

(6,,/" (" ,

()),).

#* 0,8 ). 6 , ( (" /0"9" ()" + 0. #

+*, +" (" 0,/, , (), ,!/

+"0 )" 6". ( (" *"8,/" + 0 .

#+ 0 6 ")()+" !"9 + !(" ()" ()/"

(" !"9 ,!+. ". *""8 66+ * /"! / ()" ,

(, ,! , +, ,+ !(, (),. " !"9 ()"

/" id . ( 4.1.1-14, ,()+ /" *""() )0" 2 , (,

)0, 1 ,(" "! (2) ,!+! (),8 (2B) 0"*, /" 2’ "6,),/, /

)0" 2, ) ,, !"9 6( 22)B2()A2( + .

4.1.1-14: - "

'$)- #$. &$&/ ($- #&/ '$&

"0 !"9" "! "6)+8 + *" ,6) (,()+ 60/.

!"9 *""8 /" )"- ")'+) )). #* )+8 )+.

!"9 ". /" ,") " ,! "! "6)+8 ! (

"* ,!* (+" !(" ()". /" " (),8" 60/,

, /" 66+ !"9* *""8 /"" !(" ()", ) " " ,!

"! (),8 + -) (!( ((0) "* ,!, !(" ()" /

/" 66+ +" 6( "! (),8.

#)& !'"- $')& $,+&' #&/ ))

0() "*" /, "'9"* ")+* "69, !(! + /" ,+" ,6 6)": +)"). *", *")", *!," /" 60/" !"9" , ),

0,8 -,, "*(" 9) " ) .+):+, "" !"9" 6)+8 "

60/. !"9 *""8. 6)+"! !, ")+" (()"*)( ,)/ -" +*" ("7" * 0,8 ). 6. , *",

, /" ! +,!! -, (()"*)( ,)/ ( *" , (, ,"

" ,") "" -) )+". 6 )! 6!, - (" - ,6 "6,)),

) )""(. *""8 /" (,9)(" +().

B

1

2 2’

A



1

–

53

(" , ( ") *" ("() (,0/ *""8 , !(. () ):*,

/" (:,0" *") *""8 , )"), (" 0"() /, ("'/" )0()

*""8 , ):* 6 ," 6), +"() "6)+8" !. )-"

4.1.1-7 )" (, ("'/" *""8 , ):* 6 6.)"+, ")+, "6()

1:5000:

4.1.1-7: ! $ 1:5000

+)$ #$. $!&' &(& %'

*!&* !"0& &':

!"0& 30 m

0() 6+8 )"*")," 4° C ± 0.0014 m

0() ()68 6.)"+" *"

(" ()"68

20 N ± 0.0018 m

0() 6+8 !- )"" 0.30 m/30 m ± 0.0015 m

0() ,+7"8 ):" , + 0.15 m/30 m ± 0.0004 m

0() / /"+ ):" -

")(8

0.0046 m/30 m ± 0.0046 m

0() 6+8 ),"" ,"

):"

0.0015 m ± 0.0015 m

. = ' $

/ $ =

5400

1

30

0056.0

m0056.0000031.0

=

=

( 4.1.1-15 ,()+ /" ,(+ 6()")() ,!+. ". *""8.

*", "*" * -) ) *(* 6+:" (),8" /,

66+ "(!,9, *""8 ,!+ - α E * -) /" *(* 6+:"*

(),8, /, ()* (" "(!,() *""8 , - dE .

/" 6+:" ")+ " (),8" 1:5000, !+/, !"9 ,! "

(*" -) +" "41'000°=α ε ( α ε tan5000:1 = ). )-" 4.1.1-8 6 /" (

"6() ". ,!+. *""8 ,(+ 8.+" 6()")(). ,

6+:" ,!+ (),8" !(! + n () 6( nEα α ∆ = .

/" ") () , +, (") ,!+. *""8) , /" 6.)"+ ")+ "6()

1:3000, *(* 6+:" ,!+ (),8" 6( '25'1 ==α ∆ ()0() ,!

6," *,)). /" 6.)"+ ")+ "6() 1:5000, *(*

6+:" ,!+ (),8" 6( '15"30 ==α ∆ ()0() ,! 6," 30”).

4.1.1-15: $

α ε

α ε

B

A

α E

α E dE

dE

α

C



1

–

54

4.1.1-8: $

')&

#$.

(& #$.

"# -Eαααα

*(- ! (

'!'

1:1000 3’ 26” 1’

1:3000 1’ 09” 1’

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1:7500 28” 20”

1:10000 21” 20”

1:20000 10” 10”

+$)&- #&# )

6+8" !(! + 6(+ (" 6+:"8, *)"*)0! ,(+ '!,"

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(*)+ ((), -),

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# $. +

*-/ /" (,) ).*")/(. (()"* / *!,,/, ,!+,

"6() 30″, ")+ "6() *""8 , " "6 1:300

1:400.

# $ $ . +

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# $ $ . +

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f Y – ,, " (),8" + , +, Y o(" (66 4.1.1-5),

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Y X

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6 176.74 -0.097 0.052 61 247.00 61 961.73

7 110.60 -0.112 0.060 61 140.63 61 992.11

1 140.83 -0.130 0.070 61 000.00 62 000.00

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6 (" +// 0 '*8 +/" *)" (+" )0"

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( 4.1.1-16 (*)/* )0, 2 6*,) !(" ()" ( )0" 1 )0, 2,

°−+= 1801P

2

1 α ν ν , (4.1.1-8)

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=ν σ , 1

21

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4.1.1-16: $

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pν

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1

2

3

n -1

n

d1

dn-1

dn

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XX

3α

1n−α

Y2-Y1

X2-X1



1

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62

=

1m 2

1d

2

1

0

0

σ

σ α , (4.1.1-9)

"()+: +/, *), (, ")* (,0/, (" *) +/()

*""8 +" !(" ()".

:", )" )0" 2 0,/, (" (+, 66 -

)180cos(dXcosdXX

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1P11

2

1112

1P11

2

1112

°°°°−−−−++++⋅⋅⋅⋅++++====⋅⋅⋅⋅++++====

°°°°−−−−++++⋅⋅⋅⋅++++====⋅⋅⋅⋅++++====

α ν ν

α ν ν , (4.1.1-10)

!" (, Y1, X1 )" )0" 1 6 /, (" ")()+: /" "7" -"6 !"9".

#*"* 6 ()8 !"9 -/ (" ("" 66,

=

=

2c 1m2

XXY

XY

2

Y'JJ

222

222

σ σ

σ σ , (4.1.1-11)

!" /" 2C +/ *) ) )0" 2, /" -/ *) /.

6+ -,

⋅−

⋅=

∂

∂

∂

∂∂

∂

∂

∂

=2

1

2

11

2

1

2

11

1

2

1

2

1

2

1

2

cossind

sincosd

d

XX

d

YY

Jν ν

ν ν

α

α , (4.1.1-12)

,

−−−

−−

=

1

1212

1

1212

dXX)YY(

d

YYXX

J (4.1.1-13)

0"*, /" , ,!* 66, ,08" 6*" /". +"(), *",2

1112 cosd / )XX( ν =− 2

1112 sind / )YY( ν ====−−−− . *"* 66 4.1.1-13 , 66 4.1.1-11

*"8"* *), +/ *) ) )0" 2 !(,

−+−

−−+−−−

−+−

=

+−

−+=

2

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1

2

122

112

2

1d21

12122

11212

2

1d21

2

122

112

2C 2

1

22

1d

2

1

22

1

2

1

2

1

2

1

2

1

2

1

2

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1

2

1

2

1

2

1

2

1d

2

1

22

1d

2

1

22

1

2

1

d

)XX()YY(simetricno

d

)XX)(YY()XX)(YY(

d

)YY()XX(

cossind(cossin)d(

cossin)d(sincosd(

σ σ

σ σ σ σ

ν σ ν σ ν ν σ σ

ν ν σ σ ν σ ν σ

α

α α

α α

α α

(4.1.1-14)

#* 0,8, 66 4.1.4-14 -0 (" " *"8,/" , (+// 6+/"/ '*. )*

(,0/,, *) " (" *,)+) ,()/" (,0/ ( +" )0", 0"*,

)"- () (""":



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1. (, ! *""8 1 1d ""(, 0 "6,)) /" "(

(68 66),

2. - +/ 0 , *) (4.1.1-14) - /" , ". /" +"

(""" "/"

11

11

1d

22

1

2

d

d

d

α

α

σ σ

σ σ

====

====. (4.1.1-15)

"- () !"9 ()8 /" "0 )0 2 , 9"* *",, "()+: ("/ (,0/, /" /" ")()+:" /" )0 1 (-7" (,()+ !"9.

(*)* )0, 3, 8"" )" 0,/, ("

3

2223

3

2223

cosdXX

sindYY

ν

ν

++++====

++++====. (4.1.1-16)

5") +"0" , 68"* 66, (, (,0/" *":+" (X2, Y2, d2 α2). +/ *) "6). (,0/. *"+. !(,

=

2m2m2C

2m2C2C

2

dddXdY

d

2

XY

dXX

2

XXY

dYYXY

2

Y

2222222

2222222

2222222

2222222

σ σ σ σ σ σ σ σ

σ σ σ σ

σ σ σ σ

α

α α α α

α

α

(4.1.1-17)

!" /" 2C+/ *) ) )0" 2 -/" (+, 66 4.1.1-14,

2m /" +/ *) "6,)) *""8 ( 22 ,d α ) / /" -0 /! (

22

d 22, α σ σ 0+* /!. ) 2m2C

""6"),/" "/, 6*"7,

) )0" 2 +. *""8 22 ,d α . + !" *" (" 6:,0) "*

"/", *"7,)* /" ), (" )*" ""* :" 6+) , +, +!

"*"). (), , 66 4.1.1-16 6+/"*, ("

3

22

2

1113

3

22

2

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cosdcosdXX

sindsindYY

ν ν ν ν

++++++++====++++++++==== 4.1.1-18)

[ ]

[ ])180)(2((cosd)180cos(dXX

)180)(2((sind)180sin(dYY

21p21p113

21p21p113

°−+++°−++=

°−+++°−++=

α α ν α ν

α α ν α ν . (4.1.1-19)

-/ *) (()"* (4.1.1-19) !(

−−−

−−−

−−

−−

=

−+−

+

=

∂

∂

∂

∂

∂

∂

∂

∂∂

∂

∂

∂

∂

∂

∂

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=

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1

1213

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2

3

22

2

1

3

22

2

11

3

2

3

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2

1

3

22

2

11

2

3

2

3

1

3

1

3

2

3

2

3

1

3

1

3

d

XX)YY(

d

XX)YY(

d

YYXX

d

YYXX

cossindcos)sindsind(

sincosdsin)cosdcosd(

d

XX

d

XX

d

YY

d

YY

J

ν ν ν ν ν

ν ν ν ν ν

α α

α α

(4.1.1-20)



1

–

64

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+/ *) /! 6!",

)(diag 2

d

22

dm

2

22112 1σ σ σ σ α α ==== . (4.1.1-21)

#6" (4.1.1-20) (4.1.1-21) *" (" 6+"() 66 6 0,8" +/" *)"

)0" 3 / "()+: ("/ (,0/ + ( (* +" ()". 9)"*

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[ ]

[ ][ ])180)(1n(...(cosd

...)180)(2((cosd)180cos(dXX

)180)(1n(...(sind

...)180)(2((sind)180sin(dYY

1n21pn

21p21p11n

1n21pn

21p21p11n

°−−+++++

+°−+++°−++=

°−−+++++

+°−+++°−++=

−

−

α α α ν

α α ν α ν

α α α ν

α α ν α ν

(4.1.1-22)

(, *""8 ,!+ , *"7,(- "6+( , (, !"9" ).

) )0" 1 /"" ,, *"* 6 ()8 !"9 -" ("

+/ *) 6 )0, n / !(

−

==

Cn )1n(m 2

XXY

XY

2

Y

2,n12,n2n2,n2

nnn

nnn'JJσ σ

σ σ . (4.1.1-23)

(" "). 66 6+/" -//, (" )0" '*," 6 0,8" ().

(),8 )0 !(! + (, 6)" +"() () *""8 ,!+

, 22

d ii, α σ σ /" !("

2

d

1n

1i

1n

1i2

i

i1ii1i2

1n1nYX

1n

1i

1n

1i

2

d

2

i

i1i22

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2

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1i

2

d

2

i

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2

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iin

d

)XX)(YY()YY)(XX(

dXX)YY(

d

YY)XX(

σ σ σ

σ σ σ

σ σ σ

α

α

α

−−−−

====

−−−−

====

++++++++

−−−−

====

−−−−

====

++++

−−−−

====

−−−−

====

++++

−−−−−−−−++++−−−−−−−−−−−−====

−−−−++++−−−−====

−−−−++++−−−−====

(4.1.1-24)

# 4.1.1-4: (+, ) *""8, (0,) +/, *), )0" B( (" )+"*-("* +,) (0,) *")" ()" "("

!"9 6 (), )0,.

# α σ "0&

dσ

43351721 ′′′°=α 2″ 832.281d1 = m016.0

41221852′′′′′′′′′′′′°°°°====α 2″ 300.271d 2 = m016.0

91622083′′′′′′′′′′′′°°°°====α 2″ 100.274d 3 ==== m016.0

15312054′′′°=α 2″

' +("' X Y

7.205168p′′′°=ν P 68478.139 62483.826

5.3011300z′′′′′′′′′′′′°°°°====ν Q 67709.336 62263.411

PQ

Bα1

α2

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A 68231.288 62347.833

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) 0,8" +/(" +/(" 6 )0, B

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rad106962736.9)10)(8481368.4)("2( 66

i

−− ⋅==α σ , +/( 6(

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i

−⋅=α σ

- /( *""8 , 6(: .m1056.2016.0 2422

di

−⋅==σ

- . 66, (4.1.4-24) +/(" +// ) )0" B 6(":

= =

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242

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m1087843.1d

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m1029166.1d

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m1018457.4d

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iinn

ii

ii

σ σ σ

σ σ σ

σ σ σ

α

α

α

+/ *) !(:

2

BB 44

44

m1029166.11087843.1

1087843.11018457.4

⋅⋅

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YX

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X

2

Y

2

X

2

Y

2 ====−−−−++++++++−−−− σ σ σ λ σ σ λ

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+"()) "'9, +", *, ,(, "(", /")/, "(" 0,*

2

X

2

Y

YX22tan

σ σ

σ θ

−= . +) θ 2 "7,/" (" (+, 08"" /" 6 ',/"

θ 2sin () 6 YXσ , 6 θ 2cos () 6 2

X

2

Y σ σ −−−− . 9"* *", ("

/":- +" ,(: a = 0.023 m

- * ,(: b = 0.0006 m

- ,! /")/": 2126 ′′′′°°°°====θ (, (, 6)+ (*" X (").

: #6 (), () (" (* , '6 8 !"*")/" +,

("- )+". !. " + (), -/8 ()!! ,6!

"9"8 () *") /*8. +).



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(), (.).

". "* 6 "6/, !(. ++ , 3 (), (:

), (), ( *** "6,/* *""8 .6). +"). ,!+ 10”,

"'")" (-( 6/" ( ))* ()*),

+" *"" *",

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4.1.1-17: % $ 3 %

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$(!

= _____ p = _____, ..=_____, mm/km=_____.

172°53′34″

% 91°09′55″ 281.832 -5.688

% 185°22′14″

88°45′18″ 271.300 +6.197

%

208°26′19″

87°15′48″ 274.100 +13.161

205°13′51″

"):

"*":

...

4.1.1-18: - ,

). ,

m

.,! #-" )"

Y X

H’

m

6+)" )"

Y XH"'.

m

B 68478.139 62483.826 185.132 68478.139 62483.826 185.132

281.832 241°08′58″

C 68231.288 62347.835 179.444 68231.274 62347.824 179.437

271.300 246°31′15″

D 67982.450 62239.744 185.641 67982.423 62239.722 185.626

274.100 274°57′37″

E 67709.377 62263.444 198.802 67709.336 62263.422 198.780

(67709.336) (62263.411) (198.780)

f Y = - 0.011 f X = - 0.033 f H = + 0.041

f YXH = 0.053 m 1:15 300



1

–

67

.' $#'$ $#'$ #&# )

6+8 !(! + '* (" 9) "!() (4.1.1-17) "!()

!(! + (4.1.1-18) , /* (, 6" (+" '*/" )0*

!(! + ()!,)/ )0(). #" +"". "!(), , )!*")/(*

-(, 25 6" (, )" +(" ). +"7". )0 (( 4.1.1-

19).

4.1.1-17:



1

–

68

4.1.1-18: - "



1

–

69

4.1.1-19: . 25

4.1.2. ' ('! /$+&'&# +,&$-

9) /" 0"), +! !+: (),), (* !*")/*, / )0 ("

*" ") ,!" 0". :"* )"(), -/("* (+" " "

0 "'(8 / )0, ):

#"("8"* +;

+/ ,+ ), +,; ,0* "("*;

#*"* # )".!/".

!$8)- 0* &+&' '1 $,-( – +&' !"0& !$,&

"#) &+&'* '1

)" "6)" )0" *!, (" (0,) , (, * 6)" )" /""

)0" " ,! , "6)/ )0. -! )", 6 "'(8"



1

–

70

/ "6)" )0", , ( (" ()" /*8" +" 6)" )0". ( 4.1.2-1

6 /" (),/ / (,/" +"" (,0/.

4.1.2-1:

). )0 C "7+8 / "6)" )0" B *"" (, ,!+ α β.

, b " ,! C

Aν 0,/, (" 6 ) ). )0,

( )[ ]

AC

ACC

A

2

AC

2

AC

XX

YYarctan

)XX(YYb

−

−=

−+−=

ν . (4.1.2-1)

," a c 0,/, (" ()" (,(, )""*, , ),!, ∆ABC, (+, 66

λ

β

γ

α

sin

sinbc

sin

sinba

⋅⋅⋅⋅====

⋅⋅⋅⋅====

, (4.1.2-2)

, ,! γ 0, (" )(180 β α γ +−°= .

(+, ) 0,8 ) *""8 ,!+, 0,/, (" " ,!+ () AB CB, )" )0" B "7,/, (" ( -" )" )0", "6+(

B

AA'B

B

AA'B

coscXX

sincYY

ν

ν

⋅+=

⋅+=, (4.1.2-3)

,

B

CC"B

B

CC"B

cosaXX

sinaYY

ν

ν

⋅+=

⋅+=(4.1.2-3-)

"')+" )" "6)" )0" 0,/, (" )*")0 (" + "9"8.

6 + "9"8 * -) , (, ( 6.)"+* )09, "*" / /" "'(

!+/,* )".0* ()* )0().

1"&- $!&' &+&' '1 $,-( – $ $), !) !' '1

(+)

)" "6)" )0" B *!, (" (0,) ") (+, *""8 ,!+ α β (0,)" +"() ," -6" C 6*"7, +" )" )0" (( 4.1.2-1), ("" 0.

(+, (4.1.2-3 -) ("

c

a

b

B

Cα β

γ



1

–

71

(((( )))) )cos()sin(

sinbXcos

sin

sinbXcosaXX A

CC

A

CC

B

CCB β ν β α

α β ν

γ

α ν ++++⋅⋅⋅⋅

++++⋅⋅⋅⋅

++++====++++⋅⋅⋅⋅⋅⋅⋅⋅

++++====⋅⋅⋅⋅++++==== . (4.1.2-4)

-6* /" β ν β ν β ν sinsincoscos)cos( A

C

A

C

A

C−−−−====++++ (6 ,! β "'9" (" (+,

")" (),/"), /"

b

XXcos

,b

YYsin

CAA

C

CAA

C

−−−−====

−−−−====

ν

ν

(4.1.2-5)

(" (,

β β β ν sinb

YYcos

b

XX)cos( CACAA

C

−−−−−−−−

−−−−====++++ . (4.1.2-6)

(" 66 (4.1.2-6) ,+() , (4.1.2-4) -/ ("

β α

β α β α β α

β

β α

α β

β α

β α

ctgctg

ctgXctgX)YY(

ctgctg

)YY(

ctgctg

ctg)XX(X

)sin(

sinsin)YY(

)sin(

cossin)XX(XX

ACAC

CACA

C

CACACB

++++

++++++++−−−−====

====++++

−−−−−−−−

++++

−−−−++++====

++++−−−−−−−−

++++−−−−++++====

. (4.1.2-7)

() 0 *" (" 6+"() 66 6 Y ),, (

β α

β α

ctgctg

ctgYctgY)XX(Y ACCA

B +

++−= . (4.1.2-8)

#*" 66 (4.1.1-7) (4.1.1-8) "). 6+:"8" ,(+ 6- ,!+ , ),!,

( °°°°====++++++++ 180γ β α )11

.

66 (4.1.2-7) (4.1.2-8) (, 0,( "'(, , () "* ,(" )" 0,8. 6 )! 6!, /" ! *!,", )"- ,:,0) /9 /", 6), )0, )

'*) /9 /" "6+( "9"8". 0 "9"8" )"- (0,) )*")0,

(", + "9"8, 0"*, +) 0, 6 + "9"8 " (*" -) +"

6+:"" +"() "'(" ()* )0() "*" (( 6.)"+*

/")).

1"&- $!&' &+&' '1 $,-( – $ $*&'&/ $),

(, /")( + () B CB 6)" )" )0 C,

/"0" +. AB CB ("" ") 6 )0" !"*")/". ),!, 1, *" ("

() ("" 66

0XctgYctgYX

ctg)YY(XX

C

B

CC

B

CBB

B

CCBCB

====−−−−++++−−−−

−−−−====−−−−

ν ν

ν . (4.1.2-9)

0, , ),!, 2 + ("" 6(

11 6- ,!+ , ),!, /" /" 180°, (),8" )"- /" (") (+* ,!,.



1

–

72

0XctgYctgYX

ctg)YY(XX

A

B

AA

B

ABB

B

AABAB

====−−−−++++−−−−

−−−−====−−−−

ν ν

ν . (4.1.2-9-)

,6*8"* (4.1.2-9-) (4.1.2-9) -/ ("

B

C

B

A

B

AA

B

CCAC

Bctgctg

ctgYctgY)XX(Y

ν ν

ν ν

−−−−

++++−−−−−−−−==== . (4.1.2-10)

"9"8" BX " (4.1.2-9) (4.1.2-9-) 6!"

B

AABA"B

B

CCBC'B

ctg)YY(XX

ctg)YY(XX

ν

ν

−−−−++++====

−−−−++++====. (4.1.2-11)

")." *")", "* )" )*")0. "/. ), 0,8

*!, (" ()) 66 (4.1.2-3) (4.1.2-3-). 6 (0,). ) "6)" )0" ()" 66 (4.1.2-11) * -) , !* 6.)"+" )0().

4.1.2-2: - "

# 4.1.2-1: (+, (),/" ( 4.1.2-1, ). ) ) *""8,

(0,) / "6)" )0" B (Anderson and Mikhail, 1997).

) : YA= 63 369.287 m, XA = 62 890.836 m, YC = 63 300.259 m, XC = 63 082.183 m.

""8: α = 81°17′38″, β = 64°32′28″.

$3:) (+, ," "! ,! (66 4.1.2-3 4.1.2-3-)

- , AC: b = 203.41716 m (66 4.1.2-1)

- " ,! ()" AC: "47'09340C

A °=ν (66 4.1.2-1)

- " ,!+ () AB CB: "09'52258B

A °=ν "15'42224B

C °=ν

- 0,8" ,! : "54'0934"15'42224"09'52258 °°°°====°°°°−−−−°°°°====γ

- ) ,(+ 6- ,!+ , ),!,: "00'00180°=++ γ β α

- 0,8" , () AB = c, CB = a: m050.327a ==== , m051.358c = , (66 4.1.2-2)

B

C

XB - XA XB - XC

YB - YCYB - YA

X

Y

νAB

νCB

2



1

–

73

- 0,8" ) "6)" )0": m699.62827X,m389.63048Y 'B'B ======== (( )0" )

m699.62827X,m389.63048Y "B"B ======== (( )0" B)

) #"("* + ( +" )" )0" (66 4.1.2-7 4.1.2-8)

m389.63048Y

m700.62827X

B

B

=

=

# 4.1.2-2: (+, (),/" ( 4.1.2-1 , ). ) ) *""8,(0,) / "6)" )0" B " ". ,!+ (66 4.1.2-10 4.1.2-11).

) : YA= 63 300.259 m, XA = 63 082.183 m, YC= 63 047.954 m, XC = 63 048.344 m.

""8: α = 37°39′28″, β = 97°31′31″.

$3:

- " ,! ()" CA: "40'2182A

C °=ν (66 4.1.2-1)

- " ,!+ () AB CB: "11'53179B

C °=ν , "12'42224B

A °=ν

- 0,8" ,! γ : "01'4944"11'53179"12'42224 °°°°====°°°°−−−−°°°°====γ

- ) ,(+ 6- ,!+ , ),!,: "00'00180°=++ γ β α

- 0,8" ) "6)" )0":

m392.63048YB ==== (66 4.1.2-10)m694.62827XB ==== (66 4.1.2-11, " )0" ).

# 1: #* 0,8 ) "6). )0, ()" - /,

) +"" (),, 0,8" (" -+: ( /"* 60/* '* +9" -/

60/. ' ) ). )0.

# 2: #" 0") 0,8 "), (),/, /")() 0

( 4.1.2-1. 6+""" '*," (, "'(" , (, ( 6* ")+*

(* )0 *""8* , ),!,.

!$8)- 0* &+&'/ '1 & !"0 +(8" !) !' '1 & "$)&*

( 4.1.2-3, )" / "6)" )0"12

i, / (" 6 / 6*"7,

+" )" )0" AB ( *", !(/ ()), 0,/, (" (+, 6). 66 6

)0" !"*")/" / !("

)YY(d

dYY

)XX(d

dXX

AB

AB

Ai

Ai

AB

AB

Ai

Ai

−−−−++++====

−−−−++++====

. (4.1.2-12)

#* "'(8 / )0" /, ". /" ,, dAi 6*")

-(). 6 *""8 ," " 6 * -) , 6+:"* !*

)0() *""8. (* )!, 6 ), )0(), *" (" , )0" i /8" )0" , (!(" ()"). 6 6- /". ( )0" B *"". " 6 * -) , 6+:"* !* "'(* +"* (*.

13

(" "6) )0 " 6 / (!(/ ()), 8"" )" ("

0,/, ("" 0. #+ (" (,() ,+ ( "6)" )0" , B (,+

(" (,9) )")*, )()* ")()* 6*" (.), 6)* 6*"" ,"

12 / "6). )0 / /" !0" 6+( /" )"- "*".

13 # +"* (*, 6+:" (),8" 6+( ," ()", )"!/" )"" "6()

*""8 ,.



1

–

74

ADd 0")" )0" / ,+" ()0 D, ( 4.1.2-4) 8" "6)"

)0" i - id .

4.1.2-3: 0 #

#* 0,8 ) )0 ,+. ), (), 6,/, (" + (,0/:

- )0 i (" 6 ( "(" ()" , AB:

AB

ABiAB

AB

ADA

B

AiDi

AB

ABiAB

AB

ADA

B

AiDi

d

)XX(d)YY(

d

dY

cosdYY

d

)YY(d)XX(

d

dX

sindXX

−−−−++++

−−−−++++====

====⋅⋅⋅⋅++++====

−−−−−−−−

−−−−++++====⋅⋅⋅⋅−−−−====

ν

ν

. (4.1.2-13)

% - )0 i (" 6 ( "+" ()" , AB:

AB

ABiAB

AB

ADA

B

AiDi

AB

ABiAB

AB

ADA

B

AiDi

d

)XX(d)YY(

d

dY

cosdYY

d

)YY(d)XX(

d

dX

sindXX

−−−−−−−−

−−−−++++====

====⋅⋅⋅⋅−−−−====

−−−−++++

−−−−++++

====⋅⋅⋅⋅++++====

ν

ν

. (4.1.2-13-)

4.1.2-4: 0

ν

dAi

B (YB,XB)

A (YA,XA)

i (Yi,Xi)

YB – YA

XB – XA

Y

X

D

ν

didAD

B (YB,XB)

A (YA,XA)

YB – YA

XB – XA

Y

X

i



1

–

75

1"&- $!&' 0* &+&' '1 & &)" ($- !"0&

)" / "6)" )0" *!, (" ") *""8"* , /*8" )

6)" )0". ( 4.1.2-5 ,()+ /" )+ (,0/. ). )0 A, B C

-() (, *""" ," "6)" )0" P. #-"* (" (+ "9+8" ),!,

0"*, /" ". ") ,,)98" ,!+" *"* (,(" )""*".

+* , -"" (" /" ),! (0, " ,! , ()" /

(/ +" )" )0" (, )* (,0/, )0" A,B)

AB

ABB

AXX

YYarctan

−−−−

−−−−====ν , . (4.1.2-14)

2

AB

2

ABAB )XX()YY(d −+−=

)* (" *"* (,(" )""*" 0, ,! ∠ BAP = α

APAB

2

BP

2

AP

2

AB

dd2

dddcos

⋅

−+=α , (4.1.2-15)

" ,! ()" AP

α ν ν ++++==== B

A

P

A . (4.1.2-16)

4.1.2-5: $

0, )" "6)" )0" 0,/, (" (+, +" 6). 66

P

AAPA'P

P

AAPA'P

sindXX

sindYY

ν

ν

⋅+=

⋅+=. (4.1.2-17)

)" "6)" )0" P 0,/, (" " ) )0" B, 0"*, (" "). (0, ,,)98 ,! , ),!, ABP )"*" B,

BPAB

2

AP

2

BP

2

AB

dd2

dddcos

⋅

−+= β , (4.1.2-18)

" ,!

β ν ν −= A

B

P

B . (4.1.2-19)

α

dCP

dBPdAP

AB

P

C



1

–

76

0, )" )0" P !("

P

BBPB"P

P

BBPB"P

sindXX

sindYY

ν

ν

⋅⋅⋅⋅++++====

⋅⋅⋅⋅++++====. (4.1.2-20)

"')+" )" )0" P 0,/, (" )*")0 (" + "9"8,

2

XXX

2

YYY

"P'PP

"P'PP

+=

+=

. (4.1.2-21)

6 + "9"8 " (*" -) +" 6+:"" / (" "'9" !+/,*

(* /")* 6.)"+*14

.

)" "6)" )0" *!, (" ") 0,8"* , +* ),!, / (" *"

'*) "* ( 4.1.2-5 ( *", ∆APC). )* (,0/,, "')+" )"

0,/, (" )*")0 (" "9"8 + ),!. 6 + "9"8 * -) ,

!* )0() ) ). )0 !"9 *""8 , "6)" )0".

), 0,8, ()" (" ("" 66 (),! ∆BP)

ABBPAP dcosdcosd =+ β α , (4.1.2-22)

(,

β sindsind BPAP ==== . (4.1.2-23)

6 /"() " (*" -) +" +()," +"() 60/" '" 0,8.

# 4.1.2-3: )* ()* / /" ()+:" "6), )0, P 6*""" (,

," ). )0 A, B C. (+, ) ). )0 "6,)) *""8

, ") )" / "6)" )0".

)" )":

Y = 61275.129 m XA = 60793.216 m

YB = 61421.831 m XB = 60781.472 m

YC = 61312.714 m XC = 60621.201 m

""8:

dAP = 63.177 m

dBP = 97.710 m

dCP = 136.930 m

$3:) ),! ABP∆

0,8" "! ,! ()" AB: "38'3494B

A °=ν ,

0,8" ," ()" AB: m171.147d AB = ,0,8" ,,)98"! ,! )"*" : "20'0030°°°°====α ,

0,8" "! ,! ()" P: "58'34124P

A °=ν ,

0,8" ) )0" P:m357.60757X

m143.61327Y

P

P

====

====

*() (0,) )" "6)" )0" P, 6" ) )0" .

14 #"* +"* (* 6+:" 6 ) + "9"8 " (*" -) +" 6+:""

+"() ,,! "! (),8 6 1. )"!/, )"" *", ')* 1.5.



1

–

77

4.1.3. '&!$! '1&' 0* '1 $( 8"&$!&* $#&+,* +

'&!$!+,*" – ISO4463

&)& ($($&) ($0 &'$&/ '1 #!' &)

6+:"" +"() (),8 *""8 ( 0,8) , ,!+ * "$

)0 !"")(" (+" 6("

- 6 ,": mmL75.0± ,

- 6 ,!+":L

045.0 °°°°±±±± ,

!" /" L , 6*"7, *. )0 , *")* ( ,!+, L /" () +).

6+:"" +"() (),8 *""8 , ,!+ * /

*. )0 6("

- 6 ,": mmL2± ,

- 6 ,!+": °°°°±±±±L

135.0.

!+ (" *"" /"(",* )")* - /*8" + !,(. ," (" *""

(% (),*")*. * -/ *""8 , " (*" -) *8

+. ""8 0"0* ):* */, (" +) 6 ,)/: 1) , 2)

, 3) " 4) . #* *""8 0"0*

):* * (" ()) )"! 6 6)"68" ):". (),*") * -)

() -( -6* 6 -/,.

"& ("&!$&) ($0 &'$&/ '1 #!' &)

6+:" +"() (),8 *""8 , *

(0,)" ," )" )0" *"" *"" )0" ("," *"" 6(

mmL2± .

6+:" +"() (),8 * 6*"7, +"

)0" ("," *"" 6(, 6 ,"

mmL2± ,

!" /" L , , *")* (6 L " 10 m, 6+:" (),8" 6( mm6± ) 6

,!+"

°°°°±±±±L

135.0,

( ,!+, L /" () +).



1

–

78

!+ (" *"" )")* ( /*8* "* 1 *,)", /*8" , /"* !,(,.

," (" *"" 0"0* ):* (),*")*, ( /*8" + *""8, -

/* *")*. ""8 0"0* ):* */, -) +:" 6 ,)/: 1)

, 2) , 3) " 4) . #* *""8

0"0* ):* * (" ()) )"! 6 6)"68" ):". (),*") *

-) "0 () -( -6* 6 -/,.

+):& !'"- ! 0)- $*')&/ '1 6+:" (),8" ," 6*"7, )0" ("," *"" -"""" )0"

6*"7, +" -"""" )0" 6(

mmLK± ,

!" /" L , , *")*, /" ()) / 6+( +() "):" )0" ()-"

4.1.3-1). L*8" 5 m 6+:" (),8" 6( mmK2± .

6+:" (),8" ,! 6*"7, + + (*"7,(- 6+() +" (,("" "):"

)0" 6(:

°°°°±±±± KL

0675.0,

!" /" L , , *")* " ()" + +, /" /" "'( ())

()-" 4.1.3-1).

4.1.3-1: , "

$ (ISO 4463).

$(&

10 " "

5 " ( ,

, # .)

2 /

1 1- ( , , .)

4.1.4. 1"&- )$.& +')$& %#"$ (9" $!&' $(&/ '1

(, 6)" )" )0 6)+"! ! (( 4.1.4-1) 6 0,8"

+9" '!," + (""" + –

% % Y

X , )/.

)XX(Y)XX(Y)XX(Y)XX(YP2 314243132421 −+−+−+−= . (4.1.4-1)

6+(() (*" 0,8, -/" +"() +9" *" -) 6)+

"!)+, 0"*, (", !0, ,(+/ 6)+ +"().



1

–

79

# 4.1.4-1: (+, ). ) )0 6)+"! ! (0,) +9, '!," (Kavanagh, 2003).

X Y

1 1089.981 935.049

2 1000.000 1000.000

3 1078.754 1068.139

4 1046.635 1205.498

5 1154.366 1030.252

P = 150.3 ha

4.1.5. ('$* $)"#/ $!&'

(, 6)" )" )0 A B, *!, (" () ("" 66:

(((( )))) (((( ))))

.

cos

XXd

,sin

YYd

,XX

YYtan

,XXYYd

BA

ABAB

B

A

ABAB

AB

ABB

A

2

AB

2

ABAB

ν

ν

ν

−−−−====

−−−−====

−−−−

−−−−====

−−−−++++−−−−====

(4.1.5-1)

" 0")+) 66 , '*, (4.1.5-1) ()" (" 6+( +"0" )" 6", 0"*, (" +"()+ /" 66, ( +"* )* 6*.

#6" + )" !"*")/", /"0 +" /" 6*"7, ). )0 B !(:

4.1.4-1: -

2

3

4

1

X2

X1

X3

X4

Y1

Y4

Y2

Y3



1

–

80

12

1

12

1

YY

YY

XX

XX

−−−−

−−−−====

−−−−

−−−−, (4.1.5-2)

(, 6" 0")+)" /"0" , (4.1.5-4), ("

)XX(

YY

XXXX 1

12

1212 −

−

−=− , (4.1.5-3)

!" /" mctg)YY /()XX( B

A1212 ==−− ν - !- , B. (, 6)" )"

)0" " ,! ()" B, /"0 +" !(

)YY(ctgXX 1

B

A1 −−−−====−−−− ν , (4.1.5-4)

, /"0 +" ,+" B !(

)YY(ctg

1XX 1B

A

1 −−−−−−−−

====−−−−ν

. (4.1.5-5)

"0 '!," ,! - – ," !(

222 r)KX()HY( =−+− , (4.1.5-6)

!" /" r - ,"0 ( /,() ," ( )* ") (K,H), (( 4.1.5-6),

(X,Y) (, )" "6)" )0" P / (" 6 ,. /" ")

," , )* 0"), )! (()"*, ) /"0 ," !(

222 rXY ====−−−− . (4.1.5-7)

4.1.5-1: ) $

X

Y

PC (K,H)

P (X,Y)

(K,0)

(0,H)



1

–

81

# 4.1.5-1: #"* (),/ ( ). ) "*. )0 (0,)

)" )0" "(" , EC DB (K1) .

X Y

A 1000.00 1000.00

B 1250.73 1313.61

C 1302.96 1692.14

D 934.77 1684.54

E 688.69 1160.27

$3: (+, (4.1.5-2),

EC: X = 1.1549250 Y – 651.3355

DB: X = - 0.8518049 Y + 2369.669

2.0067299 Y = 3021.004

)" )0" K1

Y = 1505.436

X = 1087.331

# 4.1.5-2: (+, ) ). , *", 4.1.5-1, (0,) )" )0"

K2 "(" , ED +" ,+" 8, / 6 6 )0" B, 6)* (0,) ,"

K2D K2E.

$3:

) 0,8" ) )0" K2

(+, (4.1.5-2), /"0 ED !(

)27.1160Y(27.524

08.24269.688X

27.116054.1684

27.1160Y

69.68877.934

69.688X

−−−−====−−−−

−−−−

−−−−====

−−−−

−−−−

(+, 66 (4.1.5-3) *" (" ()+) /"0 , BK2

)61.1313Y(08.246

27.52473.1250X −=−

, ","7"8 !8. 66 -/ ("

: 09.144XY46938.0 =−

BK2: 36.4049XY13049.2 ====++++

:" /"

102.1502Y

27.3905Y59987.2

=

=

6*"* (0,)" +"() Y , !8, /"() (66 6 ), -/ ("

15.849X =

) 0,8" , K2D K2E

62.377d

53.201d

EK

DK

2

2

=

=

): 15.579dd EKDK 22====++++

15.579dED =

BC

D

E

2

1



1

–

82

4.2. 54 6 7

" ), 6+8" )"" 6.)"+ " /! +(( 6.

((, )"" (" (,/" *,: " "

().

((" 6" *!, (" *") (""* *")*:

") !"*")/(* +"** – ")* *""8"* +"). , (/"6/ *"));

") )!*")/(* +"** – *""8"* 6"). ,!+ (.

,;

.*")/( – +")" ," (" "7,/, ).*")/(* *")*;

*")/(* +"** – *""8"* 6 )*('"(! )( 60)* ()*;

+*")/(* +"** – *""8"* 6 !+)" (" ,6 * !+*");

"/* (()"** 68 – () (" "/ )'* ( )

*"7,(- ,+" (". ") )0() (" "" 15 50 cm, ,*

60 km 100 km;

# )".!/* – +(" (" (" "'"") "(. +7"8" "(. +( +9 +")! ,* +9 (" (+, 6+8 ( 6*"7, !"

"( (,,/" !").

+, +! !+: "):/" " (" () *")" !"*")/(! )!*")/(!

+"*.

4.2.1. ('$* &)(& - #&$& &)(&

('$*( &)(&( (, )"), (" *" ("() 6+ – '""/

+"*) (" 6+ "/ "7+8 +((. 6 6*"7, )0 6"*:/

+9 ( "") *"* ("-. (),*") (+") .6)/ +6,.

"*")/( +"* (" " :

#&$& +"* (() (" 6 "7+8" +( ""),

&)(& '1 !': (!':& &)(& - () (" 6 "7+8" +(

"):. )0 – )!'(" +9 )"", ,6,. "0. '

)"").

"")(" 6" '60/ +9 "*:" ( 6)* (,)* +(* 6+/, ("

. "" *!, -) . "/ )""(.

*""8 /* (" ,6 * +" 6 (,). +( "" 6+ ("

. +"8" , !""* +"*, ,+" (" 6+ 6 , )/.

( - /"* ,:"9, +" 68" "8" ")+". ()/8" 6*"7, + "" 6+ (" . 9" +"*(. () '*

.

+"*( + *" -):

6*"7, + ) "",

,

((").

9" +"*(. ++ *"7,(- +"6. 0" .



1

–

83

)(& $$

#* 6- / +"*(. )0 ( "") ". /" (,) ("""

6.)"+":

)"" * -) 0+() ()-, -/") , /" (" "" ,!7,/,,

"" * -) ()+:" ) (" 8"! *" ()+) 0)) ")+,

+"*( + " (*"/, -) "+9" ,!.

"" (" 67,/, +"! !+7 60). - *"6/ / 6+(" : 1) " 2) , /, (" "" ()+:. "" (" , -/") ()+:/,: 1) " (, -/")") 2) ((),-, ()"). 26)

"" *!, -) +/ – +" 6+ + -/") (,!) ) (" 8. *" ()+) ")+ (, , + -/") ) (" +6 * )+ (2 mm) / ("

6 , (" 0"! " "". 26) "" /" (" ()+: ")+,()+:/, (" , ()-" -/")" )/! )", /*8" 0.5 m 6 )!'("

+9. 26) "" + ( 6* ()+:/, (" +(, 1.5 m - 1.8 m.

4.2.1-1: 2

26)" """ )"- ()+) /*8" 30 " +"8. , +

+"* "* -/") !. 6 ()+:8" "", "" (" *!, ()+) ,

"+) '," -")(" (),-+" ()"". 8 +9 "" + 6 (),-

(()"") ) (" 8"! *" ()+) ")+. ()-6/" "" ,6* (" (

/ / !"" (: , "

, $ .

)(& )

(" +" )0" 0/, +((, 6, )"- ") )+* *"7,(-*

()/8, (" " *" ") (* ( /"" ()", ) (" +((" 6"

6 *""8"* +9" () (-8"* /"0. *""8 +((. 6.

0" 0/" +(" ()* (* +"*" - (0, +(" )/. ""

6+/, (" )0*. "6 )0 (-""+/, (" , -, ...) /"()" *"() // (" +9 0)8" ")+" * "( ( /"" ,!, (),. 5)8" (+ ())

")+" / (" 6 (,) (*" ")8 6+ (" , (*, ")+,

6+* . 5)8" ")+" , (*", ")8 (+"6 )0 ) 6+ ("

, (*, ")+, 6+* . ), *""8, +"6" )0" ("

()+:/, +"*(" ,0" *") 0.

4400 114400

3300

3300 – – 5500 ccmm

11..55 – – 11..88 mm



1

–

84

4.2.1-2:

#")()+* (" "7,/" +(( 6 6*"7, )0 B. (+, )

*""8 ()* ( 68, "8, ")+,), (0,)" (, +((" 6" (+/

(),

nn

22

11

PZ

'

n

...PZ

'

2

PZ

'

1

llh

...

llh

llh

−=

−=

−=

∆

∆

∆

. (4.2.1-1)

) 0,8 6+ (" (-8"* ( -" ()" /"(), )/.

[[[[ ]]]] [[[[ ]]]]PZ

' llh −−−−====∆ . (4.2.1-2)

"6) +(( 6 +"*(" ()" (6*"7, "" A B) -/ (" (-8"*

+((. 6 (+/ (),

[[[[ ]]]]'hHAB ∆∆ ==== . (4.2.1-3)

/" 6) +( )0" , +( )0" B 0, ("

[ ]'hHH AB ∆+= .

-! 6.)"+ ,6() " +( )0, +"8" (" 0"() +9 , (,)* (*",.

"')+ +"() +((" 6" -/ (" )*")0 (" +"8

" 6. " (" +") (* , /"* - (*", 6+( +()"

!""! +"* 6.)"+ ")! /").

)(& ) "('&"' +(8" !) !' $$

" (, RA RB + "" 0/" (,)" +(" 6(" HA HB. 6*"7, ). ""

()+:" /" n "6). )0 ( "", !(. )0 (.), 0/" +(" /"

". ") !""* +"**. " (, *""" +((" 6"

+"*(. () '

n

'

2

'

1 h,...h,h ∆∆∆ , ," +"*(. () n21 d,...,d,d .

". /" (0,) +(" "6). )0 n21 H,...,H,H .

151.9936,

R100 ). 1

). 2

") ),*

151,520

1,205

152.725

152.725

0,852

151.873

1,120

0,652

151.341151.993



1

–

85

4.2.1-3: , #

) :

" # "

, )/.

AB

'

i HHh −=∆ , (4.2.1-4)

(" !"9 *""8, !"9 ). +( (., ,(+ " ") -) 6+:", )

/"() (4.2.1-4) /0"9" "" -) 6+:". *", /+" (" 6 Hf / ("

0,

H

'

iAB f h)HH( ====−−−−−−−− ∆ , (4.2.1-5)

"()+: $ (,*"),)! +15

). /" Hf ,

6+:"* !*, ,, $ Hf ("" ("

+((* 6* +"*(. (), )" ().

"() 6+:"! (),8 6+( :

, ,

$ .

#(), 0,8 + *""8 +((. 6 (,(+ 4.2.1-5 * -)

6+:"), 0,8" "')+. +((. 6 "')+. +( ""

6+ (" .

0,8" + *""8 +((. 6 !"*")/(* +"** +9 (" (+, 66 -,

i

H'h

p

1

p

1

f v ⋅

=∆ , (4.2.1-6)

!" /" ip !+/, )" *""8 +"*(" ()" / 6+( :

15 /" +"*( + 6)+" !, ) /" HB –HA = 0.

R

R1

R2

Rn

RB

∆h1

∆h2

∆hn+1

d1

d2

dn+1



1

–

86

(+: "+:),

(!"*")/( )!*")/().

!"*")/(* +"*,, * 0,8 )" +"*(" ()" ( +)

6,/, (" + (,0/:

– )"" (" 0,/, ,

i

id1p ==== ,

– )"" (" 0,/, ,

,1

p2

i

iσ

=

i

in

1p ==== ,

2

H

i

1p

∆= ,

!" (,: i - () (),8" *""8 +((" 6" +"*(" ()" (+), in -

-/ +"*(. () , () (+,) H∆ /" 6+:" (),8" *""8 +(("

6" +"*(" ()" (+) )" +"().

"() 6+:"! (),8 H∆ 6+( :

,

.

)-" 4.2.1-1 )" (, +"() 6+:"! (),8 "* 9* +"* (*.

!"*")/(* +"*, +:* )"",, , +, ,*"),)* 6*"7, + ) "",

* 0,8 + *""8 +((. 6 () (" ("" 66

[[[[ ]]]] iH

'h dD

f v ⋅⋅⋅⋅====∆ , (4.2.1-7)

!" (,: id ," +"*(. (), D ,, , +. /" )""

, 6 )"" (" ,(+//, "0" +"() +) 6+:". (),8.

"')+" +((" 6" 0,/, ("

'h

'

ii vhh ∆∆∆ ++++==== , (4.2.1-8)

, "')+" +(" "" ,

n1nn

212

1A1

hHH

...

hHH

hHH

∆

∆

∆

++++====

++++====++++====

−−−−

(4.2.1-9)

), 0,8 () (" 66

1nnB hHH ++= ∆ . (4.2.1-10)



1

–

87

# 4.2.1-1: )" (, +(" "" R100 (H100 = 151,520 m) R200 (H200 = 161,761 m).

(+, *""8 +((. 6 (0,) +(" "6). )0 1,2 3.

$3:

/

+

Rn'

ih∆ id iv ih∆ Hi

R100 151.520

1.915 0.20 +0.003 1.918R1 153.438

4.429 0.26 +0.004 4.433

R2 157.871

5.576 0.16 +0.003 5.579

R3 163.450

-1.694 0.29 +0.005 -1.689

R200 161.761

='

ih∆ 10.226 0.91 +0.015 10.241 10.241

)HH( 100200 − = 10.241

1

=H

f +0.015 (0.025)

9" *"7,(- +"6. +"*(. ++ 0 +"*(, *",.

6+(() 6.)"+" )0() +"*, !"" +"* (*") (" "

0") )"!/":

, , " * ,

" .

4.2.1-1: ) $'

&)(&

$)'&

"1*&

#$.

km

'*- " k(

#& $$

1& &)-

& '&, &).'$&

0

± 1 mm 250 7 – 8

2

± 2 mm 75 – 250 4 2

."

*

± 5 mm

25 – 75

2

2

&

."

± 8 mm 25 1 &

$&.- #$. " #('$*( &)(&"

(+, 6!8 , ").* !+:, *" (" 6:,0) "( *""8 *")*

!"*")/(! +"* ) 60/ -/ 6+ !"9. /" ) (),*") /

+, " *8" + (, ,(+ *""8, (,()+ +"9) ").



1

–

88

()"*)( ,)/ *!, (" )) 9)+8"* "," *""8. "9" (,0/!

)" " *!, (" ), (:,0), (" 8.+ ,)/ *" 60/ ",+)

:+* ,+8"* ()* (),*")* +8"* ".. (.

,(+ *""8,. 6 /". 6+ (,0/. ,)/ ("- (, 60/"

!"9":

( "),

,

.

+ !" (" " 6.)"+ +( "6(), ()8" !"9 *""8 )") (" ,

6+(() :

$ ,

, +,.

+"" ") /" ), ()!, 8"!+ ())()0 +() " + (" ,

)8" ()" *")" 6+8 + / /" ( , *", 4.2.1-1.

!6 6 ()8 !"9 *""8 !"*")/(* +"** 6+ ("

("" 0. - *" 6 ()8 !"9 , +,, (,0/" !"9"

() (" *-,/, , /", +"(), !"9" /" (" (" "8, 68, ")+, *"7,(- (" 6/"0+/,. " /": sσ - $ $ ( /""

()" /" ," +6,", l - , +6," h∆ - +(( 6 ( /" /"

6 0)8 68" "8" ")+").

' $ () 0, (" (+, ("""!

66

2l sh σ σ ∆ ⋅⋅⋅⋅==== . (4.2.1-11)

' $ ," d , 6 H∆σ ( n () ,

+,, 0, (" (+, ("""! 66

nhH ∆∆ σ σ ==== , (4.2.1-12)

, ( -6* /" l2 / dn ==== , (" 0 66 6 0,8" H∆σ .

dll2

dshH ⋅⋅⋅⋅======== σ σ σ ∆∆ . (4.2.1-13)

66 (4.2.1-12) (4.2.1-13) 6,/, /" () (),8" +((" 6" +

", ", 6+ $ $

. " ("'/ ,+ 0+ +""* 6)":* 6+

6+:" (),8 , ',/ ,," ," + *(*" ," +6,".

4.2.1-2: % $

- H∆

$& ):& $& &):& $' &)(&

'$& ) '$& )

/&1 &)(&

)9& '1&'

2d04.0d20 ⋅+±

2d04.0d10 ⋅+± 2d04.0d25 ⋅+± 2d04.0d15 ⋅⋅⋅⋅++++±±±±

/&1 &)(& 2d06.0d32 ⋅+±

2d06.0d16 ⋅+± 2d06.0d40 ⋅+± 2d06.0d24 ⋅+±



1

–

89

4.2.1-3: ! # " ( - ,1997)

+ *" +8" ()/""

'! ($- )&/ $+ "*")/( +"*

!*")/( +"*

#

.*")/(

&'$"(&' -"

")+"

#/")

#/") 30″

")0* -"*

$& $,!"$ "*")/( +"*

$ $

% (mm)

!*")/( +"*

"

, % (mm)

#

#/")

#/")

#/")

#/")

#/")

#/")

,

5

#/")

mm

#/")

#/")

120 m

3 m

mm

kmd30

,

#/")

6″

cm

Knd4 0 + 16

#/")

' (Federal Geodetic Control Subcommittee –FGCS), (Bossler, 1984), () +"). ). *" 6(+ )0()

+((" 6" -b , )/.

d

sb = , (4.2.1-14)

!" /": d - - .6) , 6*"7, "" , km, s - () (),8e

+((" 6" (, mm) , +"*(/ *" -/"/ "* *") /*8.

+).

" 6 b /"()" km / mm . "() )0() +((. 6 - b "'( /" 6

(+ " *"" ("- ()-" 4.2.2-1).

"/(, )"/,* )0() +((" 6" *"8,/" (" (+" +" )0 ,

*". #)0, +"() b (" 0, 6 "7" ,6, /+" +"() b () ("

)"/,* 6 ('/, )0().

16d0 –("0 , ()" , .")*")*, n – -/ () , +,, K – ()) (2 *, 5 * 8 *).



1

–

90

4.2.2-1: ! " (FGCS84)

!

$)

I II

$"#

I II

$9

"*")/ *""

# (km)

# (km) #

" $ (km)

3

1.6

300

3

1.6

100

3

1.6

50

3

3.0

50

3

3.0

25

(),*")

+"*( (),*")

+

"6,/ (),*") ")+"

(mm)

0.25″ #

17

0.1

0.25″ #

0.1

0.50″ #

18 / #

0.5-1.019

0.50″ #

1.0

1.00″ + / *")

1.0

-/

+"*( (),*")

, , mm/m

- , , mm/m

# (),

()

,

")+

)

# ()

%

0.05

0.02

7

1

20

1

10′

0.05

0.02

7

1

1

10′

0.05

0.02

7

1

-

10′

0.05

0.02

7

1

#21

-

10′

0.10

0.04

7

1

#

-

10′ ""( ",

0

mm22

23

24

#

mm

#

mm

#

3

25

"8

26

17 # – + +(), #"

18 (" () )0 **")

190.5 mm , (" () )0 **"), 1.0 mm (" () (),*") ( )

20 - )

21 # – ) #6+70

22 -") 23

-" ( +" (" (),*") 24

-" - 6 25

6+:" , /"* +, , /" ()/8" 6*"7, ). )0 " 25 km26 6+:" , /"* +, , /" ()/8" 6*"7, ). )0 " 10 km



1

–

91

+ $!- +!- ') &

$+ (m)

(), (m)

$ (m)

(m)

0 *

#

(+) (mm)

(* !"9 "6)+8

! (mm)

+"8" , /"* (*",

""+"6 +"

") ( )

")+ ( +(),* "*

2

4

50

0.5

D3

D4

5

10

60

0.5

D4

D5

5

10

60

0.5

D6

D6

10

10

70

0.5

-

D8

D8

10

10

90

0.5

-

-

D12

D12

4.2.2. !$8)- )& '1 ('!( '$#&('$*# &)(&

9) /" /" 6), /"() +(( 6 6*"7, +" )0" *") )!*")/(! +"* 0, (" (+, 66 -

12kAB klizcosdH +−+⋅=∆ , (4.2.2-1)

!" (,: i - +( (),*"), l - +( (!, dk - *"" ( ,, k 12 - +

,(" ,)/ "'/" 6+:"() / !(

( )k1R2

dk

2

H12 −⋅= , (4.2.2-2)

!" /" dH - *"" , (+"" , + .6) (, km), k – "'/") "'/" (,

)0* *"* ,(+/" /" +"() "'/") k = 0.13), R = 6377 km.

(, +((" 6" "7"" -(), ) (" 0 +(( 6 0,

2

)li()li(

2

zcosdzcosd

2

HHH

ABBA2k21k1

ABAB

AB2Z1Z

−−−−++++−−−−++++

−−−−⋅⋅⋅⋅====

====++++

====∆∆

∆

. (4.2.2-3)



1

–

92

"" +((" 6" +"*(" ()" ( +) )!*")/(! +"*

," ()" (+) d, , )!*")/(/ *", "7,/, (" ("" 0:

+"*( () - /"() 8

2

i

id2

1p =

+"*( () - -() 8

2

i

id

1p =

+"*( + - -() 8

[[[[ ]]]]2

n21 d

1

p

1...

p

1

p

1

p

1

1p ====++++++++++++====

==== .

0,8" + *""8 +((. 6 )!*")/(* +"** ,

'$#&('$** ($0 +9 (" (+, 66 (-() "7"" +((" 6")

[[[[ ]]]]2

i2

H'h d

d

f v ⋅⋅⋅⋅====∆ . (4.2.2-4)

0,8" + *""8 +((. 6 )!*")/(* +"** , #&* ($0 +9 (" (+, (). 66 , !"*")/(* +"*,

(-() "7"" +((" 6"), )/.

[ ] iH

'h dd

f v ⋅=∆ , (4.2.2-5)

, (), 0,8 +( )0 () /" !"*")/(! +"* (*" 4.2.1-

1).

# +"* (*, 6+:" 6 +((. 6 *""8 " 6

)!*")/(* +"** *!& &)(& '$& " #&( )" 6(

)m(h

2

)cm( d)zctg1(00075.0 ⋅+=∆ , (4.2.2-6)

, 6+:" (),8" +((" 6" *""" " 6, )!*")/(*

+"** *!& &)(& '$& " '$#&('$** ($0 6(

)d05.48.1(4 )km(h)cm( ⋅+=∆ . (4.2.2-7)

6+:" (),8" 6- +((. 6 6)" +((" 6" *""8

'$#&('$*( &)(&( " #&( )", 0, ("

Knd4 0)cm( ++++⋅⋅⋅⋅====∆ , (4.2.2-8)

!" /": – ()) (2 cm – -" )0" "", 5 cm – /" )!*")/(, ,! ""

8 cm – -" )!*")/(" )0"), 0d - ("0 , !(" ()" (hm), n - -/

() , +,



1

–

94

4.2.3-1:

)(& )$. $"'/ '1 *8"* )"" )!* *")* "7,/" (" .6) / )0.

"):* +"** "7,/, (" 8.+" +(". /" ". (+* )0*

(*:"* )!* *")* ") +(". (" (" "7,/, (* 6 " )0"

/" +(( ""6"),/, )"". /" ". +* )0* "()+) +(,

"! " )"", /, )0" ,:/, (" , '6 6+7"8 "):!

+"* (( *"8 +, 6*"7, +" (*:"" )0" *""8"* , )

(*:" "):, (.). + .6) *"8 6+" (" ( )09, 1 dm.

+! "*", ! 6 6+7"8" "):! +"* () (" ()/" (

(*8 "):. # "):! +"* "!(),/, (" ( (*8 ),9"*. (" , +, ! ()" (" .

/" )"" (*:" ')!*")/(* *")*, ! 6 6+7"8" "):! +"* ()" (" .

(+" " "):! +"* +9 (,). )0 /"(,:

6+ (" (" (*8 )!* *")*;

*/, (" (* )0" /" )"9, )"";

(+ ()" (" (" (*8 "): )!* *")*, /"

)()(! ')(";

+ (" "!(),/, +* ),9"* ( ')( * ),9"*);

, !,, 0" + (),08 + ) '!,);

,+ + (,, * /" 6 (),*")*; #- 6 (: +", +" ")+", +" ,0", (,-, ,0 ):,

6( (1) !" ((").

(+, 6 6+7"8" "):! +"* 0 ()/" +"*( *" (+"*(

"").

+"8 * "6/" "):! +"* 6+ (" (""/ ",:

#08" (" "";



1

–

96

4.2.3-2: %

)(& )$. !%&& $)&( %#"$(

"): +"* +9 "'(" +* '!,* "6,/" (" * ,"7"8 )"" 6 )"-" 6!8" ()(. )"", "* (. #+" '!,"

"()+:"" (, *"* +) ( ()* 10 m, 15 m 20 m. (+* )"*",

'!," -/ (" . ")* (" -""+/, )"*" +), -""+8,

'* (" ( )"". # +"8 () /" +"* (,). )0. +"

)0" /" (, )"()0" , +")* (*(, " /, )"*"* '!,, */,

(" ") / +( ( 6). (+, ) *""8,

0,/, (" +(" )0 )"". 6 ) /")+! ()8 "7,/, (" +"()

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