geod premer 1
TRANSCRIPT
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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
0,8 , !(* +, ...................................................................................... 45
#!( + ,*"),) 6*"7, +" )" )0"........................................................... 45
)+" ! / 08" 6+9+ ()/ )0.......................................... 50
)+8" !"9 ". *""8 !(. ()........................................ 52
!+ (),8" ")+ "6() !(. ++ .............................52
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
"7+8" / "6)" )0" "("8"* – 6)" ," "
,!+ "6)/ )0 .............................................................................................69
0,8" ) "6)" )0" "("8"* – "(" + ( +" )"
)0" (-6")......................................................................................................................700,8" ) "6)" )0" "("8"* – "(" /")(. + 71
"7+8" / "6). )0 , 6*"7, +" )" )0"
,+/ ...........................................................................................................................73
0,8" ) / "6)" )0" (+, *""8 , ...............75
4.1.3. ) )0() / )0 "* "7,/ !6/ 6
()6/, – ISO4463 ....................................................................................... 77
(+ (*) *" ). )0 !"")(" (+" ................................ 77
,( ((",) *" ). )0 !"")(" (+"............................77
6+:" (),8 -""+8 /")+. )0.................................... 78
4.1.4. 0,8" +9" 6)+"" '!," *, ) "*. )0... 78
4.1.5. "*")/ +,!. ) ....................................................................... 79
4.2. 3 #4 5 ...................... 824.2.1. "*")/( +"* - !"" +"*................................................... 82
+"*( "" ....................................................................................................... 83
+"*( + ........................................................................................................... 83
+"*( + ,*"),) 6*"7, + ) "" ...................................................... 84
#"9"8" !"9 , !"*")/(* +"*, ......................................................... 87
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
# *") (*8 .............................................................................................. 132
)! *") (*8....................................................................................... 133
# *") (*8 "): ........................................................................................ 135
#/") ,*")/ * "6/" *""8 # *")*.................... 140
6. # &$ (LAND SURVEYING), # # #
.............................................................................................................................. 142
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
6.3.4. +8" )() ++ .............................................................................. 152
:................................................................................................................. 158
.................................................................................................................. 164
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1.
1.1.
"*: +9 /" +"* ("" " "+! *)"*)0! - (( 1.1-1).3", +9 )"9, ""!," 6"*:" *(" .*!"" *(" * ". #
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1.1-1:
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1.1-1:
! " - a " -
b
Clarke (1866) 6 378 206,0 m 6 356 584,0 m
GRS80 6 378 137,0 m 6 356 752,314 m
Besel 1841 6 377 397,155 m 6 356 078,963 m
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)0* *"* "*: (" 0"() (* ('"*. #"(" +9 /
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1.1-4:
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, " 6"** ".*!"() 6"*:. *( + )+8 " - +).
1.1-5:
#(*)/* ) )0" ("8/ +9 "*:" /" -6,/, ),! (( 1.1-6). #+9
,,) ),! /" 6+:", ()" ),! (, ,+ +". ,!+. + ),!
6+ (" . ("* /* 6 /" ),! , + ( )"*"*
, B C. "*", *8. +9 ," () ),! , + (" 6/"0+/, (
,* ,+ !+/,"! ('"! ),!. !+ ('"! ),! α, β ν (, +"
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+9 (*)* , ,!+" 6*"7, / )+/ +9 (*)*
.
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1.1-6: !
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)")/ ",-" -/" +") ),* /" "'( ("8* /"* (!
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-6 (), , ), (* /"" !" (1875. !"). - 9 ),* " 6+:+/,
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#"*" 6,*"+ *""8" "7+8" ()! / ""*") '60!
() ")+ , (, ", ," "'( 6"*:/
+9. ", ")+ / )0 0,/, (" , +, ," -!
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"!'( ) (()"* (" () , /9"* (*(,. 3"! "'9, /"
. #"" "'9, !"!'(" 9" ()),"), *"/
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– 6)/" UTM) () (E – East, Y ( +""! %$
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9() ("-, * /" ) ( 0"() (,0/, .6) +") ),* (,
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),*. -! 9"! 6,*"+8, )"- -/() 6, 6*"7, . !-.
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#")()+* "() *" ,(" "( (" 6"*:" )/".
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( ""*")* "'(* 1841. !", /"* ()), !),)
!"* +(* , )0 Hermannskogel ("'$*) 6*,)* ()" (/")/*)
Hermannskogel – Hundsheimerberg.
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1.3.2. & !'"(
", ," "(6/" ()")(" !""6/", ( "!, "!"")0)
),* (, - ,-0/". " 8. /" )$ !'"( 1950 – 50. #*
,(()+:8 "!"")0. ),* /" (" + 0, 8.+* (, "*
!""),. "7,)*, (+" (+9"/ ()")( (()"* 6.)"+ (, ,(()+:8"
!"")0! ),*. 26) +") / ( +9" (, +" "6+("
*")" / )0. -6* (" ()") ", ,)8* ") *("
"*:", / 6(+ )+* )".!/* !0 0+ ( (.9)"* , !""),. ) /" ". "'() ) (()"* , /"* " (" )+ +") ().
("8" +"*", , "*",, 60/ /" (,) )".!/ &# '(
+,&$- (GPS) / -"6-"7,/" !"")(" /" )0 , ()* !"")0* (()"*, WGS84 (GRS80). GPS "7,/" )" )0 "*:,
) 60 (" 6 8.+ 6 * ()) ) (()"* +"6 6 "*:,. + (()"* 6) /" 6+*
(Conventional Terrestrial Reference System - CTRS)
(Conventional Terrestrial System - CTS). ) 0") CTRS 6 (" ,
"), *(" "*:" (!"")), X ( 6 !"") 6 6 )0, "("
,)! *"/ (0 *"/) "+), Y ( 6 !"") " , + ("8"! / "+) ,+ /" X (,, Z /" ,(*"" , +, ("8"!
/ (" )/" "*:" "'(" , ", 1900. 1905. !".
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(()"*, " / /")/" ,,/" '60 (+/()+. , *",
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*")* "( GRS80, 8"!+* /"* /")/*, ( "7""
'60" *")", /* " -) "0 +9* ,("+*.
1.3.1-1:
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1.3.1-2:
1.3.3. !
#" !"")(" 9" ,", (+ )0 +9 "*:" * )", ), -
+(,. "'"") +9 (),*) +( -/". !"*")/(* +"** /"()" +9
#!. (" /" (" (" ,), +(, +9 (!") 6+/, (" $'('$*(
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"'/, !" + /" J. B. Listing /9 1872. !". "7,)*, +""" /+"
" ,)0, ("8 + * , (, /, +9 !" + 6 1 m 2 m
(Sickle, 2001) ) )+ /" "'/ +9" /" " +. +) (
/" 6()") , )!'(" 6"*:" +9. (+/ )0 6"*:" +9
* (+/ + )"6)"), )/. *" (" +")( (), 8"" +"()
60)* *"()* )!'(" +9 (, 60)". #+9 /"! !+)!
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!+" /+" ,) / +(, "90 0(+, ")8" ()") . #+9 !" /" *)"*)0 "!, 9) /" )!'( 6"*: +9. /" "!" 6!,) "!" ,"!,). 6 )+! 8"!+! - (, 60), /"
/60//. /" (+ "+*" (" 6"*:. *( , 8"/ ,,)98(). /" ), 8"!+ - - - + -6 "(*. "7,)*, (* 6"*:
'60 +9 +9 !" (), "(", "* *"()* 100 m.
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),* WGS84) 6+/, (" . 6! 6 )"9" , "6, 6
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!"*")/(. - "(. , )*")/(" +(" " , /" *",)*
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6)" "(" +(" )0, +(" )0 , +* (()"*, , ,)"- 0,/,
(" *"* )"! * +! ()"" (' GPS "
- , 2002) / !(:
XCYBAhH ⋅⋅⋅⋅++++⋅⋅⋅⋅++++++++==== (1.3.4-1)
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(" 6). )0 * -) + ( /" )0 +9 2 x 2 km).
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1.3.5-1: (
1.4.
!'( !'0 6,/" / "7". ""*") !"!'(! ().
/" (* () /" +9 "*:" 6+:", /" +9 + 8*" /" *!," /")+) '60, )")/, -"6 "'*/. /" )")/ *,
"*: (" *" (*)) +*.
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– - /"/.
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1.4.1. $0)& $!&'& '( $!&' " $)& $*,*
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"("* "* ")* *"/,. (" 6+/", (+
((* ")!) (" /"),/, /". )" )0 "7,/, (" , (, ) (()"* ! "'9, +" (" 0/ (, /
/")/ 6 ( 1.4.1-1. 9/ 6"*: ,(+/" /" *(*
"'*/ , , /"/ 6( 1 dm/km. " " )")/" -/" 6 /" ,
/"* )* (()"*, ( ")* *"/* 21° ()0" !"!'(" ," –
("* 6. 6" ()", *8 " )")/" 6. 6.
( (" "(+ (""* ,(+*:
( " , + "+);
#/"/ /" ';
"8 *"/ (" "(+ + / – 8"!+ /"/ "()+: X
(, )! (()"* , +, /" /"/ "+) - Y ( )!
(()"*
1.4.1-1: ( - ))
,(-!"+" /"/" *"/ "" (" "(+/, .
+,!* )* (()"*, / (+" )0" "7" /" $)"#(
$!&'( - Y, X. (" " - 0, ( "!)+* )*, X ( ("
,,/" +"() Y = 500 000,00 ) (+" )0" ()0 ")! *"/
*/, )" +"" 500 000,00 m, (, )" 6 ")! *"/
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*8" 500 000,00 m. 7", 6 () )* (()"*,, (" Y
)" ,(,/" (" -/ 6", )/. 6 ("*, 6, ,(,/" (" -/ 7 ( *", 7 500 000.00
m). ,! ) – X ), 60+ ()/8" )0" /"/" "+).
,:"8"* ! *"/ +"+ (" "'*/ , '*,
dd ⋅= ω ∆ , (1.4.1-1)
!" /"
,R24
Y
R2
Y4
4
2
2
⋅⋅⋅++=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°.
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-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
====⋅⋅⋅⋅====
====⋅⋅⋅⋅−−−−++++====
# 1.4.2-2: )" (, *,(" )":41,6302460X
11,4115327Y
====
====. 0,) "*,("
)":
$3:
"*,(" )" 6(":
09,76360649999,0 / 41,4606302X
35,414329999,0 / )00,750000011,7532411(Y
========
====−−−−====
",/ ," ( "( (, 9"* "*", - ,)" +(" +9) d +
/"/" d ( (","* ,) 0, (" "* 66,
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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 *"/.
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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"( "*");
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#"*" *"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 ()
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+,! ) (()"* ( "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 /") (
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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/".
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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 -()
)() '*. (()"*.
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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
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+ , ), "*" /"()" + 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 -()
)().
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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/, *)"*), /"/ (.
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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’.
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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)
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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
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+,!* )* (()"*,, / )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
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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
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3.1.4-1: ,
+) 6 6 N ( +"()
,! , ()""*
#+ + + 0 90
,! + - 90 180
" - - 180 270
5")+) - + 270 360
3.1.5. + $)"#/ $&/ $!&'
( 3.1.5-1 ,()+ (, + (, ) – " ),d( ν 3 +,!"
)X,Y( PP )" )0" P . (, )" " )" ),d( ν , +"() +,!.
) 0,/, (" *, 66
3.1.5-1:
ν
ν
cosdX
sindY
P
P
⋅=
⋅=, (3.1.5-1)
, , (, 6)" +,!" )", " )" (" 0,/, *, 66
P
P
2
P
2
P
X
Y
tan
XYr
=
+=
ν
, (3.1.5-2)
,
P
P1
P
P
X
Ytan
X
Yarctan −==ν . (3.1.5-3)
3 (" "'"") + ( 6)+* (*"* X (" / /" " ("8"* *"/,
6" /"/", ) (" ,! α 60+ ( ν 6+ (" !$,&( "#(.
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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
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°+= 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: -
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# 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).
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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′ )
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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 ″, ).
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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
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!" /" 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).
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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. #& ($0
#!*")/ /"()" "'( /"()+ *") ,(()+:8 *"" ).
)0 , .6)/ + / /" +"* ( , !,() (":"* ("* 6(*
)""* !" (, )" +6," "*+" !" *" )!,/"
))"/" /" "(, ( ,(" +"9)0. . "" # /"
*":+a.
#!( *" /" *"8":
*8, ! ("; (()+:8, *)"*)0" (+" 6 6+7"8" )!'(! "*";
8, -""+8, /")+. "): "8"(. -/");
8, ). )0 6 "6/, ')!*")/(! "*".
#!(, *", 0" !( +. #!( + "()+: (, 6*9:".
+. / – !(. () /" !"")(* *""8* , ,!+ +"6,/,
)/ ()-6+" !"")(" )0" )")/ 6+7"8 "*". 0" +"6"
!(* ()* 6+/, (" #&( '1(.
," !(. () *"" (":
") ("")(* :*"*, *"* )* – ):*);
") (*"* ).*")/(. *")).
#" !"0&, (+/ !(/ )0 6*"7, +" (,("" ()" )")* (" *"
"#.
#!( + *" -) "'( ,:
+*"6/ + (.6) +);
*"6/ + (()).
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&'$"(&' $( + ($- !"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.
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4.1.1-1: -
4.1.1-2: ) –
4.1.1-3: – . C D
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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: * $
"
"(
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6 !"")(" (+" 6 (*8" "): +9 (" , (+"*, "* "9"8* 6 "/!
!+! /"), -"6 -6 (" +/ *" "(),/ ()".
#/") !(" *"" 67,/" (" +* 6*" 1:2500, 1:5000 1:10 000
)) /*. 0" ()/"" "'"")" *"" ()+/, (" ,$)&(,
+/")+" )0" !(" *"" 1. 2. " ,$&( ),9"*. #/")+" ()"
!(" *"" 1. " ()+/, (" ,$&( ),9"* "-:* /" 0.6 mm, ()"
!(" *"" 2. " 0.2 mm.
(+, )()(, 9), 67,/" (" , !(" *"" , 6*" 1:5000
1:10000, / (:
), *", ( ((* )* 6+ + ();
")" ()/"" )0" +"* +"7"" )0" * ),9"*;
, )()(" 9)" "), 6""* ),9"* "-:" 0.8 mm;
, !7"+(! " "), ,)* ),9"* "-:" 0.5 mm;
#", ()+" ("), ""* /* :,-0()* ),9"* "-:" 0.5
mm) (" "): ("), ""* /* :,-0()* ),9"* "-:" 0.2
mm) (0! (*8, (* ", ()+" ')!*")/(" *")"
(*8;
") *""" ()" ()" ""* /*, 0,(" ("* /* (* ),9"* "-:" 0.2 mm).
(": ( +" +9" )()(. 9) , /* (" ,*"/ !(. )0
+9 "", 67,/" (" /"()+" ( *"" 6 " (":". ,*"/
!(. )0 *"" 1. 2. " +9 (" )()(* 9)*, -/ 1
:". !+" !( (":, ,*"/ !(. )0 +9 (" "" -"6
-6 !" )()(. 9).
!(" *"" 67,/" (" /"* +9" ()+ '*) 100 cm ( 70 cm
70 cm ( 50 cm, 6+( +"0" )()(" 9)" 6-" 6*"".
) #!' &) 67,/" (": (" ").* ()+8* ,)+ /" ,0/, )()(" 9)"
,9)" () "', +: -/ )0 -"6 /. /" *!,
6 +8" )() 6"*:9) 6 )() "")();
)"-" +8 "*" ,0/* !" /" "*" 6+9"
"')!*")/(* *")*.
(" !(. )0 "7,/, (":
"*")/(* "+"** (!"" +"*),
!*")/(* +"**,
# *""8*.
(" )0 , +/ !(/ *" "7,/, (" !""* +"**, ,
,0/, "*" ()/ +"*( *". )+*, *"8,/" (" )!*")/( +"* (" +( 6 # *""8* )('*/* (0().
&'$",* ()/"" !"")(" (+" +9 (" , (""* (,0/"+*:
6-! 9)""8 ,9)"8 )0 , +""* -*,,
6-! 8"" "',(),
6-! 9"8 !7"+(! " (":,
6-! ".*!"() *"" 60). *")!/ *""8 -" ,
()/"/ *",
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()/" *" /" , ,(-!"+/ /"/ *")(* (()"*,.
"(),/ ()/"" *"" +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
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)+" ! *!,,/" ), ,,)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
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#* 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
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!"-( 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″
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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" +.
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(" ,!+! "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+ ("
$ "()+: ($" )'' ! , ( –
. #"* ")+* "* (),8, 0"() (" (',/" (
"6() ! (1:1000, 1:5000 (.) , (, 8 60/ )"""
"*"+* (()"*)(* ,)/* , ("- (" !,-" !"9", +"()
")+! (),8 /" 60/. ")+ "6() + ( /" *"7,(-!
"7"8 +9" 60). ++, " )"- /" ()) /, (,)"
)0() / )0 !. 9"* *", ")+ "6() + 6(
4894 / 11762 / 36.0 = (( 1/4800 /" (" 6,,/" , ()),).
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4.1.1-12: +
')$& #& * 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
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–
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 ’
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–
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 ()"
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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)"*
(,0/, ** n !(. )0 , )+"* !(* +, / 608" )0" 1 6+9+ )0 n , )" )0" n 0,/, (" (+, 66 -
[ ]
[ ][ ])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
in
2
X
1n
1i
1n
1i
2
d
2
i
i1i22
in
2
Y
iinn
iin
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
α4
α3
νz
νp
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$3:
) 0,8" +"() ". ,!+ () ). 6:
) , j
iν ∆Y ∆X Y X
P 68478.139 62483.826
281.832 241°08′57.7″ -246.851 -135.993
A 68231.288 62347.833
271.300 246°31′14.6″ -248.838 -108.091B 67982.450 62239.742
) 0,8" +/(" +/(" 6 )0, B
- ) (),8" *""8 ,! 6(:
rad106962736.9)10)(8481368.4)("2( 66
i
−− ⋅==α σ , +/( 6(
.rad10401772.9 2112
i
−⋅=α σ
- /( *""8 , 6(: .m1056.2016.0 2422
di
−⋅==σ
- . 66, (4.1.4-24) +/(" +// ) )0" B 6(":
= =
−++
= =
−+
= =
−+
⋅=
−−+−−−=
⋅=
−+−=
⋅=
−+−=
2
1i
2
1i
242
d
2
2
i
i1ii1i2
i3i3XY
2
1i
2
1i
242
d
2
i
i1i2
i3
2
Xn
2
1i
2
1i
242
d
2
i
i1i2
i3
2
Yn
m1087843.1d
)XX)(YY()YY)(XX(
m1029166.1d
XX)YY(
m1018457.4d
YY)XX(
iinn
ii
ii
σ σ σ
σ σ σ
σ σ σ
α
α
α
+/ *) !(:
2
BB 44
44
m1029166.11087843.1
1087843.11018457.4
⋅⋅
⋅⋅−−
−−
%) 0,8" *") "(" !"9
(+, +/" *)" "'9" (" )"()0 * ,!! ()""
-
0)()( 2
YX
2
X
2
Y
2
X
2
Y
2 ====−−−−++++++++−−−− σ σ σ λ σ σ λ
" 21 ,λ λ / "()+:/, "9"8 )"()0" /"0" ( /"0"
+"()) "'9, +", *, ,(, "(", /")/, "(" 0,*
2
X
2
Y
YX22tan
σ σ
σ θ
−= . +) θ 2 "7,/" (" (+, 08"" /" 6 ',/"
θ 2sin () 6 YXσ , 6 θ 2cos () 6 2
X
2
Y σ σ −−−− . 9"* *", ("
/":- +" ,(: a = 0.023 m
- * ,(: b = 0.0006 m
- ,! /")/": 2126 ′′′′°°°°====θ (, (, 6)+ (*" X (").
: #6 (), () (" (* , '6 8 !"*")/" +,
("- )+". !. " + (), -/8 ()!! ,6!
"9"8 () *") /*8. +).
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#& ) " '$!(&+&&( $'$"
(" )* *""8 , !(* +, 6.)"+ 0,8" +( !(. )0
)*" *"" +") (6")) ,!+, ) !+* !(* +, , 3
(),. +/ (), ("- 6 6/ /+* (+"*". ,"7/ ())
(), (.).
". "* 6 "6/, !(. ++ , 3 (), (:
), (), ( *** "6,/* *""8 .6). +"). ,!+ 10”,
"'")" (-( 6/" ( ))* ()*),
+" *"" *",
())+,
#* - (():, )", -)"/", ...). )-" 4.1.1-17 6 (, "6,)) *""8 ))* ()* , 3 !(*
+,. )-" 4.1.1-18 6 (, "6,)) 0,8 ) +( )0 !(! + , 3 (),.
4.1.1-17: % $ 3 %
'&, +"$ &'& "# 3$+&'&
"#
3$. "0&
m
&
$+,m
$(!
= _____ 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
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.' $#'$ $#'$ #&# )
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:
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4.1.1-18: - "
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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"
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/ "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
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(((( )))) )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" )"- /" (") (+* ,!,.
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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
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- 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 ,.
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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
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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
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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
$3:) ),! ABP∆
0,8" "! ,! ()" AB: "38'3494B
A °=ν ,
0,8" ," ()" AB: m171.147d AB = ,0,8" ,,)98"! ,! )"*" : "20'0030°°°°====α ,
0,8" "! ,! ()" P: "58'34124P
A °=ν ,
0,8" ) )0" P:m357.60757X
m143.61327Y
P
P
====
====
*() (0,) )" "6)" )0" P, 6" ) )0" .
14 #"* +"* (* 6+:" 6 ) + "9"8 " (*" -) +" 6+:""
+"() ,,! "! (),8 6 1. )"!/, )"" *", ')* 1.5.
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4.1.3. '&!$! '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 /" () +).
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!+ (" *"" )")* ( /*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" $!&' $(&/ '1
(, 6)" )" )0 6)+"! ! (( 4.1.4-1) 6 0,8"
+9" '!," + (""" + –
% % Y
X , )/.
)XX(Y)XX(Y)XX(Y)XX(YP2 314243132421 −+−+−+−= . (4.1.4-1)
6+(() (*" 0,8, -/" +"() +9" *" -) 6)+
"!)+, 0"*, (", !0, ,(+/ 6)+ +"().
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# 4.1.4-1: (+, ). ) )0 6)+"! ! (0,) +9, '!," (Kavanagh, 2003).
X Y
1 1089.981 935.049
2 1000.000 1000.000
3 1078.754 1068.139
4 1046.635 1205.498
5 1154.366 1030.252
P = 150.3 ha
4.1.5. ('$* $)"#/ $!&'
(, 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
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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)
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# 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.
$3:
) 0,8" ) )0" K2
(+, (4.1.5-2), /"0 ED !(
)27.1160Y(27.524
08.24269.688X
27.116054.1684
27.1160Y
69.68877.934
69.688X
−−−−====−−−−
−−−−
−−−−====
−−−−
−−−−
(+, 66 (4.1.5-3) *" (" ()+) /"0 , BK2
)61.1313Y(08.246
27.52473.1250X −=−
, ","7"8 !8. 66 -/ ("
: 09.144XY46938.0 =−
BK2: 36.4049XY13049.2 ====++++
:" /"
102.1502Y
27.3905Y59987.2
=
=
6*"* (0,)" +"() Y , !8, /"() (66 6 ), -/ ("
15.849X =
) 0,8" , K2D K2E
62.377d
53.201d
EK
DK
2
2
=
=
): 15.579dd EKDK 22====++++
15.579dED =
BC
D
E
2
1
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4.2. 54 6 7
" ), 6+8" )"" 6.)"+ " /! +(( 6.
((, )"" (" (,/" *,: " "
().
((" 6" *!, (" *") (""* *")*:
") !"*")/(* +"** – ")* *""8"* +"). , (/"6/ *"));
") )!*")/(* +"** – *""8"* 6"). ,!+ (.
,;
.*")/( – +")" ," (" "7,/, ).*")/(* *")*;
*")/(* +"** – *""8"* 6 )*('"(! )( 60)* ()*;
+*")/(* +"** – *""8"* 6 !+)" (" ,6 * !+*");
"/* (()"** 68 – () (" "/ )'* ( )
*"7,(- ,+" (". ") )0() (" "" 15 50 cm, ,*
60 km 100 km;
# )".!/* – +(" (" (" "'"") "(. +7"8" "(. +( +9 +")! ,* +9 (" (+, 6+8 ( 6*"7, !"
"( (,,/" !").
+, +! !+: "):/" " (" () *")" !"*")/(! )!*")/(!
+"*.
4.2.1. ('$* &)(& - #&$& &)(&
('$*( &)(&( (, )"), (" *" ("() 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" .
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)(& $$
#* 6- / +"*(. )0 ( "") ". /" (,) ("""
6.)"+":
)"" * -) 0+() ()-, -/") , /" (" "" ,!7,/,,
"" * -) ()+:" ) (" 8"! *" ()+) 0)) ")+,
+"*( + " (*"/, -) "+9" ,!.
"" (" 67,/, +"! !+7 60). - *"6/ / 6+(" : 1) " 2) , /, (" "" ()+:. "" (" , -/") ()+:/,: 1) " (, -/")") 2) ((),-, ()"). 26)
"" *!, -) +/ – +" 6+ + -/") (,!) ) (" 8. *" ()+) ")+ (, , + -/") ) (" +6 * )+ (2 mm) / ("
6 , (" 0"! " "". 26) "" /" (" ()+: ")+,()+:/, (" , ()-" -/")" )/! )", /*8" 0.5 m 6 )!'("
+9. 26) "" + ( 6* ()+:/, (" +(, 1.5 m - 1.8 m.
4.2.1-1: 2
26)" """ )"- ()+) /*8" 30 " +"8. , +
+"* "* -/") !. 6 ()+:8" "", "" (" *!, ()+) ,
"+) '," -")(" (),-+" ()"". 8 +9 "" + 6 (),-
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/ / !"" (: , "
, $ .
)(& )
(" +" )0" 0/, +((, 6, )"- ") )+* *"7,(-*
()/8, (" " *" ") (* ( /"" ()", ) (" +((" 6"
6 *""8"* +9" () (-8"* /"0. *""8 +((. 6.
0" 0/" +(" ()* (* +"*" - (0, +(" )/. ""
6+/, (" )0*. "6 )0 (-""+/, (" , -, ...) /"()" *"() // (" +9 0)8" ")+" * "( ( /"" ,!, (),. 5)8" (+ ())
")+" / (" 6 (,) (*" ")8 6+ (" , (*, ")+,
6+* . 5)8" ")+" , (*", ")8 (+"6 )0 ) 6+ ("
, (*, ")+, 6+* . ), *""8, +"6" )0" ("
()+:/, +"*(" ,0" *") 0.
4400 114400
3300
3300 – – 5500 ccmm
11..55 – – 11..88 mm
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4.2.1-2:
#")()+* (" "7,/" +(( 6 6*"7, )0 B. (+, )
*""8 ()* ( 68, "8, ")+,), (0,)" (, +((" 6" (+/
(),
nn
22
11
PZ
'
n
...PZ
'
2
PZ
'
1
llh
...
llh
llh
−=
−=
−=
∆
∆
∆
. (4.2.1-1)
) 0,8 6+ (" (-8"* ( -" ()" /"(), )/.
[[[[ ]]]] [[[[ ]]]]PZ
' llh −−−−====∆ . (4.2.1-2)
"6) +(( 6 +"*(" ()" (6*"7, "" A B) -/ (" (-8"*
+((. 6 (+/ (),
[[[[ ]]]]'hHAB ∆∆ ==== . (4.2.1-3)
/" 6) +( )0" , +( )0" B 0, ("
[ ]'hHH AB ∆+= .
-! 6.)"+ ,6() " +( )0, +"8" (" 0"() +9 , (,)* (*",.
"')+ +"() +((" 6" -/ (" )*")0 (" +"8
" 6. " (" +") (* , /"* - (*", 6+( +()"
!""! +"* 6.)"+ ")! /").
)(& ) "('&"' +(8" !) !' $$
" (, 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
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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
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(+: "+:),
(!"*")/( )!*")/().
!"*")/(* +"*,, * 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)
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# 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) ").
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()"*)( ,)/ *!, (" )) 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 ⋅+±
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+((" 6" -b , )/.
d
sb = , (4.2.1-14)
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+).
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# (km)
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+ $!- +!- ') &
$+ (m)
(), (m)
$ (m)
(m)
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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+:"() / !(
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dk
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!" /" dH - *"" , (+"" , + .6) (, km), k – "'/") "'/" (,
)0* *"* ,(+/" /" +"() "'/") k = 0.13), R = 6377 km.
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2
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2
zcosdzcosd
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ABBA2k21k1
ABAB
AB2Z1Z
−−−−++++−−−−++++
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∆
. (4.2.2-3)
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"" +((" 6" +"*(" ()" ( +) )!*")/(! +"*
," ()" (+) d, , )!*")/(/ *", "7,/, (" ("" 0:
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id2
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id
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+"*( + - -() 8
[[[[ ]]]]2
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1p ====++++++++++++====
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d
f v ⋅⋅⋅⋅====∆ . (4.2.2-4)
0,8" + *""8 +((. 6 )!*")/(* +"** , #&* ($0 +9 (" (+, (). 66 , !"*")/(* +"*,
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)!*")/(* +"** *!& &)(& '$& " #&( )" 6(
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)d05.48.1(4 )km(h)cm( ⋅+=∆ . (4.2.2-7)
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'$#&('$*( &)(&( " #&( )", 0, ("
Knd4 0)cm( ++++⋅⋅⋅⋅====∆ , (4.2.2-8)
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8 cm – -" )!*")/(" )0"), 0d - ("0 , !(" ()" (hm), n - -/
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4.2.3-1:
)(& )$. $"'/ '1 *8"* )"" )!* *")* "7,/" (" .6) / )0.
"):* +"** "7,/, (" 8.+" +(". /" ". (+* )0*
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"! " )"", /, )0" ,:/, (" , '6 6+7"8 "):!
+"* (( *"8 +, 6*"7, +" (*:"" )0" *""8"* , )
(*:" "):, (.). + .6) *"8 6+" (" ( )09, 1 dm.
+! "*", ! 6 6+7"8" "):! +"* () (" ()/" (
(*8 "):. # "):! +"* "!(),/, (" ( (*8 ),9"*. (" , +, ! ()" (" .
/" )"" (*:" ')!*")/(* *")*, ! 6 6+7"8" "):! +"* ()" (" .
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6+ (" (" (*8 )!* *")*;
*/, (" (* )0" /" )"9, )"";
(+ ()" (" (" (*8 "): )!* *")*, /"
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+ (" "!(),/, +* ),9"* ( ')( * ),9"*);
, !,, 0" + (),08 + ) '!,);
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6( (1) !" ((").
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+"8 * "6/" "):! +"* 6+ (" (""/ ",:
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4.2.3-2: %
)(& )$. !%&& $)&( %#"$(
"): +"* +9 "'(" +* '!,* "6,/" (" * ,"7"8 )"" 6 )"-" 6!8" ()(. )"", "* (. #+" '!,"
"()+:"" (, *"* +) ( ()* 10 m, 15 m 20 m. (+* )"*",
'!," -/ (" . ")* (" -""+/, )"*" +), -""+8,
'* (" ( )"". # +"8 () /" +"* (,). )0. +"
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6+70 + * 0,+) 0".
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4.2.3-3: % "
)(& "+!"0&# $%
6, ' )"" /(! -/") /"()" "(" )"" +")* + /
( (, /(! -/"). ( /(! -/") (,), ,!" (.) -""" )"",
6 , 6+ (" . #/")+8" -""+8" ("
/(! -/") "*") (, "8"(" !""6/". (, *,/" 0" + / ("
(", , )"*"*. ( *,/" (()/ (" 6 , . +
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*" 1+030 60+ /" )0 0") )(" ,: 1 km 30 m). #"
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)0" */, (" (0,) )" ") ""*") (+, /. (" )(
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%). )0 !"")(" *"" -/") -""+/, (" )/ ()-6,/,
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(+" )/ -"""" )0" ()+: (" +" )- ( 6* ()* )"()0" )0". 7", , 6.+), )(", -""+/, (" (+" )0" "(" )(" (
()/"* -/")* (,), ,!, , 9,* (.) "7,/" 8.+ (). (+,
)(, + (" ( ()" ((" 4.2.3-4 4.2.3-6) // (" ()+ )( (+
)0 60+ 6+* ()*.
(( / )(" "'9" (" +"**. +"* (" (8 ()/"" """.
# 6+9"* +"*, 0,/, (" +(" ,6,! ' – (+. )"()0.
)0 , (" /(! -/"). (+, (0,). +( (()+: ("
()-" 4.2.3-2) (+, 0"! (" ) )(".
(+ + * -""+8 )(" "6/" +"* , /(!
-/") – )(" *,/" (,6, ') !(":
#" )(" (" ()-6,/, "" +"6,/, ( )* ""* *")*
!"*")/(! !""! +"*, , (, ( 6.)"+* /");
"*" + (" ()-6,/, )/* *"* -""!*, ()" )0" , (, (
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#" (+" )0" ()+: (" 0 // /" 60" 6 ();
)( (" -""+/, ,!" )"()0" )0" – "(";
(( (" (*/, (+" )"()0" )0" )(" (0") )(", 0") +"
- #, (" +" - , / +" – , .")*"), (.);
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)(, + (" ( ()" ( 6* )0 8.+* ()*;
")+ (" )0* ()" 0) ")*"), ""* mm (,
/")* /" ,!0/" "+7");
*"() -/"+ )0, , 6( (" /0"9" ,( )"()0 6 )0"
)(, *", #3 0+120.68;
(+, ()" +( )0 (()+: ("
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4.2.3-4: '$
4.2.3-5 : 0 $
.1
1
2
3
z1 p1
z2 p3z2
p3
.2.3
100
H100
HVHa
l1
l2l3
.1
1
2
3
z1 p1
z2 p3z2
p3
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100
H100
HVHa
l1
l2l3
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4.2.3-1 : - $
4.2.3-6: ! $
4.2.3-2 : $
+" )0" / ' ) (
#1 0+000.00 140.32
#2 0+090.40 141.32
# #3 0+180.10 144.32
#4 0+310.30 146.21
#5 0+410.20 156.21
)(& $1&/ $%
#" ,6,! ' )(", 6 + /")+8" /(! -/") ". /"
)"" (*) + (" -/") ()/8, /" 6+( +()" *,/" !-
)"". #"0 ' )"" "'9" (" "(" )"" +"). +
(1,208)101
108,981,296
109,031,245
108,761,512224
109,072+ 1,334(+ 0,003)
1,20762101
110,27107,7352,54160a2
(2,470)a
109,290,913
109,680,522
109,500,701
107,735- 2,020(+ 0,003)
2,47150a
Ima = - 0,686treba = - 0,680
fn = +0,006 m
Dozvoljeno
H101 = 109,072
H100 = 109,752
H101-100 = - 0,680
110,20109,7520,451501001
PrimedbaHVH = HV - ldhldVizuraStanica
(1,208)101
108,981,296
109,031,245
108,761,512224
109,072+ 1,334(+ 0,003)
1,20762101
110,27107,7352,54160a2
(2,470)a
109,290,913
109,680,522
109,500,701
107,735- 2,020(+ 0,003)
2,47150a
Ima = - 0,686treba = - 0,680
fn = +0,006 m
Dozvoljeno
H101 = 109,072
H100 = 109,752
H101-100 = - 0,680
110,20109,7520,451501001
PrimedbaHVH = HV - ldhldVizuraStanica
60,330Hn V =⋅
[ ] 13,2h −=−
[ ] 47,327H =
m016,0d36 =
81,330Hn V =⋅
[ ] 04,4h −=−
[ ] 77,326H =
!
0+090,40
2
1
3
4
"" - 5
0+410,20
" -
" -
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2. :
3. % :
4. (+:
5. - :
6. ) :
7. - " " :
8. ) :
9. - " :
10. - " :
11. - :
( ) [ ]hHHf abh∆−−=
kmh d36)mm( ±=∆
hf h
∆≤
[ ] ih
i dd
f v ⋅=
[ ] hf v =
nn
'
n
22
'
2
11
'
1
vhh
...
vhh
vhh
+=
+=
+=
∆∆
∆∆
∆∆
[ ]ab HH'h −=∆
'
nnB
'
3bc
'
2ab
'
1Aa
hHH
...
hHH
hHH
hHH
∆
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∆
+=
+=
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AAV lHH +=
nVn
2V2
1V1
lHH
...
lHH
lHH
−=
−=
−=
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12. ) :
4.3. 54 (3) 6 7
4.3.1. ('! !$8)- $'$&# 0*
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8 /" 8" 8"!+/ 69)) ,6() .
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(1 '( 0 21 ")+ 3 "6"+ ()"). )") (" 6"
+(* 20200 km ("7" (, , 6 -). + /" (" , (,
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+ ()") "*),/" (!" +" '"+"/" , L '"+")* ("!,. L1 ("
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()") /"*). (+, " ,)+8 -6" ")8 (! 0, ("
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&'$& #(&' 0" 6"*:(" ()". ("7"" (, 9* (+") ( :"*
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()") ,)8 (8 ".. '*/ (), *") 0(+
()"), 6+()+" ()),( ()") .) 6 , ()")". + ) ()
6 (" , +6,.+/ -6 , !(, () (, ()" ("7"" ,
60)* "+* 6"*:" ,!" (( 4.3.1-2).
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$&1 '( 0" (+ / (",/, " GPS /"*. (0
("!*") /"()" " (()"* 6 / (, ( /+9" 6)""(+. ("-! 60/
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GPS "*;
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(+! , ,0 (" " + *!,() 9"8 GPS. #*" GPS (" *",
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GPS /"* (" "" "* -/, '"+"/ : .
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(+, *""8 , ()") /"* ( ))"/"). ," (" *!,
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)0() 10 m 30 m. # (,)! 68 6.)"+
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#"6 ("+( 6.)"+ 9"8" /"*.
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4.3.2-1: 1 , ! $
4.3.2-2 : 1 , $
%$&,*& $')& '/& GPS +,&$-
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+ /"* 0"*, (+ / *" ()/8 ( '6)
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+ +9" GPS /"* / (" 6" !"")(* )0*. -0 /" /" GPS
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6. (LAND SURVEYING),
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