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, 2002

. - .
. - .
.
.
.

,

, 2002


, , .
I II .
.
,
, .

, ,
. .
, ,
, ,
, ,
, ,
,
. I II
.
:
. : 15 21, 36 42, 49 51, 61 64, 66, 67, 71 73;
. : 11 13, 22 25, 52 55, 65, 74, 75;
. : 26 35, 68 70, 76;
. : 7 10, 14, 43 45;
. : 1 6, 46 48, 56 60.


1.
, .
.
,
.
. .
251,45 0,005, 1,316 0,0005 ,
. ,
n- , - 5. -
5, n- . 35,18 35,176. ,
, 5 : 152,.25
152,2, 0,435 0,44.
, ,
. , : 55,35g.
, .
, , , ,
. . 350 000 .
3 5. 0,0015 , 102,350 .

, . , -
.

, - .

2.
,
. .
, .
:
1.
, - .
28,17+3,2+0,025+12,3854=43,7804
43,8.
2. ,
- .

= 34,215 0,102 0,48 = 1,6751664


1,68.
3. , . :
2,752 = 7,56.
4. ,
. : 6, 25 = 2,50 .
5. .
6. -
.

3.

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

. .

.
.

4. .
4.1.
Sistem international Si ( ,
1965 .)
(rad).
,
. 4.1
, .
().
.
.
1.
.
360 , . (1 0)
60 (60 ) (1 ) 60 (60 ).
10 = 60 ; 1 = 60 .
315018 30 .
- . .
400 , (g). (1g)
100 , (). (1) 100
, ().
1g = 100c; 1c = 100cc.
, :
125g 75c 85cc 125,7585g.
(gon)
(mgon) (mmgon)
1gon = 100mgon;
1 mgon = 100 mmgon.

g
=
(4.1)
.
360 400g

, :
10

g = = +
(4.2)
,
9
9
9 g
g
.
= g
10
10
1: = 62 45 32 .
, (4.2), -
. (32 : 60 = 0,53 ),
45,53 . (45,53 : 60 = 0,7588),
62,7588. (4.2) :
= 62.7588
62.7588
g = 62.7588 +
= 69.7320g .
9
2: g = 85.1735g.
, (4.3).
85.1735
= 85.1735
= 77.1421 .
10

0,1421 60 = 8,526
0,526 60 = 31,56 .
= 77.1421 77 08 32 .
(4.3)

2.
.
- .
(rad). ,
(. 4.1).

)

=
=
(4.4)
.
360 400g 2R
R = 1 (4.4)
:
) "
=
=
=
(4.5)
"
(4.6)

) g c cc
=
=
=
,
g c cc

)
= ;
)
= ;
(4.7)
)
" = "
)
g = g ;
)
(4.8)
c = c ;
)
cc = cc
, :
180
=
= 57, 2958

= 3437,75
= 206265
200g
g =
= 63, 6620g

c = 6366,20c
cc = 636620cc.
, ,
,
, .
3:
(. 4.2)

CD

,
=
4. f,
,
S
= 20 m.
:
CDD
DD = f
f = SCD tg .
. 4.2


- , tg
:
) f
= ,
S
)
f = S . f , ,

f =

c
c

S=

4c
.20 m = 1, 2 cm .
6366, 20

4.2.
1.
() (),
.
a
1
=
= 1: M .
(4.9)
A M
, .
.
250, 500, 1000, 2000, 5000, 10000 .. -, -,
, -, -. (4.9)
:
1: =150,45 m 1:2500.
A 150, 45
a=
=
= 0, 0602 = 60, 2 mm .
M
2500
2: 1:5000 = 52,5 mm
.
A = a M = 52,5 . 5000 = 262 500 mm = 262,5 m.
3: , , = 21,8 mm
= 214,25 m .
A 214, 25
M = =
= 9828 10000
a 0, 0218
= 10 000.

. ..
. ().
2.
, .
. ,
.
, . ,
, . 1 5
cm. ,
, (, 2, 3 ..). - n
0,5 2 mm. n ,
,
t.

A
t= .
(4.10)
n
- ,
,
(. 4.3).
. 4.3
0,1 .
,
t.
4: 1:500 t = 0,5 m.
, . 1 cm = 5,00 m.
a
5
= 10 .
(4.10) n = =
t 0,5
1 cm (. 4.4), 10 .
( 6,4 m).

. 4.4

, - .
3. ()
. ,
n p q, n = p.q.
.
(3 5 mm) q .
- q .
- , .
q ,
.., -1 -
. .
t ,
.
5: 1:5000 t = 1 m.
, = 2 cm, 100 m.
A 100
= 100 . q: n = 100 = 10.10 = 5.20.
: n = =
t
1
- p = 10 q = 10. = 10
q=10 (. 4.5). L = 163,4 m.

. 4.5

5.
.
( ) .
, -
.
2 5 mm. - ,
.
,
(. 5.1). ,
.
, (.
5.1), ,
. (. 5.1)

. 5.1

, ,
.

. 5.1a

. 5.1a

,
.

.

. 5.1

.
.
(. 5.2) ,
R. , ,
.

. 5.2

. 5.2a


(- 2 mm) (. 5.2).

.
.

,
,
(. 5.2).

. 5.3

,
(. 5.3).
,
, .
, ,
N (. 5.4). N, (m)
. 200g (. 5.4).
,
. , m ,
.

. 5.4

. 5.4

, ,
m.
, , N,
.
.
. - ,
, .
R. - -.
, ,
.
,
2 mm.

Mm
=
" ,
(5.1)
nR
n , ;
Mm .
,
= 1 2 . -.
:
30 40 m
(. 5.5).

. 5.5

,
. l1 [mm].
, n
l2. . 5.5
l l l l
tg(n) = 2 1 = 2 1 " ,
S
S
l "
=
.
nS

- ,
, . .. .
(. 5.6).

. 5.6

. 5.7

,
. ,
.
,
(. 5.7).
,
.
. ,
. ,
.

6. ,
.
, .
,
, .
,
.

. 6.1

,
,

,
(. 6.1).

-
,
, ,
.
,

. 6.2

, -
.

, .

,
(. 6.2).
,
, .
-
(, , ,
.. .) (. 6.3).
(. 6.4).

. 6.6

. 6.3

. 6.4

, -
,
(. 6.5).
,

, .
, ,
(
0,07 m). ()
.. 12 , .. 26 .

- 20 m.
()

. 6.5

, .
.
, .
, ,
1,0 1,5 m, 0,2 0,3 m.
,
. , ,
, .
, , .
.
,
( , , .)
. , ,
.

.
.

.
3 4 cm
1,5 3 m. 0,5 m
. ,
.
, ,
(. 6.6).
,
,
. ,

.
. 6.7

-, (. 6.7).
.
, ,
.
- ,
,
(. 6.8).
, (. 6.9).
.

. 6.8

. 6.9

, - .
,
.

. 6.10

. 6.11

,
(. 6.10). C D 2 3 m
. , . .
, ,
. . . ,
- .
. . .
. , , , ,
(. 6.11).
. , . ,
- .
, 30 . 100 m 15 mm.
.
, ,
. , . (. 6.12). , . 1,
, . D1 1.
D1 1 , D1B1, .. . 2.
. D .
D, :

, .
(. 6.13).

. 6.12

. 6.13

,
. (. 6. 14).

. 6.14

II


7.

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

-
.
,
.
, .
.
, .. ,
.
,
.
B L H, X Y
H, . -
X Y,
H.

8.
.
6. ,
. .

, .

. 8.1

.

. 6
4 . , 180
. 60 . 4 ,
. 1:1 000 000.
.
: -34; -35; L-34; L-35.
1:1 000 000
1:500 000, 1:200 000, 1:100 000.
:
1:1 000 000 1:500 000,
, , , .
1:200 000 1:1 000 000 36 ,
I XXXVI.
144 1:100 000
1 144 (. 8.3).
1:100 000 1:50 000, 1:25 000, 1:10 000 :
1:100 000 1:50 000
, , , .

. 8.2

. 8.3

1:50 000 4 , : , , ,
1:25 000. 1:10 000,
1 4 (. 8.4).
1:100 000 1:5 000, 1: 100
000 256 1:5 000, (1) (256) (. 8.5).
[17] 1:2 000
1:10 000. 1:10 000 25 1:2 000 (. 8.6).
- 1:2 000
.

1:100000,
1:50 000, 1:25 000 1:10 000
1:100000


1:5 000
1:100000

. 8.4

. 8.5

8.1

1:2 000
1:10 000

. 8.6

1: 500 000
1: 200 000
1: 100 000
1: 50 000
1: 25 000
1: 10 000
1: 5 000
1: 2 000



K-34-
K-34-XXXVI
K-34-144
K-34-144-
K-34--
K-34---4
K-34-144-(256)
K-34--4-XXV

9.
:
, , ,
. ,
.

, .
,
h (. 9.1).

. 9.1

, -
,
(.. -), .
.

. 9.2

10.
1.
,
. .
: .
.
.
, - .
, ,
- .

(. 10.1).

. 10.1

. 10.2

,
, .
: ,
.
, (. 10.2).
(. 10.3):
0.2 m,

, . 136.4

4.
, .

. 10.3

4 6 137.5. , , . .

.
: ,

,
(. 10.4).
=
SAB. ,
.
134.4
. 10.4
.
S
a
= AB ,
(10.1)
hA1 H AB
(10.2)

a = S AB .

hA1

H AB

= S AB

134.4 134.2
= S AB .0, 25 .
135.0 134.2


.
, . .
.
,
.
: , , .
. -
,
.
1/2
, 1/4
.

.
(. 10.5).

2.
.

.
-
. 10.5
,
. -
, 10 .


- .
X Y . . XA YA,
.
X K = X A + X
(10.3)
YK = YA + Y .
X Y .
(. 10.6).

. 10.6

. . .
S3 = X S2 = Y . :
X K = X B X
(10.4)
YK = YB Y .
. ,
S1 + S2 S3 + S4 d X Y A
B.

. :
d
XK = X A +
S ,
S3 + S4 4
(10.5)
d
YK = YA +
S .
S1 + S2 1


X Y - .

.

3. .



. ,
. . 10.7 . 307 m.
(. 10.8)
. .

. 10.7

. 10.8

, . .
S, ,
h. h = 1 m.
hCB = x . - H1,
SCB. :
SCB
x
h
=
(10.6)
x = h.
.
SCB S AB
S AB
.
(10.7)

HC = H1 + h.

SCB
S AB


:
. . . 10.9 .

. 10.9


. .
. i
,
(.
10.10) h

h
h
= arctg
i = tg = .
(10.8)
. 10.10
a
a
, i

i % = 100 tg = 100i .
(10.9)
: h = 2 m, = 6.7m. :
h
2
i = tg = =
= 0.298507
a 6.7
= 18.4675g .
i % = 100 tg = 29.85% .

:
:
h
(. 10.10), .
:


(.
10.11).

,

. 10.11

. . 10.11 ,
= 330.

4.

, i%
h
h
a=
.100 .
(10.10)
i%
,
h
a=
(10.11)
.
tg
, ,

, .
.

. 10.12

:
1. ,
- ;
2. , ;
3. , -
.
, . . ,
. . . . . ,
. D. ADB.

5. .

,
.

:
, .
.
(. 10.13).

. 10.13

,
, , ,
. .
. -
, , .


.
. . ,
. (.
10.14 ).

. 10.14

. 10.14



. ,
.
, (. 10.15).
, - , ',
, . '
. . .
' ' , . '
', , .

. 10.15

6.
, .
, .

, , ,
.
. 10.16
,
. .

. 10.16

7.
,
h.

, (. 10.17).

. 10.17



1
(10.12)
Vi = h ( Si 1 + Si ) .
2
n
1
V = h( S1 + 2S2 + 2S3 + ... + Sn ) .
(10.13)
2
,
h'.
1
V = h Sn .
(10.14)
3
:
1
1
V = h( S1 + 2S2 + 2S3 + ... + Sn ) + h ' Sn .
(10.15)
2
3
: D (. 10.21) .
. : HA = 104.3 m, HC = 99.7 m h = 1 m. S0 , S1 ,..., S5
S0 = 600 m2; S1 = 580 m2; S2 = 420 m2; S3 = 380 m2; S4 = 320 m2; S5 = 210 m2.

. 10.18

:
1
1
1
V = h( S1 + 2S2 + 2S3 + 2S4 + S5 ) + h '( S0 + S1 ) + h '' S5 .
2
2
3
1
1
1
V = (600 + 2.580 + 2.420 + 2.380 + 2.320 + 210) + .0,3(600 + 580) + .0,3.210 = 2303 m3.
2
2
3

III


11.
, ,
, . .
:
,
,
.
.
.
, , .

.
Y n x1 , x2 , x3 ,K , xn ,
:
Y = f ( x1 , x2 , x3 ,K , xn ) .
(11.1)
Y,
xi (i = 1, 2,K , n)
2

f
f 2 f 2
MY =
m +
m +K +
x 1 x 2
x
1
2
n

(11.2)

2
mn ,

MY ;
mi xi ;
f
xi


li .

xi

(11.2) , MY ,
mi .
(. 15.6 cm, 9.3 cm, 6.7).
,
.
:
1.
.
2.
. :
;
.
3. , .
,
:
1. .
2. , , .
3.
.
4.

MY .
: a = 137.28 m, b
= 185.72 m = 57.8500g,
: ma = 5 cm, mb = 7 cm, m = 2c.
.
1. ,
ab sin
S=
(11.3)
.
2
2. (11.2)
2

. 11.1

S
S
S
ms = ma2 + mb2 +
a
b

(11.4)

3. :
s ab cos
s b sin
s a sin
=
=
=
;
(11.5)
;

2
a
2
b
2
4. (11.5) (11.4).
2

(11.6)

2 m 2

b sin
2 a sin
2 ab cos
ms =
ma +
mb +

2
2
2

.

,

c
, m c .

185.0, 789
2 173.0, 789
2 185.137.0, 615 2
ms =
0,05. +
0, 07 +

2
2
2

6366
ms = 33.62 = 5,8 m2.

12.
,
, , , - .
,
- , -
.
(
), ,
.
, .

:
1. - (-) .
2. .
,
- , , - ,
.
l1 , l2 , l3 ,K , ln n l, .
- , x ,
ml - M x .
- .

.
1. li
(12.1)

li = li x0 ,

x0 - li (i = 1, 2, 3, n).
2. - x
[ l ] .
(12.2)
x = x0 +
n
x
.
3. .
i = x li .
(12.3)
:
[ ] = 0 ,
(12.4)
(12.5)

[ ] = [ l ] .

(12.4) (12.5)
[l ] n. ,
:
[ ] = n ,
(12.6)
(12.7)

[ ] = { [ l ] [ l ] } .


[l ]
[l ]
=

(12.8)
,

n
, - ,
, .
4.
[]
m=
(12.9)
.
(n 1)
5. -
m
[]
M =
=
(12.10)
.
n
(
n 1)
n
.
:
m
mm =
(12.11)
,
2(n 1)
(12.12)

mM =

mm

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

m 1
x
= ;
N= .
x N
m
: 6 .
. 12.1. - x
m, M M . (12.1)
(12.13)

M =

(12.13) . 12.1.
12.1

l, m

l, cm

m = 23,34 / 5 = 2,1 cm

1
2
2
4
5
6

135,27
135,24
135,28
135,22
135,25
135,26

5
2
6
0
3
4

-1,7
+1,3
-2,7
+3,3
+0,3
-0,7

2,89
1,69
7,29
10,89
0,09
0,49

-8,5
+2,6
-16,2
0
+0,9
-2,8

x0 =

135,22

20

-0,2

23,34

-24,00

M = 2,1/ 6 = 0,9 cm
.

M = 0, 9 :135, 2 =
= 1:15000

[l ]
[l ]
[ ]
[]
[l ]
=
3,3
n
x=
135,253
[l ]

3,3
n
= 0, 033 n = 0, 2 [l ] = 0, 66
[l ]
3,333

n
. 12.1 , (12.6) (12.7)
.
:
1. - x = 135.253 m.
2. m = 2.1 cm.
3. - Mx, = 0.9 cm.
4. M, 1:15 000.


(, , ).
.
li , li i- (i = 1, 2,K , n) , a di
,
(12.14)
d = l l .
i

li ,
. ,

[d 2 ] .
2n
-

(12.15)

m2 =

1 [d 2 ] .
n
2 2
(12.15) (12.16) .
,

[d ]
= i .
(12.17)
n
, ,

(12.18)
d = d ,
(12.16)

M =

(12.15) (12.16). ,

[ d ] 0, 25 d .
(12.19)
: .
. 12.2.
- ,
.
12.2

l , m
1
2
3
4
5
6
7
8
9
10

135,27
165,84
103,18
115,02
141,75
95,21
128,98
101,31
65,76
99,15

l , m

d , cm

x ,m

d2

135,25
165,80
103.23
115,06
141,83
95,19
128,94
101,29
65,74
99,12

+2
+4
-5
-4
-8
+2
+4
+2
+2
+3
2

135,260
165,820
103,205
115,040
141,790
95,200
128,960
101,300
65,750
99,135
36

4
16
25
16
64
4
16
4
4
9
162

m = 162 / 20 = 2,8 cm
M = 2,8 / 2 = 2, 0 cm
M = 2 /165,82 = 1: 8 291
M = 2 / 65, 75 = 1: 3 287
2 < 0,25 36

d 2
[d ] < 0, 25 d

. 12.2 , .
- .
- (165,84 m) - (65,75 m) ,
.
[d ]

13. .

12 .
.
- - -
.
, . p

k
pi =
(13.1)
,
mi2
k , mi i- , i
=1,2,3,, n.
- .
k , .
k .
- .
.
: m1 = 25cc , m2 = 30cc , m3 = 20cc , m4 = 50cc
. ,
.
k
m22 , . k = 302 = 900 . (13.1)
900
900
900
900
900
p2 =
p3 =
p4 =
,
,
,
=
,
625
900
400
2500 2500
p1 = 1, 44 , p2 = 1, 00 , p3 = 2, 25 , p4 = 0, 36 .

.
1. . . (13.1).
p1 =

2.
. ,
.
3. . , . -
. (13.2).
:
- x ,
,
i- mi ,
- M x .
, :
1. x0 12

li = li x0 .
(13.2)
2. (13.1).
3. ( )
[ p l ]
x = x0 +
(13.3)
.
[ p]
4.
i = x li .
(13.4)
5. , :
[ p ] = 0 ,
(13.5)

[ p ] = [ pl ] .
(13.5) (13.6),
[p l] [p]. ,
:
[ p ] = [ p ] ,
(13.7)
(13.6)

[ p ] = { [ pl ] [ pl ] } .

(13.8)


[ p l ]
[ pl ]
=

(13.9)
,
[ p ] [ p ]
, 12.

6.
[ p]
(13.10)
.
=
n 1
7.

[ p]
mi =
=
(13.11)
.
pi (n 1)
pi
8. -

[ p]
M =
=
(13.12)
.
[ p ](n 1)
[ p]
. . x , , m5 , M .
. 13.1.
13.1
p
p
p

pl
pl

l
g
mcc
1
2
3
4
5

65,8920
65,8945
65,8975
65,8930
65,8950

30
17
40
35
25

1,36
4,24
0,76
1,00
1,96

0
25
55
10
30

0
106
41,8
10
58,8

23,2
-1,8
-31,8
13,2
-6,8

31,55
-7,63
-24,17
13,20
-13,33

731,96
13,73
768,61
174,24
90,64

0
-190,75
-1329,40
132,00
-399,90

x0 =

65,8920g

[ pl ]
= +23,2cc
[ p]
x = 65,89432g

[ p]

[ pl ]

9,32

216,6

[ p ]
-0,38

= 0, 04

k =

m42

[ p ] = 0, 373

[ p]
1779,18

[ pl ]
-1788,0

[ p l ] = 8, 8

= 1225 , ,

.
. 13 .1 , [ pl ] [p] (13.7)
(13.8),
[ pl ]
= 23, 2cc ,

[ p ]
[ pl ]
= 23, 240cc ,

[
p
]


= 0, 04cc .
:
1.
1779, 2
=
= 21cc .
4
2.
21
m5 =
= 15cc .
1,96
3. -
21
M =
= 7cc .
9, 23
- ,
x = 65,89432g 7cc .

,
.
.
, ,

d p < 0, 25 d p ,
(13.12)

:
(13.13)
(13.14)

[ pd 2 ]
2n

Mi =
- .
2 pi

(13.12) di (12.17) (12.18).



[ pd 2 ]
.
2(n 1)

, ,
- .
(13.15)

IV


14.
, ,
X, Y, H.
X Y, ..
AB (. 14.1) S AB , .
S AB . S AB , BA
. AB BA 200g, .. AB = BA 200g.
BA . BA < 200g "+"
, BA > 200g "".

. 14.1

. 14.2

:
X Y
, ;
SAB,
SAB S.
1.
, ,
X AB YAB . . 14.2 ,
X AB = cos AB S AB = X B X A
(14.1)
YAB = sin AB S AB = YB YA .
X AB YAB
X Y
X B = X A + X AB = X A + S AB cos AB
(14.2)
YB = YA + YAB = YA + S AB sin AB .
: X A = 1409.08 m, YA = 2104.43 m, S AB 103.04
m AB = 129.3814g . B (XB, YB).
:

X AB = cos AB S AB = 45.88 m
YAB = sin AB S AB = 92.26 m
X B = X AB + X AB = 1409.08 45.88 = 1363.20 m
YB = YAB + YAB = 2104.43 + 92.26 = 2196.69 m.

2.
SAB S AB BA
SAB = S

AB = arctg

(14.5)

YAB
X AB

. 14.3

. 14.3 , AB 0g 400g.
X Y:
XAB YAB , AB 0g
100g.
XAB , YAB , 100g< AB < 200g.
XAB YAB 200g< AB < 300g.
XAB YAB 300g< AB <400g.
AB r, ..
. | X AB |
| YAB |
(14.6)

r = arctg

| YAB |

| X AB |

. 14.4

r, ,
, AB (. 14.4)

AB = r ,

X AB >0

YAB >0,

AB = 200 r , X AB <0 YAB >0,

(14.7)

AB = 200 + r , X AB <0

YAB >0,

AB = 400 r , X AB >0 YAB >0



BA = AB 200g .

(14.8)

S AB
X AB
YAB
2
2
S AB = SBA = X AB
+ YAB
=
=
(14.9)
cos AB sin AB
: , B, C, D X Y.
S AB , SBC , SCD , SDA AB , BC , CD , DA .

.
14.1
X

1
2
1
2
1
2
1
2

A
B
B
C
C
D
D
A

4023.48
2020.14
2020.14
1531.45
1531.45
2530.30
2530.30
4023.48

2113.38
5001.26
5001.26
3115.18
3115.18
1213.12
1213.12
2113.38

r = arctg

| YAB |

X12

Y12

-2003.34

2887.88

61.3897

-488.69

-1886.08

83.8599

998.85

-1902.06

69.2158

1493.18

900.26

34.5404

| X AB |

12
200-r
138.6103
200+r
283.8599
400-r
330.7842
r
34.5404

S12

3514.71
1948.36
2148.38
1743.58


15.

, .. . ,
, , - .

1.
.
, .
. 15.1. (1) (2)
.

. 15.1


, .
.

2.
,
(. 15.2), ,
(. 15.2). ,
, (200g).

. 15.2

. 15.2

. . ,
, . .
, . 1

. 15.3

. , ,
, (. 15.3).
, , . 1
, .
, .
, . 2 (. 15.3). .
( ),
,
. , ,

(. 15.3). .
. . ,
.
, ( 1,5 2 m),
,
.

. 15.4

. ,
, (. 15.4) . , ,
.
, .
. .

, .
. , . .

, .
24.

3.

(. 15.5).
( X) .
1, 2,K i,K
1, 2,K i,K , .
X .
, ,
X i Yi
.

. 15.5

(. 15.6) .
,
.
( ) . 1, 2,K i,K
(. 15.5), X i
Yi , .
, . X i
1, 2,K i ,K , .
Yi 1, 2,K i,K
. ,
.
(23),
, .

. 15.6

16. -
() .
- :
-, -
, , (),
-.

16.1. , ,

1.

. 16.1, . 16.2.
: (
) (1), () (2),
(3) (6)
7.
: Z
, V (4),

H (5), .
, ,
:
, .

. 16.1

- (. 16.2 16.3) :
1, 1.1, 1.2, - 1.3 ( ) , 1.4
1.5 , . 16.4.
.
() 2 6.
.
3, , -
3.1 3.2. ,

,
.

.


.

.

: I ,
II ,
.


200g.
V (4)
() 4.1
4.2
.

.
. 16.2
(5)
() 5.1 5.2
.
.
7 6,
. : 6.1
, 6.2,
6.3, 6.4 ( ),
6.5 , 6.6 6.7
(1 . 16.16),
(8 . 16.16) (2
. 16.14).
() 8, ,
8.1 8.2 ( ),
, .
9 (. 16.1),
- , 9.1, ,
,
, .
.

.
,
. .
- ,
,
. ,
1015 - .
, .

, ,
: ( ), ( )
, (-
), , , ,
.
2.
.
, . 16.3, ()
. : 1, 2 ( ,
), 3 ( ), 4
( ) 5 (
), 6 (
, ) 1, 2
3 (. 16.4).

. 16.3

. 16.4

. 16.5. , ,
B1 A1 . (
) , , ,
B1 A1 . ,
. , ()
, B2 A2 , ,
W .

. 16.5

. 16.6

W - . ,
, .. W
.
.
Z .
. 16.6 - . ,
, : hh, vv () dd
d1 -d1 .
(), .. . ,
, ,
, , .
:
1. . (-
) ,
- W .
.
() :
2. ,
.
3. ,
A1B1 ,
.
( ), ,
,
.
4.
, ( ) (
) .
3. .
. :
) , - 30 (10II);
) 5 30 (1,5II10II),

10 30 (3II10II)
5 10 (1,5II3II);
) , - 5 (1,5II).
. - : ,
( ).
, ,
,
.
, ,
ZEISS/Jena (), .
. .
h 080 (. 16.7.).
,
(1), ,
(2).
(3),
, (4) .
(. 16.8)
: (-)
100, () 50.

(. 16.8)
(5) (. 16.7),
.
.
(Hz) (V)
,
.
a = 10c , .

,
,
. 16.7
12.
. 16.8 : 208,23g 220,08g .

. 16.8a

. 16.8

, ,
.
- heo 080 heo 120,
.
Theo 080 A : T05 (Wild/), Th51 (Opton/), KO-S
(Kern/) .
.
.
Theo 030 (. 16.9). , ,
(1) (2).
, ,
. (3).
(6.3 . 16.1) ,
(4), . -

a = 1g .
, (. 16.10).
, : Hz
V, , .
n = 100 , 1 10 . ,
- t = a / n = 1c .
. (0,1 0,2) t = 10 20cc . ,
, , ,
. . 16.10 : 372,08g
291,86g .

. 16.9

. 16.10

(5) ,
,
(18).
Theo 020 (. 16.11) - .
(1),
( 2),
10.
(3) ,
(
, 4).

. 16.11

. 16.12

. 16.13

Theo 020 (. 16.12), ,


. (1) (2)
, (3) (4),
, . (5)
(6).
Theo 020 (. 16.13). (1) ,
.
: T16 (Wild/), Th41 Th42 (Opton/), DKM1
(Kern/), T5 T10 (), T60E (Sokkia/) .
.
Theo 015 (. 16.14).
(1) (2) .
(3) . ,
, - ,
. ,
. (1) (. 16.15).
, Hz V ,
( ), .
. ,
.
.
: , - ,

( ).


. .
a = 1g , n = 500 ,
t = a / n = 20cc . ,
20 . .
16.14 373,766g.

. 16.14

. 16.15

(4) .
: T1 1A(Wild/), K1A 1 (Kern/) .
. .
t = 1 2cc .
.
.
- .
,
, - ,

. , ,
.

,
.
.
Theo 010
(. 16.16).
-.

(1)


,
(1.1)

.


.

(2)
(3)

. 16.16
.
(4)
.
(5) (6) ,
(. 16.17) .
, , - a = 20c .
, n = 1000 t = a / n = 2cc .

. 16.17a

. 16.17

, (7)
, .. (. 16.17).
( 200g).
: (
291);
( 7 10c = 70c );
( 6),
0, 2,
: 291,7602g.
, - (4)
(2) (3).

heo 010 A (. 16.18).


-, . (1)
(2) Theo020A (. 16.12).
- ,
.
(. 16.19).

-
. .
: ,
, .
,
. (4)
(. 16.19)
126,1990g.
,
(5).
. 16.18

. 16.19a

. 16.19

heo 010 (. 16.20)


(1) ,

.
.
: T2 (Wild/),
Th2
(Opton/),
DKM2

DKM2-A
(Kern/), Te-B1 (/), T2 (),
TM1A (Sokkia/) .

16.2.

-
,
, .

,
.

,

. 16.20

- .
, , ..
, .
- :
H ,
V ,
Z ,
L ,
L , .. ()
,
hh ,
vv .
,
, , ,
: ,
, 100 g .
(

, ):
1. L V, ( L V)
. ,
.
:
, , .
200g. 1/2 , ,
. .
. ,
() .
.
,
1/2 .
,
, .. L
V. ,
.
f () L V

f ( ) = .sin .tg ,
(16.1)
,
, .
, , = 0 (200)g
g
= 0 . L V ,
.
2. hh V ( vv V )
, .
,
.
:
, (. 16.21).
.
, (. 16.21).
, .

. 16.21


, .
:
3 (. 16.4).
, .
.
,
, ,
, - .
3. Z H .
, H Z ,
. 100g
.
f (c) c
c
f ( c) =
= c .sec ,
(16.2)
cos
, . = 0g, f (c) = c .
:
( ) ,
(. 16.22)
O1 . , 200g
( ) (. 16.22)
O2. f (c) c
, f (c) = c , 1 (2 200g) = 2c, 1 2

. :
1 = 115,3150g,
1 = 1 = 115,3300g,
g
O2 = 315,3450 ,
2 = 2+ = 315,3300g.
2c=1 ( 2 200g)= 3,00c c = 1,5c.
, .
,
2 ( ).

. 16.22

: 2 - ,
, :
:

1 2,
(. 16.22). (1) (. 16.4),
, .
: 1
2 ,
( )
(
).
.
,
.
4. V (..
). ,
, .
f (i ) i :
f ( i ) = i .tg .
(16.3)
( = 0g) , - ,
-. Z H
.
: ,
1 2 .

(16.4)

2 f ( i ) = O1 O2 200g ,

, , .. Z H .
, H V
.
: - ,
.

, 1 2 , ..
(16.5)

Ocp =

O1 + O2 200g

),

2
f (i ) .

16.3.
1.
. ,
,
v .
:

,
,
,
(
). L

5 , ,
. (.
16.23): 5
1 = 1400,
2 = 2602 L
= 2 1 = 120,2 . v = L : 5 =
120.2 : 5 = 24 .
- ,
-,

. 16.23
.
:

, ,
, .
- 16 40
.
. ,
, , .
, ,
. 1 3.
(. 16.24):
D , .
1 2 ,
L = O2 O1 .
L2 L
= 2arctg
.
(16.6)
D
D

. 16.24

. ,
.
: ,
, 5, 20, 50, 100, 200, 500,
1000 m, I II I II .
= I II
(. . 3).


, .
.
2.
. (0
10) , ,
. , .
:
(. 20g),
,
.
(. 100) 0,1 - .

.
.
. (. 20g),
.
(
) (
).
.
(. 100 10,00). 0,1, . 3 4.
.
3.
(. 16.25) E C ,
e .
O

(
)
:
(50 60 m), ,
20 50g

. I II
,
I OII
= OI OII.

.
i = 2(c i ) , c
. 16.25
,
Y
, (. 16.26). ,
. Y = 2c, X,
i .

.

. 16.26

4.
,
, .. .
: ,
, ..
, .
, Z1 .
1g Z2 .
, , ,
.
Z = Z2 Z1 1g

,
A1 . ,
A2 .
A1 .
A2 . A2 A1 .
3 4 , 200g
A1 A2 ,
.

i
= ,
(16.7)

i = arcsin(sin Z sin A) = sin Z sin A


(16.7)
,
( )
A = A2 A1 .

17.
, -
.
- .

17.1. , ,
,
1.
(. 17.1).
, , ,
. (1)
, () (2),
, (3),

. 17.1


( ) .
(ON/OFF)
.
-
(-),
,
.
( )
,
.
.
2.
.
. ,
() () , -
, (. 17.2). ()
, , .
,
, .
,
.
, ..
, .
, .
( )
, .
.
.

. 17.2

, -
. -
:
,
(. 17.3).

,
, ,
.
,
.
( )
. 17.3
,
. - .

. 17.4


(. 17.4). , ,
, (
1: 1,01).
. ,
.
.
- .
- , ,
90.

. 17.5

(. 17.5). ,
, ,
, .
. ,
, .
,
. ,
.
, ,
, .
,
. , ,
, . -
. - .
1.
.
,
(.
17.6), ()

.
. -
, 256
.
.
1,6g.

128 .
. 17.6

.
( ) 1000
128 000 31,25 . -
4096 , 1000
4 096 000 , 1.
-, ,
- , : ()
, ( ). ,
,
. - ,
.
, ..
. : )
; ) ) -
. -
.
.
3.

- .


. ,
() , ,
,
, , .
()
, ,
, , , , ,
. -
,
, ,
. ,
39.
:
( ).
.
.
4.
.
,
: - ( ),
.
( - ) , ,
, ,
.
.
. - ,
(),
. .
-.
.
Kern /, Opton/ .
. (. 17.7).
( , ,
, , .)
() . ,
(. ,
.).

( ,
.).

. 17.7

(39) , .
5. ()
,
. ,
: , , ,
. , ..

, .
. :
( )
(
).
THEOMAT T2000
Wild/ (. 17.1). ,
, 0,1.
, .
.
(. 17.7):
1. :
ON ( OFF);
: SET TIME t
RUN ( t = 0 20 ., t = 1 1 .);
: SET MODE 40 RUN 2 RUN ;
n : SET FIX n RUN, n 1 5;
2.
ON.
DSP HzV 2 3 .
: ,
, : Hz, V
HzV. REP,

, .
STOP.

: SET Hz0 RUN.
3. (
). - : SET MODE 78 RUN
RUN.

REC .
NR RUN
NR RUN, REC.
4.
. ERROR
: 11 12 , 51 58
..

TEST 0, 1
BATT, 2 .
, CE.
: T1000, T1010, T1610, T1100, T1800, T105 T107 (Wild,
Leica/), 2 (Kern/), Eth2 Eth50 (Zeiss/ ), DT2E, DT4E, DT500 DT600
(Sokkia/), DT101, DT 102, DT 103, DT 104 DT106 (Topcon/) .
( )
39.

17.2.
,
-: 1. L V, . LI V; 2. hh V; 3. Z H 4. H V.

- .

. , ,
.
.
, ,


. , ()

.
, .
( ) ,
, - : 1)
, , -
, ,
(
) 2) (
) ,
. ,
,
,
. ,
(. ),
.



.
, - ,
, , .
.

(THEOMAT T 2000)
.
THEOMAT T2000 (. 17.1 17.7):
( ).
,
, .
( ) SET MODE 15 RUN,
. ,
RUN, . 200 g,
( ), RUN
. 3 .
, 0. ,
1II, 100g, ,
.

, ,
, STOP RUN.
.
. , - 100 .
, .
SET MODE 11 RUN. 1
Hz C, 2 3 . RUN
3 100,0000, .
, 1 2 , 3
. -
45 , , , RUN
CE
.
( ).
, .
1 ,
. 200g 2 .
, :
, . 3
1 2 .
3. , 200 g
3. , .
SET 2 C II SET 4C II ( SOKKIA/) (. 17.8 17.8)
, 2 20.
.
,
. 15- () . , ,
60 - .
.
( )
.
.

. 17.8

. 17.8


.. , ..
, . :
YES,
,
, ,
. SHFT 0 SET,
. PROG,
2
Correction (). Tilt offset
( 2)

, Tilt angle
. , ,
SHFT 0 SET, . 200g,
,
SHFT 0 SET, ,
.
CECA.
, Tilt
angle, X Y
100g.
. - 100 m
(). PROG.
2.Correction, 2.Collimation ( ).
YES,
.
, .
( YES), .
YES
, NO . NO
(Re-observe?). YES
.
, ,
, () .
,
-.
. .
SET5F (. 17.9 17.9) SOKKIA/,
, 20,
, ,
4 ,
3000 , .
() : (THEO), (EDM), (S
O) (CONF). .
4 , .
.

. 17.9

. 17.9a

() :
, . , , .
. ,
(CONF), 2.Tilt correction ( ).
: = 90,0000g X1 Y1
. , ,
200 g,

= 270,0000g, ,
X 2 Y2 . X = ( X1 + Y1 ) / 2
Y = ( X 2 + Y2 ) / 2 . - - - 10II,
EXIT .
: 0 SET,
0,0000g. SET X1 Y1 .
200g ( ), , X 2 Y2
, SET . ,
.. . - 400 120,
EXIT. ENTER,
.
X3 Y3 , .
200g , X 4 Y4 .
X Y 3 4 10II, EXIT
, .
.
REC ELTA 13 C (ZEISS/) (. 17.10 17.10)
, ,
, 4 , 40
, 24 , ,
-.

. 17.10

. 17.10a

(ADJUST/PREPARE) 5
, .
1,
. ENTER (Input and
measurement), : Measure pos. 1: ENTER.
ENT ,
.
ENT
: 1.
; 2. 3. 0 . MEN
.
4,95,
ERROR: LIMIT EXCEEDED MEN INPUT AND MEASUREMENT
MENU.
2, SZ
SK .
,
ENT. 200g,
ENT . SZ SK
NZ NK . (+) ,
() . MEN SZ SK
.

SZ SK 2,55 5,15,
ERROR: LIMIT EXCEEDED. MEN
ADJUST/ PREPARE.
,
1.Levelling, ,
, SZ, SK , NZ NK
. MEN .

LEV ().

18.



,

,
,

.



, ,
,
. 18.1

(6).

. ,
R ,
(.
18.1). ,
, (
). -, 400g.
( 18.1).

:
1. , .
, .

18.1

28
40

66, 64 82
227, 69 88

266, 64 48
27, 69 38

34
50

=
=

R-OR
R
I
II
O
R
O +(O 200)
2
g c cc
g c cc
cc
g c cc
6
7
8
9
0, 15 03
0 ,00 00
0, 00 00
0,0
161, 20 18
161, 05 15 161 ,05 080
-7,0
260, 01 71
259, 86 68
259,86 757
7,7
330, 79 53
330, 64 50
330,64 597
9,7
(16 45)
(56 33)
(56 434)
+10,4
+ 15 03 x 4
=
60 12
1= +2,6
(16 45)
66, 64 65
0, 00 00
0,0
227, 69 63
161, 04 98
10,0

15
16

326, 51 74
396, 29 50

126, 51 26
196, 29 12

48
38

326, 51 50
396, 29 31

(15 94)

(14 24)

(170)

(15 09)
+ 64 65 4

- .

.
I
II
OI
OII
g

1
24

24

24

2
28
40
15
16

28
40
15
16

c cc
3
0, 15 24
161, 20 42
260, 01 98
330, 79 72
(17 36)

133, 38 62
294, 43 66
393, 25 32
64, 03 20
(10 80)

c cc
4
200, 14 82
361, 19 94
160, 01 44
130, 79 34
(15 54)

333, 38 12
94, 43 30
193, 24 90
264, 02 80
(09 12)

2c

5
42
48
54
38
(182)

50
36
42
40
(168)

133, 38 37
294, 43 48
393, 25 11
64, 03 00
(09 96)
38 37 x 4

259, 86 85
330, 64 66
(56 49)
58 60
(15 09)
0, 00 00
161, 05 11
259, 86 74
330, 64 63
(56 48)
=
53 48
09 96
=

cc
10

11
12.08.1999.
17
: ,

-2,6
-9,6
5,1
7,1
0.0

[ ] = 411,18
1,4
11,4

9,3
6,3

-7,9
-4,9

5,6
-1.4

0,0

2=
56 33
56 49
56 48
169 30 : 3 =
56 433
3=

0,0
-3,0
1,7
-3,3
-4.6
-1.2

1,2
-1,8
2,9
-2,1
0.2

m=

411,18 /(3 2) = 8,3cc

M = 8,3cc /

3 = 4,8cc

fmax

No
.
28
40
15
16

1
00
115
68
50

2
00
98
85
66

3
00
111
74
63

f cc
max
0
17
17
16

,
, .
2. , , ( )
.
.
3. ( ).
, ,
.
, , :
4. . ,
. .
5. . ,
, .. ,
, , , .
:
6. , ()
. ,
.
0,5 cm. - ,
,
, .
7. , . ,
, :
, ,
100g .
,
. ,
, , .
, ,
:

.
. , -

. ,
(, )
, .
0,2 2 mm.
.
,
, , ,
,
100g.
,
(
) .
8. , ..
- .
.
:

;
;
,
( ,
, -
);
,
.

,
, .
, ,

.

1.
,
, -
.
,
,
.

(. 18.2)
:
( - ,
, ).
. 18.2
( 18.1),
,
, ,
,
.

3 . ,
200g
, , ,
, 4
. . ,
, 200g.
, - ,
, .. , n
. ,
.
, = 200g/n. n = 3 ( 18.1)
, = 66 67g. ,
0g, 2 .
:
: ,
- 0 g, ,
, .

.
, -
, , - 0 g,
,
.
: , ,

, 0g, - 66g,
.
: , ,
,
- 133g.
:

I
II
g
1. 5 2c = O O 200 .

, , ,
.
. . ,

, -
.

,
( ).
.:

OI OII = 2c

: 17 36 15 54 = 1 82 ..

2. 6 O ,
, :

OI + OII 200g

).

2
, ..
6 3 4. : 16 45 = (17 36 + 15 54 )/2
..
3. 7 R ,
6
, 0,00 00g. , R ,
, , ..
.
.
, .
: 7 4
( ) ,
6. : 56 33 + 415 03 = 16 45 ..
4. 8 R
R .
:
7 : (56 33 + 56 49 + 56 48)/ 3 = 56 434.
:
1. 9
, .. = R R .
2. 10 i = i , : = [ ] /,
(i = 1, 2, ..., ). [ ] = 0 . [ ].

(18.1)

m=

[ ]
( n 1) ( k 1)

R
m
M =
(18.2)
.
n

2.

, - .
(), .

. 18.3

: (. 18.3) .
, . ,
- 0g ( ,
).
, . ,
, . (
I ) (. 18.3). ,
. , .
,
. . (. 18.3).
. ( II), ,
, . ,
.
() . =III.
(. 18.3). - , 3, n
, n

(18.3)

O O k .400g

),

n
k = 1, 2, ... .
,
= O O .
:
= 0, 76 24g
:
= 0, 76 24g
= 7, 83 68
= 3, 12 13

(3 ) = = 7, 07 44
= = 2, 35 89
= ( 3 )/3 = 2, 35 813

19.
:
1. , .. ,
;
2. .

1.
( , .) 12,



(.
19.1).


mm,
,

, .. 12.



i ,

e sin i
(19.1) i = arcsin
,
Si
. 19.1
i
,

Si () ,
.
,
( 19.1) :
1. 2 , 3
Re .
2. 4 i ,
. .
3. 5 Si e (
).
4. 6 7 sin i i .
5. i 3
,
i ( 8) R 9
R = Re + R .
7, 8 9 .
19.1.

12

. . .
.

= Re R
Re
(g c cc)
(g c cc)
1

12e

7
0,0000
14
73,1481
28
182,4658
10
311,5362
12() 336,1532

(3036)
+15325 =

(1504)

S
e
(m)

sin =

e
S

sin

(g)

R = 7

(g)

63,8468
136,9952
246,3126
375,3830
0,0000

646,320
781,570
524,350
758,430
1,437

0,001874
0,001537
-0,001822
-0.000715

0,1193
0,0978
-0,1160
-0,0455

0,0000
-0,0215
-0,2353
-0,1648

(5376)

0,0556 -0,4216

7660

+0,11934 = +0,4772

3036

0,0556

R = Re + R
(g c cc)
9

0,0000
73,1269
182,2305
311,3714

(7288)
+4216

1504

2.
(. 19.2)
: () ,
,

. 19.2

(. ). (. )
, . -,

, .
= mm,
. . 19.2,
, 19.1, .

20. () .

,
(. 20.1). h
. ,
, .
, - ,
(. 20.2). z ( )
. - 100g, 100g,
- 100g. 100g:
(20.1)

+ z = 100g .

. 20.1

. 20.2

,
,
, .
,
,
. -
, .
- ,
.
( 8 10I).
100g (300g
). - ,
i .
i.


1. -

. .

30 m (. 20.3). , ,
, ,
, .
z1 . (. 20.3), z2 .

(20.2)

2i = ( z1 + z2 ) 400g .

. 20.3

,
.
.

.
. -

z1 = 99, 85 50g ,
2i = 400g = 3g ,
z1 = z1 i = 99, 87 00g ,
z2 = 300, 11 50 ,

=399, 97 00

i = 1,5c ,

z2 = z2 i = 300, 13 00

= 400, 00 00

.
,
z1 z1 ( z2 z2 ).
,
. .
.

, z1
z1 ( z2 z2 ).
(. 20.3).
2 (. 16.4).
2.
, -
, . ,
.
. ,
.
- ,

.
.
THEOMAT T 2000 (. 17.1).
: SET MODE 10 RUN. .
2 3 .
RUN, .
. ,
2 3 . RUN,
CE .
SET 2 CII (SET 4CII) (. 17.8).
V indexing, 2.Manual. () 3
ZA Face 1.
30 . SHFT 0 SET. ZA Face 2.
SHFT 0 SET,
.

REC ELTA 15 C (ZEISS/) (. 17.10).


(ADJUST/PREPARE) 5 V INDEX/HZ COLLIMATION
COMPENSATOR, . 1
.
(. 17.2).


,
.
, .
.
( 20.1).
20.1.

.

24
1,48

28
2,01
40
1,51
15
0,00

2i = OI OII 400

Z =

II

O + 400 O

II

OI = Z I
g c cc

OII = 400 Z II
g c cc

cc

g c cc

97,4616

302,5362

-22

97,4627

100,7694

299,2270

-36

100,7712

103,8964

296,1008

-28

103,8978

16
101,1852
-18
101,1861
298,8130
1,51
-
(33). J (
) Si (
, ).

2i , .
I II

(20.3)

Zcp =

OI + 400 OII

).

21. .
,
. (. 21.1). A,
A,

,

,
,

,
: N

, M

+X

.
. 21.1

:
,

I .

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

.
,
.
, ,
(). .
, .. ,
. ,
, .. ,
, , .
.
, .
, ,
, , , ,
. ,
.
(. 21.2) - - , ,
0180 (0200g), 1 (1g).
, , .

. 21.2

. 21.3

(. XI) (.
21.3), , , 20 40
( ). , ,
, .
,
, .

. 21.4

. 21.5

- ,
. (. 21.4) (. 21.5).
,
(. 21.6). , ,
, (. 21.6) (.
21.6). ,
O .
, i . AiM
(21.1)

AiM = Oi OM .

. 21.6


, , , 0g
.
:
(21.2)

Ai = AiM +

:
(21.3)

i = AiM + + .

,
. ,
,
.
.
4 10.
, .
VI


22.
,
.
. - 1/4000 (2.5 cm 100 m),
- . 20, 30 50 m,
, 10 cm .
( ),

.

(20C),

. 22.1

(10 kg).
- 12 mm. -
. - , - .

() (. 22.1, . 22.2).

. 22.2

. ,
:
,
;
, .
.
, , , , 11
.
:
1. .
2. - (. 22.1),
.
3. ,
, . (20 m).
4. , . ,
, ,
.
5. ,
, 10 kg,
45 . . 1 (. 22.1).
6. , 1
. , . 1
, .
7. .
. - ,
, .
8.
() , , (
) .
(22.1)
D = nl + l ,
l, , l .
9. , . . .
. . .
.
, :
1. 56 cm, .
2. -
1020 cm.
3. .
4. , ,
.
5. .
.

4
5
4
4
5

6
4
6
2
6

16,45
9,36
1,98
16,67
19,75

6
6
6
2
6

16,39
9,33
1,96
16,68
19,71

.
.

136,42
89,345
121,97
56,675
139,71

136,39
89,33
121,96
56,68
139,67

15
10
2
8
18

(I + II)

12

No


I
II

II

136,45
89,36
121,98
56,67
139,75

No

100m

100 m

100 m

,
,
. . 22. 1.
22.1

1:500
1:1000
1:2000


4%
1:4000
2,5cm
1:3000
3,3cm
1:2000
5,0cm

4% 8% 1:3000
3,3cm
1:2000
5,0cm
1:1500
6,5cm

8%
1:2000
5,0cm
1:1500
6,5cm
1:1000
10cm

,
.
(11), , -
.

23.


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



, . : ,
.
.
1. ,
, .
.
(. 23.1) . N, A B,
M N AB . a, b, h
D
a+b
D = a + b h2
(23.1)
.
2ab

. 23.1

. 23.2

(. 23.2) A B .
M
. 1 . M 2 M1M3 M 2 M 4 . m,
b . a, b, c
(23.2)
D = a+b+c .
2. .
AN. . B .
x, y (. 23.3)
D = x2 + y2 .
- , ,
. . A . B
x, y1 , y2 (. 23.4).
(23.3)

(23.4)

2
D = x2 + ( y2 y1 ) .

. 23.3

. 23.4

, .
.

. ,
,
, 2 - .



. -
. ,
.
1. . A B, (. 23.5).
. C,
A
B.
AC = a BC = b.


(23.5) D = a + b 2ab cos .

6.

. A B,
(.
23.6). . C
. 23.5

, , a. f = + + 200 .
=

f
3

(23.6)

D=

a sin
.
sin

. 23.6

. 23.7

7. . . A B
.
, (. 23.7). . C1 C2 . ,
, a b. :
a sin
D=
(23.7)
;
sin( + )
b sin
.
sin( + )

. ,
11 .
(23.8)

D=

24. . ,
,


, . (. 24.1, 24.1a).

. 24.1

. 24.1

() .
b, S.

b
b
S=
.
(24.1)
tg
, :
) ;
) .

. :
1. ( );
:
1.1.
:
1.1.1 ( );
1.1.2 ( 002, , .).

1.2. ,
(BRT 006, .)
2. ( ).
:
( );
( ).

- (
), .
, 6366.
.
(. 24.2),
:

. 24.2

. 24.3

;
3 4 ;
,
(. 24.3).
, L1 L 2 L = L 2 L1 .
(1000, 2000, 3000),
.

S = KL + c ,
(24.2)
K = ctg , c .
K - 100, 50
200.
(24.2)
S = KL .
(24.3)
(. 24.3), L1 = 1400 ;
L 2 = 1626 ,
S = KL = K ( L 2 L1 ) = 100 (1, 626 1, 400) = 100 0, 226 = 22, 60 m.
- .
D
z.
D = S cos2 = KL cos2 ,
D = S sin2 z = KL sin2 z .
,
. .



1% ,

. 24.4
.

. ,
, ( 3 5 m) ( 100 m) (. 24.4).
, K c,
:
S1 = KL1 + c S2 = KL2 + c .
: S1 = 4, 62 m S2 = 98, 43 m,
L1= 10461000 = 0,046 m; L2= 19861000 = 0,986 m. :
4,62 = 0,046K + c; 93,81 = 0,940K; c = 4,62 0,046K;
98,43 = 0,986K+c; K = 99,80; c = 0,03 m.
- 1%,
, K = 100 c = 0.
:
, , , .,
1% .

2

m m .
+
K L
,
1:100 300 m 1:400 100 m.
(24.4)

mS = S

- .
, ,
. .
,
. .
.
002. . 170 m 2 5
cm. .
, - .
. ,
BRT-006, .
60 180 m. 60 m . . ,

. BRT-006 6 10 cm 100 m.
. -
.
( )
.
-2
1 m,


.
(. 24.5)
. 24. 5
,
(24.6)

D=

ctg

2
2
b =2 m e ;
.
:
. ;
. ;
;

.
2
.
.
(24.7)

D = ctg

25.
-, . .
.

, .

( ),
.
A B
(. 25.1),
. A, . B,

.
,
,
t1 .
,

. 25.1
. A t2 .
= t2 t1 .

. -
, ,

(25.1)
S =v ,
2
v ;
,
.

C
v= ,
(25.2)
n
C = 299 792 458 m/s ;
n ,
( ).

. .
(25.1)
2

mS mv m

=
+
,
S v
mS , mv , m S, v .
, (25.1)
, .
:
, .
- , ,
. - ,
.
, , ( ),
. - ,
.
.
( ).
,

= .
(25.4)

v
S=
.
(25.5)
2
-
f ( = 2f ) ,
v
S=
(25.6)
.
4 f
(25.3)

f, v
,

S=
(25.7)
.
2 2
,
2 , .
= 2N + 0 ,
(25.8)

S = ( N + N ) ,
(25.9)
2

N
=

/
2

, .
0
N ,
.
(25.9) . 25.2.



, .
. 25.2
:
1. .
2. , ,
, ,
, .
3. , .
4.
, ,
.
(25.6),

2

2 mv 2 2
S +
S .

. 1 . 4
:
mL = (a + bSkm ) , mm mL = a + bppm ,
(25.11)
(25.10)

2
v 2 mf
mS =
mv +
4f
f

mL S ;
a ,
;
b
, ppm .
a b
.

k = k + k . 25.1, ,

. .
[48].
, .
, , ,
:
- 400 m - 1000 m;
/2
;
.

() , 0,4 m
. , 1,3 m,
.

24 m,
.
- , ,
5 10 m. 1 m,
2 m, . 25.3.
.

. 25.3

,
.
5 10 ,

ki = S Sm , i = 1, 2,K , n ,
(25.12)
S , Sm .
n
- ,
n (S S )
m
k =
(25.13)
.
n
1
k ki .. .
.
k .

.
() 1550 km. . 1/300 000.
.
() 2 5 km.
.
. .
() - 0,3 3 km .
.
- .
(0,1 + 0,1 ppm).

,
, .

VII


26. .
.

1.


,

. 26.1

.
.
,
(. 26.1).
. 26.1 ,
H B = H A + hAB .
(26.1)
hAB , B ,
, A.
A B
hAB = H B H A ,
hBA = H A H B ,
(26.2)
hAB = hBA .
,
:

.
-
, ,
, .
, .
12
,
. ,
, .

2.
A B
,
.
,
.

a ,
A b ,
B.
. 26.2 ,
hAB
hAB = a b .
(26.3)
. 26.3
- 3.5 m,
A B 150
. 26.2
m.
, -
- -,
,
, , .
, A B
.
( ). . 26.3, A
, .
A ( ). J A
.
b B .

(26.4)

hAB = J A b .

,



.

. 26.3

3.
,
. ,
.
.
, () .
, ,
,
.
,
- .

.

:

1 km
, - 0,5 mm.
I II , .
.

1 km
0,5 mm 3 mm. III IV ,
, .

1 km
3 mm 10 mm.
,
. 26.4
.
:

;
( )
.

4 m, 3 m 2 m, , .
, ,
. .
, .
. - 4-
. , .

.
.

,
. ,
,
,
, (. 26.5).
. 26.5

27. .
,
.
, (. 27.1).

.

,



..

,
. 27.1

,
.. .

:
() ;
.

H .
, ,
.

.
,
.
, -
.

,

.

,

,
. 27.2,
. 27.2

, . 27.2.
,
.
, ,

. 27.1, :
V, ;
L;

L;
Z;
(hh) (vv) .

:
1.
V.


.

(. 27.3).
200g
. 27.3
.

D
, .
(. 27.3) ,

,
a
d
.
.
2. (hh)
V. ,
C ,
.

.
b
,
c
, a,
b, c d (. 27.4)
, .
B
.
3. L
. 27.4
Z
. ,
.

. 27.5

,
A B (. 27.5).
6070 m. , , .
A, a1 .
, . B,
b1 . . 27.5 ,
hAB
hAB = a1 b1 ,
(27.1)
A B,
. . 27.1
,

. ,
, .
( 34 m) , .
. B, , ,
b2 .

. a2
, . A, , ,

a2 = hAB + b2 .
(27.2)
, . A,
. 27.2. ,
, ,
. 27.2 ,
.
,
. A .
. 27.2, , ,
.
B D, . 27.4.

28. .


.
, .

( ),
:
, . Z0 ,
(. 28.1). ,
. P.
. . P
, (. 28.1).

, (. 28.1).
- .

( ) ( ),
.

. 28.1

. 28.2 Ni025,
.

. 28.2

1,
. 2 ,
. () 3,
1 . .
10, -.

:
V, ;

L;
(hh) (vv) .
,
. ,
.
:
1. L V
.
2. (hh) V
.
3.
.
5060 m. 5 , 5
(. 28.3). , ,
. ,
,
. , ,
, (
) ,
4 . ,
3 mm 5 mm .
- .

. 28.3

4. , ,
.
. ,
, , .
. A (. 27.5) . 27.2,
, B D
(. 27.4) , .

. 27.1.
27.1



. B



. B

a1 = 1576

a2 = 1651

a1 = 1620

a2 = 1684

b1 = 1237

b2 = 1300

b1 = 1282

b2 = 1345

hAB = +0,339 m; a2 = 1639 ; = 12 mm

a2 = hAB + b2

hAB = +0,338 m; a2 = 1683 ; = 1 mm

29.
1.
,
.
1. , 16.
2. , 16.
3.
.

(..
) .
,
.
( ,
),

m. = 0.1 ,
(29.1)
.

60
m.. =
(29.2)
,
v
v .
- ,

60
0.1 =
(29.3)
,
v

600
=
(29.4)
.
v
.
- . 29.4

1200
=
(29.5)
.
v

, 5060 m
. , ,
,
. 12 mm
, ,
. -, .
,
.
,
. , ,
.
4.
.
1011 , , 5060 m
S1 (. 29.1).

. 29.1

h12 , h 23 ,K , h10,11 ,
S1 , ,
1, 2,, 11, S2 , -
, , .

1, 2, 3,, 11 S1
(.. ) ,
. ai ,
:
h12 = a2 a1 ,
(29.6)

h23 = a3 a2 ,
KKKKKK
h10,11 = a11 a10 .

S2
, . ai ,
:
h12 = a2 a1,
(29.7)

h23 = a3 a2 ,

,
KKKKKK
a10
.
h12 = a11
- 23
mm , ,
.
5. , 24.

2.
1. ( ).
10
, , .
, 0.2 mm,
, ..
, , ,
.
0.02 mm.
.
, , .
, .
.
2.
. ,
-.
(100 mm) 0.5 mm.
3. . ,
, , 2030 m
. - 3 ,
.
, , .
4. .
. ,
5060 m .
,
.
.
, .
100g . ,
.

30.
()

,


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.
,

,

(. 30.1).

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.


, CCD .
. 30.1

.

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,
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30.2
. 30.2
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.


- :
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50% . , ,

5500 m 1 (8 ).
1 8800 m.
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, - .
- -
. .

DiNi 21 Carl Zeiss


1. . 30.3 DiNi21.
:
1) ;
2) ;
3) ;
4) ;
5) ;
6) ;
7) ;
8) ;
9) ;
10) ;
11) ();
12) ;
. 30.4
.
. 30.3

. 30.4

<ON/OFF>,
.
<MEAS> (8) . 30.4,
<DIST>.
,
. ,
. :
<MENU>;
<INFO>;
<DISP>;
<PNr>;
<REM>;
<EDIT>;
<RPT>;
( ) <INV>;
<INP>.
. -
.
, (. 30.4).
.
4 - .
,
. ,
, ,
. <MOD>
.

2.

<MENU> (. 30.4).
,
<> <>. ,
<YES>.
<SET INSTR. PARAM.>
:
<HEIGHT UNIT>.
, <MOD>.

<INPUT UNIT>.
( ),
<DISPLAY R>.
0.001 m/0.0001 m 0.01 ft/0.001 ft .
,
<SHUT OFF>. <OFF> <10 min>
10 min, .
<SOUND>. <ON>
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.
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Tp, Cp.
,
,
.

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:
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dz (
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Db;
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4.
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Db Df.
Db ,
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, ,
.
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( 10). ,
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DiNi21 , .
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.
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,

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.
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,
.
(. 30.5).

. 30.5

A B , . 1 . 2 (.
30.5). .
. 30.5 .
, .
5.

<MENU> (. 30.4). <SET
REC. PARAM.>. <PARAMETER SETTING>
( REC500 REC E),
( REC500/LN-CTL ..), .
<RECORDING OF DATA>
, :
<RECORD>
<iMEM>,<V.24> <OFF> ;
<ROD READINGS> <R-M> ,
,
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<Yes>, <No>.
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7.

- .
, .
.
<MENU> (. 30.4).

<DATA TRANSFER>.
:
<INTERFACE 1> ;
<INTERFACE 2>
. ,
DiNi21 . ,
- ( , ,
, ..)
8. :
1 km :
:
0.7 mm;
1.3 mm;
:
2.0 mm.
:
:
1.5 m 100 m;
1.5 m 100 m;
:
1.3 m.
:
:
15 mm;
20 mm;
:
30 mm.
, :
0.1 mm;
10 mm.
2.5 sec.
:
26x;
40 mm;
100 m 2.2 m;
100 m 0.3 m.
:
(
) 15;
,
0.5.
4 21 .
:
400g/360;
1g/1;
0.1g/0.1.
, :
<->;
<--->.

.
:
;
;
;
.
:
2000 ,
1 .

On-line RS232 C/V24


.
NiMH 6 V 1.1 Ah, 1 .
-20 C +50 C.
125 mm/176 mm/295 mm.
2.5 kg.
NA2002/NA3003 Leica

NA2002
NA3003

NA2000, .
NA3000,

1990
.

NA2002/NA3003

. 30.6
:
GRM10 REC .
GIF10/GIF12 .
DELTA/LEVNET , .
.
. 30.6 NA3003.
:
1 km :
:
0.9 mm/0.4 mm ( NA2002,
NA3003);
1.5 mm/1.2 mm;
:
2 mm/2 mm.
:
:
1.8 m 60 m;
1.8 m 100 m;
:
0.6 m.
1 cm 5 cm.
2 8 .
, , ,
.
, :
NA2002 1 mm 0.1 mm;
NA3003 0.1 mm 0.01 mm;
4 sec.
:
<-> NA2002 NA3003;
<---> NA3003.
:

1 99.

, 2 20.
( ) 1
20.
:
REC GRM10 GPC1;

.
:
24x;
36 mm;
100 m 3.5 m.
:
(
) 10;
,
0.8 NA2002 0.4 NA3003.
8/2 mm.
:
400g/360;
1g/1;
0.1g/0.1;
GEB79 NiCd 12 V 500 mAh, 1 .
2.5 kg.

31.
,
,
. . .
31.1 , A B.
.
.
:
- 150200 m 3.5 m,
( ). ,
x1 , (. 31.1).
, , (),
. a
A, b
x1 . ,
, .

.

. 31.1

, . 31.1 a
, A, b
, ( ,
x1 , x2 ..).
.
A ( . 31.1 . 1,
). , . . x1
, ,
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. x1 . 1 .

, B,
.
.
. A
, B .
31.1
1.09.1999 .

.

1
.. A


Ni025 15310
. .

.
.
m
2
118

x1

, mm

, m

3
2053

1327

0943

Hi , m

7
541.253

8
..A

-2

1.110

x2
x3

2247

541.843

-1

2841

0.071

2318

x2

-2

150
1963

0872

1.969

x3

-2

114
2198

1014

0.949

544.685

545.419

545.080

.. B

-2

98
3

x1
0.516

1843

68

-2

130
1

1872

1462

0.736
-2

168
.. B

2209

S = 846 m a = 14501 b = 10661

0.337

H B H A = +3.827 m

fh = ( a b ) ( H B H A ) = +13 mm
fh = 30 mm
vik =

fh

Skm = 28 mm

Sik


. -
, a b ,
= a b
hAB
hAB = H B H A .

hAB = ( a b ) ( H B H A ) ,
fh = hAB
(31.1)

. .
,
(31.2)

fh = 30 mm

Skm .

.
- , ,

. ( fh < fh ) ,
.
,
A B . ,
,
f
vik = h Sik ,
(31.3)
S

..
. (
) ,
. , , ,

. 31.1. , -

f
vik = h ,
(31.4)
n
n .
.
hij = hij + vij .
(31.5)
-
. ,
A () :
H1 = H A + hA1 ,
(31.6)

H2 = H1 + h12 ,
H3 = H2 + h23 ,

H B = H3 + h3B .
.
, ,
. hA1 = hA, x + hx ,1 .
1

B 31.6.
, .

. ,
,
, ,
fh = a b ,
(31.7)
. A . B H A = H B .

32.
1.
, ,,
, . .

. ,
.
, ,
.
. - ,
.
:
,
,
.
.
, .

1.
.
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.
() 100 m
0, 1, 2, 3 ..,
. ,
, 20 cm
.
,
20 m ,
, ,
. , .

.
.

.
.
2.
, ,
- . 12 km
, .
, .

. 32.1

. 32.1
: S1, ,
. 100 ,
a1 . , . 32.1 ,
.. 100 .
, , . 32.1 . A, ()
, 2, 4, 5, 6, 8,
31 32. ci ,
. .
S1 () 1 b1 ,
. S1
. . S2 ,
1, ,
. a2
1,
33 34, 12, 14, 16, 17, 18 22, 2 . B,
. ci , ..
. 101
b2 . , , .
. ,

. ,
.
3. , .

. -
, ( S100,S , SS ,1 ,
1

S1,S SS ,101 ),
2
2
a b ,
= a b
hAB
hAB = H B H A .
. 31.1 . 31.2.
- ( fh < fh )
, ( h100,1

h1,100 ) . 31.3, . 31.4.


. 31.5. ,
() , .
(
1), ( H1 = H100 + h100,1 ).
:
HS = H100 + a1 ,
1

(32.1)

HS
2

= H1 + a2 .


( ).
, ( ,
)
Hi = Hk ci .

(32.2)

31 . . 32.1
, . 32.1.


Ni025 15310

+5

. 100

2545

, m

Hi,
m

, mm

. .
H, m .

, m

32.1.
1.09.1999 .

10

544.261

541.716

.100

A0

2200

542.06

A0

2350

541.91

2100

542.16

542.38

1880

1.134

142
6

1730

542.53

1650

542.61

31

1590

542.67

31

32

1470

542.79

32

542.855

..1

+6

. . 1

1411

2897

545.752

34

2710

543.04

34

33

2630

543.12

33

12

2560

543.19

12

14

2420

543.33

14

16

2350

543.40

16

2340

543.41

17

18

1110

544.64

18

. . 2

1040

544.71

..2

22

0970

544.78

22

17

2.136

166

11

0800

. 101
S= 308m

0761
a=5442

= 30 mm

544.997

. 101

H B H A = +3.281 m

b=2172

fh = ( a b) ( H B H A ) = 11 mm
fh

544.95

Skm = 17 mm ;

vIK = fh / S SIK

.
(.
AutoCAD, ArcView .) , .
,
. .

10 - .
- 1:1000 ( 1:2000) 1:100 ( 1:200) .
X, ML
Y, MH
, , - -
, .
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, . . 32.2 ,
AutoCAD.

. 32.2



,
. ,
. 20 50 m
.
1.
.
.
5 10 m , .
, .
.
.
2. ,
. 32.1.
(. 32.1).

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3. ,
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.
, .

2.
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1. .

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10 50 m.
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5, 6 7,
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.
.
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(. 100 . 32.3).
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100.
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100. , S1
,
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S 1
. S2 ,
. 18, .
S2 , ,
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31 .
.
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32.4 , _.

. 32.4

, m

, mm

. .
Hi, m

Ni025 15310


H, m

, m.

32.2.
1.09.1999 .

10

11

-4

. 100

577.643

1360

576.283

.100

1990

575.65

1840

575.80

1730

575.91

10

1670

575.97

10

1720

575.92

1780

575.86

15

1600

576.04

15

16

1590

576.05

16

0.088
17

1520

576.12

17

25

1310

576.33

25

1400

576.24

24

23

1450

576.19

23

22

1440

576.20

22

29

1240

576.40

29

30

1250

576.39

30

31

1200

576.44

31

32

1120

576.52

32

39

0910

576.73

39

38

0980

576.66

38

37

1040

576.60

37

36

1060

576.58

36

576.191

18

24

92

-4

18

1448

1627

577.818

1810

576.01

1640

576.18

1540

576.28

1480

576.34

14

1370

576.45

14

13

1470

576.35

13

12

1600

576.22

12

1740

576.08

11

576.32

19

11
19

88

1500
0.525

20

1370

576.45

20

21

1270

576.55

21

28

1150

576.67

28

27

1260

576.56

27

26

1390

576.43

26

33

1200

576.62

33

34

1100

576.72

34

35

0970

576.85

35

42

0740

577.08

42

41

0910

576.91

41

40

1020

576.80

40

576.712

. 101

. 101

S = 180m

1102

a = 2987

b=2550

H B H A = +0.429 m

fh = ( a b ) ( H B H A ) = +8 mm
fh = 30 mm Skm = 13 mm
f
vIK = h SIK
S


.
. ,
.
0.2, 0.5 1 m.
.
2. ,

.
, ., .
.
. .
2050 m ,
.
.

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,
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3. ( )
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.
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.
.
,
,
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, .

33.

, , .

. 33.1

A B . 33.1 :
= S AB ctgZ AB ,
hAB
(33.1)
+ J A TB + f = S AB ctgZ AB + J A TB + f ,
hAB = hAB
(33.2)
S AB . A . B ;
Z AB ;
J A . A ;
TB . B ;
f ,

1 k 2
f =
S .
(33.3)
2 R AB
. 33.3 R = 6371 km,
k = 0.106 .
, ,
, , ,
,
- , .
300 m ( f = 6 mm)
. . 33.1 f
.
33.1
S AB ,[m]
0
100
200
300
400
500
600
700
800
900
0
0.00 0.00 0.00
0.01
0.01
0.02
0.02
0.03
0.04
0.06
1000
0.07 0.09 0.10
0.12
0.14
0.16
0.18
0.20
0.23
0.25
2000
0.28 0.31 0.34
0.37
0.41
0.44
0.48
0.51
0.55
0.59
3000
0.63 0.68 0.72
0.77
0.81
0.86
0.91
0.96
1.02
1.07
4000
1.13 1.18 1.24
1.30
1.36
1.43
1.49
1.56
1.62
1.69
5000
1.76 1.83 1.90
1.98
2.05
2.13
2.21
2.29
2.37
2.45
6000
2.54 2.62 2.71
2.80
2.88
2.98
3.07
3.16
3.26
3.35
33.1 33.2 S AB . A . B .
, 33.1 33.2
S AB
:
= S AB
cos Z AB ,
hAB
(33.4)
+ J A TB + f = S AB
cos Z AB + J A TB + f ,
hAB = hAB
(33.5)
. A . B . ,
S AB

,
, sin Z AB
33.4 33.5.

, A B
, .. . A . B
hAB
:
hAB
= S AB ctgZ AB + J A TB + f ,
hAB
(33.6)
= hBA
= SBActgZBA J B + TA f .
hAB

(33.7)

, 1.20 1.21 ,
, ,
( k = 0.106 )
f . 33.3,
, ..
.

h + hAB
(33.8)
.
hAB = AB
2


. ,

. [19]
d = 14 cm

(33.9)

Skm .

,
, ,
4 cm 100 m.
300-400 m
(33.10)

fh = 4 cm

S2

1002

[29]
25 mm 100 m.
[19]

(33.11)

fh = 14 cm

Skm .

[4]

(33.12)

fh = 60 mm

2
Shm

.

A B
( H B H A ) = hij ( H B H A ),
fh = hAB
(33.13)
( H A = H B ) :
fh = hij .
(33.14)
- ,

fh 2
vij =
Sij .
(33.15)
S2
. 33.2 .
33.2.

1.47 1.90

1.49 1.85

255.68 101.1602 -5.070


1.49 1.50

1.53 1.50

269.01 99.8227 +0.749


1.50 1.80

320.33 99.2347 +3.781


1015

1.60

S = 1611.89 m

320.30 100.6797 -3.760


1.46

1.47 1.50

268.99 100.1721 -0.737


4

365.09 99.2049 +4.570


401.80 101.4071 -8.912

255.69 98.6395 +5.085


3

11

1.51 1.50
401.78 98.5911 +8.903

10

Hi

365.11 100.7905 -4.554

1.51 1.50

hji

8
1.50

Zij

J
7

Sij

hij

Zij

Sij

1
2
1006 1.48

574.111

+8.908 583.033

12

+11

-4.562

13
14
578.662 1006

+14

+5

+5.077 588.115

+6

-0.743

587.378

+9

+3.770

591.157 1015

H1015 - H1006 = + 12.495 m

h= +12.450

fh = hij ( H1015 H1006 ) = 45 mm


fh = 14 cm
vik =

Skm = 178 mm
fh

S2

Sik2


(, , , .). .
.
. 33.2 Z1 Z2 ,
S AB .

h = S AB cotg Z1 S AB cotg Z2 = S AB (cotg Z1 cotg Z2 ).


(33.16)

.

. 33.2

34.
,
, .

,
, . , ,
( 2 m),

,
. .
, hAB
A B . ,
, .
.
, , . 34.1
. ( ),
,
,
. A B ,
, . 34.1. OA OB
. ,

= ( HI OA ) ( HII OB ) = (OB OA ) ( HII HI ),


hAB
(34.1)
OA OB , HI HII
, .
( HII HI ) .
B , A .
OA OB

= ( HII OA ) ( HI OB ) = (OB OA ) + ( HII HI ) .


hAB
(34.2)

. 34.1

h + hAB
(O OA ) + (OB OA )
(34.3)
hAB = AB
= B
.
2
2
. 34.3 , A B
.

. , ..
, ,
11.5 mm. -
, .
1 mm.
10 ,
0.1 mm, . -

.
, -
.
- .
0.010.02 mm [2].

,

.
.
, ,
.

35.
, hAB
A B ,
. ,
- ,
, .
( -, ,
, ),
, .
,
(..
).
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(. ).
, ,
(). - ,
.

Pi = Pi + P + Pt + P0 ,
(35.1)
Pi ,
P ,
P ,
Pt ,
P0 .
,
.
.
- , .


.
.

.
, .
.
Pi
. 35.1, ,
. A

hAi = C ( PA Pi ) ,
(35.2)
PA A , . 35.1,
Pi i , . 35.1,
C , .. ,
(. 1 mm ).
C . 35.1
, P t
, .
35.1.

P =

Pi + Pj

600
610
620
630
640
650
660
670
680
690
700
710
720
730
740
750
760

t =

-5 C
13.12
12.90
12.70
12.50
12.30
12.11
11.93
11.75
11.58
11.41
11.25
11.09
10.93
10.78
10.64
10.50
10.36

0 C
13.36
13.15
12.93
12.73
12.53
12.34
12.15
11.97
11.79
11.62
11.46
11.29
11.14
10.98
10.84
10.69
10.55

+5 C
13.61
13.39
13.17
12.96
12.76
12.56
12.37
12.19
12.01
11.83
11.67
11.50
11.34
11.19
11.04
10.89
10.74

+10 C
13.85
13.63
13.41
13.20
12.99
12.79
12.60
12.41
12.23
12.05
11.88
11.71
11.55
11.39
11.23
11.08
10.94

ti + t j
P =

+15 C
14.10
13.88
13.65
13.43
13.22
13.01
12.82
12.63
12.44
12.26
12.08
11.91
11.75
11.59
11.43
11.23
11.13

+20 C
14.35
14.12
13.88
13.66
13.45
13.24
13.04
12.85
12.66
12.47
12.30
12.12
11.95
11.79
11.63
11.48
11.32

+25 C
14.59
14.36
14.12
13.89
13.68
13.47
13.26
13.07
12.87
12.69
12.51
12.33
12.16
11.99
11.83
11.67
11.52

+30 C
14.84
14.61
14.36
14.13
13.91
13.69
13.49
13.29
13.09
12.90
12.72
12.54
12.36
12.19
12.03
11.87
11.71

Pi + Pj
2

600
610
620
630
640
650
660
670
680
690
700
710
720
730
740
750
760


A B,
H HA
C= B
(35.3)
,
PA PB
H A H B , PA PB
, . 35.1.

.
, 5 km,
- 400 m.
- , 10 16 .
.
12 m.
. 1 2 P1 = 748 mm Hg- P2 = 734.6
mm Hg- t1 = 20.4 C t2 = 18.4 C.
. 35.1. h12 .
t = 19.4 C
P = 741.7 mm Hg-. . 35.1 P0 = 740 mm Hg- t0 = 15 C
C0 = 11.43 .

P = P - P0 = 741.7 - 740.0 = +1.7 mm H g C p = 0.034
t = t t0 = 19.4 15.0 = +4.4

Ct = +0.176 .


C = C0 + CP + Ct = 11.43 - 0.034 + 0.176 = 11.572

h12 = C ( P1 P2 ) = 11.572 ( 748.8 734.6 ) = +164.32 m.

VIII


36.
36.1.

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


. :
.
:
, .
, .. .



B L .

.

. P
, ..
,


X Y (. 36.1).
. 36.1

,
: X
, Y .
, X
(. 36.2). , I
, .
0 400g . . A . B
AB , . B . A AB .
200g : BA = AB + 200g . 400g ,
400g .

. 36.2

. 36.3

XYZ (. 36.3). O
. Z , X
, Y , 90 X .

, ,
, GPS (Global

Positioning System), - (51).


()
.
WGS 84,
WGS 1989, ( 1 m) .
GPS .

36.2.
, ,
, (, .)
. -
,
.
, .. .

. , ..
, .
, (),
, .
- , . ,
, - . ,
(. 36.4).
. , ,
. (),
1.
, (. 36.4).
() ,
, .
.
,
3- 6- , 3 6 .
3- 6- .
1:5000 -,
, - 1:5000.

. 36.4

. n
0 :
0 = 3n
0 = 6n 3 .
8 9 = 24 = 27
4 5 = 21 = 27 .
36.1


24

(m)
8 583 287,14

(m)
4 873 312,96

(m)
8 412 564,64

(m)
4 737 629,60

27
9
36.2

9 525 413,81

4 745 502,18

9 367 903,85

4 651 694,18

(m)
(m)
(m)
(m)
21
4
4 635 272,85
4 871 135,12
4 483 122,96
4 720 127,85
27
5
5 573 964,60
4 871 375,18
5 350 718,12
4 607 274,65
, X
, , ,
.
, .
, . ,
Y 500 km (. 36.4). ,
500 000 m. ,
, - - 500 000 m.
, ,
.
. 36.1 36.2 3 6 .
UTM (Universal Transversal Mercator),
, ,
0,9996 .
,
. ,
, ,
. ,
, .
-
, ,
.

36.3.
- (. 36.5) (
). ,
. ,
.

. 36.5

, .
.

X = const Y = const . , , ,
, , -
. ,
. ,
. ,
. 1:50 000 1:25 000 2
4 cm, 1 km,
. - 10 cm,
. 1:1000 1:500 ,
.
, , ,
, ,
.
, ,
, .

.
0,2 mm .
,
: ,
, ., ,
.

37.
(
, )
.

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

. 37.1

, , ,
GPS [15], [20], [56], [58], [59], [60], -
, (51).
GPS
- ()
.
:
, , , ,
, , ,
, ( )
, , .
.
.
()
(). , , ,
. ,
. ,
, . ,
.
(. 37.1) 1:2 000, 1:5000
.
, , ,
. , ,
, , , , ,
, .
. ,
, .
, ,
.
().
, ,
.
: ( ) (
) .

.

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

, ()
().
IX

()
38.
38.1.
() ,
.
X,
Y , ( ), .
, , ,
() , .
, ,
, .
X Y H
.

i
: RAi ,
Z Ai

DAi

S
Ai
, J A
si
(.
38.1) (. 38.2).
, ..



XY,

RAB RAC
B
C
(
,

. 38.1

). AB
.
OA XY,
:
OA = AB RAB .
(38.1)

. 38.2

, . ,
, OA
.
RAi i
XY, A
(38.2)

Ai = RAi + OA .

, Si ,
Di Zi (. 38.2).
: Ai DAi
X i Yi (14)
, XY .
Hi
(33) : H A , Z Ai ,
J A si .
.
- .
,
.
, , -
.
, .
- -,
.., , -
.
.

38.2.
:
,
( ),
;


, , , ,
, ;
, ,
, , , ;
;
;
;
, ,
, .
.

.
,
[19] GPS (51), [20].

.
.
.
,
. ,
. ,
( XIV), (
XV) GPS (51).

,
( ).

, , , - 1:25 000
.
, , ,
.
-,
- ,
- ( ) (40).

1:2 000 1:5 000, .
, ,
,
.
, .
, 30%
. ,
1:4.
, .
- , -,
.
, 6.
, ,
, , ,
, .

,
.
-
, , -
1.
(22),
(24), (25)
(39). ,
, . 22.1.

,
, 56.
(26)
(33) .
,
:
(38.3)

fh = 30

[ S ] km

, (mm )

(38.4)

fh = 18

[ S ] km

, (cm ) .


, :
(38.5)

m =

p f 2
,
n

(38.6)

mS =

p f2
S S ,
nS

mh =

p f2
h h,
nh

(38.7)

f fh ,
n nh ,
fs ns ,
p , pS ph (13) .

.
1:2000 1:10000 (. 38. 3),
,
. 3,5 mm, 7 mm.
, ,
, ,
. ,
,
7 mm. 1:500 1:1 000 ,
50/80 cm,
Y. - (8).
.

. 38.3


. , , ,
.
(. 38.4) ,
,
.

. 38.4

38.1

....................................................................................................................
....................................................
....................

...................................................
.

. . . .
,
, ( 38.1).
,
.

39.

, .
:
1. ;
2. ;
3. .

39.1.
1.
,
, () , ..
(24). ,
, ,
.
.
(26).
.
2.
-
, . -
DAHLTA 010 (010 010 ) DAHLTA 020 BRT 006 Redta 002 Zeiss/.
Redta : RDS ( Wild/) Rta4 (Opton/), ,
DK-RV DK-RT ( Kern/), .

. 39.1

. 39.2

DAHLTA 010 (. 39.1) e THEO 020,


.
(),
(. 39.2). , . ,
: , 100 (

) , , .


, : 10, 20, 50, 100, +10, +20, +50 +100.
,
(. 39.3).
( Z = 100g ) +10 10
(. 39.4). 200,
(. 39.3 39.4).

. 39.3

. 39.4

4-
, ,
(. 39.5).
1,40 m , .
:

. ,
,
,
(. 39.3).
, .
L = 29,1 cm 100,
, .. D = 29,1 m.
cm

,
(. 39.3). : 20, h = 20 . 0,219 = 4,38 m.
, ,

,

.

,

2,
200.

,

,
.
DAHLTA
. 39.6
. 39.5
010 B (. 39.6) .
DAHLTA 020 010 - , DAHLTA 020
Theo 030 ,
. +50 50,

200,
200.
BRT 006 (24)
. 60 m,
180 m. ,
.
3.

( ) ( ).
.
:
) - ,
) - ,
)
) ( ).
- -
() (25).
,
. ELDI 1, 2 3
Th2 Opton/. ,
Wild Kern ( - Leica/), AGA Geodimeter ( Spectra Precision) /, Sokkia,
Topcon Pentax/ .,
, .
- ,
, .
. , . . EOT 2000, RECOTA, SM11 (Zeiss/), 5 () .

. ,
.
, ,
.
, ,
,
, , (
, ),
. ,
. GRE3 GRE4 Wild ( Leica)/, SDR Sokkia/,
REC Opton/, Alphacord Kern ( Leica/) .
. -
, .. . , ,
TACHIMAT TC 2000 (Wild, Leica ).
,
, MS-DOS,
, , .

. -.
: Leica ( Wild
Kern)/, Zeiss/, Spectra Precision ( AGA) , Trimble/ (+ Spectra
Precision + Zeiss), Sokkia Topcon/ .
. 39.1 ,
-. 5, mR (
)
, 6
(IM) , /
(MC).
39.7, , , , , : TC2003 (Leica/),
Powerset 4010(Sokkia/), Geodimeter 608S (Spectra Precision/), GTS 713 (Topcon/), Elta C
20 (Zeiss/) Trimble 5600 (Trimble/).

. 39.7a

. 39.7

. 39.7

. 39.7

. 39.7

. 39.7

39.1.
-

ms = a + bD km
,

(km)
3

ms
mR
a, b
(cc)
(mm)
4
5

mm

(kg)
(IM/MC)
6

TC/TCR 307
5.4
2, 2
3/20
8000/ 4.5
Leica/
TC/TCR 305
5.0
2, 2
3/15
8000/ 4.4
TPS-

TC/TCR 303
5.0
2, 2
3/10
8000/ 4.4
TC/TCR 705
5.0
2, 2
5/15
4500/ 5.0
TC/TCR 703
5.0
2, 2
5/10
4500/ 5.0
TPS-
TC/TCR 702
5.0
2, 2
1/6
4500/ 5.0
TC 1010
3.5
2, 2
10/10
/MC
5.6
TC 1610
5.0
2, 2
1/5
/MC
5.6 TPS-
TCM/TCA1100/L
5.0
2, 2
10/10
/MC
6.1
()
TC 1105
5.0
2, 2
5/15
/MC
5.0
:
TC 1103
5.0
2, 2
5/10
/MC
5.0
TCM/R/A,TCRM,

TC 1102
5.0
2, 2
1/ 6
/MC
5.0
.
TC 1101
5.0
2, 2
1/ 5
/MC
5.0
TCM /TCA1800L
3.5
1, 2
1/3
/MC
6.4
TC/TCA 2003L
3.5
1, 1
0.1/1.3
/MC
7.0
TPS-
TDM 5000
5.0
1, 2
0.1/1.3
/MC
7.0
R-.. 80 m; L- ; M-; -
Sokkia/
SET XL
4.2
2, 2
2/2
/MC
7.5

MONMOS
1.0
0.8, 1
1/6
/MC
6.1
(SET 2C (II)
4.2
3, 2
2/6
/MC
7.5

SET 3C (II)
4.0
3, 3
2/10
/MC
7.5
)
SET 4C (II)
2.8
5, 3
10/15
/MC
7.4
SET 5F/W
1.6
3, 2
2/15
3000/5.5/5.6
Powerset 1000
3.5
2, 2
1/3
1300/
5.6
Powerset 2000
3.5
2, 2
1/6
1300/
5.6

Spectra
Precision
(AGA)/

Powerset 3000
Powerset 4000
Powerset 2100
Powerset 3100
Powerset 4100
Powerset 1010
Powerset 2010
Powerset 3010
Powerset 4010
SET 500
SET 600
SET 4110R
SET 411 MA

3.3
2.4
3.5
3.3
2.4
3.5
3.5
3.3
2.4
2.4
2.0
2.4
2.4

2, 2
2, 2
2, 2
2, 2
2, 2
2, 2
2, 2
2, 2
2, 2
3, 2
3, 2
2, 2
2, 2

2/10
10/15
1/6
2 /10
2 /15
1/3
1/6
2 /10
10/15
2/15
2/19
10/15
10/15

1300/
1300/
3000/ 3000/ 3000/ 5000/
5000/
5000/
5000/
4000/ 2000/ 5000/MC
5000/

Geodimeter 640S

5.8

2, 2

0.1 /3

Geodimeter 620S

5.0

2, 2

1/5

Geodimeter 610S

2.9

2, 2

1/10

Geodimeter 608S

2.5

3, 3

1/15

Trimble 3305
3303

1.6
2.0

5, 3
3, 3

0.1/10
0.1/15

IM/
/MC

3.5
3.5

Trimble 3602
3603

5.0
5.0

2, 2
2, 2

0.1/7
0.1/10

8000/
8000/

6.7
6.7

Trimble 5601
5602
5603
5605

5.8
5.0
2.9
2.5

2, 2
2, 2
2, 2
3, 3

0.1/3
1/5
1/10
1/15

8000/

6.4

4.2
3.4
1.8
1.4
1.0
4.4
4.4
4.2
3.6
4.4
4.4
4.2
3.6
5.0
5.0
5.0
3.4
5.8
5.8
5.8
4.0

3, 2
3, 3
3, 2
3, 5
5, 5
2, 2
2, 2
2, 2
5, 3
2, 2
2, 2
2, 2
2, 2

/MC
/MC
2000/
2000/
500/
3000/
3000/
3000/
3000/
5000/
5000/
5000/
5000/

5.8
5.8
4.9
4.9
4.9
5.9
5.9
5.9
5.6
5.9
5.9
5.9
5.9

2, 2
2, 2
2, 2
3, 3

2/6
10/15
2/15
2/18
10/30
1/2
2/6
2/10
2/15
5/ 3
5/ 6
10/10
10/15
5/3
5/6
10/10
10/15
2/10
2/10
2/10
10/20

2.6

2, 2

6.0

3, 2

7.0
7.0
4.0

3, 2

/MC
/MC
/MC
/MC

5.6
5.6
5.3
5.3
5.3
5.4
5.4
5.4
5.4
5.0
5.0
5.4
5.4

100

80

6.3
6.3
6.3

6.3

()

Trimble

Topcon

()

Topcon

()

GTS-6/6A
GTS-6B
GTS 211 D
GTS 212
GTS 213
GTS 300
GTS 311
GTS 312
GTS 313
GTS 710
GTS 711
GTS 712
GTS 713
GTS 601(AF)
602(AF)
603(AF)
605(AF)
GTS 223
225
226
229
GTS
800/800
601/801
802/802
GPT 1003
1004
GPT 2003
2005
2006

2, 2

5/3
5/6
10/10
2/15
2/18
2/10
2/15
2/18

3300

100 m
3600

80 m
.
5600

600 m
. -.
.

210

310

710

600
..
MS DOS

5000/

5.8

12 000/

4.9

30 000/
MC

7.8/
7.9

800

3000/

5.1

1000

3800/

5.0

220

2000
GPT 2009-

Zeiss/

(
)

2009

4.0

10/27

AP-L1A

1.0

3, 2

2/6

/MC

9.5

GMT- 100
RecElta RL
RecElta RL- S
RecElta 15
RecElta 14
RecElta 13
Elta R 45
Elta R 50
Elta R 55

4.2
8.0
6.0
1.8
2.0
2.5
2.0
1.2
1.6

2, 2
5, 3
2, 2
5, 3
3, 2
3, 2
3, 3
5, 3
5, 3

2/10
2/5
2/5
2/10
2/8
2/5
2/10
5/15
5/15

2000/
/MC
/MC
/MC
/MC
/MC
1900/
1900/
1900/

8.6
5.6
5.6
5.2
5.2
5.2
3.5
3.5
3.5

RecElta 13C/15C
13CM,13CMS

2.5

2, 2

0.1/ 5

1000/MC

5.2

RecElta 14 C
Elta S 10
Elta S 20

1.6
3.5
3.5

3, 2
1, 2
2, 2

0.1/ 8
0.1 / 3
0.1 /10

1000/
3000/MC
1000/MC

5.2
8.2
8.7

Elta C 20

3.0

2, 2

0.1/7

1000/

6.2

Elta C 30

3.0

2, 2

0.1 /10

1000/

6.2

MS-DOS,
- 200 m

, .

486 DOS ,
, .

:
Move / Sprint

.
:
80 100m, ,
( Kodak Grey %)
, 90% 600 m;
,
4 5 m ;
;
() ,
(
);
, ;
,
100g;
;
() ,
, ;
- , . - ;
;
- ;
-
;
;
;
360 - ,
;
(
), ,
;

, ,
(, ).
.
;
( ) ,
,
. ,
, .
, . -

, ,
. , ,
;
() ,
;
:
* ;
* , ;
* PC ;
MS-DOS , ,

PCMCIA ( Mb)
,
;
,
, - , ,
, - .

. ,
,
.
;
GPS ,
,
(51).

39.2.
:
( 17),

.
, ,
.

. SET 2C II SET 4C II (. 17.8) : ,
50100 m .
Z1. CE-CA . SHFT I
Signal checking, Signal.
, .
CE-CA, , 3,
Z2. CECA, SHFT I Signal checking. Signal.
, .
CE-CA , , 3
Z3. Z2 Z1 2I 30II Z3 Z1 2I 30II, .
- 2I 30II,
-.
.
, 0 mm.
. 100 m,
. , ,
. 10
S AB .
, , ,
, . 10
SCA SCB .
(38.8)

K = S AB ( SCA + SCB ) .


- 3 mm, .

40.
: (
- ), ,
, ,
, ,
( ,
, )
() ,
.
.
: , , ,
( ), ,
, (
), ( ), ,
, , .
( 1:500 1:1000)
.

, .
,
, . 40.1:
40.1

1000
1
1:500
1:1000
1:2000
1:5000
1:10000
17
15
600
150
I
300400
30
25
700
300
II
400600
50
35
500
III
800950
600800
70
50
600700
IV
9501200
8001000
130
80
700900
V
12001400 10001200

,
1:2 000, 1:5 000 1:10 000 40.2 40.3.
40.2

I
II
III
IV
V

m
1:2000
1:5000
1:10 000
45
8060
140100
40
6050
10080
35
5040
8060
30
4035
6050
25
50
3530

40.3

1:10 000
1:5 000
1:2 000

m


12
12
12
12
250
300
200250
250300
200
250
150200
200250
150
180
150
150180

1:500 1:1000
23 cm, - .
:
80 m ;
100 m (, , .);
130 m ( , , , .);
150 m 180 m 1:500 1:1000 .
.
300 m
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2
44
12
121
122
123
.
.
12

3
1000
2000
1000
1000
1000

- - - Z, S,
R,
g
g
m

4
1755
3001
1490
1535
1440

5
1378
2500
1245
1268
1220

6
394,27
100,38
250,71
257,84
270,45

7
99,80
103,48
100,41
96,98
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8
75,5
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49,0
53,5
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H =

9
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2,50
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1,27
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11
0,24

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13

5,46
0,32
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14
1,14
7,96
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15
654,59

1,27
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H=
=H+h

16
653,45
646,63
653,03
655,86
655,93

17
(653,43)
(646,61)
()
()
(. )

9
158,12
264,63

10
100,25
99,08

11
-0,31
1,56

12
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0,16

100
8



=+h, m

50
7



=+J, m

20
6

h = h - s. m

10
5
-0,030
0,156

h (m)

4
75,0
108,0

: .

Z,
()

: 010

D, m

s, m

h = h s , m

(100,39)

: 30. 09. 1999 .

3
1,40
1,40

h , m

=H +J

40.2

1
2
22 42
J=1,48 20

,
m

-
-
D, s, m
m



R, ()

1
43
J = 1,46
H=
= 653,13
H=
= 654,59

: Theo 020B

J, m

: 17. 06. 1999 .

13
654,56

14
652,85
654,72

15
(652,84)
(654,74)

210
211
212
213
.
.
42

2,40
1,40
1,40
2,40

48,3
52,1
18,3
37,9

0,301
0,321
-0,130
-0,178

43,88
265,41
68,74
76,32

(158,11)

96,03
96,08
108.98
105,96

3,02
3,21
-2,60
-3,56

0,62
1,81
-4,00
-5,96

655,18
656,37
650,56
648,60

Dahlta 010 (. 39.1).


(. 39.5). ,
,
. ( 40.2).
1 J , 2
. 3 s ( ) .
1,40 m, , ,
, .
D ( 4),
, 5, 6, 7 8 ,
. ,
, 9 10.
, ,
, - .
200
.
.
Dahlta 020
.
BRT 006 (24). ,
. D
. Dahlta ( 40.2),
5 8 .
SET 4CII (. 17.8a).
10/20 (5 mm + 3 mm/km),
2,8 km. (I).
:
:
SHFT EDM ,
1. Meas mode ( ), :
1. Fine meas ( ),
2.Coarse meas ( )
3.Track meas ( ).
:
1. Single meas ()
2. Repeat meas (, .. ).
NO 2. Prism const,
.
NO 3. ppm ( ),
:
1. 0 set (,.. ),
2. Temp&Press ( ),
3. ppm ( ).
:
MENU, :
1. Config (uration), 16 ,
, - : ,
, , 10 20,
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, , , (
) ,
, .
2. Card, , .
NO MENU, 2. Card. - Job file,
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, , 2 , 3
.

3. Code, MENU, ( 13 )
.
:
NO REC ,
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1. . - Station data,
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, ppm
(N, E, Z , N, Z), YES. ,

S, V, H.
2. . S, V, H,
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S, V, H (offset) - , , :
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N, E, Z + S, V, H - .
S, V, H
N, E, Z.
, . S, V, H, ,
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Target , Ht - - - YES
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(IC), , . Target 365 Record end.
,
NO Press function keys to select operation,
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9 .
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Online. COMMS. CARD RECEIVE.
,
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. SDR RAW.
TPLAN RAW,
DEK.
,
, .
SET 2CII,
2 (3 mm +2 mm/km), 4,2 km.
SET 5F (. 17.9a).
20 (3 mm +2 mm/km),
1,6 km. . 5 ,
4 .. () ,
.
:

,
.
EDM THEO

S-O

CONF

CONF : 1. Configuration 2.Tilt correction, 3. Key select



1. Configuration .
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Enter : 1. data output
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COMMS. SDR. RECEIVE
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SDR . ,
PC FILE NAME: [C: () .SDR],
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DEK. EXIT . FILE PRINT,
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, - :
COMMS, FILE, DIRECTORIES, 2
[ . ] , . ( . ) FILE,
, DEK:
FILE NAME: [C: () .DEK],
OK. FILE, PRINT .
WILD TC1610 (. 40.2 40.2).
1 (2 mm + 2 mm/km),
5 km. REC 64Kb ,
.
.

. 40.2

. 40.2

:
1. . MENU, 4. CONF
5. UNITS. : DIST 1, ANGLE 2, P/T 3
, , . ENTR
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.
.

2. . MENU,
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3. . MENU 1. SET,
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4. . MENU, 1.SET 4. hr
().
5. . MENU 3. REC 3.
PORT. MODUL RS232 ( GRE ).
6. ( 1 14). MENU 3. REC, 4. FILE DATA
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8 .
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ALL
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Rec Elta 13C (. 17.10).
5 (2 mm + 2 mm/km),
2,5 km. FCT,
TAB FCT. , -
, .
.
FCT .
:

, 5 ADJUST/PREPARE, 6.
UNITS. ,
ENT ,
ENT. :
Hz
V : GON
V-REF
: ZENITH
SD
: METER
Hz REV
: +
TEMP
: C
PRESS
: TORR
COORD : YXZ.
MEN (YES/NO).

1. . , 6
DATA TRANSFER, 3. RECORDING.
: INTERNAL (PC) EXTERNAL (RS 232-C)
.
2. . , 7 SET,
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3. DEL PROJECT; 6. DATA FRO OTH. PROJECT; 7. CHANGE PROJECT; 8. UPDATE PROJECT.
2, NAME:......... .DAT. ENT,
, ENT 9. YES. ,
ABC.
3. . INP
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(INST), (ADCO), (SCLE), (TEMP),
(PRESS) (PPM).
, MEN
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: , , ,
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ENT, . Input P.I.
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4.
ENT MEASURE.
, FCT 4 :
Rno , R-M (D)-Hz-V,
R-C , , . X, Y, Z, h RMC R-M
R-C. Rno
(
).
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.
, .
, ENT
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.
, .
.
, ENT
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, PCMCIA , .
,
INTERFACE 2 ( INTERFACE 1 ).
INTERFACE 2 PCMCIA .

41.

.
.

, D
H.
.
D .
H.
( 40.1). 10
s , cm. 8 S
L , :
S (m) = 100 L(cm) = L ,
(41.1)
D ( 9):
(41.2)
D = S sin2 Z .
11 12, , h , :
h = D ctg Z .
(41.3)
13 14 h = h s .
H
H = H + J , 15. 16 H
:
= + h .
(41.4)
- , 17,
, ,

:
= 0, 04 D + 0,1 ctg Z .
(41.5)
, .
,
.
Dahlta ( 40.2). 5, 6, 7 8,
, h ,
11. , 15,
, 40.1.
BRT 006. 40.1,
3, 4, 5 8 , 10 .
40.2 5, 6, 7 8.
, .
BRT.
- , .. ,
, -
.
(). - O
( ) :
k

(41.6)

O =

( i Ri ) ,
i =1

k
i Ri ,
k .
R
:
= ( R + O ) .
(41.7)

400g, 400g. ,
D ,
X Y:
X = X + D cos
(41.8)
Y = Y + D sin .
: )
- ,
) ,
( ,
).
,
(TPLAN [33], GEO[42] .),
X, Y H.
X Y
:
( ),
,
, , X Y
(. 41.8 ).
41.3 41.4,
.

( , ), .
, ,
-.
( ), ,
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, .
.
TPLAN (
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TPLAN
TPLAN Taskm,
autoexec.bat
AUTOEXEC.BAT : @ . 'taskm'

Task Manager: (c) V1.0 1990,
,
TskManager: Already installed.
'taskm'
.
.
'.TMP'.
.TMP . .
, .
( ) .
,
. .
.
'.lis'. .
( '.lis')
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TPLAN

===========================================================================
: vitocha
.
.
7.
(0,1,2,3,4,5,6,7,8 9).
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( ). . vitocha0
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vitocha3 - , vitochha4, vitocha5 vitocha6 .
() :
======================================
||

||
||
||
||
||
||
||
||
||
||
||
||
||
||
||
|| DOS
||
|| ESC
||
======================================
II.
1. : ,
.

2. ,
.
3. DOS TPLAN.
4. ESC DOS, a
.
III.
" " ,
:
============================================
||

||
||
||
|| Pe2 vitocha.kor -
||
|| Pe2 vitocha.dpi -
||
|| PIEK GRE(.)
||
|| Pe2 vitocha.gre - GRE
||
|| Fowf -
||
|| Pe2 fowf.lis -
||
============================================

- , .
'.kor'. Pe2,
, .
'.kor' :
) () .
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- 3 ( 30022 22)
- 4 ( 40022 22)
- 5 ( 50022 22)
- 6 ( 60022 22)
- 7 ( 70022 22)
- 8 ( 80022 22)
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1
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[Pe2 vitocha.dpi] .
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:
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Ms= c1[mm]+c2*S[km]
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.
(1, 2 3) .
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(Ns), (I), (Nt),
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Nt = 0 .
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.
()
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.
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[vitocha.dpi]
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[FOWF] '.dpi' '.dek' () ,
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. .
:
1. 'Wild'

8 25 5
5
0
2
4 0 5 60 0
0 0 0 0
410040+00000001 42....+00110054 43....+00000152
110041+00110056
21.102+09734349
22.102+09332080 31..00+00206941
51....+0005+005 71....+00000150
110042+00110056
21.102+29734652
22.102+30667219 31..00+00206941
51....+0005+005 71....+00000150
110043+00110080
21.102+36359536
22.102+10179699 31..00+00532464
51....+0005+005 71....+00100151
110044+00110080
21.102+16359951
22.102+29819733 31..00+00532464
51....+0005+005 71....+00100151
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[PE2 FOWF.LIS] .
IV.
" " , :
===================================================
||

||
||
||
|| Pe2 vitocha.dpm -
||

|| WDPM -
||
|| POPM -
||
|| PIPM -
||
|| Pe2 wdpm.lis 'wdpm'
||
|| Pe2 popm.lis - 'popm'
||
|| Pe2 pipm.lis - 'pipm'
||
|| SPOL -
||
|| Pe2 spol.lis - 'spol'
||
|| SGM - ()
||
===================================================
[vitocha.dpm]
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[vitocha.dpi]. -
.
[vitocha.dpm] :
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TA 2.
on lin of lin. of line SGM.PLT TA 2.
SGM
SGM.LPT .
V.
" " , :
===================================================
||

||
||
||
|| Pe2 vitocha.dgm -
||
|| Pe2 vitocha.dtn - .
||
|| WDNM - .
||
|| PONM - .
||
|| PINM - .
||
|| Pe2 wdnm.lis - 'wdnm'
||
|| Pe2 ponm.lis - 'ponm'
||
|| Pe2 pinm.lis - 'pinm'
||
|| SNX -
||
|| Pe2 snx.lis - 'snx'
||

|| SGM - ()
||
===================================================
[vitocha.dgn]
.
[vitocha.dgn] :
- - [vitocha.dpi];
- - , .

;
- - -
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[vitocha.dtn]
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Ms= c1[mm]+c2*S[km]+c3*sqr(S[m]), ,
[mm], - , ,
[mm] - .
.

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.
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VI.
" " , :
===================================================
||

||

||
||
|| Pe2 vitocha.dps -
||
|| Pe2 vitocha.dos -
||
|| OGS -
||
|| Pe2 OGS.LIS -
||
|| Pe2 vitocha.kpt -
||
||| NGS -
||
| SFA - cstre [SFA.*]
||
===================================================
[vitocha.dps]
. [vitocha.dps] :
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:
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[vitocha].dli,
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:...................

07 123 46 78 -84 67 -53 69 45 75 *


22 238 567 898 -890 900 456 *
...........................................................
.
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78 -84 , 78, 79, 80, 81, 82, 83 84.
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ACSTRE .
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16 32- 640 KB
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(43.2)

XC = X C + yC cos AB + 300g = X A + xC cos AB + yC cos AB + 300g

YC = YC + yC sin AB + 300g = YA + xC sin AB + yc sin AB + 300g

X C = X C + yC cos AB + 300g = X A + xC cos AB + yC sin AB

YC = YC + yC sin AB + 300g = YA + xC sin AB yC cos AB ;


(43.3)

X D = X D + yD cos AB + 100g = X A + xD cos AB + yD cos AB + 100g

YD = YD + yD sin AB + 100g = YA + xD sin AB + yD sin AB + 100g

X D = X D + yD cos AB + 100g = X A + xD cos AB yD sin AB

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2.
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.
.
,
Zephyr (Stealth .).
4 kg

XIV



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

52.
( ) (. 52.1).
A B . P
1 2 . P .
P
( ), .
-
.


.
, ,
-
,
.

.

. 52.1
,
.
, b = AB . A B ,
, 1 2 . AP BP
P .
.

1.


. (. 52.1).

YB YA

(52.1)

AB = arctg

(52.2)

( AB + 50g ) = arctg

(52.3)

2
2
;
DAB = X AB
+ YAB

(52.4)

3 = 200 (1 + 2 ) ;

(52.5)

DAP =

(52.6)

AP = AB 1 ;

XB X A

DAB sin 2
;
sin 3

= arctg

YAB
X AB

X AB + YAB

X AB YAB

DBP =

DAB sin 1
;
sin 3

BP = BA + 2 .

AP < 0 , a ako BP > 400g 400g .


X P = X A + DAP cos AP ;
X P = X B + DBP cos BP ;
(52.7)
YP = YA + DAP sin AP ; YP = YB + DBP sin BP .
(52.8)
- P
(52.7) (52.8).
X P YP
- 12 cm. .
, .
,
:
20 cm 1:2000;
10 cm 1:1000;
5 cm 1:500, , .
.
, .
(52.4) (52.8)
,
, :
Y Y + X A ctg2 + X B ctg1
XP = B A
(52.9)
;
ctg1 + ctg2
(52.10)

YP =

X A X B + YA ctg2 + YB ctg1
.
ctg1 + ctg2

.
.
: . 52.1 52.2
. 47 . 52.2.
52.1.

X
Y

X
Y
15
52641,84
86794,84
22
50299,36
89404,74
18
53098,74
88505,76
24
50838,17
87202,75
20
51731,15
88118,86
26
49805,94
88463,35
52.2.

.
15

18
. 52.2
20

18
47
20
24
22
20
47
15
22
24
15
47

0,0000
36,6461
54,9646
102,4503
0,0000
37,3273
68,5640
103,1664
0,0000
97,3984
184,9367
212,2766

1017,661

1071,482

694,080

18

264,1367

(52.3). i i . 47
, 15 18 18 20.

.
52.3.


XP =
YP =

YB YA + X A ctg2 + X B ctg1
ctg1 + ctg2

X A X B + YA ctg2 + YB ctg1
ctg1 + ctg2

A = 18

YA = 88505, 76

X A = 53098, 74

1 = 34, 6024g

ctg1 = 1, 654964

B = 15

YB = 87694,94

X B = 52641,84

2 = 36, 6461g

ctg2 = 1,540955

P = 47

YP = 87762,80

X P = 52326,83

A = 20

YA = 88118, 76

X A = 51731,15

1 = 51,8601g

ctg1 = 0,943206

B = 18

YB = 88505, 76

X B = 53098, 74

2 = 31, 2367g

ctg2 = 1,871809

P = 47

YP = 87762, 68

X P = 52326,82

ctg1 + ctg2 = 3,195919

ctg1 + ctg2 = 2,815015

2.
(. 52.3),
:
Y Y + X A tg AP + X B tgBP
XP = B A
(52.11)
;
tg AP tgBP
(52.12)

YP = YB + X P tgBP X B tgBP .

. 52.3


. :
1. ik
. (52.1). . 52.4.
2. . 52.2 RI , k .
3. Oik
(52.13)

Oik = i, k Ri ,k ,

i , k .

.
4. i .
(52.14)

ik

,
n
n i - .
5.
'i ,k = Oi + Ri, k .
(52.15)
6.
Oi =

i, k = i,k 'i, k .
(52.15)
.
. 52.4 15, 18 20.
47.
(52.11) (52.12), . 52.5.
52.4.

No . .

ik
18
47
20
24

83,3859
138,3590
185,8440

22
20
47
15

180,2182
217,5517
283,3859


Rik

X = 52641,84
15 Y = 86794,94
0,0000
83,3859
83,3913
36,6461
120,0374
54,9646
83,3944
138,3559
102,4503
83,3937
185,8416
O15 =
83,3913

54
31
24
55

X = 53098, 74
18 Y = 88505, 76
0,0000
180,2182
180,2207
37,3273
180,2244
217,5480
68,5640
248,7847
103,1664
180,2195
283,3871
O18 =
180,2207

No . .

ik
22
24
15
47
18

. .
ik = Oi + Rik
+

Oik = ik Rik

153,4147
250,8139
338,3590
17,5517


Rik

52.5.

54
25

37
12
37

37

. .
ik = Oi + Rik
Oik = ik Rik
+

20 Y = 88118,86 X = 51731,15
0,0000
153,4147
153,4169
97,3984
153,4155
250,8153
184,9367
153,4223
338,35,36
212,2766
365,6935
264,1367
153,4150
17,5536
O20 =
153,4169

22
14
54
19
54

55


XP =

YB YA + X A tg AP + X B tgBP
tg AP tgBP

YP = YB + X P tgBP X B tgBP
A = 18

YA = 88505, 76

X A = 53098, 74

AP = 248, 7847g

tg AP = 0,962531

B = 15

YB = 87694,94

X B = 52641,84

BP = 120, 0374g

tgBP = 3, 071542

P = 47

YP = 87762, 71

X P = 52326, 76

A = 20

YA = 88118,86

X A = 51731,15

AP = 365, 6935g

tg AP = 0,597916

B = 18

YB = 88505, 76

X B = 53098, 74

BP = 248, 7847g

tgBP = 0,962531

P = 47

YP = 87762, 72

X P = 52326, 78

tg AP tgBP = 4, 034073

tg AP tgBP = 1,560447 AP

.
, ,
.
.

3.

M P P (. 52.4).

( ),
. -
,

. 52.4

.
.
.
, .
, .
, ,
. .

4.
P , :
bm

MP =
sin2 '1 + sin2 '2 = m ,
(52.16)
2

sin '
3

MP =

(52.17)

m
sin '3

2
2
DAP
+ DBP
= m

m ( ) 1 , 2 ;
b = DAB

;
= 636620cc ;
3 = 200g (1 + 2 ) - P ;
DAP DBP .
m ,
. (.
cc
1c , m = 30 )
.
,
b , DAP DBP . -

3 = 100g .
: . 52.3.
cc
1. . (52.16), 1 = 34, 6024g ; 2 = 36, 6461g ; m = 30 ; b = 1770, 78 m.

MP =

30.1770,8
0,8992.636620

0,5172 + 0,5442 = 0, 77 m.

cc
2. . (52.17), 3 = 128, 7525g ; m = 30 ; S AP = 1071, 48 m; SBP = 1017, 66 m.

MP =

30
1071, 52 + 1017, 72 = 0, 077 m.
0,899.636620

5.
.
.
-
0,12m ( DAP + DBP )
MP =
= m .
(52.18)
sin '3
, .
. 52.3
0,12.30(1, 0177 + 1, 0715)
MP =
= 0, 084 m.
0,899
. (52.18) 10% -
. (52.16) (52.17).
,
:
1
1
MP = m
+
(52.19)
,
2
h1 h22

h1 h2 () S AP SBP .
:
1. . 52.5.
2. P
, 1 2
ri =
Dik
r1 =

. 52.5

;
DPA

r2 =

.
DPB

3. 1 2
12 P .
4. 1 r2
h1 , 2 r1 h2 .

5.
.
. 52.5 :
r1 = 6,3 cm; r2 = 5,9 cm; h1 = 5, 7 cm; h2 = 5,3 cm.
(52.19)
1
1
M P = 30
+
= 7, 7 cm.
2
5, 7
5,32
, ,
.

53.
P
-

A,
B , C ,
P
( ) (. 53.1).
1
2 .

,
.

. 53.1
.
,
, P
.
, - . , ,
(1 = 2 = 120) .
.
, .
, , .
- , ,
. .
:
1. .
2. P 1 2
.
3.
( A , B , C , ..). P
.
.

. 53.2

, ,
. -
.
.
,
. .
- .
: P = 49 . 53.2
. 15, 18, 20, 24
26 . 52.1 .

53.1.
53.1.



49
24
0,0000
15
172,6488
18
236,2907
20
273,6822
26
354,1991
. 53.2. i i .
. .
, , :
1. A = 15 , B = 20 , C = 24 , F = 26 , P = 49 .
2. . 1 , 2 , 3 .
3. AB BC .
4. B AB P ( 100g 1 ).
A D .
5. B BC P ( 100g 2 ).
C E .
6. D E .
7. DE .
A, B, P B, C, P.
53.2.

1. YB YD = YB YA ( X B X A )ctg1 ;
X B X D = X B X A + (YB YA )ctg1 ;

2.

3. YB YE = YB YC + ( X B X C )ctg2 ;
;
5. YE YD = YB YD (YB YE ) ;

4. X B X E = X B X C (YB YC )ctg2
6. X E X D = X B X D ( X B X E ) ;

7. I = (YB YD )( X E X D ) ( X B X D )(YE YD ) ; 8. II = (YE YD )2 + ( X E X D )2 ;


I
;
10. YP = YB Q( X E X D ) ;
II
X P = X B + Q(YE YD ) ;

9. Q =

11.
:

A = 15

YA = 86794,94

X A = 52641,84

1 = 101, 033g

B = 20

YB = 88118,86

X B = 51731,15

2 = 126,317g

C = 24

YC = 87202, 75

X C = 50838,17

3 = 80,5169g

D = 26

YF = 88463,35

X F = 49805,94

P = 49
YB YA = 1323,92
X B X A = 910, 69
ctg1 = 0, 016234
( X B X A )ctg1 = 15 78

+ (YB YA )ctg1 = 21, 49

YB YD = 1309,14

X B X D = 932,18

ctg2 = 0, 438678
(YB YD )(YE X D ) =
= 2915507,15
( X B X D )(YE YD ) =

YB YC = 916,11

X B XC = 892,98

+ ( X B X C )ctg2 = 391, 73

(YB YC )ctg2 = 401,88

YB YE = 524,38

X B X E = 1294,86

II = 5575555, 42

YE YD = 784, 76

X E X D = 2227, 04

Q = I II = 0,39170440

= 731537,58
I = 2183969,57

YB = 88188,86

X B = 51731,15

Q( X E X D ) = 872,34

Q(YE YD ) = 307,39

YP = 87246,34

X P = 51423, 76

YPA = 451,58

YPB = 872,34

YPC = 43, 77

YPF = 1216,83

X PA = 1218,08

X PB = 307,39

X PC = 585,59

X PF = 1617,82

tgPA = 0,370731

tgPB = 2,837893

tgPC = 0, 074745

tgPF = 0, 752142

PA = 377,3986

PB = 78, 4321

PC = 204, 7496

PF = 158,9463

1 = 101, 0334

2 = 126,3187

3 = 80,5169

PB = 78, 4320

PB = 78, 4318

PB = 78, 4294

cc

1:1000 = 44

cc
1:2000 = 72


PB .
A , B C , 1 2cc . .
,
PB , PF 3 , .
, ..
2

0, 2M 2
2
=
+ m ,
3D
M ;
D ;
m - ;
(53.1)

= 636620cc .
-
.
.

1.
,
. -
.
:

1. R .
2. 1 2 .
3. .
.
1.
, :
(53.2)

M P2

(53.3)

M P2 =

m2 (12 + 22 )

,
4F 2
m ;
F 123, . 53.3.

=

mR2 (12 + 22 + 32 )

,
4F 2
mR
m
, mR =
.
2

2 F = r2 r3 sin 2 + r1r2 sin 1 r1r3 sin(2 + 1 ) ;


(53.4)
(53.5)

r1 =

cc
;
DPA

r2 =

cc
;
DPB

r3 =

. 53.3

cc
.
DPC

1 , 2 , 3 :
12 = r22 + r32 2r2 r3 cos 2
(53.6)

22 = r12 + r32 2r1r3 cos(1 + 2 )


32 = r12 + r22 2r1r2 cos 1 .

F 1 (53.2).
: . 53.3.
: SPA = 129909,33 cm; SPB = 92491,39 cm;
SPC = 58722,35 cm. : 1 = 101, 0334g ; 2 = 126,3178g ; mR = 20cc .
(53.4, 5, 6) :
cc
cc
r1 =
= 4,900 ;
r2 =
= 6,883 ;
2
2
DPA
DPB
12 = 72, 49 ;

22 = 224,86 ;

2 F = 88, 01 ;

M P2 = 5, 6 cm.

r3 =

cc
2
DPC

= 10,841 ;

32 = 300,58 ;


(53.7)

MP =

mR

( DPA DBC )2 + ( DPB DAC )2 + ( DPC DAC )2


.
DPA sin 2 + DPC sin 1 DPB sin(1 + 2 )

2. ( )
1
1
1
M P = mR
+
+
(53.8)
,
2
2
h1 h2 h32
h1 , h2 , h3
() 1 , 2 3 .
(. 53.4)
52.
h1 = 14, 4 cm, h2 = 8, 2 cm,
h3 = 8, 0 cm.

. 53.4

(53.8) mR = 20cc
M P = 3,9 cm.

54.
P
A B , a = DAP , b = DBP , .
54.1.



.
. 54.1
:
1. , , A B .
2. A a = S AP .
3. B b = SBP .
4. P .

a b
(54.1)

(YP YA )2 + ( X P X A )2 = a2 ,

(54.2)

(YP YB )2 + ( X P X B )2 = b2 .

. 54.2. ,
.
.
: 47
15, 18 20. . 52.1 .
52.2.
54.1.


YP = YA + F (YB YA )

c2 = (YB YA )2 + ( X B X A )2
2F =
K=

A = 18
B = 15

B = 18
P = 47

XP = X A + F ( XB X A) +

c2
a2
c2

+ K (YB YA )

F2

a = 1071, 48

b = 1017, 66

YA = 88505, 76

X A = 53098, 74

YB = 86794, 94

X B = 52641,84

YB YA = 1710,82

X B X A = 456, 90

YP = 87762, 62

X P = 52326,85

P = 47

A = 20

K ( XB X A )

c2 + a2 b2

b = (YP YB )2 ( X P X B )2
c2 = 3135662, 68

a2 : c2 = 0, 366133

P = 0, 268250

YB YA = 967, 68

K 2 = 0, 097883

X B X A = 314, 99

a = 1148069,39
b = 1035631,88

(c2 + a2 b2 ) =
= 3248100, 20
2 F = 1, 035858
F = 0, 517929

2
b.
= 1035631,88

K = 0, 312862
2

a = 694, 08

b = 1071, 48

c2 = 2019994, 02

YA = 88118,86

X A = 51731,15

a2 = 481747, 05

F 2 = 0,112271

YB = 88505, 76

X B = 53098, 74

b2 = 1148069, 39

K 2 = 0,126219

YB YA = 386, 90

X B X A = 1367,59

c2

= 0, 238489

b. = 1017, 66

YB YA = 743,13
X B X A = 771,90

(c + a b ) =
= 1353671, 67
2 F = 0, 670136

2
b.
= 1148069, 39

K = 0, 355273

YP = 87762, 63

X P = 52326,84

F = 0, 335068

b = 1071, 48

(54.3)

MP =

ma2 + mb2
sin 3

ma mb a b , 3
.
, .
, 3 = 100g - .
: . 47 . 15 . 18,
ma = 5 cm mb = 4 cm
3 = 128, 7515g .
M 47 =

52 + 42
6, 4
=
= 7,1 cm.
0,899
0,899

55.


(. 55.1), .
( A, B, C , D...) P
, .

- .

- .

,
. 55.1
.
1. , - -
. , III IV , V .
2. -
2 km. - - 1:5.
3. 35g 165g .
4. - .
- 22g.
5. , 2cc
- 28 .
6. , , - 0,5
cm, .
7. ,
, ,
2
,
6n

, n .
8. , ,
mp - :
(55.1)

mR =

0,10 m V ;
0,07 m VI ;
0,05 m VII .


t ( ), q (
), l . , n

n = t +q+l .
(55.2)
.
X p , Yp
Ol ( ), .

n
=
t
+
l ) , .
(
( )
( n = q ) , .
( n = t + q + l ) .

.
(55.3) Ri,k = i ,k Oi ,
Ri,k , i, k , Oi

( i, k ) ,

( )

i, k ,

i , (. 55.2).
.
:
Ri,k = Ri, k + vi, k ;

(55.4)

i, k = i0,k + i ,k ;
Oi = Oi0 + Oi ,

Ri,k vi ,k ;
i0, k Oi0

. 55.2

;
i ,k Oi .
(55.3) (55.4) :
(55.5)

vi ,k = Oi + i ,k + i0,k Ri ,k Oi0
fi, k = ai0, k Ri,k Oi0 .

i ,k
i ,k = ai ,k xi + bi, k yi + ak ,i xk + bk ,i yk ,
(55.6)
xi , yi , xk , yk , ai ,k , bi, k , ak ,i , bk ,i
:
ai ,k =

sin i0, k

(55.7)
bi ,k =

Di0,k

cos i0, k
Di0,k

yi0, k

( )
Di0, k

, ak ,i = ai ,k ,

xi0, k

( )

2
Di0, k

, bk ,i = bi ,k .

0
0
0
xi, k , yi,k , Di,k

(i, k ) , .
i, k , ,

vi ,k = Oi + ai ,k xi + bi ,k yi + ak ,i xk + bk ,i yk + fi ,k .
(55.8)

, ( i A, B, C...)
P , , xi = 0 yi = 0 , k P
(55.9)

vi ,k = Oi ai ,k xk bi ,k yk + fi ,k .

i P , ( k A, B, C...) ,
xk = 0 yk = 0 ,
vi ,k = Oi + ai ,k xi + bi ,k yi + fi ,k .
(55.10)
. i A , k B ,
xi = 0 yi = 0 xk = 0 yk = 0 :
vi ,k = Oi + fi ,k .
(55.11)
, - .
.
n
n
=
.
n +1
-
T
V PV = min , :
V = AX + f ;
(55.12)

(55.13)

1
x1
f1
a11 a12 ... a1k



a

x
f
a
... a2k
V = 2 ; X = 2 ; f = 2 ; A = 21 22
.
.
.
.
.
. ... .


an1 an 2 ... ank


n
xk
fn
N = AT PA ;
p1
0
P=
.

(55.14)
(55.15)

N 1

0
0
.
0

0
0
;
.

pn

NX + F = 0 ;
F = AT Pf ;
N11
N
N = 21
.

N1k

(55.16)

0
p2
.
0

N12
N22
.
N2 k

... N1k
... N2k
;
...
.

... Nkk

F1
F
F = 2.
.

Fk

X = N 1 F ,

Q11 Q12
Q
Q22
= Q = 21
.
.

Qk1 Qk 2

... Q1k
... Q2 k
N 1
,
...
.

... Qkk
. , ..
Qi, k = Qk ,i .
,
NQ = QN = E ,
(55.17)
E .
(55.16) (55.12).
:
(55.18)

V T PV = f T pf + F T X = [ Pff .k ] .

(55.18) , ,
.
. .

.
Vi, k = ai ,k Oi Ri, k .
(55.19)
, . (55.12) (55.18)
, .
:
1.
V T PV .
nk
2.
1
ml =
(55.21)
.
pi
(55.20)

3.
mii = Qii .
(55.22)
: . 55.2.
55.1 55.2.
49 .
55.1.

15
18
20

X
52641,84
53098,74
51731,15

55.2.
. .

15

18
20
49
24
22
20
49
15
22
24
49
15
18

20

22
24
26

X
50299,36
50838,17
49805,94

Y
89404,74
87202,75
88463,35

18

Y
86794,84
88505,76
88118,86

0,0000
54,9646
94,0102
102,4503
0,0000
37,3273
60,8101
103,1664
0,0000
97,3984
125,0155
184,9367
264,1367

. .

24

15
49
20
22
24
15
18
20
26

49

0,0000
18,9065
64,9632
129,4263
0,0000
172,6490
236,2900
273,6822
354,1967

:
1. .
18, 7 (2 49 5
).
2. .
YB YA
aAB = arctg
.
XB X A
15, 18, 20, 22, 24, 26.
:
15,18 = 83,3859g ; 15,20 = 138,3590g ; 15,24 = 185,8440g ;
18,22 = 180, 2182g ; 18,20 = 217,5517 g ; 20,22 = 153, 4147g ;
20,24 = 250,8139g .
3. P = 49 .
49 52 .
0
0
x49
= 51423, 76 m; Y49
= 87246,52 m.

4.
, 18.
(55.3). .
5.
. 55.2 (55.7), (55.8) (55.9)
.
V15,18 = O15 + f15,18 ,
V15,49 = O15 a15,49 x49 b15,49 y49 + f15,49 ,
V15,24 = O15 + f15,24 ,
V18,22 = O18 + f18,22 ,
V18,20 = O18 + f18,20 ,
V18,49 = O18 a18,49 x49 b18,49 y49 + f18,49 ,
V18,15 = O18 + f18,15 ,
V20,22 = O20 + f20,22 ,
V20,49 = O20 a20,49 x49 b20,49 y49 + f20,49 ,
V20,18 = O20 + f20,18 ,
V24,15 = O24 + f24,15 ,
V24,49 = O24 a20,49 x49 b24,49 y49 + f24,49 ,
V24,22 = O24 + f24,22 ,
V49,15 = O49 + a49,15x49 + b49,15y49 + f49,15 ,
V49,18 = O49 + a49,18x49 + b49,18y49 + f49,18 ,
V49,20 = O49 + a49,20 x49 + b49,20 y49 + f49,20 ,
V49,26 = O49 + a49,26 x49 + b49,26 y49 + f49,26 ,
V49,24 = O49 + a49,24 x49 + b49,24 y49 + f49,24 .
0
6. P, k aP ,k , bP, k

fP,k .

.

0P, k = arctg =

yk yP0
xk xP0

(55.7)
aP ,k = bP,k tg0P,k

.
. 55.3
Oi0 = 204, 7496g

55.3.
K
P

Xk

tg0P , k

sin 0P , k

ai ,k

YP

XP

Y0

X 0

0P , k

cos 0P, k

aP , k = bP, k tg0P, k

SP , k

RP , k

bik
fik

0,600917

1,826
1,825

0,799311
236,2907

-2,428
-7 cc

-0,347612

-1,703
-1,703

Yk

18

88 505,76

53 098,74

49

87 246,52
1259,24

51 423,76
1674,98

RP0 , k = 0P , k Oi0
0,751794
41,0456g
2095,53
236,2900

15

86 794,94

52 641,84

-0,370731

49

87 246,52
-451,58

51 423,76
1218,08

20

88 118,86

51 731,15

49

87 246,52
872,34

51 423,76
307,39

26

88 463,35

49 805,94

49

87 246,52
1216,83

51 423,76
-1617,82

24

87 202,75

50 838,17

49

87 246,52
-43,77

51 423,76
-585,59

377,3986g
1299,09
172,6490

0,937639
172,6488

-4,595
2 cc

2,837893
78,4321g
924,91
273,6825

0,943158

6,492
6,493
-2,288
3 cc

-0,752142
158,9463g
2024,36
354,1967

0,601095

1,890
1.890

-0,799178
354,1991

2,513
-24 cc

-0,074537

-0,808
-0,808
10,811
0 cc

0,074745
204,7496g
587,22
0,0

0,332344
273,6822

-0,997218
0,0

7.
.
0
0
fi, k = i,k Ri, k Oi ,

. 55.4.
8.
V15,18 = O15 54
V15,49 = O15 1, 703x49 4,595y49 29
V15,24 = O15 + 24
V18,22 = O18 25
V18,20 = O18 + 37
V18,49 = O18 + 1,826x49 2, 428y49 + 88
V18,15 = O18 12
V20,22 = O20 22
V20,49 = O20 + 6, 492x49 2, 288y49 3
V20,18 = O20 19
V24,15 = O24 46
V24,49 = O24 0,808x49 + 10,811y49 55
V24,22 = O24 + 25
V49,15 = O49 1, 703x49 1, 703y49 + 2
V49,18 = O49 + 1,826x49 2, 428y49 7
V49,20 = O49 + 6, 492x49 2, 288y49 + 3
V49,26 = O49 + 1,890x49 + 2,513y49 24
V49,24 = O49 0,808x49 + 10,811y49 + 0
. 55.5 .
55.4.

. .

ai ,k

Ri,k

18
20
49
24

83,3859
138,3590

185,8440

180,2182
217,5517

ai,k = Oi + Ri,k

15 Y = 86794, 94 , X = 52641, 84
0,0000
83,3859
54,9646
83,3944
94,0102

102,4503
83,3937
O = O / n
83,3913
15

22
20

Oi = ai, k Ri, k

83,3913
138,3559
177,4015
185,8416

180,2207
217,5480

54

31
24
55

18 Y = 88505, 76 , X = 53098, 74
0,0000
180,2182
37,3273
180,2244

54
25

37

49
15

283,3859

60,8101
103,1664
O = O / n
18

22
24
49
15
18

241,0308
283,3871

180,2207

20 Y = 88118, 86 , X = 51731,15
0,0000
153,4147
97,3984
153,4155
125.0155
184,9367
153,4223
264,1367
153,4150

O = O / n
153,4169

153,4169
250,8153
278,4324
338,35,36
17,5536

385,8440
50,8139
115,2774

24 Y = 87202, 75 , X = 50838,17
0,0000
385,8440
18,9065
64,9632
385,8507
129,4263
385,8511
O = O / n
385,8486

385,8486
4,7551
50,8118
115,2749

24

12
37

153,4147
250,8139
338,3590
17,5517

20

15
49
20
22

180,2195

37
22
14

54
19
54

55
46

21
25
46

46

55.5

O15

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18

-1,000
-1,000
-1,000

O18

O20

O24

O49

-1,000
-1,000
-1,000
-1,000
-1,000
-1,000
-1,000
-1,000
-1,000
-1,000
-1,000
-1,000
-1,000
-1,000
-1,000

X 49

Y49

-1,703

-4,595

1,826

-2,428

6,492

-2,288

-0,808

10,811

-1,703
1,826
6,492
1,890
-0,808

-4,595
-2,428
-2,288
2,513
10,811

f
-54,000
-29,000
24,000
-25,000
37,000
88,000
-12,000
-3,000
-19,000
-22,000
-46,000
-55,000
25,000
2,000
-7,000
3,000
-24,000
0,000

9.
, -1.
:
, :
1. ;
p ;
u .
2. :
v ;
h .
3.
to = e ;
to = t ;
to = m .
phe.
;
n ;
k ;
( ) m ;
) f
( ) c .
,
:
18 7 0 0 3.

, ..
(pve), , ,
.
(
phm), :
;
;
;
.
.
(18) :
3
5 1,000
6 0,808
7 10.811
0
1

:
1.
O15 = 20,86cc

mo = 21,36cc ;

O18 = 19,91cc

mo = 18,14cc ;

O20 = 21, 08cc

mo = 22,71cc ;

O24 = 18, 70cc

mo = 22,37cc ;

O49 = 7,52cc

mo = 17, 73cc ;

x49 = 2,38 cm

mx = 4,35 cm;
my = 2,35 cm.

y49 = 1, 66 cm
2. ,

55.6

1
2
3
4
5
6
7
8
9

v (cc)
-33,14
-11,73
44,86
-44,91
17,09
59,72
-31,91
-1,15
2,08

. .

. .

mv

mi

(cc)

29,01
27,76
29,01
31,13
31,13
30,55
31,13
23,10
27,97

(cc)

21,36
22,96
21,36
18,14
18,14
19,10
18,14
27,64
22,71

10
11
12
13
14
15
16
17
18

v (cc)
-0,92
-27,30
-16,41
43,70
5,93
-7,85
-8,70
-16,79
27,41

3.
= 14278,24

[pvv] = 14 278,24
= 11,0
= 7,0
= 36,03
= 18
= 7
4.
0
O15 = O15
+ O15 = 83,3913 0, 00209 = 83,38921g ;
0
O18 = O18
+ O18 = 180, 2207 + 0,00199 = 180, 22269g ;
0
O20 = O20
+ O20 = 33, 7489 0,00211 = 33, 74679g ;
0
O24 = O24
+ O24 = 385,8486 0, 00187 = 385,84673g ;

. .

..

mv

mi

(cc)

27,97
28,24
24,36
28,24
24,21
31,37
24,57
31,89
22,50

(cc)

22,71
22,37
26,54
22,37
26,68
17,72
26,35
16,77
28,14

0
O49 = O49
+ O49 = 204, 7496 0, 00075 = 204, 74885g ;
0
X 49 = X 49
+ x49 = 51423, 76 0, 024 = 51423, 736 m;
0
Y49 = Y49
+ y49 = 87246,52 + 0,017 = 87246,537 m.

10.
,
. . 55.7 (55.7)
. 55.6 , .
55.7
tgi, k
Yk
Xk
i
Ri , k = ai ,k Oi
Ri,k
vi,k
Ri , k = ai ,k Oi

Yp
Xp
k
Ri,k
Y
X
1

399,99669

0,00000

-33,1cc

15

86 794,940

52 641,840

-0,370738

2
3

94,00897
102,45479

94,01020
102,45030

-12,3cc
44,9cc

49

87 246,537
-451,597

51 423,736
1218,104

172,64934
172,64880

4
5

399,99551
37,32901

0,00000
37,32730

-44,9cc
17,1cc

18

88 505,760

V14 =
53 098,740

5,4cc
0,751773

6
7

60,81605
103,16321

60,81010
103,16640

59,5cc
-31,9cc

49

87 246,537
1259,223

51 423,736
1675,004

236,28989
236,29070

8
9

244,68333
383,80491

244,68350
383,80470

-1,7cc
2,1cc

20

88 118,860

V15 =
51 731,150

-8,1cc
2,837616

10
11

119,66791
399,99727

119,66800
0,00000

-0,9cc
-27,3cc

49

87 246,537
872,323

51 423,736
307,414

273,68128
273,68220

12
13

18,90489
129,43067

18,90650
129,42630

-16,1cc
43,7cc

V16 =
49 805,940
51 423,736
-1617,796
V17 =
50 838,170
51 423,736
-585,566
V18 =

-9,2cc
-0,752142
354,19741
354,19910
-16,9
0,074777
0,00278
0,00000
27,8cc

26
49

88 463,350
87 246,537
1216,813

24
49

87 202,750
87 246,537
-43,787

- 12cc.
0,5cc, .

,
n t + l . 55.3.
.
, ( i A, B, C )
P , , xi = 0 yi = 0 , k1 P
(55.9),
Vi, k = Oi ai ,k xk bi ,k yk + fi ,k .

i, k = Oi + Ri,k , Oi = 0 ,

. 55.3


(55.23) Vi, k = ai,k xk bi,k yk + fi,k .


n
p=
.
n +1

0
fi, k = i,k i,k .

(55.23) :
[ paa ]dx + [ pab]dy + [ paf ] = 0 ;
[ pab]dx + [ pbb]dy + [ pbf ] = 0 .

. (55.12) (55.16).
.
N , Q, F , X
N12 [ paa ] [ pab]
N
N = 11
(55.24)
=
,
N
N
21
22 [ pba ] [ pbb]
Q12
Q
F1 [ paf ]
dx
Q = 11
X = .
, F= =
,

dy
Q21 Q22
F2 [ pbf ]
Q
N
N
N
(55.25)
Q11 = 22 , Q12 = Q21 = 12 , Q22 = 11 ,

(55.25)

2
= N11 N12 N12
.

:
X = N 1 F = QF
(55.27)

dx = Q11F1 Q12 F2
dy = Q21 F1 Q22 F2 .

X = X 0 + dx ;
Y = Y 0 + dy , (55.23).


[ p]
(55.28)
.
=
nk

(55.29)

mx = Q11 ;

my = Q22 ,


(55.30)

ms = mx2 + m2y = Q11 + Q22 .

.
:
1. [ p ] = [ pff .2]
.
'
2. Vi, k = i ,k i,k


.
:

. 55.4.
. 55.1
55.8.
49
.
. 55.4

55.8

. .

15

18
47
20
24
22
20
47
15

18

0,0000
36,6461
54,9646
102,4503
0,0000
37,3273
68,5640
103,1664

. .

20

22
24
15
47
18

0,0000
97,3984
184,9367
212,2766
264,1367

1.
13, 5 (2 P = 47
3 ).
2.
YB YA
AB = arctg
.
XB X A
15, 18, 20, 22, 24.
:
15,18 = 83,3859g ;

15,20 = 138,3590g ;

18,22 = 180, 2182g ;

15,24 = 185,8440g ;

18,20 = 217,5517g ;

20,22 = 153, 4147g ;

20,24 = 250,8138g .
3. P = 47
47 51
0
X 47
= 52236, 77 m;

0
Y47
= 87762, 72 m.

4.

, 3. , 3.
(55.23). .
5.
V18,47 = a18,47 x47 b18,47 y47 + f18,47 ;
V15,47 = a15,47 x47 b15,47 y47 + f15,47 ;
V20,47 = a20,47 x47 b20,47 y47 + f20,47 .
6.
55.9

. .

18
47
20
24

83,3859
138,3590
185,8440

22
20
47
15

i, k

180,2182
217,5517
283,3859

22
24
15
47
18

153,4147
250,8139
338,3590
17,5517

Ri,k

15 Y
0,0000
36,6461
54,9646
102,4503

Oi = ai, k Ri, k

i, k = Oi + Ri,k

= 86794,94 X = 52641,84

O15 = Oi / n

83,3859
83,3944
83,3937

83,3913
120,0374
138,3559
185,8416

83,3913

= 88505, 76 X = 53098, 74

20 Y
0,0000
97,3984
184,9367
212,2766
264,1367

= 88118,86 X = 51731,15

O18 = Oi / n

O20 = Oi / n

180,2207
217,5480
248,7847
283,3871

180,2207
153,4147
153,4155
153,4223
153,4150

31
24
55

18 Y
0,0000
37,3273
68,5640
103,1664

180,2182
180,2244
180,2195

54

25
37
12
37

153,4169
250,8153
338,35,36
365,6935
17,5536

153,4169

54

37
22
14

54
19
54

55

7.

55.10
k
i
47
18

Yk

Xk

tgi0, k

sin i0,k

ai ,k

Yi

Xi
X 0

cos i0,k

bi ,k

Y0

si0,k
i0, k

i, k

fi, k

87 762,72
88 505,76
-743,04

52 326,77
53 098,74
-771,97

0,962524
1071,47
248,7845

-0,693478
-0,720478
248,7847

4,120
-4,281
-2cc

47
15

87 762,72
86 794,94
967,78

52 326,77
52 641,84
-315,07

-3,07163
1017,78
120,0368

0,950878
-0,309567
120,0374

-5,948
-1,936
-6cc

47
20

87 762,72
88 118,86
-356,14

52 326,77
51 731,15
595,62

-0,59793
693,97
365,6927

-0,513190
0,858275
365,6935

4,708
7,873
-8cc

8.
55.11

dx
dy
1
2
3

4.120
-5,948
4,708

-4,281
-1,936
7,873

-2
-6
-8

0,75
0,75
0,80

55.12
N

1
2
3

dx

dy

56,995

25,062
66,149

= 3142,042

9.
55.13

Q
1
2

0,021
-0,008

-9,545
-35,255

[ pff ] = 81, 200

F
-0,008
0,018

-9,545
-35,255

10. , . 47,
. 55.14.
55.14
Vi, k
dx
0,080
= 4,32cc
dy

0,563

mx = 0, 63 cm

V47,18 = 4, 74

X
Y

52326,769

my = 0,58 cm

V47,15 = 6, 61

87762,726

ms = 0,86 cm

V47,20 = 3,94

[ pvv] = 62,104
[ pvf ] = 62,104
11.
,
.

55.15
k
i
47
18

47
15

47
20

Yk

Xk

tgi, k

Yi

Xi

i, k

Y0
87 762,726
88 505,760
-743,034

X 0
52 326,769
53 098,740
-771,971

i, k
0,96251615
248,78421
248,78470

87 762,726
86 794,940
967,786
87 762,726
88 118,860
-356,134

V47,18

-4,9

52 326,769
52 641,840
-315,071

-3,07164493
120,03678
120,03678

V47,15

-6,3

52 326,769
51 731,150
595,619

-0,59792291
365,69314
365,69350

V47,20

-3,6


,
.
n = q .

i P , ( k A, B, C...) ,
xk = 0 yk = 0 , (55.10)
Vi, k = Oi + ai ,k xi + bi,k yi + fi, k .
, , .
. ,
:
[aa ]xi + [ab]yi [a ]Oi + [af ] = 0
[ab]xi + [bb]yi [b]Oi [bf ] = 0

(55.35)

[a ]xi [b]yi nOi [ f ] = 0.


.
(55.14) (55.18).
, (55.9).
.
,
Vp, k = p, k Op Rp ,k .
.

[]
(55.33)
.
=
nk
,

mx = Q11 ;

(55.34)

my = Q22 ;

m0 = Q33 .


ms = mx2 + m2y = Q11 + Q22 .

(55.35)

: . 55.5.
. 55.1 55.16.
49 .
55.16
.
49

. .
24
15
18
20
26

. 55.5


0,0000
172,6490
236,2900
273,6822
354,1967

:
1.
5, 3 (2
49 1

).
2.
V49,15 = O49 + a49,15x49 + b49,15y49 + f49,15 ;
V49,18 = O49 + a49,18x49 + b49,18y49 + f49,18 ;
V49,20 = O49 + a49,20 x49 + b49,20 y49 + f49,20 ;
V49,26 = O49 + a49,26 x49 + b49,26 y49 + f49,26 ;
V49,24 = O49 + a49,24 x49 + b49,24 y49 + f49,24 .
3. 49
49 52 .
0
X 49
= 51423, 76 m;

0
Y49
= 87246,52 m.

4.
49
. 55.3
0
= 204, 7496g .
O49

5.
. 55.17.
0
O49
= 204, 7496g

55.17.
Yk

K
I

Xk

tgi0, k

sin i0, k

ai ,k

cos i0,k

bi ,k

Ri,k

fi, k

0,600917
0,799311
236,2907

1,826
-2,428
-7cc

YI

XI

Y0

X 0

18
49

88 505,76
87 246,52
1259,24

53 098,74
51 423,76
1674,98

si0,k
Ri0,k = i0,k Oi0
0,751794
2095,53
236,2900

15
49
20
49

86 794,94
87 246,52
-451,58
88 118,86
87 246,52

52 641,84
51 423,76
1218,08
51 731,15
51 423,76

-0,370731
1299,09
172,6490
2,837893
924,91

-0,347612
0,937639
172,6488
0,943158
0,332344

-1,703
-4,595
-2cc
6,492
-2,288

26
49

872,34
88 463,35
87 246,52

307,39
49 805,94
51 423,76

273,6825
-0,752142
2024,36

273,6822
0,601095
-0,799178

3cc
1,890
2,513

1216,83
87 202,75
87 246,52
-43,77

-1617,82
50 838,17
51 423,76
-585,59

354,1967
0,074745
587,22
0,0

354,1991
-0,074537
-0,997218
0,0

-24cc
-0,808
10,811
0cc

24
49

6.
V49,15 = O49 1, 703x49 1, 703y49 + 2 ;
V49,18 = O49 + 1,826x49 2, 428y49 7 ;
V49,20 = O49 + 6, 492x49 2, 288y49 + 3 ;
V49,26 = O49 + 1,890x49 + 2,513y49 24 ;
V49,24 = O49 0,808x49 + 10,811y49 + 0 .
-

S
dx
dy
dO
f
1
2
3
4
5

-1,703
1,826
6,492
1,890
-0,808
7,696

4,595
-2,428
-2,288
2,513
10,811
4,014

-1,000
-1,000
-1,000
-1,000
-1,000
-5,000

2,0
-7,0
3,0
-24,0
0,0
-26,0
491,588

7.
52, 604dx 15, 441dy 7, 696dO 42, 078 = 0 ;
15, 441dx + 155, 4371dy 4, 014dO 59,372 = 0 ;
7, 696dx 4, 014dy + 5, 000dO + 26, 000 = 0 .

N
F
S
dx
dy
dO
1
2
3

52,604

1
2

-15,441
155,437

NR

-7,696
-4,014
5,000

-42,078
-59,372
26,000
638,000


FR

dx

dy

dO

52,604

-15,441
150,905

-7,696
-6,273

-42,078
-71,724

-5,298
-8,603
6,204
-20,596
9,003
-19,290
-19,290

-12,612
76,610
19,290
562,549

-12,612
76,610
19,290
562,549

-12,612
72,908

-12,612
72,908

3,613

dx

1
2
3

1,000

16,862
491,558

dy

20,476
491,558

20,476
491,558

dO

1,000
1,000
1,000


NE
FE

dx

dy

dO

1
2
3

1,000

0,294
1,000

0,146
0,042
1,000

0,200
0.027
0.004
0,044
T

0,800
0,475
-4,667

0,240
-0,483
-5,667

0,240
-0,483
-5,667


0,281
-4,667
1,000
F
0.004
0,007
0,012

0,044
0,012
0,277

0,019
0,007
0,277

-42,078
-59,372
26,000

0,200
0,281
-4,667

FxT + f f = 49,558 .
8. ,
. 49
V49,15 = 5, 034cc ;

V49,18 = 2, 652cc ;

V49,26 = 18,320cc ;

V49,20 = 8,320cc ;

V49,24 = 7,547cc ;

0
X 49 = X 49
+ dx = 51423, 762 m;
0
Y49 = Y49
+ dy = 87246,523 m;
0
O49 = O49
+ dO = 204, 74912cc .

9.
491,56
=
= 15, 7cc ;
53
mx = 15, 7 0, 027 = 2, 6 cm;
mO = 15, 7 0, 277 = 8, 2cc ;

my = 15, 7 0, 007 = 1,3 cm;


ms = 2, 62 + 1,32 = 2,9 cm.

10.
O49 = 204, 74912g
k
i
15
49

18
49

20
49

26
49

Yk

Xk

tgi, k

Yi

Xi

Ri,k = i ,k Oi

Y0

X 0

Ri,k

86 794,940
87 246,523
-451,583

52 641,840
51 423,762
1218,078

-0,370734
172,64927
172,64880

Vi, k =

-4,7cc

53 098,740
51 423,762
1674,978

0,751793
236,29043
236,29070

Vi, k =

-2,7cc

51 731,150
51 423,762
307,388

2,837903
273,68302
273,68220

Vi, k =

8,2cc

49 805,940
51 423,762
-1617,822

-0,752139
354,19726
354,19910

Vi, k =

-18,4cc

88 505,760
87 246,523
1259,237
88 118,860
87 246,523
872,337
88 463,350
87 246,523
1216,827

24
49

87 202,750
87 246,523
-43,773

50 838,170
51 423,762
-585,592

0,0747450
0,00076
0,0000

Vi, k =

7,6cc

- 0,5c,
, .
XV

56. . , ,


. ,
. -
. .
.

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

1.
- 1:25 000
. , ,
.
, .
.
.
, ,
. (56.1)

:
56.1

1
2
3
4
5

1:500
1:1000
1:2000
1:5000
1:10 000


[m]
20
20
40
60
75

130
150
200
300
400

[m]
1000
1200
2000
3000
4000



[m]
150
180
250
400
500

.

, .
,
.

.
, , .
. ,
30% .
,
- 1:5.

.

2.
,
. ,
: , ,

(6).
30 cm.
- ,
(6), (. 6.5).

3.

- 0,01 gon (1) .
5 mm.

. ,
.
,
. 5 mm.
, ,

.

.
,
.
.
.
f
o
. f . 56.2,

n .
56.2

o
f

1:500/1:1000
1:2000
1:5000
1:10 000

0, 015 n
0, 02 n
0, 03 n
0, 04 n


0, 02 n
0, 025 n
0, 05 n
0, 06 n

- . 57.2,
.

4.
.
, .

. ,
.
, ,
- 1/3 .
.
.
( I IV)
.
. ,
, .

5.

, .
,
.

fh
. ,

( fh < fh )

, .

31, .

6.

. ,
Si,i +1 i,i+1
X i ,i +1 Yi,i +1 (. 56.1).

. 56.1

,
(57.1,2,3; 58; 59; 60).

i :
(56.1)

i,i +1 = i 1,i + i 200g .

(56.1) i 1,i
i - 200g, 200g, 200g,
200g. , 400 , 400 (. 56.1).
Si,i +1 i,i+1
i i + 1 :
X i ,i +1 = Si ,i +1 cos i ,i +1
(56.2)
Yi,i +1 = Si,i +1 sin i ,i +1 .
:
X i +1 = X i + X i,i +1
(56.3)
Yi +1 = Yi + Yi,i +1 .
56.3

4%
4 8%
:
8%
4%
4 8%
:
8%

15%

15%

fS , m a b
1:500
0,10; 0,005
0,10; 0,015
0,10; 0,025
0,10; 0,010
0,10; 0,020
0,10; 0,030

1:1000
0,10; 0,010
0,10; 0,020
0,10; 0,030
0,10; 0,015
0,10; 0,025
0,10; 0,35

:
1:2000

1:5000

1:1000

0,10; 0,015 0,20; 0,030

0,30; 0,050

0,10; 0,020 0,20; 0,050

0,30; 0,070

0,10; 0,020 0,20; 0,060

0,30; 0,080

0,10; 0,30

0,30; 0,150

0,20; 0,120

: (56.1), (56.2) (56.3) .

(56.1)
(56.3),
, .. .
.
, ,
, .
, .
(56.1), (56.2) (56.3).
fS

fS =

(56.4)

f x2 + f y2 m,

f x f y X Y . (.
56.3) fS

fS = a + b [ S]

(56.5)

m,

[S] [m], a b
, .
fS - ,
f x f y X Y
.
, (TPLAN, GEO
.).

57. ,
57.1.

BA (. 57.1),
. i
Sik (. 57.2). , ,
(. 57.1).

. 57.1

57.1

1283=A
15=B
57.2

X, m
Y, m
45626,63
82753,46
45738,127
82672,86


, g
160,1525

..

,
g

1283

15
14
1283
13
14
12
13
11

238,0190
349,9440
0,0000
220,3900
0,0000
188,7420
0,0000
159,5080

111,9250

137,58

220,3900

146,36

188,7420

207,49

159,5080

162,55

14
13
12

i , g

Sik , m

11

12
10

0,0000
223,7250

223,7250

175,54

.
, .
,
.
- .
:
1. . . BA
(. 57.1)
Y
BA = arctg BA .
(57.1)
X BA
2. (.
57.3)
:
.
BA .
Y X .
i Sik
.
3. (56.1)
.

= + i n 200g ,
(57.2)
n .
4. Sik cm
Yik X ik (56.2).
5.
(56.3) , Y X .

57.3

i , i +1

= a

i 1, i

Si ,i +1

+ +
i

+ V + 200


Y = S sin

VY

X = S cos

15 B
1283 A
14
13
12
11

160,1525

137,573

72,0775

146,36

1321,51

62,16

92,4675

207,49

206,04

24,49

81,2095

162,55

155,52

47,28

40,7175

175,54

104,77

140,84

64,4425

139,82

118,57

74,10

111,9250
220,3900
188,7420
159,5080
223,7250

10

+ [ ] = 1064, 4425

= [V ]
+ n 200 = 1064, 4425

[ S ] = 831, 76 [ Y ]

f = ......

V =

(Y Y ) = 717, 41

[ X ] = 348,87
( X X ) = 348, 87

fY = ......

fX = ......

= 717, 41

VX

82672,860 m

45738,127 m

15 B

82753,460 m

45626,630 m

1283 A

82885,97

45688,79

14

83092,01

45713,28

13

83247,53

45760,56

12

83352,30

45901,40

11

83470,87

45975,50

10

= n = K K
f
n

vY =

fX
fY
S = ... v X =
S = ... f =
s
[S] i
[S] i

f X2 + f Y2 = ... f = (... [ S ] + 0,10) = ...

(57.3)

:
Y Y = Yik

X
= ik ,
Y = YA , X = X A Y = Y10 X = X10 .
.

,

,
.

S A3
,
.
. 3 (. 57.2).
. 57.2


A3,2 3,2
(. 57.3).
X

. 57.3

.
, (. 57.4)
.

. 57.4

,
1
(. 57.5).
1 = AA1 .
(57.4)

. 57.5


,
.
, - , , ,
. :
(57.5)

M =

2
mS
+ i

m
2
S

mS ;
m ;
S,i , ,
, :
(57.6)

2
m [ S ] m
M = S
+
S n + 1

[ S]
3

n ,

mS

;
S
[ S ] [m];
n .

57.2.
1. ()
,
CA BD (. 57.4), .. .
i Sik (. 57.5).
(. 57. 6).

. 57.6

57.4

X, m
45061,029
46160,460
46243,747
45626,631

1288=C
1245=A
1253=B
1283=D


,g
4,2456

Y, m
82078,029
82151,460
83516,331
82753,465

256,6989

57.5

..

,
g

1245=A

1288=C
1
1245=A
2
1
3
2
4
3
5

108,1256
373,2906
173,1877
399,9997
211,8176
0,0000
161,0292
399,9992
235,7856
399,9976

265,1650

1
2
3
4

i , g

Sik , m

174,30
226,8120
202,34
188,1824
230,85
238,9700
181,05
164,2120
160,05

5
6
7
1253=B

4
6
5
7
6
1253=B
7
1283=D

180,5799
399,9979
222,9149
399,9974
159,6020
0,0000
28,3727
360,5777

219,4180
200,20
177,0825
149,62
240,3980
123,32
332,2050

.

.
. ,
, .
:
1. , , D (57.1)
CA BD (. 57.6).
,
.
2.

f ,

, :
(57.7)

f = ( [ ] ) + k 200g ,

k , :
n 2

k
=
(57.8)
,
n
n + 2

n . k
.
3. f -

f , . 57.2 ,

i . ,
:
f
(57.9)
v = ,
n
n .
f v i
.
(. 57.6), , 1:2000
f :
f = 0, 02 n = 6c

f < f . v =

f
n

f =84

cc

= 9cc .

(57.2) 9,
10 .
v = f .
(57.10)


4. = i vi
(57.1) . ,
BD .
5. (56.2)
X i Yi , .

, ,
fx fy:

(
)
f y = [ Y ] ( Y Y ) .
f x = [ X ] X X

(57.11)

. fx fy (57.11)
fS , .
6. fS fS , . 57.6 ,
fx fy X Y ,
:
fx
vikx =
S
Sik ik
(57.12)
fy
viky =
S .
Sik ik
, cm
. : f x = 0, 04 m , f y = 0,11 m , fS = 0,12 m

fS = 0,015

[ S ] + 0,10 )

m = 0,66 m.

7. X = X + vx , Y = Y + vy .
(56.3) ,
. , .
. .
.
.


, - ,
(57.13)

m
M = S
S

[ S ] 2 + m [ S ] 2

n,

192
(57.6).
m
1
cc
S =
, m = 50 , [S]=1421,73 m n=9
S
2000
4n

2
2
1 1421.73 50 1421.73
M =
+
.9 = 0,12 m.
.
.
4.9
192
2000
636620
,
.

57.6

i , i +1

= a

i 1, i

Si ,i +1

+ +
i

+ V + 200


Y = S sin

VY

X = S cos

VX

1288 C

1288 C
4,2456

1245 A

265,1650

10

226,8120

202,34

201,98

11,99

84,4078

230,85

223,96

55,98

123,3787

181,05

168,98

-65,00

87,5916

160,05

157,02

31,00

107,0105

200,20

198,99

-22,00

84,0939

149,62

144,97

37,00

124,4929

123,32

114,30

-46,28

10

332,2050

10

= [V

+ n 200 = 2056, 6989

[ S]

= 1421, 73

cc
f = 84

V =

c
= n = 2
f
n

= 9,33

46160,46 m

1245 A

82306,03

46241,02

82508,03

46253,02

82732,01

46309,01

82901,00

46244,02

83058,03

46275,02

83257,04

46253,03

83402,02

46290,03

83516,33 m

46243,75 m

1283 D

256,6989

1283 D
+ [ ] = 2056, 6905

82151,46 m

240,3980

c 1253 B

96,2245

177,0825

80,56

219,4180

164,2120

154,56

238,9700

174,30

188,1824

69,4116

[ Y ]

1283 D

(Y Y ) = 1364, 87

[ X ] = 83,25
( X X ) = 83, 29

fY = 0,11

fX = 0, 04

= 1364, 76

9 =6

VY =

fY
[S ]

Si

fS

= fY2 + f X2 = 0,12 m VX =

fY
[S ]

Si

f = 0, 015 [ S ] + 0,10 m = 0, 66 m

2.
,
.
, f fS , -
,
. , ,
. ,
,
.
. - ,
.
3.

.
(. 57.7) : . .
: . . . ,
, ,
.

. 57.7

(. 57.7)
. . , . . . ,
(. 57.7 ), .
(. 3) (. 1, 2, 3), ,
(. 4, 5 ).
4.
,
fS - ,
.

.
f x f y
fS fS
(57.14)

f = arctg
S

fy
fx

, fS , .
.
, fS S3,4 (. 57.8).

. 57.8

,

.

57.3.
.
.
,
(. 57.9, ).

. 57.9

. 57.9


Y ,
.
(. 57.9) (X = 82151,46 m, Y = 46160,46 m)
A , SAB SA5.
A2

(57.15)

A2 = AB + + 'A 200g .

,
f :
(57.16)

g
f = i ( n 2 ) 200

g
f = i ( n + 2 ) 200
,
n .
57.7

..

,
g


i , g


Sik , m

58

1245=A
57
58
59
57
18
59
1245=A

0,0000
179,7650
0,0000
69,3480
247,8430
0,0000
277,8080
0,0000

179,7650

144,79

69,3480

160,54

152,1570

118,68

122,1920

159,70

57
59
18

1245=A

18
58

48,2990
124,8245

76,5255

145,95

. 57.7
, , .
( = , Y = Y), fx fy
:
f x = [ X ]
(57.17)
f y = [ Y ] .
(. 57.8) ,
(. 57.6).
(. 57.9),
(1=1000,00 m, Y1=1000,00 m)
( 1,2=100,0000g). ,
, .

57.8

i,i 1 = i 1 +

Si,i +1

Y = S sin

Vy

X = S sin

150,0000

144,79

102,38

-102,38

129,7675

160,54

143,31

-72,36

399,1180

118,68

-1,64

118,67

351,2775

159,70

-110,64

115,17

-1

273,4720

145,95

-133,46

-59,07

-1

+i + V0 + 200

Vx

1245 A
58

179,7650

57

69,3480

59

122,1920
76,5255

1245 A

82151,46 m

46160,46 m

1245 A

82253,85

46058,08

58

82397,17

45985,71

57

82395,54

46104,38

59

82284,91

46219,54

18

82151,46 m

46160,46 m

1245 A

-1

25

152,1570

18

25

25
25
25
150,0000

58

58

[ S ] = 729, 66
n

+ [] 599, 9875
n

+ n 2000 = 600, 0000

= [V ]

[Y ] = 0, 05

+0, 03 = [ X ]

(Yi Yi 1 ) = 0, 00

0, 00 = ( X i X i 1 )

f y = 0, 05

+0, 03 = f y

f = 1 , 25

V =

= 2
f
n

n = 4 , 47
cc

= +25

Vy =

fy
[S ]

Si

fS =

f y + fx = 0, 058 m

Vx =

fx
[S ]

Si

f = (0, 015 [ S ] + 0,10) m = 0,505 m

58.
,
, .. .



,

i Sik
. 58.1

(. 58.1).

, ,
. -
:
1. ( A1 ) .
, . 50,0000g, 100,0000g ..
2. ( A1 ) , i Sik
. , , (57.1).
, . . A1 A1
, . ,
1, 2, 3, A, 1, 2, 3, B (. 58.2).
1, 2, 3 , [ X ] [ Y ]
B (. 58.2).
3. AB
. S AB S AB

S AB , . B AB S AB
. S fS (56.5),
, .

. 58.2

4. S , (. 58.2)
q:
= AB AB = 94,4155g ;
(58.1)
S
q = AB = 0,99998 .
(58.2)

SAB
5.
A1 :
A1 = A1 = 144,4155g .
(58.3)
6. Sik q
Sik :
(58.4)

Sik = q Sik .

7. (. 58.3) ,
A1 , i
Sik . . .
: . ( = 46160,46 m, y = 82151,46 m) . ( = 45626,63 m, y =
82753,46 m). (. 58.1).
18, 17,16, 15 (. 58.1).
58.1

, g


i , g


Sik Sik, m

18

1245 = A
17
18
16
17
15
16
1283 = B

0,0000
197,1845
0,0000
204,5680
0,0000
183,1035
0,0000
247,0835

197,1845

145,94
188,45

17
16
15

204,5680
182,48
183,1035
171,90
247,0835
137,58

58.2

1245 A
18

i,i 1 = i 1 +

Vy

Si,i +1

Y = S sin

50,0000

145,94

103,20

103,20

47,1845

188,45

127,23

139,02

51,7525

182,48

132,54

125,43

34,8560

171,90

89,48

146,77

81,9395

137,58

132,08

38,51

+i + V0 + 200

X = S sin

82151,46m

46160,46 m

1245 A

Vx

197,1845

17

18

204,5680

16

17

183,1035

15
1283

16

247,0835

15

82735,99

[ S ] = 826.35
n

+ [] 881, 9395
n

+ n 2000 = 881, 9395

= [V ]

f = ......

V =

= 2
f
n

n = .....

Vy =

fy
[S ]

Si

[ Y ] = 584, 53

552, 93 = [ X ]

(Yi Yi 1 ) =

= ( X i X i 1 )

fy =

= fy

fs = f y2 + f x2 =

Vx =

fx
[S ]

Si

46713,39

1283 B'

f = ......... [ S ] + 0.10 m = ..........m

58.3

i,i 1 = i 1 +

+i + V0 + 200

Si,i +1

Y = S sin

Vy

X = S sin

1245 A
18

111.83

-93.75

141.6000

149.63

-114.56

146.1680

136.56

-121.04

129.2715

154.05

-76.28

176.3550

49.93

-128.20

204.5680

16

183.1035

15

247.0835

1283 B

[ S ] = 729, 66
n

+ [] 976, 3550
n

+ n 2000 = 976, 3550

= [V ]

f = .......

V =

= 2
f
n

82151.46 m
144.4155
197.1845

17

Vx

n = .....

Vy =

fy
[S ]

Si

[ Y ] = 602, 00

533, 83 = [ X ]

(Yi Yi 1 ) = 602, 00

533, 83 = ( X i X i 1 )

fy =

= fy

fs =

f y + fx = ..........m

Vx =

fx
[S ]

Si

46160.46 m 1245 A

82263.29

46066.71

18

82412.92

45952.15

17

82549.48

45831.11

16

82703.53

45754.83

15

82753.46 m

45626.63 m

1283 B

f = ...... [ S ] + 0.10 m = .......m

59.

, (. 59.1).

. 59.1

,
, , , , ..

, .
:
, , D, . (. 59.1).
, S2,3
, S3, C .
1 , 2 , 3 , C S1,2
1, 2 3.
:
1. . A ,
, .1 .
2. 1 ,2 S A 1 b , (.
59.1).
3. BA S AB (. 59.1).
59.1
A

YA [m]
XA [m]
tg BA
B
BA
Y [m]
X [m]
S = Y /sin
B

YAB [m]

XAB [m]

2
2
+ YAB
SAB= X AB

- 0,635492
5636,02
2375,94
4689,15
3865,92
163,9604g
946,87
- 1489,98
1765,39 m

4. AA1 S A1 :
b sin
S A 1 =
(59.1)
.
sin ( 1 + 2 )
A
B

. 59.2.
59.2

94,71 m
b
67,8695g
1
74,3502g
2
142,2197g
+
1

SA1

105,20 m

SA1
SAB

sin

+
A

AB

AB

SAB = XAB /cos

BA

BA

1765,39 m
1765,39 m

59.3

105,20 m
1765,39 m
84,3675g
0,057803
3,6819g
88,0494g
111,9506g

5. AB1 A :
S
sin = A1 sin ;
(59.2)
S AB
(59.3)

A = 200g ( + ) .

. 59.3.
6. A S A 1 , (57.2),
(. 59.4).

59.4.

i,i 1 = i 1 +
+i + V0 + 200

Si i +1

Y = S sin

Vy

X = S sin

Vx

B
163.9604

111.9605

169.5475

172.1550

242.1525

192.9125

-65
75.9144

105.20

97.76

-2

38.86

45.4554

141.31

92.54

-2

106.79

17.6039

161.51

44.09

-2

155.37

59.7499

129.34

104.34

-2

76.43

-65
-65
-65
-72

5636.02

2375.94

5733.76

2414.81

5826.28

2521.61

5870.35

2669.99

5974.67

2753.43

52.6552
D

[ S ] = 537, 36
n
+ [] 1052, 6884
n

+ n 2000 = 1052, 6552

= [V ]

[ Y ] = 338, 73

377, 45 = [ X ]

(Yi Yi 1 ) = 338, 65

377, 49 = ( X i X i 1 )

f y = +0, 08

0, 04 = f y

f = +3 , 32

V =

= 2
f
n

n = 3 , 35

Vy =

fy
[S ]

Si

fs =

f y + fx = 0, 09 m

Vx =

fx
[S ]

Si

f = 0, 015 [ S ] + 0.10 m = 0, 45 m

60.
,

(. 60.1).
, ,
.
.

,
m
m
g
(60.1) Ai ,k = Ak ,i 200 .

. 60.1

.

,
Aim,k + Akm,i 200g

(60.2)

Aim,k =

(60.3)

Aim,k = Ri,k R

.
2
,
.
, t = 1
. ,
, N m.
(. 60.1).
. Ai,km Ri,k
N m :
Nm

60.1

A 1
2

B 4

Nm
2
Nm
3
A 1
Nm
B 4
2
Nm
3


R
g
20,1050
132,6875
35,6025
182,3575
348,1775
74,5550
220,8500
21,3025
80,3500
26,6525

. 60.2.


Aim
,k = R R

Nm


Ai ,mk

112,5825

112,5788

146,7550
312,5750

146,7462

146,2850
346,7375

146,2938

346,3025

60.2

A 1
2

i,i 1 = i 1 +

Vy

Si,i +1

Y = S sin

82.8164

176.54

170.15

47.08

119.3164

138.52

132.19

-41.39

91.0239

115.33

114.19

16.21

+i + V0 + 200

X = S sin

236.5000

171.7075

B 1

[ S ] = ......
n

+ [] 491, 0239
n

+ n 2000 = 400, 0000

= [V ]

f = = 91, 0239

V =

= 2
f
n

n = ........

Vy =

fy
[S ]

Si

[ Y ] = 416, 53

21, 9 = [ X ]

(Yi Yi 1 ) = 416, 53

21, 9 = ( X i X i 1 )

fy =

= fy

fs =

f y + fx = ..........m

Vx =

fx
[S ]

Si

Vx

3989.96 m

2794.09 m

A 1

4160.11

2841.17

4292.30

2799.78

4406.49 m

2815.99 m

B 4

f = ......

[ S ] + 0,10 m = ....... m

,
.
,
-.

,
N m .

.
,
m
. Ai ,k

. 60.2

i, k (. 60.2):
(60.4)

i, k = Aim, k + ( + ) = Aim, k + ,

;
.

. (+) , ()
N m N 0 .

. ( ) 1
. ( ) .
, - .
= + (60.4).
.
,
Aim,k (. 60.1).
i, k :
(60.5)

= i, k Aim, k .

.
() () ,
(58), .

XVI


61.
, ,
. ,
,
, . -
(13),
- .

61.1.
1
17, 21 40 1 (. 61.1).
. 61.1, . 61.2 (
).

. 61.1

61.1

H ( m)
17
21
40

61.2


L ( km )


h ( m )

1,4
3,940
0,9
2,049
1,1
4,543
h
H , .. H = H + h . p (
) L km:
p = 1/ L .
- , 13.
61.1

L
H
H
p
p
pH
pH

p
(km)

1
2
3

641,388
1
643,265
2
649,874
3
61.1.

645,328
645,314
645,331
H 0 = 645,314

[ pH ] =
[ H]

(mm)

(mm)

(m)

1,4
0,9
1,1

14
0
17

0,71
1,11
0,91
[ p ] = 2, 73

9,94
0
15,47
25, 41 =
[ pH ]

-4,7
9,3
-7,7

-3,34
10,32
-7,01
[ p ] = 0, 03

15,68
96,00
53,95
165, 63 =
[ p ]

-46,76
0
-119,17
165, 93 =
[ pH ]

93

H = 645,323 3

[ p ]
n 1

= 9,1 , mm;

mH =

[ p]

= 5,5 mm.

m0 1 km
, p = 1 L = 1 km.

61.2.
. 61.2 () 6.
. A, B C
, , . 61.3.
,
, : - 6
,
(. 6,7 ), X Y ,
A, B C 6 (57)
( 6,7 X 6 Y6 ).

. 61.2

61.3

A
B
C

X
(m)

Y
(m)

4 704,14
4 744,51
3 861,54

4 315,87
5 610,94
4 736,41

. . . .

[ S ]

[]

[X ]

[Y ]

(g)
164,3784
115,2816
284,3672

(m)
748,72
924,84
515,45

(m)
893,9702
1543,0676
1173,9768

(m)
-443,89
-484,36
398,76

(m)
549,36
-745,62
128,78

:
1.
( A , B C ), ,
S ,
- , 6,7 .
[ ] [ S ] .
. 61.3.
2. 61.2.

= H + [ ] k .200g ,
6,7
(61.1)

k = n, n 2 n + 2 , p , n
:
c
p = ( c = 6 ).
(61.2)
n
-
.

6,7

61.2.

6,7

1
2
3

7
7
5

58,3486
58,3492
58,3440

46
52
0

06,7 = 58,3440

[ p ] =
[ p]

(cc)

(g)

[ p] =

0,86
0,86
1,20

2,92

(cc)

39,56
44,72
0
p ] =
84,28

251,47
458,90
1002,25
p ] =
1712,62

-676,66
-1033,24
0
p ] =
-1709,90

-17,1
-23,1
28,9

-14,71
-19,87
34,68
p ] =
-0,10

289

6,7 = 58, 34689 ,

[ p]
n 1

m =

= 29,3cc ,

[ p]

= 17,1cc .

3. 6,7
. , ,
f . , = f / n,
. ,
X Y [ X ] [ Y ] .
. 61.3.
4. 61.3 61.4 X 6 Y6
. , [ X ] [ X ]
X 6 Y6 6 ,
[ S ] :
c
( c = 1 ).
[ S ]
. 6
.
p=

(61.3)

X 6

61.3.

1
2
3

[ S]

X 6

(km)

(cm)

X
(cm)

0.749
0.925
0.515

4 865.25
4 865.15
4 965.30

10
0
15

X 60 = 4 260,15

[ p X ] =
[ p]

pX

p
1.34
1.08
1.94

[ p ] = 4.36 [

13.4
0
29.1
p X ] =

(cm)
-0.3
9.7
-5.3

pX

0.12
101.62
54.49
p ] =

-4.02
0
-154.23
pX ] =

-0.402
10.476
-10.282
p ] =

42.5

-0.208

156.23

-158.25

97

X 6 = 4 260, 247

[ p ]
n 1

1
2
3

[ p]

= 4, 2 cm.

Y6

61.4.

MX =

= 8,8 cm,

[ S]

Y6

(km)

(cm)

0.749
0.925
0.515

4 865.23
4 865.32
4 865.19
Y60 = 4 865.19

Y
(cm)
4
13
0

p
1.34
1.08
1.94

[ p ] = 4.36 [

pY
5.36
14.04
0
p Y ] =
19.40

(cm)
0.4
-8.6
4.4

pY

0.21
79.88
37.56
p ] =

2.14
-120.74
0
pY ] =

0.535
-9.288
8.536
p ] =
-0.216

117.65

-118.60

[ p Y ] =
[ p]

44

Y6 = 4 865.234

[ p]
n 1

MY =

= 7, 7 cm,

[ p]

= 3, 7 cm,

M 6 = M X2 + MY2 = 4, 22 + 3, 72 = 5, 6 cm.
5. 6
, (57). f X f y ,
fS . ,
.
.

62.
,
.
.
, .

62.1.
1, 2 3
. 62.1. . 62.1,
. 62.2 ( h ,
).
.

. 62.1

- . 1, , 1 2 (
62.1). p = 1/ L km,
H11,2
62.1

5
7
29
30

H (m)
420, 940
494, 165
428, 326
435, 864

62.2

1
2
3
4
5
6
7

L (km)
1,06
1,40
0,84
0,91
1,20
1,05
0,94


h (m)
5,216
2,178
13,958
4,259
32,055
21,984
51,229

p1,2 = p1 + p2 = 1, 65 . 1 2
(1,2)
1
1
L1,2 =
=
= 0, 61 km.
p1,2 1, 65

H36,7 . 3 , 6 7,
p6,7 = p6 + p7 = 2, 01 ( 62.2).
(6,7)
1
1
L6,7 =
=
= 0,50 km.
p6,7 2, 01
62.1
L

(km)

1
2

1,06
1,40

426,156
426,158

8
0

H 0 = 426,148

[ p H ] =
[ p]

pH

(mm)

(m)

0,94
0,71

[ p] = 1,65

(mm)
7,52
0

-3,4
4,6

[ pH ] = 7,52

-3,2
3,3

[ p ] = 0,1

46

H11,2 = 426,1526

62.2

L
6
7

[ p H ]
[ p]

472,181
472,169

12
0

H 0 = 472,169
=

p H

(mm)

(m)

1,00
0,94

(km)

0,95
1,06

[ p ] = 2,01

(mm)
11,4
0

-6,3
5,7

[ pH ] = 11,4

-6,0
6,0

[ p] = 0,0

57

H36,7 = 472,1747

2 (
62.3), : 4 30
(1,2,3)
L1,2,3 = L1,2 + L3 = 0, 61 + 0,84 = 1, 45 km
(5,6,7)
L6,7,5 = L6,7 + L5 = 0,50 + 1, 20 = 1,70 km.
H2 2 :
H11,2,3 = H21,2 + h3 = 440,1106 m,
H24 + h4 = 440,123 m
H26,7,5 = H26,7 h5 = 440,1197 m,
:
p1,2,3 = 1/ L1,2,3 = 1/1, 45 = 0, 69 ,
p4 = 1/ L4 = 1/ 0,91 = 1,10

p6,7,5 = 1/ L6,7,5 = 1/1, 70 = 0,59.


62.3
(km)

. 2

H
H
p
pH
p
(mm)
(mm)
(m)

(1,2,3)

1,45

440,1106

0,69

8,0

5,5

0,91

440,123

124

1,10

13,64

-4,4

-4,8

1,70

440,1197

91

0,59

5,37

-1,1

-0,7

(5,6,7)

H 0 = 440,1106

[ pH ] =
[ p]

[ p ] = 2,38 [ pH ] = 18,51

[ p] = 0,0

80

H2 = 440,1186

2 -
. 2 ,
.
V1,2 (1,2) V1,2,3

V1,2 =

V1,2,3 L1,2
L1,2,3

8,0.0, 61
= 3, 4 mm.
1, 45

H1 1
H1 = H11,2 + V1,2 = 426,1526 + 0, 0034 = 426,1560 m.
H3 3:
V6,7,5 L6,7 1,1.0,5
V6,7 =
=
= 0,3 mm
L6,7,5
1, 70
H3 = H36,7 + V6,7 = 472,1747 0, 0003 = 472,1744 m.
( 62.4)

( H + h ) .
= H Hi = H
(62.1)
[ p ] = 0 . [ p ] = 164, 74
, ,
, m0 1 m
( p )
167, 74
= m0 =
=
= 6, 4 mm.
nk
73
62.4
.

1
1

2
3

L
(km)
1,06


H
= H H
H

(m)
426,1560

1,40
0,84

0,84

4
5

0,91
1,20

1,20

6
7

1,05
0,94

440.1186

472,1744

(mm)
0

(m)
426,156

0,94

426,148
426,1606

8,0
-4,6

0,71
1,19

5,7
-5,5

440.1140

4,6

1,19

5,5

440.123
440.1194

-4,4
-0,8

-1,10
0,83

-4,8
-07

[ p ] =

0,2

[ p ] =

472,1736

0,8

0,83

0,7

472,181
472.169

-6,6
5,4

0,95
1,06

-6,3
5,7

[ p ] =

0,1

62.2.
-
, .

. 62.2

. 62.2, 4 9
:
1. ( )
S
.
, .
4,7 9,10 ( - , ).
, , ,
. [] [ S ] .
2. :
) 1 2 4,7
(62.2)

4,7 = H + [ ] k .200 p =

n ;

1
,
n

p = p1 + p2 .
) , 62.2, 1,2
4,7 1,2
(1,2) n1,2 = 1/ p1,2 ;
) 9,10 9 ,
62.2, , 4 5 (1,2,3),
n1,2,3 = n1,2 + n3 ;
) 1,2,3 (1,2,3) 1,2
(1,2):

1,2 = 1,2,3

n1,2
n1,2,3

4,7 :
4,7 = 1,2
4,7 + 1,2 .
)
[ p ] = 0 ( 62.4);
)
: f ,
.
3.
( 61.2):
)
X Y [ X ] [ Y ] ;
1,2
) , - X 1,2
4 Y4

1 2 p1,2 = p1 + p2 [ S ]1,2 = 1/ p1,2 , p = 1/ [ S ]


;
) X 9 Y9
9 4 5 (1,2,3) [ S ]1,2,3 = [ S ]1,2 + [ S ] 3 .
X
Y
) 1,2
1,2
:
X
X
1,2
= 1,2,3

[ S ]1,2
,
[ S ]1,2,3

Y
Y
1,2
= 1,2,3

[ S ]1,2
,
[ S ]1,2,3

4:
X
X 4 = X 1,2
4 + v1,2 ,

Y
Y4 = Y41,2 + v1,2
.

[ p ] = 0 ;
)
,
61.2.

63.
,
, .
, -
,
. ,
(, ,
, , , .).
:
0,3 2 km, 5,
cc
100g 300g , f = 20 n , n
, - 1/ 35 000,
- 1/20 000,
1:3, 1 2cc .

.

.

, - .
(. 63.1).
63.1 63.2. mR = 10cc ,

mS = ( 10 + 5 Dkm ) mm.
() .

. 63.1

63.1

X (m)
A 31
4 864,324
B 29

(g)
AA = 161,16 48
BB = 52, 62 18

Y (m)
3 184,486

6 116,869

5 253,252

63.2


.
= +

S = S + S

86, 48 26g

16, 4cc

86, 48 096

221, 8416g

5,8cc

221, 84102

179, 36 48g

6,8cc

179, 36548

239, 16 72g

15, 2cc

239, 16872

164, 39 82g

26, 2cc

164, 40 082

S A,1

615, 384 m

2,1 mm

615, 3861

S1,2

726, 359 m

1, 4 mm

726, 3576

S2,3

480, 684 m

1, 6 mm

480, 6856

= f = 26cc

679, 8391
3,9 mm
1. r . t = 3 ,
n = t + 2 , nS = t + 1
S3,B

679, 843 m

n = n + nS = 2t + 3 , k = 2t . ,

r = n k = 3 .
2. . ,
, , :

H + A + 1 + 2 + 3 + B KP + k .200g = 0,
(63.1)

X A + X A,1 + X1,2 + X 2,3 + X 3, B X B = 0,


YA + YA,1 + Y1,2 + Y2,3 + Y3, B YB = 0.
3. . :

X i, k = Si, k cos i,k ,


Yi, k = Si, k sin i,k ,

(63.2)

i ,k = H + A + 1 + .... + i K .200g ,

i = i + i Si,k = Si,k + Si,k


,
:

(63.3)

a)

A + 1 + 2 + 3 + B + f = 0;

b)

( YB YA ) + ( YB Y1) + ( YB Y2 ) + ( YB Y3 )
A
1
2
3

+
cc
S + cos 2,3
S + cos 3,
B S + f X = 0;
+ cos A,1S + cos 1,2
A,1

1,2

2,3

3, B

( X X ) + ( X X ) + ( X X ) + ( X X )
A A
B
1 1
B
2 2
B
3 3
B
c)
+ sin A,1S

A,1

S
+ sin 1,2

1,2

cc
S
+ sin 2,3

2,3

B S
+ sin 3,

3, B

+ fY = 0.

( 63.1) i
i , X i ,k Yi,k
i Si, k (63.2),

f , f X fY .

ai , bi
ci . :
i : ai = 1 ,

bi = ( YB Yi ) / cc

ci = ( X B X i ) / cc .

a =0
Si ,k : i
, bi = cos i,k
ci = sin i, k .
,
63.1.
63.3 V ,
a, b c B ( r , n ), f ,
(63.3)
BV + f = 0 .
(63.4)
4. . f , f X fY
63.1. B B a, b c
. 63.3.
, ,
. mR = 10cc ,
cc
2
m = mR 2 = 14 . p = c / m pS = c / mS2 .
2
c = m , p = 1 . . 63.3 mS ,

.
c = m2

63.3
B*

ai
1,00

bi = ( YB Yi ) / pcc

ci = ( X B X i ) / pcc

biS

ciS

= cos i,i +1
-3,25

= sin i,i +1
1,97

m (cc)

P = c / m2

mS (mm)

PS = c / mS2

14

1,00

1,00

-2,59

1,26

14

1,00

1,00

-1,58

0,74

14

1,00

1,00

-1,05

0,20

14

1,00

1,00

14

1,00

A1

0,72

0,60

13

1,16

0,46

0,89

14

1,00

23

0,72

0,70

12

1,36

3B

0,18

0,98

13

1,16

1
2

12

63.1

(g)

A 25
A 31

(g)
161, 36 48

S (m)

47, 84 74

615,384

420,183

449, 604

69, 68 90

726,359

645,572

332, 918

49, 05 38

480,684

334,806

344, 909

88, 22 10

679,843

668,239

125, 071

Y (m)

X (m)

86, 48 26
1

221, 84 16

179, 36 48

239,16 72

B 29

164, 39 82
52, 61 92

B 23

(52, 62 18)
+ [] = 1058, 6192

( + n.200) = 2052, 6218


f = 26cc
f = 20cc
f< f

[ S ] = 2502, 270 [ Y ] = 2068, 800


(Y Y ) = 2068, 766

fY = 0, 034

n = 45cc

0, 043 = f X

fS /[ S ] = 1/ 45 500 ;

X (m)

3 184, 486

4 864, 324

A 25
A 31

3 604, 669

5 313, 928

4 250, 241

5 646, 846

4 585, 047

5 991, 755

5 253, 286
(5 253, 252)

6 116, 826
(6 116, 869)

Y (m)

1252, 502 = [ X ]
1252, 545 = ( X
fS =

X )

2
2
f X + fY = 0, 055 mm

( fS /[ S ]) = 1/ 20 000 ;
fS /[ S ] < ( fS /[ S ])

B 29
B 23

63.2
.

.
.
(g)

Y (m)
X (m)
Y (m)
X (m)
(g)
S (m)
A 25
161,36 480
A 31
1

86, 48096
221,84102

179,36548

239,16872

B 29

164, 40 082

B 23
f = 0cc
0

47,84576

615,3861

420,173

449, 617

69, 68678

756,3576

645,559

332,940

49, 05 226

480, 6856

334,799

344,918

88, 22 098

679,8391

52, 62180

(52, 62 18)

668,235

A 25

3 184, 486

4 864, 324

A 31

3 604, 659

5 313, 941

4 250, 218

5 646, 881

4 585, 017

5 991, 799

5 253, 252

6 116, 869

B 29

125,070

(.)

B 23

()
fY = 0, 000 m

f X = 0, 000 m.

5. X 2 Y2 ,
. 2 - .
mF F [1], [50], X 2 Y2 ,

1
mF =
= QF ,
(63.5)
pF

a
b
p .1
p

QF =

aa
bb
p
p
p .1

(63.6)

c
p .2
,

cc
p .2

S F , X 2 Y2 ,
:
X 2 = X A + X A,1 + X1,2 ,
(63.7)
Y2 = YA + YA,1 + Y1,2 .
. ,
(63.1), :
( Y2 YA ) A + ( Y2 Y1) 1
S ;
X 2 = X 2
+ cos A,1S + cos 1,2
A,1
1,2
cc
Y2 = Y2 +

( X 2 X A ) A + ( X 2 X1 ) 1
cc

+ sin A,1S

A,1

S
+ sin 1,2

1,2

X Y X 2 Y2
S . S . 63.3,
.
X X 2 :
X = 1, 67,
A

X = 1, 01,

SX

A,1

= 0, 73 SX = 0, 46 .
1,2

Y Y2 :
Y = 1, 23,
A

Y = 0,52,
1

YS

A,1

= 0, 68 YS = 0,89 .
1,2

.
6. . -
. 63.4, B* ,
X Y , s 1/p S .

63.4.
*

PV
. = B* .K

1,00

-3,25

1,97

-1,67

1,23

-0,72

1,00

-16,42

cc
mm
-16,42

1,00

-2,59

1,26

-1,01

0,52

-0,82

1,00

-5,80

-5,80

1,00

-1,58

0,74

0,16

1,00

6,85

6,85

1,00

-1,05

0,20

0,15

1,00

15,18

15,18

1,00

1,00

1,00

26,18

26,18

0,73

0,68

0,73

0,68

2,82

0,86

2,45

2,45

0,46

0,89

0,46

0,89

2,70

1,00

-1,38

-1,38

0,72

0,70

1,42

0,73

2,23

1,63

1
2

A1

12
23

0,18

0,98

1,16

5,00

-6,38

7,42

-1,49

3,32

7,87

3B

0,86

-4,55

-3,91

[ p ] = 1294, 503

7,87

(63.4) -
[1], [45] K : N K + f = 0 , N = B P1 B*
.
N , B P1X , B P1Y S = B P1s ,
. 63.5.
63.5
N = B P1B*
K1

K2

K3

5,00

-8,47
21,95

4,17
-9,69
8,43

B P1X

B P1Y

-2,68
8,71
-3,73

1,75
-4,51
4,27

S = B P1s

-0,23
-0,23
7,99
7,99
3,45
3,45
X X
Y Y
=

4,48
2,97
p
p
7. .
- [1], [50] . 63.6 63.7, K ,
Q = N 1 .
: K = Q F , [ p ] = f .3 = 1294,526 (
f N R ) = K f = 1294, 488 (
).
8. (. 63.4).
* . 63.4 K
B
p = B* K ,

[ p ] = 1294,503 ,

[ p ] = f .3 = K f .
63.6.

K1
5,00

N
K2
8,47
21,95

.
K3
4,17
-9,69
8,43

NR
5,000 -8,470 4,170
7,602 -2,626
4,046

NK+ f =0

BP1X

BP1Y

-26
-43
34

-2,68
8,71
-3,73
4,48

1,75
-4,51
4,27
2,97

-26,23
-35,01
37,45
-

-26,23
-35,01
37,45
-

1/ NiiR


-26,000
-87,044
25,654

[ p] = f .3 = -1294,526

-2,680
4,170
-0,056

1,750
-1,546
2,277

-0,00
0,02
-0,04

-26,230 -26,230
-79,444 -79,444
31,918 31,921

-0,2000
-0,1315
-0,2472

0,758 = 1/ pX 2 0,762 = 1/ pY2

63.7.

E

1,000

1,000

5,246
10,450
-7,889

5,246
10,450
-7,890

1,000
1,000
1,000

NE
-1,000


1,694
-1,000

-0,834
0,345
-1,000

5,200
11,450
-6,341

0,536
-0,548
0,014

-0,350
0,203
-0,563

K1

K2

K3

1,000

26,178

9,262

-6,341

1/ NiiR

0,594

0,202

-0,062

0,202

0,161

-0,062

0,085
Q

V PV = K f

K = Q f

0,200

-26

26,238

0,085

0,132

-43

9,285

K f = - 1294, 488

0,247

0,247

34

6,355

f .3 = -1294,526

9. . .
63.2.
10. . . 63.2
( 63.2). f , fY
f X , , (63.1)
, ..
11. . m ,
1,
[ p ]
1294,50
= m =
=
= 20,8cc ,
r
3
2:
1
mX =
= 20,8 0, 758 = 18,1 mm,
2
pX
2

mY =
2

1
= 20,8 0, 762 = 18, 2 mm
pY
2

M 2 = m2X + mY2 =
2

1
1
+
= 25, 6 mm.
pX
pY
2

( 1/ pX 2 1/ pY2 X Y ).

Q :

1
= P1 BP1 Q BP1
(63.8)
pF

) (

a b
a c
1 a
= Q11 2 Q12 2 Q13
PF p p
p p
p p
2

b
b c
c
Q22 Q23 Q33 .
p
p p
p
1
= 4, 48 2, 682.0,594 + 2. ( 2, 68 ) .8, 71.0, 202 + 2. ( 2, 68 ) . ( 3, 73) . ( 0, 062 ) +

pX
2

+8, 712.0,161 + 2.8, 71. ( 3, 73) .0, 085 + 3, 732.0, 247 = 0, 756

1
= 2,97 1, 752.0,594 + 2.1, 75. ( 4,51) .0, 202 + 2.1, 75.4, 27. ( 0, 062 ) +

pY
2

+ 4,512.0,161 + 2. ( 4,51) .4, 27.0, 085 + 4, 272.0, 247 = 0, 762.

( B P X Y . 63.5).

64. -
I, II, III IV
. ,
.

1:10 000, , [19].


, ,
. - -
. , ,
, , .
( )
.
- 3 , 5
, 1 2,
, - 1:35 000. .
: ,
(ppm), ,
.
w .

(64.1)

[ ww ]

,
6n
n .
: 15 V 20 VI .

0,10 m V 0,07 m VI .
mR =

. 64.1

47 48 (. 64.1)
, 4 : 2315, 2319, 2341 2343.
64.1, 64.2.
mR = 10cc , ms = ( 5 + 5 Skm ) mm.
.
64.1
..
X (m)
Y (m)
2315
2319
2341
2343

649,81
6471,85
4403,60
4365,90

7746,35
4951,47
7231,09
5016,31

1.
, .
X Y ( t ), -
, O

( s ), .
, k = 2t + s = 2.2 + 5 = 9 . nR = 20 ,
nS = 6 ( ,
mS / 2 ), n = nR + nS = 20 + 6 = 26 .
r = n k = 17 .
64.2

2319

2315
47
48
2343

R
g c cc
0, 00 00
36, 37 16
72, 74 84
102, 08 77

2341

2343
47
2315

0, 00 00
69, 29 97
115, 44 08

1308,009
-

11,5
-

2343

2319
48
2315
47
2341

0, 00 00
28, 90 44
57, 60 97
61, 13 05
100, 87 82

1182,352
1982,421
-

10,9
4,9
-

47

2315
2341
2343
48
2319

0,0000
116, 97 48
207, 92 90
242, 54 22
281, 08 24

1307,995
1108,151
-

11,5
10,5
-

2319
47
2343

0,0000
125,0840
258,2437

1166,055
1108,161
-

10,8
10,5
-

48

.
.

ms


S (m)

(m)

1892,039
1166,042
-

14,5
10,8
-

Scp = ( Sik + Ski ) / 2 mcp = mS / 2


(m)

(mm)

1308,0020

8,1

1108,1560

7,4

1166,0485

7,6

2. . R S i
X , Y O :
Y
Rik = ik Oi = arctg ik Oi ,
(64.2)
Xiu
(64.3)

Sik =

( X k Xi ) 2 + ( Yu Yi ) 2 .

3. .
, ..
(64.4)
X = X 0 + x , Y = Y 0 = y , O = O0 + O ,
:
R = R + R S = S + S .
(64.5)
R S
:
(64.6)

ikR = Oi + aikR xi + bikR yi aikR xk bikR yk + fikR ,


S
ik
= aikS xi + bikS yi aikS xk bikS yk + fikS ,

(64.7)

0
aikR = sin ik
/ Sik0 ,
0
aikS = cos ik
,

0
bikR = cos ik
/ Sik0 ,
0
bikS = sin ik
,

0
, ik
= Rik + Oi0 ;
fikR = ik
ik

fikS = Sik0 Siki .

i k , x y .
4. ( 64.1).
- .
,

. ,
. R ,
O = R ,
Ocp , = R + Ocp , = .
25, 30 40 3, 2 1 km.
5. . ,
(

64.2), 2343,48
47,2341
.
-, .
,
.
6. S
R
R
a , b , aS , bS ( 64.3).

47 48
Y Y
i ,k = arctg k i ,
(64.8)
X k Xi
a

b . (64.7), , S mm,
/ S = 636620cc / Smm = 0, 6366 / Skm . a R = bR tg .

.
ik
Rik
Oi = ik Rik

g c cc
g c cc
g
c cc

2315
47
48
2343

95,9519
198,0405

2343
47
2315

298,9164
14, 35 51

2319
48
2315
47
2341

398,0405
55,6496
98,9164

64.1.

ik = ik ik

= Rik + Oicp
ik
g

cc

.. 2319
X = 6471,85 m, Y = 4951,47 m
0,0000
95,9519
95,95235
36,3716
132,32395
72,7484
168,70075
102,0877
95,9528
198,04005
[ ] = 0,0
Ocp = 95,9523
5
.. 2341
X = 4403,60 m, Y = 7231,09m
0,0000
298,9164
298,91535
62,2997
368,21505
115,4408
298,9143
14,35615
Ocp = 298,91535
[ ] = 0,0
.. 2343
X = 4365,90 m, Y = 5016,31 m
0,0000
398,0405
398,03953
28,9044
26,94393
57,6097
398,0399
55,64923
61,1305
59,17003
100,8782
398,0382
98,91773
Ocp = 398,03953

-4,5
4,5

10,5
-10,5

9,7
3,7
-13,3
[ ] = 0,1


Y
X
S
(g)
(m)
(m)
(g)
(m)
2343
48

266,8403

47

274,4326

26,9439

1182,352

485,605

1078,028

93,7842

1008,156

1102,878

108,026

168,2150

1308,002

626,260

-1148,332

(168,2150)
2341

64.2.

Y
(m)

X
(m)

5016,310

4365,900

2343

5501,915

5443,928

48

6604,793

5551,954

47

(7231,053)
7231,090

(4403,622)
4403,600

2341

7. f R ( 64.4).
, , R ,
( 64.3),
O = R , Ocp , = R + Ocp
R
f R = . f = 0 .
8. . . 64.3
O, x y
f . mR mS ,
p = c / m2 p = c / m2 , c = m2 . Scp
R

mS

cp

mS
2

64.3.

k
Yk
Xk
tgik
0
aR
i

2315
47
2341
47
2343
47
48
47
2319
47
2319
48
2343
48

Yi

Xi

Yik

Xik

S
aki
bkiS

7746,350
6604,793
1141,557
7231,090
6604,793
626,297
5016,310
6604,793
-1588,483
5501,915
6604,793
-1102,878
4951,470
6604,793
-1653,323
4951,470
5501,915
-550,445
5016,310
5501,915
-485,605

6649,810
5551,954
1097,856
4403,600
5551,954
-1148,354
4365,900
5551,954
-1186,054
5443,928
5551,954
-108,026
6471,850
5551,954
919,896
6471,850
5443,928
1027,922
4365,900
5443,928
-1078,028

1,0398058
0,720768
0,6931760
-0,5453867
0,4788062
-0,8779206
1,3393007
-0,801283
-0,598285
10,2093755
-0,9952372
-0,0974826
-1,7972934
-0,8738467
0,4862015
-0,5354930
-0,4720698
0,8815612
0,4504568
-0,4107110
-0,9117656

ik
Sik0

ik
bikR
0

Sik

fikS = S S (mm)

51,24217
1583,8056
168,21393
1308,0385
1308,0020
259,16982
1982,4233
1982,421
293,78419
1108,1559
1108,1560
332,32358
1892,0057
1892,039
368,70140
1166,0246
1166,0485
226,94389
1182,3521
1182,352

0,2897
-0,2786
0,2330
0,4273
36,5
-0,2573
-0,1921
2,3
-0,5717
0,0560
-0,1
-0,2940
-0,1636
-33,3
-0,2578
-0,4813
-23,9
-0,2211
0,4909
0,1

64.4.
f

. . .
0
O0 = 0 R = R + Ocp

f R = 0

O = R

V R = O Ocp

R
g
2319

2315
47
48
2343

c
cc
0.0000
36.3716
72.7484
102.0877

c
cc
95.9519
132.3236
168.7014
198.0405

Ocp =
2341

2343
47
2315

0.0000
69.2997
115.4408

298.9164
368.2139
14.3551

Ocp =
2343

2319
48
2315
47
2341

0.0000
28.9044
57.6097
61.1305
100.8782

398.0405
26.9439
55.6496
59.1698
98.9164

Ocp =

c
cc
95.9519
95.9520
95.9530
95.9528
95.95242
298.9164
298.9142
298.9143
298.91497
398.0405
398.0395
398.0399
398.0393
398.0382
398.03948

c
cc
99.95242
132.32402
168.70082
198.04012

[ f R]=
298.91497
368.21467
14.35577

[ f R]=
398.03948
26.94388
55.64918
59.16998
98.91768

[ f R]=

cc
-5.2
-4.2
5.8
3.8
0.2
14.3
-7.7
-6.7
-0.1
10.2
0.2
4.2
-1.8
-12.8
0.0

c
cc
95.9519
132.3238
168.7007
198.0405

Ocp =
298.9164
368.2146
14.3551

Ocp =
398.0405
26.9453
55.6496
59.1708
98.9164

Ocp =

c
cc
95.9519
95.9522
95.9523
95.9528

cc
-4.0
-1.0
0.0
5.0

95.95230

0.0

298.9164
298.9149
298.9143

12.0
-3.0
-9.0

298.91520

0.0

398.0405
398.0409
398.0399
398.0403
398.0382

5.4
9.4
-0.6
3.4
-17.6

398.03996

0.0

64.4

. . .
0
O0 = 0 R = R + Ocp

f R = 0

O = R

V R = O Ocp

R
g

47

2315
2341
2343
48
2319

cc

0.0000
116.9748
207.9290
242.5422
281.0824

cc

51.2422
168.2139
259.1698
293.7842
332.3236
Ocp =

48

2319
47
2343

0.0000
125.0840
258.2437

cc

51.2422
51.2391
51.2408
51.2420
51.2412

368.7014
93.7842
226.9439

[ f R]=
368.70060
93.78460
226.94430
[ f R]=

368.70060

cc

51.24106
168.21586
259.17006
293.78326
332.32346

51.24 106
368.7014
368.7002
368.7002

Ocp =

0
fik = ik
Rik + Oi0

cc

11.4
-19.6
-2.6
9.4
1.4
0.0
8.0
-4.0
-4.0
0.0

cc

51.2409
168.2146
259.1708
293.7846
332.3238
Ocp =
368.7007
93.7846
226.9453
Ocp =

cc

cc

51.2409
51.2398
51.2418
51.2424
51.2414

-3.6
-14.6
5.4
11.4
1.4

51.24126

0.0

368.7007
368.7006
368.7016

-2.7
-3.7
6.3

368.70097

-0.1

64.3.
.
. -

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

64.3
.
. -

21
22
23
24

V=

VS

. .

2319

2315
47
48
2343
2343
47
2315
2319
48
2315
47
2341
2315
2341
2343
48
2319
2319
47
2343

2341

2343

47

48

V=

2319

2341

. .

47

2341
2343
48
2319

47

48

4
x

-1
-1
-1
-1

7
y

4
x

8
y

-0,294 -0,164

-1
-1
-1

0,233
-1
-1
-1
-1
-1

-0,257
-1
-1
-1
-1
-1

-0,518

-0,258

-0,481

-0,221

0,491

0,518

-0,056

-0,258
0,518
-0,221

-0,481
-0,056
0,491

0,427

0,192

0,290 -0,279
0,233 0,427
-0,257 0,192
-0,518 0,056
-0,294 -0,164
-1
-1
-1

0,056

f
cc/mm

-5,2
-4,2
5,8
3,8
14,3
-7,7
-6,7
10,2
0,2
4,2
-1,8
-12,8
11,4
-19,6
-2,6
9,4
1,4
8,0
-4,0
-4,0

-5,200
-4,658
5,061
3,800
14,300
-7,040
-6,700
10,200
0,470
4,200
-1,865
-12,800
11,411
-18,940
-2,665
9,400
0,942
7,261
-4,000
-3,730

VR
VS

2343
O

mR

2319

2341

2343
O

48

4
x

7
y

0,878 -0,479
0,598 0,801
0,097 0,995
-0,486 0,874

4
x

-0,097

(mm)
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10

P
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000
1,000

mR

47

(cc)
mS

8
y

-0,995

f
cc/mm

36,5
2,3
-0,1
-33,3

36,899
3,699
-0,100
-32,912

(cc)
mS
(mm)
8,1
14,9
7,4
14,5

P
1,524
0,450
1,826
0,476

25
26

48
2319
2341
2343
47
48

2319
2343
-0,294 -0,164
0,233 0,427
-0,257 0,192
-0,546 0,232
-0,518 0,056

-1,677

3,677

-0,882
0,912
-0,258

0,472
0,411
-0,481

-0,221
0,518
0,039

0,491
-0,056
-0,046

-23,9
0,1
0,2
-0,1
0
0
0

0,089

-0,296

-18,2

-24,310
1,423
-0,997
0,560
0,205
0,148
-0,469
-16,407
-16,407

7,6
10,9

1,731
0,842
-1/4
-1/3
-1/5
-1/5
-1/3

64.6.
.
.
( i)

V (cc)
VS (mm)

f S (mm)

VS = VS + fS (mm)

VS = VS + fS (mm)

V R = (cc)
V S = S S (mm)

2319

2315
47
48
2343

1.8
-6.9
-

-5.2
-4.2
5.8
3.8

-5.2
-2.4
-1.1
3.8
O = -1.2

-4.0
-1.2
0.1
5.0
[ V ] = -0.1

1.000
1.000
1.000
1.000

-4.0
-1.0
0.0
5.0
0.0

2341

2343
47
2315

6.2
-

14.3
-7.7
-6.7

14.3
-1.5
-6.7
O = 2.0

12.3
-3.5
-8.7
[ V ] = 0.1

1.000
1.000
1.000

12.0
-3.0
-9.0
0.0

2343

2319
48
2315
47
2341

13.7
10.2
-

10.2
0.2
4.2
-1.8
-12.8

2315
2341
2343
48
2319

-13.1
6.2
10.2
3.7
1.8

11.4
-19.6
-2.6
9.4
1.4

5.4
9.1
-0.6
3.6
-17.6
[V ] = -0.1
-3.5
-15.2
5.8
11.3
1.4
[V ] = -0.2

1.000
1.000
1.000
1.000
1.000

47

10.2
13.9
4.2
8.4
-12.8
O = 4.8
-1.7
-13.4
7.6
13.1
3.2
O = 1.8

5.4
9.4
-0.6
3.4
-17.6
0.0
-3.6
-14.6
5.4
11.4
1.4
0.0

. -
( k)

V (cc)

f (cc)

VR = V + fR (cc)

VR = VR O (cc)

VS (mm)

f S (mm)

VS = VS + fS (mm)

VS = VS + fS (mm)

-6.9
3.7
13.7

8.0
-4.0
-4.0

1.1
-0.3
9.7

-2.4
-3.8
6.2

.
.
( i)
R

. -
( k)

.
VR = V + fR (cc)
VR = VR O (cc)
f R (cc)

48

2319
47
2343

1.000
1.000
1.000
1.000
1.000

64.4
V = (cc)
R

P
1.000
1.000
1.000

V S = S S (mm)
-2.7
-3.7
6.3

O = 3.5
47
S
48

2341
2343
48
2319
2319
2343

-30.4
8.3
3.3
32.5
22.5
-3.7

36.5
2.3
-0.1
-33.3
-23.9
0.1

6.1
10.6
3.2
-0.8
-1.4
-3.6
[pvv]=1322.528

[ V ] = 0.0
6.1
10.6
3.2
-0.8
-1.4
-3.6

-0.1
1.524
0.450
1.826
0.476
1.731
0.842

6.2
10.6
3.2
-0.8
-1.4
-3.6

9. O
. O ,
-1, i ,
x y f
, p = 1/ ni , ni .
. 64.3. .
,

p = pik + pki , .
10. .

V = A X + f , P ,
(64.9)
V V R V S , X x y 47
48.
64.4.

.
N

x1

y1

x2

y2

:
NX + F = 0

2.298

-0.394
3.299

-0.521
-0.145
2.751

-0.142
-1.849
-0.259
3.179

53.269
-54.750
36.673
-28.093

54.510
-53.838
38.499
-27.164

54.510
-53.838
38.499
-27.164

0.003
0.006
-0.006
-0.016

f pf =
NR
2.298

-0.394
3.231

-0.521
-0.234
2.616

-0.142
-1.873
-0.427
2.015

4946.769 4953.869

4953.869

FR

SR

53.269
-45.614
45.446
-43.827

54.510
-44.490
47.635
-41.812

54.510
-44.490
47.635
-41.812

f pf . 4 = 1325.245 1325.245

I
NiiR

-0.43516
-0.30950
-0.38228
-0.49628

64.5.

f

E
1.000
1.000
1.000
1.000

1.000

N
-1.0000

0.1715
-1.0000

47

FE

0.2267
0.0724
-1.0000

0.0618
0.5797
0.1632
-1.0000
48

-23.7206 -23.7206
13.7697
13.7697
-18.2091 -18.2091
20.7504 20.7504

1.0000

X -20.5581 25.7256 -13.8226 21.7504


Q

-23.1806
14.1176
-17.3723
21.7504

SE

X = QF

1/ Nii

0.4861
0.1185

0.1185
0.4852

0.1076
0.0756

0.0994
0.2936

0.4352
0.3095

53.269
-54.750

-20.5598
25.7279

0.1076
0.0994

0.0756
0.2936

0.3955
0.0810

0.0810
0.4963

0.3823
0.4963

36.673
-28.093

-13.8213
21.7517

f pf =

4946.769

1.000

X * F + f * Pf =
= V PV

1325.233

- [ p] = min

NX + F = 0 ,
(64.10)

N = A PA , a F = A Pf .
64.4 ( ) 64.5
( ). X , Q , ,
X = QF . f Pf 4 = 1325, 245 = X F + f Pf = 1325, 233 = [ p] .
:
0
X 47 = X 47
+ x47 = 5551,954 0, 0206 = 5551,9334 m ,
0
Y47 = Y47
+ y47 = 6604, 793 + 0, 0257 = 6604,8187 m,
0
X 48 = X 48
+ x48 = 5443,928 0, 0138 = 5443,9142 m,
0
Y48 = Y48
+ y48 = 5501,915 + 0, 0218 = 5501,9368 m.

11. . X . 64.3
V = AX + F . 64.6 .
) ik :
(64.11)

ik = aikR xi + bikR yi aikR xk bikR yk ;

:
) ik
(64.12)

= ik + fikR ;
ik

) Oi :
(64.13)


Oi = ik ;
ni

) R :
R
Oi , [ ] i = 0 .
(64.14)
ik
= ik
) S :
S = AS X + f S .
[ p] = 1322,528,
(. 64.4 64.5).
64.5.

(64.15)

Yk

Xk

ik (g)

Sik (m)

Yi

Yik
2315
47

7746.350
6604.8187
1141.5313
7231.090
6604.8187
626.2713
5016.310
6604.8187
-1588.5087
5501.9368
6604.8187
-1102.8819
4951.470
6604.8187
-1653.3487
4951.470
5501.9368
-550.4668
5016.310
5501.9368
-485.6268

2341
47
2343
47
48
47
3219
47
2319
48
2343
48

Xi

(g)
ik

Sik (m)

Xik

V ik (cc)

VS (mm)

6649.810
5551.9334
1097.8766
4403.600
5551.9334
-1148.3334
4365.900
5551.9334
1186.0334
5443.9142
5551.9334
-108.0192
6471.850
5551.9334
919.9166
6471.850
5443.9142
1027.9358
4365.900
5443.9142
-1078.0142

51.24086
51.24 217
-13.1
168.21455
168.21393
6.2
259.17084
259.16982
10.2
293.78460
293.78419
4.1
332.32376
332.32358
1.8
368.70071
368.70140
-6.9
226.94527
226.94389
13.8

1583.8014

1308.0082
1308.0020
6.2
1982.4316
1982.4210
10.6
1108.1591
1108.1560
3.2
1892.0382
1892.0390
-0.8
1166.0470
1166.0485
-1.5
1182.3485
1182.3520
-3.5

12. . 47 48
S 64.5. = ,
R R = R [ R] / ni ( 64.4),
S = S S . ,
( . 64.6). .
13. . 1
mR :

[ p ]

1322,53
= 8,8cc .
nk
17
:
mx = Q11 = 8,8 0, 486 = 6,1 mm,
= mR =

47

my

47

= Q22 = 8,8 0, 485 = 6,1 mm,

M47 = Q11 + Q22 = 8,8 0,971 = 8, 7 mm.


mx

48

my

48

= Q33 = 8,8 0,396 = 5,5 mm,


= Q44 = 8,8 0, 496 = 6, 2 mm,

M48 = Q33 + Q44 = 8,8 0,892 = 8, 3 mm.

65.

. , ()
, , ,
.
.
,
( , , .)
:
1. ;
2. ;
3. .
( ) - 2,
.
:
1. .

2. .

1.
,
.
.
:
x, y xy ;
X , Y XY ;
X , Y xy XY ;
X 0 , Y0 XY;
[ X ] ; Y = [Y] ,
(65.1.1)
X0 =
0
n
n
x0 , y0 xy ;
[ x] ; y = [ y ] ,
(65.1.2)
x0 =
0
n
n
n ; a, b
xy XY ;
;
m .
a, b, m .
XY
X , Y
(65.1.3)

(65.1.4)

2 + 2 = min,
x y
x = X X ,

y = Y Y .
(65.1.5)
:
a = X 0 x0 ;
b = Y0 y0 ;
(65.1.6)
p
p
1+ q
tg =
; m=
=
.
(65.1.7)
q +1
sin cos
p q :
[x y ] [yx ]
p = m sin =
;
(65.1.8)
[x2 ] + [y2 ]
(65.1.9)

q = m cos 1 =

(65.1.10)

xI = xI x0 ;

(65.1.11)

X I = X I X 0 ;

[y y ] + [x x ]
[x 2 ] + [y 2 ]

yI = yI y0 ;
YI = YI Y0 ;

x = X I xI ;
y = YI yI .
(65.1.12)
:
X I = xI + a ( yI y0 ) p + ( xI x0 ) q,
(65.1.13)
YI ' = yI + b + ( xI x0 ) p + ( yI y0 ) q .
(65.1.14)
:
A = a + y0 p x0 q ; B = b x0 p y0 q,
(65.1.15)
(65.13, 65.14) :
X I = xI yI p + xI q + A,
(65.1.16)
YI = yI + xI p + yI q + B,
(65.1.17)
I = 1, 2, 3, K k .
:

[ x x ]

(65.1.18)

MX =

(65.1.19)

M S = M X2 + MY2 =

(65.1.20)

m=

MY =

[ y y ]
n

[ x x ] + [ y y ]

.
n



DiXY
,k
Dixy
,k

(65.1.7).
65.1.1 65.1.2.
:
[ X ] = [ x] [ y ] p + [ x]q + kA ;
(65.1.21)
[ Y ] = [ y ] + [ x] p + [ y ]q + kB .
,
.
, .

65.1.1.

, -, ,
[m]
[m]
[m]
y
x
X
Y
X
Y

515 92352,439
560 84759,620
1244 88697,044
255809,103
x0 =

20359,231
17042,702
17379,409
54781,342

[ x]
n

y0 =

84778,635
85622,843
86502,430
256903,908
[ y]
n

26014,364
17771,625
21624,425
65410,414

X0 =

[X ]
n

84778,635
85622,840
86502,433

Y0 =

[Y ]
n

26014,360
17771,621
21624,433

mm
y
x
0
+3
-3
0

+4
+4
-8
0

x
y

18800901,493

88603,034

18260,447

85634,636

21803,471

y x

-15013422,848

xi = xI x0

yI = yI y0

X i = X I X 0

YI = YI Y0

[x y ] [ y x ] = I

+33814324,34

515

+3749,405

+2098,784

-856,001

+4210,893

x x

-31921294,636

560

-3843,414

-1217,745

-11,793

-4031,846

y
y

+7241236,369

1244

+94,010

-881,038

+877,794

-179,046

[y y ] [X x ] = II

-24680058,267

0,001

0,001

0,000

0,001

x2

+28838706,90

y 2

+6664025,120

+3543,024

[x2 ] + [y 2 ] = III

+35502732,02

p = I / III

+0,95244288

-68152,382

q = II / III

-0,69515941

= 80,2802g

m = 1,000038

x = X i xI

y = YI yI

515

-4605,406

+2112,109

-2968,398

560

+3831,621

-2814,101

1244

+773,784

+701,992

-0,001

p
tg =
3,124396
q +1

0,000

Mx =

[ x x ]
n

= 0, 2 cm; M y =

M s = M X2 + MY2 =

[ y y ]
n

[ x x ] + [ y y ]
n

= 0, 6 cm;

= 0, 6 cm

515,560
D XY
Dxy = 8285,546 m;
D XY = 8285,857 m;
m=
xy

= 1, 000038

65.1.2.



a = 2968,398; p = 0,95244288
A = a + y0 p x0 q = +76016,868
b = 3543, 024; q = 0, 69515941
B = b x p y q = 68152,383
0

X I = xI yI p + xI q + A;
YI = yI + xI p + yI q + B

515
1
2
3
4
5
6
7
8
9
10

y
x
X
Y
92352,439
20359,231
84778,635
26014,360
85000,000
18000,000
84784,346
18292,392
85832,860
18000,000
85038,235
19085,644
85921,088
18971,457
84139,874
19465,815
85000,544
18969,271
83861,337
18588,384
85920,204
17364,628
85670,017
18975,147
86853,689
17650,354
85682,443
19951,339
86973,205
18957,166
84474,213
20463,540
87982,206
19120,383
84626,342
21474,311
87447,424
18177,309
85861,543
20677,475
87829,343
17420,000
86199,260
20810,372
957121,002
202989,800
934618,685
223806,398
5,6
DY
Dxy = 976, 234 m;
D XY = 976, 271 m;
m=
= 1, 000038
D xy

[ X ] = [ x] [ y ] p + [ x]q + kA = 934618, 689;
[Y ] = [ y ] + [ x] p + [ y ]q + kB = 223806, 401

2.

- .
:
X i = a0 + a1 xi + a2 yi ;
(65.2.1)
Yi = b0 + b1 xi + b2 yi .
(65.2.2)
a0 , a1 , a2 , b0 , b1 , b2 :
a0 = X 0 a1 x0 a2 y0 ;
(65.2.3)
b0 = Y0 b1 x0 b2 y0 .
(65.2.4)
X 0 , Y0 , x0 , y0 (65.1.1) (65.1.2).
(65.2.5)
(65.2.6)

I
II
III
IV
, a2 = , b1 = , b2 =
,
V
V
V
V
I = y 2 x X [ x y ] y X ;

a1 =

(65.2.7)

II = x 2 y X [ x y ] x X ;

(65.2.8)

III = y 2 x Y [ x y ] y Y ;

(65.2.9)

IV = x 2 y Y [ x y ] x Y ;

(65.2.10)

V = [ x 2 ][ y 2 ] [ x y ]2 ,
x = x x0 ,

y = y y0 ,

X = X X0 ,

Y = Y Y0 .

:
[ x x ] + [ y y ]
(65.2.11)
m0 = mx =
;
mp = m0 2 .
2n 6


65.1.

.
65.2.1.


A
x,
y, m

515
560
1244
325
545

515
560
1244

X, m

Y, m

92352,439
84759,620
88697,044
85000.000
87829,343
438638,446
[ x]
x0 =
n
87727,6892
xi = xI x0

20359,231
17042,702
17379,409
18000.000
17421,001
90201,343
[ y]
y0 =
n
18040,2686
yI = yI y0

84778,635
85622,843
86502,430
84784.346
86199,260
427887,514
[X ]
X0 =
n
85577,5028
Xi = X I - X0

26014,364
17771,625
21624,425
18292.392
20810,372
104513,178
[Y ]
Y0 =
n
20902,6356
YI = YI - Y0

4624,7498
-2968,0692
+969,3548
-2727,6892
101,6538

2318,9624
-997,5666
-660,8596
-40,2686
-619,2676

-798,8678
45,3402
924,9272
-793,1568
621,7572

5111,7284
-3131,0106
721,7894
-2610,2436
-92,2636

0,0000

0,0000

0,0000

X , m
Y , m
84778,667
85623,022
86502,286
84784.330
86199,209

26014,352
17771,563
21624,296
18292.401
20810,566

mm
vy
vx
-32
-179
144
16
51
0

12
62
129
-9
-194
0 mm

x2 = 38588016, 08

y 2 = 7195814, 60

[ xy ] = 13091063, 92
[ x y ] 2 = 1,713759546.1014
[ xX ] = 705864, 71
[yY] =14662635,06
[ xY ] = 40743745,37

0,0000

yX = 2862737, 69


III
I = y 2 x X [ x y ] y X =
b1 =
= 0, 95238487

V
= 3, 23970148.1013

I
a1 = = 0,3047803564
V
a2 =

-
B

II
= 0, 952308949
V

b2 =

II = x 2 y Y [ x y ] x X =

IV
= 0,305025068
V

= 1, 0122268479.1014

a0 = X0 a1 x0 a2 y0 = 76019, 7356 b0 = Y0 b1x0 b2 y0 =


= 68150, 622

III = y 2 x Y [ xy ] [ yY ] =


[ x x ] + [ y y ]
m0 = mx =
2n 6

IV = x 2 y Y xY x Y =

= 1, 01234945.1014


X i = a0 + a1xi + a2 yi ;

= 3, 242302249.1014

Yi= b0 + b1xi + b2 yi .

mp = m0 2
V = x 2 y 2 [ x y ] = 1, 06296255.1014


m0 = 0,17 m
mp = m0 2 = 0, 24 m
515,560
D xy = 8285, 546 m

D XY = 8285,857 m

m=

D XY
Dxy

1, 000038

, - , ,
(. 325 . 5644) .


Xi = a0 + a1xi + a2 yi

a0 = 76019, 736


a1 = 0.3047803564

a2 = 0,952308949

Yi= b0 + b1xi + b2 yi

b0 = 68150, 622

b1 = 0, 95238487

b2 = 0,305025068

1
2
3
4
5
6

A , m
y
x
85000,000
18000,000
85832,860
18000,000
85921,088
18971,457
85000,544
18969,271
85920,204
17364,628
86853,689
17650,354

, m
X
Y
84784.505
18292,543
85038,353
19085,757
84140.108
19466,092
83861,626
18588,408
85670,036
18975,127
85682,444
19951,318

7
8
9
10

86973,205
87982,206
87447,424
87829,343
864760,563

18957,166
19120,383
18177,309
17420,001
182630,569

84474,268
84626,472
85361,579
86199,171
849838,562

20463,534
21474,496
20677,516
20810,254
197785,035

5,6
D xy = 976, 234 m;

D XY = 976, 270 m;

m=

D XY
Dxy

= 1, 000037


[ Xi] = ka0 + a1[ xi ] + a 2 [ yI ] = 849838, 663
[Yi ] = kb0 + b1[ xi ] + b2 [ yI ] = 197785, 558

XVII

()

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100 hm2

1000
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. 66.1

1, 2 3 - .
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S1,16 S18,12 + S1,18 S16,12 + S1,12 S16,18


S1,16 sin 2 S1,18 sin(1 + 2 ) + S1,12 sin 1

1,3.1, 4 + 1, 4.2,1 + 1,0.1, 4

= 113 mm = 11,3m.
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2
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sin 3

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ms
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FP (Feature Point)

FL (Feature Line)

FA (Feature Area)

FC (Feature Complex)

NO (Node)

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TP (Text Placement)
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68.2

CND (Connected Node Primitive)


EDG (Edge Primitive)
END (Entity Node Primitive)
FAC (Face Primitive)
RNG (Ring Table)
TXT (Text Primitive)
.AFT (Area Feature Table)
.CFT (Complex Feature Table)
.LFT (Line Feature Table)
.PFT (Point Feature Table)
.TFT (Text Feature Table)
PJT (Point Join Table)
LJT (Line Join Table)
AJT (Area Join Table)
CJT (Complex Join Table)
ATE (Area To Edge)

. 68.3 - .
68.3

B
(Boolean)
I
(Long Integer)
S
(Short Integer)
R
(Long Floating Point)
F
(Short Floating Point)
T

T,n
n-
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Null
Y

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68.4
(Entity Node Primitive END)

ID_END
ID_PFT
Cont_Face
Coordinate


I
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.PFT
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Y/Z

P
N


3
U/N ,
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3, .
01

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68.5
(Connected Node Primitive CND)

ID_CND
ID_PFT
Cont_Face
Coordinate


I
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.PFT
X
Null

Y/Z

P
N

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U/N ,
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3, .
01

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68.6
(Edge Primitive EDG)

ID_EDG
ID_LFT
Start_Node
End_Node
Right_Face
Left_Face
Right_Edge
Left_Edge
Coordinate


I

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68.7
(Face Primitive FAC)

ID_FAC
ID_AFT
ID_RNG


.AFT
RNG

I
I
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P
N
N

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3 ( )
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68.8
(Ring Construction RNG)

ID_RNG
ID_FAC
Start_Edge

I
I
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P
N
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68.9
(Text Primitive TXT)

ID_TXT
ID_TFT
String
Shape_Line

. .
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()

I
I
T/T,n
CY

P
N
N
N

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Feature Table).
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END CND (. 68.4 68.5),
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1:1
M:1 ( .
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Null,
(
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68.10
(Point Feature Table .PFT)

ID_PFT

I
ID_CND / ID_END
I

N .

,

P
N

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Feature Table).
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EDG (. 68.6), (
).

1:1 M:1 (
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Null,
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68.11
(Line Feature Table - .LFT)

ID_LFT

P
ID_EDG

N
N .

,

P
N
N

:
0, 1 2 (, - ). T. 68.12
0, 1 2.
,
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AFT (.AFT Area Feature Table).
, .
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0, 1 2 (. 68.13).
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.
68.12
0, 1 2 (Area Feature Table .AFT)

ID_AFT

I
ID_AreaToEdge
ATE
I
N

,

P
N
N

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0, 1 2 EDG (. 68.6).

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EDG (. 68.6).
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True, False.
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68.13
(AreaToEdge ATE)

ID_AreaToEdge
ID_EDG
Forward/Reverse
ID_Feature_Class
ID_AFT

AFT
EDG


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I
I
B
S
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P
N
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N
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68.14 o o 3 (Area Feature Table - .AFT)

ID_AFT

I
ID_FAC
FAC
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N .

P
N
N

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TXT (. 68.9),
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1:1.
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68.15
(Text Feature Table .TFT)

ID_TFT
ID_TXT


I

I
TXT
N .
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P
N

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.
.
68.16
(Complex Feature Table CFT)

ID_CFT

I
N .

, , .

P
N

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(Point Join Table PJT);
(Line Join Table LJT);
(Area Join Table AJT);
(Complex Join Table CJT).
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68.17.
(PJT, LJT AJT)

ID_Connection
ID_Feature_Class
ID_Feature
ID_Primitive
From_To


I
P

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N
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N

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N

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68.18.
(Complex Join Table CJT)

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69.
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1:1000 1:500.

,
.
.
.
5 10 cm.
.
-
1/3 .. 15 20 cm.


. 74.1.
74.1

(, )

1:1000
1:1000
1:1000

1:5000

1:5000

75. II

1:500

1:2000

,
1:1000 1:2000.
30 ha 1:2000 1520 ha 1:1000.
1 2 m .
3 (18 ).
, :
1. 17
2. 1 .

2 .

, 34 .

56. .
. (
). .
1c .
, :
(75.1)

1:2000

(75.2)

1:1000

f = 2c n
f = 1,5c n

n e .

. 1 cm.
.
,
(22, 24, 25). . 22.1.
.
. 80100 m.
fh :
(75.3)

fh = 30 [ L] mm ,

L .

.
.

.
1:1000
1:5000, .
, 50/50 cm.
1:2000 ( 50/50 cm)
.
1:5000,
.
( ACAD), .
7

, .
, .
, ()
, ,
42.
40.

. ,
() . 5c .
. 75.1
75.1

1:2000
1:1000

150
80

150
100

180
130
- 30 m.
).
. 10 ha
1:2000 60 80, 1:1000 150 350.
-.
, .
8
,
.
,
56
, .
1:2000 0.40 m 1:1000 0.20 m.
, -
( 0.25 m).

" ",
. .
,
, .
, TPLAN GEO.
60/60 cm ( 50/50 cm)
(ACAD).
,
(42).
( ).
1 2 m,
,
.

.
.

.
.
"SOKKIA" "COMMS"
. , ,
TPLAN.
. ,
. ACAD
, .
. ,
.
.


, .
.
.
0.5 mm, 1/3 .
1
,
. 74.1.

76.

6 ( )
I .

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

1.
. 76.1 4 11
. .
.
, :
1)
. .

. 76.1

2) .
3) .
4) .
5) .
6) .

2. .


. , ( ,
X Y ),

. -
(.. ), ,
.
- (..,
), , ,
.
. . 76.1.
.
76.1

.
R
.
S
433
51
91
51
63
63
101
97
97
70
91
433
433
9
91
91
97
9
9
50
91
55
55
433
50
96
101
101
95
96
96
94
55
55
93
433
94
63
70
94
92
433
433

45930.45
0.0000
93
428.527
92
45870.86
0.0000
70
441.836
92
45024.91
0.0000
50
511.270
96
45055.94
0.00
0.0000
55
428.543
9
0.00
0.0000
50
412.391
97
0.00
0.0000
50
407.656 101
0.00
0.0000
55
418.342
0.00
0.0000
94
418.348
94
0.00
0.0000
95
416.313
95
0.00
0.0000
50
367.554
0.00
0.0000
93
804.198
93
0.00
0.0000
51
444.582
0.00
0.0000
94
448.382
51
0.00
0.0000
51
620.237
51

X
.
.

Y
R
S

87378.14 7
2
6.9559
70 31.0260 55
620.243
88774.97 6
2
25.8188
93 25.8188 101
795.502
87832.06 6
2
38.3580 433 66.6876 51
416.284
88870.72 0
0
0.00 4
2
52.0930
50 83.8768 9
412.380
0.00 3
2
73.7219
97 131.5675
407.623
0.00 3
2
67.1526 101 166.1590
511.284
0.00 6
1
134.9289
95 178.4024 101

152.7334
804.182

0.00 5
2
95 187.6142 50
0.00

0.00
55

5
1
32.6666 94


.
R
.
S

50.3692

101

67.7044

91

159.7733

86.7119

433

135.9789

92

144.8478

149.7162

70

194.3677

96

210.3503

195.7257

97

258.3621

333.3638

328.2013

91

361.4886

85.8568

70

156.1932

250.5687

95

288.0944

92

388.6010

143.5188

193.9583
367.542
16.7272

0.00 5
3
63 188.7987 70
63 448.376
0.00 4
1
180.7937
63 215.6888 94
50.6246
444.578

76.6804
441.819

0.00 4
2
93 107.4639 51
0.00

246.7582

148.8403

220.2679
795.496

:
BT ;
BRP ;
BRD ;
NT . -
.
X Y .
,
, . -

.

O
.
, ,
.
O .
NP ,
.
R .
ND ,
.
S .
NR - - .
NR NP R
, .. NR
NP R NT (
NR [ 1] = 1
NP R),
NR NP R
NT .. NR
,
NP R, .. NR
NT. , ,
NR , 1 - NP
R, .. , 1
NP R, .
NS - - .
NS ND S
, .. NS
ND S
NT ( NS [ 1] = 1

ND S), NS
ND S NT
.. NS ,
ND S, ..
NS NT. ,
, NS , 1
- ND S, .. , 1

ND S, .
,

BRP = NR [ BT + 1] 1 ,
(76.1)
:
BRD = NS [ BT + 1] 1 .
(76.2)

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

, .. . .2
(. 76.1):

: < >
< X > < Y > < > < > ,
, < X > < Y > .
, ,
() .
,
(. ) ,
, 0.
:
..1 ..R1 ..2 ..R2 ..N ..RN
, ,
.
,
,
, 0.
:
..1 ..S1 ..2 ..S2 ..N ..SN
,
.
,
(. I := 0 ) - NR NS 1 (..
NR [ 1] := 1 NS [ 1] := 1 ,
NT NP R, .
ND S.
. 1 ( I := I + 1)
(..
NT [ I ] , X [ I ] . BP BD
,
. 0 , ,
( O [ I ] := 0 ) . , -
0.0000 g
(, , ),
O , (. 0.0001g),
.
.
BP > 0 (.. ) J,
1 BP 1.
,
, , , ..
. J BP ,
BP
. NP R
NR [ I ] NR [ I ] + BP - 1 . (
) J
NR [ I ] + J - 1 NP R.
NR [ I ] ,
J NR [ I ]

, . IPos , ( IPos := NR [ I ] ) . ,

IPos + J - 1 , ..
NP [ IPos + J - 1] , R [ IPos + J - 1] .

0 ( BP = 0 )

, .. - J
,
. , .. BD > 0 ,

J (
, BP = 0 ) 1, BD 1.
,
, , , ..
. J BD ,
BD
. ND S
NS [ I ] NS [ I ] + BD - 1 . (
) J
NS [ I ] + J - 1 ND S. ,
J
NS [ I ] , . IPos ,

( IPos := NS [ I ] ) .

,
IPos + J - 1 , ..
ND [ IPos + J - 1] ,
S [ IPos + J - 1] .
,
NP R, . ND S , I + 1 -
. , I + 1 -
- NR - NS.
- , NR [ I + 1] := NR [ I ] + BP

NS [ I + 1] := NS [ I ] + BD .
-
(.. BP = 0 ) (.. BD = 0 )
, .

,

. ,
, , ,
I 1 I := I + 1
.

. BT (
) I
.
:
1) I := 0; NR [ 1] := 1; NS [ 1] := 1 .
2) I := I + 1
3) NT [ I ] , X [ I ] , Y [ I ] , BP, BD .
4) O [ I ] := 0
5) BP = 0 10.
6) IPos := NR [ I ]

7) J 1, BP
1.
8) NP [ IPos + J - 1] R [ IPos + J - 1] .
9) J.
10) BD = 0 15.
11) IPos := NS [ I ]
12) J 1, BD
1.
13) ND [ IPos + J - 1] S [ IPos + J - 1]
14) J.
15) NR [ I + 1] := NR [ I ] + BP; NS [ I + 1] := NS [ I ] + BD

16) , 2.
17) BT := I
18) .
. 76.2
. NP ND
. ( ) ,
, . . ( )
, , .
. NP ND (
) . 4.

76.2

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26

ND
91
5
92 15
63 14
92 15
97
7
96 10
433
1
9
6
91
5
97
7
9
6
101
3
55
9
50
8
94 12
101
3
95 11
96 10
55
9
93 13
63 14
94 12
94 12
51
2
433
1
51
2

S
428.527
620.243
441.836
795.502
511.270
416.284
428.543
412.380
412.391
407.623
407.656
511.284
418.342
418.348
804.182
416.313
367.542
367.554
804.198
444.578
448.376
444.582
448.382
441.819
620.237
795.496

NS
1
3
5
7
7
9
11
13
14
16
18
19
22
23
25
27

NT
433
51
101
70
91
9
97
50
55
96
95
94
93
63
92

X
45930.45
45870.86
45024.91
45055.94
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

Y
87378.14
88774.97
87832.06
88870.72
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

O
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000

NR
1
8
14
20
20
24
27
30
36
41
43
48
53
57
61
63

NP
51
2
93 13
70
4
55
9
101
3
91
5
92 15
63 14
70
4
93 13
101
3
433
1
92 15
97
7
50
8
433
1
51
2
70
4
96 10
433
1
55
9
50
8
9
6
91
5
50
8
97
7
9
6
50
8
101
3
91
5
55
9
95 11
101
3
97
7
9
6
433
1
94 12
95 11
50
8
91
5
101
3
95 11
96 10
50
8
55
9
94 12
70
4
55
9
93 13
63 14
70
4
95 11
433
1
51
2
63 14
94 12
70
4
94 12
93 13
51
433
51

2
1
2

R
0.0000
6.9559
31.0260
50.3692
67.7044
159.7733
388.6010
0.0000
25.8188
25.8188
86.7119
135.9789
144.8478
0.0000
38.3580
66.6876
149.7162
194.3677
210.3503
0.0000
52.0930
83.8768
143.5188
0.0000
73.7219
131.5675
0.0000
67.1526
166.1590
0.0000
134.9289
178.4024
195.7257
258.3621
333.3638
0.0000
152.7334
187.6142
328.2013
361.4886
0.0000
193.9583
0.0000
16.7272
32.6666
85.8568
156.1932
0.0000
50.6246
188.7987
250.5687
288.0944
0.0000
180.7937
215.6888
246.7582
0.0000
76.6804
107.4639

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59

148.8403
0.0000
220.2679

60
61
62

4.


NT. 433 . 76.2 1 (
), 91 5 ( ) ..
,
NP , ND,
.

NT, X, Y O ,
, .
-.
:
. 1

1 BRP ( ), NP,
BRD ( ), ND, ..
NP, . ND .
( NP, . ND),
1 BRP, . BRD.
NP
( , ) ND ( ,
), , .
NP, . ND
, 1 -
BT ( ) 1.
NT , .
( N), 1
BT.
NT ( ),
,
NT.
,
NP,. ND
,
NT . , ,
NP, . ND ,
, .
, , - .
( NP, . ND
), ,
1 ( ), NP, . ND
, , -
( NT) ..

, .. NP, . ND. ,
,
, - (..
NP, . ND NT),

.

NP (. ND) :
1) I 1, BRP
(. BRD) 1.
2) J 1,
BT 1.
3) NP [ I ] = NT [ J ] (. 6.
4) J.
5) , NP[I] (. ND [ I ] ) NT.
.
6) NP [ I ] = J (. ND [ I ] = J ).
7) I .
8) .

5.
(
)
, ( )
R ( ) S ( ) ,
. , NP ND
, .. .
, :
I ,
( ).

J ,
( ).
IJ ( )
R, . S. (.. ,
. I J), IJ
0.
I1 ,
I NP R (. ND S).
I2 ,
I NP R (. ND S).
I1 I2
NP R (. ND S), (
) I .
:
I1 = NR [ I ]
(76.3)
I 2 = NR [ I + 1] 1
NP R, ,
:

(76.4)

I1 = NS [ I ]

I 2 = NS [ I + 1] 1
ND S, ,
.

I2 < I1 , I (,
. 76.3 , . 76.4) .
I2 = I1 , , I
. ,
.
,
.
.
.

I1 I2 , . 76.3 . 76.4.
I .
,
, J ,
, , R
, . S . IJ,
I1 1 I2 .

. NP, . ND,
I1 I2 , ..
NP, . ND, ,
I. I NP,
. ND ,
.

NP ( ) ND (
). ( ,
) J ( ,
). ,
R, . S
IJ . -
. ,
1 NP,

. ND I1 I2 , - ..
, (..
I1 I2 J ,
), , .
IJ ( , )
0, , .
(
) :
1) I1 I2 76.3. 76.4.
, .
2) Ako I2 < I1 6.
3) IJ I1 , I2
1.
4) NP [ IJ ] = J (. ND [ IJ ] = J ) 7.
5) IJ .
6) IJ = 0 . .
7) .

6.


. , ()

(76.5)

W = 1 + 2 + 3 200g ,

1, 2 3 .
W ,

:
m =
(76.6)
mR =

W 2

W 2

3N

6N

m mR .
(
) ,
. .
:
,
.
.
Wi . 76.5.
. 76.6.
, :
I, J K , ,
.
.
IJ, JI, IK, KI, JK KJ ()
I J, J I, I K ..
R (, ,

, .. ).
, .. ,
(), . 5. . 5
, ,
0. I, J K
( , ),
K J, KJ 0
.
,
.
BI, BJ BK
I, J K ( ).
, , .
W
. 76.5. W , ,
,
(.
SUMW , W ,
). , . BrTr

1. , ,
,
.

. 76.6,
,
.
.
, I, J K .
. 76.2

- I , 1
BT ( ) 1.
( NT)
,
.

I
( NT). ,
,
I. I1 I2 (. 76.3)
I
NP R. NP I1
I2 ,
76.2
I , .


J K. , I
J K , J
K I1 I2 NP.
J I K I. -
J K. 6
I, J K .
IK,
I1 I2 - 1 1.
NP ,
I. K , . IK
, NP I1
( , I) I2 - 1
( , I) .
IK ( I2 - 1
), , K

I, , J (
I , ) .
IK
:
K
NP, .. K := NP [ IK ] .
K < I . , K ( - NT) I . , K ,
, .
IK, ,
, ,
1 ( )
NP.
(.. K I NT),
, . 5.
K I.
KI.
KI
: 0 K I
K I R,
. K .
( IK
) NP.
K := NP [ IK ] ,
K < I
K I. K > I
KI ,
, J.
( ) IJ,
IK + 1 I2 1. IK
- I2-1 ( ),
I K, - ,
IJ J.
NP,
IK + 1 I2 , ..
I, ,
IK.
IJ
:
J
NP, .. J := NP [ IJ ] .
J < 1 . , J ( - NT) I. , J ,
, , .
IJ, ,
, ,
1 ( )
NP.
(.., J I NT),
, . 5.
J I.
JI.
JI
: 0 J I
J I R,
. J
( IJ

) NP.
J := NP [ IJ ] ,
J < 1
J I. J > 1
JI ,
J K.
J K. JK
(..
), K J.
, KJ ,
0. , JK > 0 KJ > 0 (..
J K), I,
J K ,
. J K , J
IJ,
, , 1
- .
, I, J K,
. R[IK], R[IJ], R[KI], R[KJ],
R[JI] R[JK]. IK, IJ, KI,
KJ, JI JK R. ,
.
:
BI =| R[IJ]- R[IK] |,
BJ =| R[JI]- R[JK] |,
(76.7)
BK =| R[KI]- R[KJ] | .
,
BI, BJ BK - 200g (
- 200g ). ,
400g (
). , 400g
BI, BJ BK.
W . 76.5.
, , SUMW,

. BrTr ( )
. SUMW BrTr
I.

. 76.6.

:
1) SUMW BrTr 0.
2) I 1, BT
( ) 1.
3) I1 := NR[I], I2 := NR[I + 1]- 1.
4) I2 I1 27.
5) IK I1,
I2 - 1 1.
6) K := NP[IK].
7) K < I 26.
8) K I
(. 5). KI
.
9) KI = 0 26.
10) IJ IK + 1 ,
I2 1.
11) J := NP[IJ].

12) J < I 25.


13) J I
(. 5). JI
.
14) JI = 0 25.
15) K J
(. 5). KJ
.
16) KJ = 0 25.
17) J K
(. 5). JK
.
18) JK = 0 25.
19) BI :=| R[IJ]- R[IK] |; BJ := | R[JI]- R[JK] |; BK := | R[KI]- R[KJ] | .
20) BI > 200g BI := 400g - BI.
21) BJ > 200g BJ := 400g - BJ.
22) BK > 200g BK := 400g - BK.
23) W := BI + BJ + BK - 200g .
24) SUMW := SUMW + W * W, BrTr := BrTr + 1.
25) IJ.
26) IK.
27) I.
SUMW
SUMW
28) BrTr > 0 MR :=
; MB :=
;
6N
3N
29) .

7.

(. 76.3),
.. .

.433

51

O101
50

R 101,50
R 101,97
R 101,96
R 101,70
R101,51

R 101,433

101,50
101,97
101,96
101,70
101,51
101,433
97

101

70
96

. 76.3

. 101 ( ) 433, 51 70
96, 97 50.
O101 ..
,
.
.
. 76.3
X

.
. 101 . 433, . 51 . 70
101,433, 101,51 101,70.
O101
:
= 101,433 R101,433 ,
O101
(76.8)

= 101,51 R101,51 ,
O101
= 101,70 R101,70 .
O101

:
O + O + O
O101 = 101 101 101
(76.9)
3
,
:

101,96
= O101 + R101,96 ,
(76.10)

101,97
= O101 + R101,97 ,

101,50
= O101 + R101,50 .

.
. I,
1 BT ( ) 1.
( NT)
(.. )
,
O. -,
, :
, , ..
.
. ,

,
,
.
I
:
SUMO (
) BrO ( )
0.
NT (
I,
) , .. X[I] > 0 Y[I] > 0 . ,
I ( )
,
. ,
I
1 ( )
.
NT ,
I1 I2 (. 76.3)
I NP R.
I2 I1 , I
,
.
I2 > I1 J,
I1 I2 1.
NP ( ,
I), I1 I2.
NP I1 I2
,

I .76.8,
.76.9. :
K
NP, .. K := NP[J] .
NP
, .. X[J] > 0 Y[J] > 0 . ,
, J,
I. J
I
, 1 (
) NP.
DX := X[K]- X[I] DY := Y[K]- Y[I] .
ALFA ,
arctg, ,
.
0g 400g .

I - Ori := ALFA - R[J] . , Ori < 0 , Ori := Ori + 400.

, .. SUMO := SUMO + Ori .
1, .. BrO := BrO + 1 .
J BrO > 0 , ..
I.
,
I O[I] := SUMO/BrO . ,
I O.

I .

:
1) I 1, BT
( ) 1.
2) SUMO BrO 0.
3) X[I] 0 Y[I] 0 16.
4) I1 := NR[I], I2 := NR[I + 1]- 1
5) I2 I1 16.
6) J I1,
I2 1.
7) K := NP[J] .
8) X[K] 0 Y[K] 0 14.
9) DX := X[K]- X[I]; DY := Y[K]- Y[I] .
10) ALFA, arctg,
, .
0g 400g .
11) Ori := ALFA - R[J] .
12) Ori < 0 Ori := Ori + 400 .
13) SUMO := SUMO + Ori; BrO := BrO + 1 .
14) J .
15) BrO > 0 O[I] := SUMO/BrO .
16) I .
17) .

8.
. 7 ,
()
, (.76.4).
. 76.4

I K
:

OI I.
RIK I K RKI K
I.
I
IK
K
= + R .

(76.11)
K I
KI
(76.12)

= IK
200g .
KI

OK K
RKI .
(76.13)
OK = KI
, :
NC .
NC ,
, ,
, ,
.. - . , ,
NC ( NC)
(
, ,
NC ),
NC ,
NC (
NC)
, ..
NC ,
.
,
NC. ,
NC,
NT , ..
. , ,
NC
.
K NC.
K1 NC, ..
NC.
.
K 0. I,
1 BT ( ) 1.
( NT)

, NC
, -
. I ,
NT[I] (.. O[I] > 0 ),
K 1 NC
( NC[K] := I ).
I. NC. K1
K.
NC ,
. I
0. (,
). I
1 , .
NC ,

NC,
.

NC
, .
( )
NC
, .. NC .
NC ,
.. ,
.. , .
II
NC , .. II := NC[I] .
I1 I2 (.76.3)
II NP R.
I2 I1 , II
, ..
.
, ,
I 1.
.
, NC (
II)
(.. I2 > I1 ) IK,
I1 I2 1.
NP, I1 I2
, II.
:
J
NP IK (
, II), .. J := NP[IK] .
NP
IK (
J) , .. O[J] > 0 . ,
J .
IK, ,
, 1
NP I1 I2 , .
, O[J] 0 ,
NC ,
. ,
NT ( NT[J] 0 , ..
), NC
. IK
, NP
I1 I2 .
O[J] 0 NT[J] > 0 , ,
J,
II, -
J II.
( ) J
II. JII
. 0
J II ,
R, .
( )
JII 0, J
IK,
IK 1 ( )
NP. ( JII > 0 ) ,
J
NC. K 1 ( NC 1)
NC J, .. NC[K] := J .

NT J , .. NT[J] := -NT[J] ,
, NC ,
.
IK.
,
I. : I
K ( NC).
, ,
I 1.
I - K NC
I K , ,
NC . I 1

NC. ,
, NC
, .. K .
,
NC
K .
I ,
NC
- . ,
NC ( ,
), I K
( , .. I = K )
,
I .

NC.
M, K1 + 1 K
1. ,
NC,
,
.. .
M :
SUMO (
) BrO ( )
0.
I
NC ( I := NC[M] ).
I1 I2 (. 76.3)
I
NP R.
NC.
, IK,
I1 I2 1.
NP ( ,
I), I1 I2 . KK
NP
( KK := NP[IK] ).
NP ( KK)
, .. O[KK] > 0 . , KK
I
IK ,
- . ( O[KK] > 0 )
KK
I, ( ).
( ) KKI
0, I
IK, 1 (
) ,

NP. ( KKI > 0 ) ,


KK I,
R[KKI].
76.11, 76.12 76.13. KK
I (AL := O[KK] + R[KKI]) , 0g
400g 400g , 400g .
.76.12 I
KK (AL := AL - 200g ) ,
, 400g .
I
. 76.13 Ori := AL - R[IK] .
, 400g .
I
SUMO (
) SUMO := SUMO + Ori .
1 ( BrO := BrO + 1 ).
IK.

I (O[I] := SUMO/BrO) .
M,
NT (
, .. ).

:
1) K := 0 .
2) I 1, BT (
) 1.
3) O[I] 0 6.
4) K := K + 1 .
5) NC[K] := I .
6) I.
7) K1 := K .
8) I := 0 .
9) I := I + 1 .
10) II := NC[I] .
11) I1 := NR[II]; I2 := NR[II + 1]- 1 .
12) I2 I1 23.
13) IK I1,
I2 1.
14) J := NP[IK] .
15) O[J] > 0 22.
16) NT[J] 0 22.
17) J II
, . 5. JII
.
18) JII = 0 22.
19) K := K + 1 .
20) NC[K] := J .
21) NT[J] := -NT[J] .
22) IK.
23) K > I 9.
24) M K1 + 1 , K
1.
25) SUMO := 0; BrO := 0 .
26) I := NC[M] .
27) I1 := NR[I]; I2 := NR[I + 1]- 1 .

28) IK I1,
I2 1.
29) KK := NP[IK] .
30) O[KK] 0 40.
31) KK I
, . 5. KKI
.
32) KKI = 0 40.
33) AL := O[KK] + R[KKI] .
34) AL > 400 AL := AL - 400 .
35) AL := AL - 200 .
36) AL < 0 AL := AL + 400 .
37) Ori := AL - R[IK] .
38) Ori < 0 Ori := Ori + 400 .
39) SUMO := SUMO + Ori; BrO := BrO + 1 .
40) IK.
41) O[I] := SUMO/BrO .
42) M.
43) I 1, BT
1.
44) NT[I] :=| NT[I] | .
45) I.
46) .

9.

-
- ().
, I

( ).
,

. ,
,
.
. 76.11
.
,

, - ,
,
- , ..
, .

,
, .. ,
.
(. KF), .
, , ..
(. KF := 1 ). (
),
,
.
KF 0.
I,
1 BT ( ) 1.
NT .

. / ,
I, ,

. (
),
. ,
.
I1 I2 (. 76.3)
I
NP R. I2 I1 ,

I, ,
. ( I2 > I1 )
, IK,
I1 I2 1.
NP ( ,
I) I1 I2 . K
NP
( K := NP[IK] ). K , .. .
X[K] > 0 Y[K] > 0 ,
IK, ,
. ( X[K] = 0 Y[K] 0 )
K ,
I K ( / ). ,
( ), . 5.
I K. ,
, K I.
,
( ) :
I K
IIK ( IIK > 0 )
IIK S ( S[IIK]).
K X[K] := X[I] + S[IIK]* COS(AL)
Y[K] := Y[I]+ S[IIK]* SIN(AL) . - KF 1 ( KF := 1 )
.
IK, , IK
.
I K
IIK ( IIK = 0 ) .
K I.
( ).
KI . ( KI > 0 ),
KI S (
S[KI]). K
X[K] := X[I] + S[KI]* COS(AL) Y[K] := Y[I] + S[KI]* SIN(AL) . - KF
1 ( KF := 1 )
. IK, ,
IK .
(
) IIK KI ( IIK := 0 KI := 0 )
I K ( ). K
, I. - KF
. IK,
, IK .

IK I.
- KF. :
KF 1 ( KF = 1 , .. ). ,
( I)
.

, (
I), .

(, KF ),
, ..
I.
KF 0 ( KF = 0 , .. ). ,
( I)
.
,
. .

:
1) KF := 0 .
2) I 1, BT (
) 1.
3) X[I] 0 Y[I] 0 17.
4) O[I] 0 17.
5) I1 := NR[I]; I2 := NR[I + 1]- 1 .
6) Ako I2 I1 17.
7) IK I1, I2
1.
8) K := NP[IK] .
9) X[K] > 0 Y[K] > 0 16.
10) AL := O[I] + R[IK] .
11) AL > 400 AL := AL - 400 .
12) I K
, . 5. IIK
.
13) IIK > 0 X[K] := X[I]+ S[IIK]* COS(AL) Y[K] := Y[I] + S[IIK]* SIN(AL); F := 1 ;
16.
14) K I
. KI
.
15) KI > 0 X[K] := X[I] + S[KI]* COS(AL) Y[K] := Y[I] + S[KI]* SIN(AL); F := 1 .
16) IK.
17) I.
18) KF = 1 1.
19) .

10.
1)
, . 3.
2) NP NS
, . 4.
3) , . 6.
.
4) , . 7.
.
5) , . 8.
.
6) ,
. 9. .


1.

00
10
20

0,00..
11,11..
22,22..

1,11..
12,22..
23,33..

2,22..
13,33..
24,44..

3,33..
14,44..
25,55..

4,44..
15,55..
26,66..

5,55..
16,66..
27,77..

6,66..
17,77..
28,88..

7,77..
18,88..
30,00..

8,88..
20,00..
31,11..

10,00..
21,11..
32,22..

30
40
50

33,33..
44,44..
55,55..

34,44..
45,55..
56,66..

35,55..
46,66..
57,77..

36,66..
47,77..
58,88..

37,77..
48,88..
60,00..

38,88..
50,00..
61,11..

40,00..
51,11..
62,22..

41,11..
52,22..
63,33..

42,22..
53,33..
64,44..

43,33..
54,44..
65,55..

60
70
80

66,66..
77,77..
88,88..

67,77..
78,88..
90,00..

68,88..
80,00..
91,11..

70,00..
81,11..
91,11..

71,11..
82,22..
93,33..

72,22..
83,33..
94,44..

73,33..
84,44..
95,55..

74,44..
85,55..
96,66..

75,55..
86,66..
97,77..

76,66..
87,77..
98,88..

00
10
20

0.00000
0.18519
0.37037

0.01852
0.20370
0.38889

0.03704
0.22222
0.40741

0.05556
0.24074
0.42593

0.07407
0.25926
0.44444

0.09259
0.27778
0.46296

0.11111
0.29630
0.48148

0.12963
0.31481
0.50000

0.14815
0.33333
0.51852

0.16667
0.35185
0.53704

30
40
50

0.55556
0.74074
0.92593

0.57407
0.75926
0.94444

0.59259
0.77778
0.96296

0.61111
0.79630
0.98148

0.62963
0.81481
1.00000

0.64815
0.83333
1.01852

0.66667
0.85185
1.03704

0.68519
0.87037
1.05556

0.70370
0.88889
1.07407

0.72222
0.90741
1.09259

00
10
20

0.00000
0.00309
0.0617

0.00031
0.03040
0.00648

0.00062
0.00370
0.00679

0.00093
0.00401
0.00710

0.00123
0.00432
0.00741

0.00154
0.00463
0.00772

0.00185
0.00404
0.00802

0.00216
0.00525
0.00833

0.00247
0.00556
0.00864

0.00278
0.00586
0.00895

30
40
50

0.00926
0.01235
0.01543

0.00957
0.01265
0.01574

0.00988
0.01296
0.01605

0.01019
0.01327
0.01636

0.01049
0.01358
0.01667

0.01080
0.01389
0.01698

0.01111
0.01420
0.01728

0.01142
0.01451
0.01759

0.01173
0.01481
0.01790

0.01204
0.01512
0.01821

1.


g
00
10
20
30
40

0

0 00
9 00
18 00
27 00
36 00

1

0 54
9 54
18 54
27 54
36 54

2

1 48
10 48
19 48
28 48
37 48

3

2 42
11 42
20 42
29 42
38 42

4

3 36
12 36
21 36
30 36
39 36

5

4 30
13 30
22 30
31 30
40 30

5 24
14 24
23 24
32 24
41 24

7

6 18
15 18
24 18
33 18
4218

8

7 12
16 12
25 12
34 12
43 12

9

8 06
17 06
26 06
35 06
43 06

50
60
70
80
90

45
54
63
72
81

45
54
63
72
81

46
55
64
73
82

47
56
65
74
83

48
57
66
75
84

49
58
67
76
85

50
59
68
77
86

51
60
69
78
87

52
61
70
79
88

12
12
12
12
12

53 06
62 06
71 06
80 06
89 06

00
00
00
00
00

54
54
54
54
54

48
48
48
48
48

42
42
42
42
42

36
36
36
36
36

30
30
30
30
30

24
24
24
24
24

18
18
18
18
18

0.00
0.10
0.20
0.30
0.40


0 00.0
5 24.0
10 48.0
16 12.0
21 36.0


0 32.4
5 56.4
11 20.4
16 44.4
22 08.4


1 04.8
6 28.8
11 52.8
17 16.8
22 40.8

3

1 37.2
7 01.2
12 25.2
17 49.2
23 13.2

4

2 09.6
7 33.6
12 57.6
18 21.6
23 45.6

5

2 42.0
8 06.0
13 30.0
18 54.0
24 18.0

6

3 14.4
8 38.4
14 02.4
19 26.4
24 50.4

7

3 46.8
9 10.8
14 34.8
19 58.8
25 22.8

8

4 19.2
9 43.2
15 07.2
20 31.2
25 55.2

9

4 51.6
10 15.6
15 39.6
21 03.6
26 27.6

0.50
0.60
0.70
0.80

27 00.0
32 24.0
37 48.0
43 42.0

27 32.4
32 56.4
38 20.4
43 44.4

28 04.8
33 28.8
38 52.8
44 16.8

28 37.2
34 01.2
39 25.2
44 49.2

29 09.6
34 33.6
39 57.6
45 21.6

29 42.0
35 06.0
40 30.0
45 54.0

30 14.4
35 38.4
41 02.4
46 26.4

30 46.8
36 10.8
41 34.8
46 58.8

31 19.2
36 43.2
42 07.2
47 31.2

31 51.6
37 15.6
42 39.6
48 03.6

.
.

0.90

48 36.0

49 08.4

49 40.8

50 13.2

50 45.6

51 18.0

51 50.4

52 22.8

52 55.2

53 27.6


g
0.0000
0.0010
0.0020
0.0030
0.0040

0.0
3.2
6.5
9.7
13.0

0.3
3.6
6.8
10.0
13.3

0.6
3.9
7.1
10.4
13.6

1.0
4.2
7.5
10.7
13.9

1.3
4.5
7.8
11.0
14.3

1.6
4.9
8.1
11.3
14.6

1.9
5.2
8.4
11.7
14.9

2.3
5.5
8.7
12.0
15.2

2.6
5.8
9.1
12.3
15.6

2.9
6.2
9.4
12.6
15.9

0.0050
0.0060
0.0070
0.0080
0.0090

16.2
19.4
22.7
25.9
29.2

16.5
19.8
23.0
26.2
29.5

16.8
20.1
23.3
26.6
29.8

17.2
20.4
23.7
26.9
30.1

17.5
20.7
24.0
27.2
30.5

17.8
21.1
24.3
27.5
30.8

18.1
21.4
24.6
27.9
31.1

18.5
21.7
24.9
28.2
31.4

18.8
22.0
25.3
28.5
31.8

19.1
22.4
25.6
28.8
32.1

2.

=0,101 R=6381 km.
S,m
0
1000
2000
3000
4000
5000
6000

0
0.00 m
0.07
0.28
0.63
1.13
1.76
2.54

100
0.00m
0.09
0.31
0.68
1.18
1.83
2.62

200
0.00 m
0.10
0.34
0.72
1.24
1.90
2.71

300
0.01 m
0.12
0.37
0.77
1.30
1.98
2.80

400
0.01 m
0.14
0.41
0.81
1.36
2.05
2.88

500
0.02 m
0.16
0.14
0.86
1.43
2.13
2.98

600
0.02 m
0.18
0.48
0.91
1.49
2.21
3.07

700
0.03 m
0.20
0.51
0.96
1.56
2.29
3.16

800
0.04 m
0.23
0.55
1.02
1.62
2.37
3.26

900
0.06 m
0.25
0.59
1.07
1.69
2.45
3.35

3.

b=

t=

b1 + b2

t1 + t2
2

b=

b1 + b2

-5

10

15

20

25

30

600
610
620
630
640

13.12
12.90
12.70
12.50
12.30

13.36
13.15
12.93
12.73
12.53

13.61
13.39
13.17
12.96
12.76

13.85
13.63
13.41
13.20
12.99

14.10
13.88
13.65
13.43
13.22

14.35
14.12
13.88
13.66
13.45

14.59
14.36
14.12
13.89
13.68

14.84
14.61
14.36
14.13
13.91

600
610
620
630
640

650
660
670
680
690

12.11
11.93
11.75
11.58
11.41

12.34
12.15
11.97
11.79
11.62

12.56
12.37
12.19
12.01
11.83

12.79
12.60
12.41
12.23
12.05

13.01
12.82
12.63
12.44
12.26

13.24
13.04
12.85
12.66
12.47

13.47
13.26
13.07
12.87
12.69

13.69
13.49
13.29
13.09
12.90

650
660
670
680
690

700
710
720
730
740
750
760

11.25
11.09
10.93
10.78
10.64
10.50
10.36

11.46
11.29
11.14
10.98
10.84
10.69
10.55

11.67
11.50
11.34
11.19
11.04
10.89
10.74

11.88
11.71
11.55
11.39
11.23
11.08
10.94

12.08
11.91
11.75
11.59
11.43
11.28
11.13

12.30
12.12
11.95
11.79
11.63
11.48
11.32

12.51
12.33
12.16
11.99
11.83
11.67
11.52

12.72
12.54
12.36
12.19
12.03
11.87
11.71

700
710
720
730
740
750
760

4.
1:2000, 1:1000 1:500
1:2000
1:1000

1:500


:
-
-

4.
1:2000, 1:1000 1:500
1:2000
1:1000

1:500

()

- (
)




-
-
- ,

()

()
-
-
-
()


1. , . . ., , 1998.
2. , ., . , . . I ., ., ,1990.
3. , ., . . II ., ., , 1991.
4. ., . , . , . , . , . .
, ., , 1991.
5. , . ., . . , . . , . . . . , . . , . .
. , ., , 1984.
6. , . ., . . , . . , . . . . ., , 1983.
7. , . ., . . , . . , . . , . . .
, . ., , 1988.
8. , . . . ., , 1980.
9. , . ., . . . - . .,
, 1978.
10. . , ., , 1978.
11. , . . ., , 1970.
12. . . , ., ,
1982.
13. , . , ., , 1957.
14. , . . . . ., , 1969.
15. . ., . . GPS . ., 1997
16. , . . ., , 1979.
17. 1:10 000, 1:5 000 1:2 000
1:10000 1: 500. ., 1985.
18. . ., ,1996.
19. . ., ,
1986.
20.
(GPS), , ., 1995.
21. . ., , 1969.
22. , ., , . . . . ., ,
1988.
23. , . . . ., , 1982.
24. , . . ., , 1979.
25. , ., . , . , . , . . , ., , 1982.
26. , ., . .
. ., , 1986.
27. , ., . . . ., , 1987.
28. , . . . . ., , 1972.
29. 1:1000 1:500, ., , 1995.
30. , . ., . . , . . . . . , 1983.
31. , ., . . , I II. ., , 1973.
32. , . . ., , 1988.
33. TPLAN, . ., ., 1993.
34. - , , ., 1995.
35. .
36. , ., . , . . .
., , 1983.
37. .
38. . ., , 1988.
39 , . ., . II . ., , 1981.
40. , . ., . . , . . . . ., , 1978.
41. , . . . ., , 1981.
42. . . : . . , .,
1986.
43. , . . . , 1983.
44. , . . . . ., , 1984.
45. DIGEST.
DGIWG, . , 1992

46. , ., . , . . I . II . ., , 1977 1982.


47. , ., . , . . . ., , 1983.
48. , . . . . . ., 1962.
49. , ., . , . , . , . , . .
, ., , 1985
50. ., . , . , . , . .
. ., , 1986.
51 ., . , . , . , . , . . , ., ,
1982.
52. , . ., . . . , .,
, 1980.
53. , . ., . ., . ., , 1986
54. 1 : 1000 1 :
500. ., -, 1993.
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