Professional Documents
Culture Documents
. - .
. - .
.
.
.
,
, 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. ,
- .
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
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,
(14.7)
AB = 200 + r , X AB <0
YAB >0,
(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
. 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).
. 16.19a
. 16.19
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)
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=
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,
.
,
.
, .
.
( 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
a2 = hAB + b2
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.
()
,
,
.
,
,
(. 30.1).
,
.
, CCD .
. 30.1
.
.
,
, ..
.
,
. .
30.2
. 30.2
.
, . -
:
,
( ).
.
( ).
.
- :
( )
50% . , ,
5500 m 1 (8 ).
1 8800 m.
(
). ,
, .
, - .
- -
. .
. 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>
, <OFF> . :
; ,
; ,
.
<Language> .
<E__300> <G__300> .
<INPUT>
, :
<Max. dist.>.
<Min. sight> ( ) 0
1 m. 0, .
<Max. diff.>
0 0.01 m ( 0 ).
<Refr. Coeff.> 1 +1.
,
.
3.
-
,
<ESC>.
.
. ,
<DISP>.
3 4 .
( ,
) ,
, .
<Point>.
<MEAS> (8) . 30.4.
R
HD.
. ,
<PNr>
, <REM>.
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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.
:
(
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1 km :
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1.5 mm/1.2 mm;
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2 mm/2 mm.
:
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1.8 m 60 m;
1.8 m 100 m;
:
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1 cm 5 cm.
2 8 .
, , ,
.
, :
NA2002 1 mm 0.1 mm;
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:
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:
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.
,
,
. . .
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.
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1.09.1999 .
.
1
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.
m
2
118
x1
, mm
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3
2053
1327
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7
541.253
8
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1.110
x2
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2247
541.843
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2841
0.071
2318
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150
1963
0872
1.969
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114
2198
1014
0.949
544.685
545.419
545.080
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98
3
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0.516
1843
68
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130
1
1872
1462
0.736
-2
168
.. B
2209
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
..
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n
n .
.
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-
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A () :
H1 = H A + hA1 ,
(31.6)
H2 = H1 + h12 ,
H3 = H2 + h23 ,
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.
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1
B 31.6.
, .
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,
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32.
1.
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31 32. ci ,
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2
2
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- ( fh < fh )
, ( h100,1
(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 .) , .
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X, ML
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1.
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Ni025 15310
H, m
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32.2.
1.09.1999 .
10
11
-4
. 100
577.643
1360
576.283
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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
.
. ,
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0.2, 0.5 1 m.
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2. ,
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2050 m ,
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33.
, , .
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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
1.53 1.50
1.60
S = 1611.89 m
1.47 1.50
11
1.51 1.50
401.78 98.5911 +8.903
10
Hi
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
h= +12.450
Skm = 178 mm
fh
S2
Sik2
(, , , .). .
.
. 33.2 Z1 Z2 ,
S AB .
. 33.2
34.
,
, .
,
, . , ,
( 2 m),
,
. .
, hAB
A B . ,
, .
.
, , . 34.1
. ( ),
,
,
. A B ,
, . 34.1. OA OB
. ,
. 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
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
) , , .
, : 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
.
.
() (. 40.1
5). .
, ,
( , ,
, , , ,
.).
. 40.1
.
, .
, -
.
.
.
,
.
-
. . ,
.
, .
, ,
.
, .
, (, , , ,
.) ,
. , ,
: , ,
, , ,
, . ,
.
(,
), ,
.
. ,
. , , ,
, ..
.
.
,
, .
. (,
)
, .
,
, ,
.
. 5 10
. ,
, ,
,
. , ,
( -)
,
, .
,
, .
, , ,
.
, , , -
, - .
,
. .
.
- ( ) .
.
, .
,
.
,
.
. S
(40).
.
( 40.1). J .
2 - ,
, ,
. .
,
, 10 00 ( 1 m ) ,
(. 38.2), 3, 4 5
,
.
, ,
6 7.
, .
40.1
: .
, mm
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
96,29
8
75,5
100,1
49,0
53,5
44,0
H =
9
75,5
99,8
49,0
53,4
43,9
10
1,38
2,50
1,24
1,27
1,22
11
0,24
12
13
5,46
0,32
2,54
2,56
14
1,14
7,96
1,56
15
654,59
1,27
1,34
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
-1,71
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)
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
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
3. Code, MENU, ( 13 )
.
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NO REC ,
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2. . S, V, H,
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Online. COMMS. CARD RECEIVE.
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SET 2CII,
2 (3 mm +2 mm/km), 4,2 km.
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20 (3 mm +2 mm/km),
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2, NAME:......... .DAT. ENT,
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41.
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H.
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AUTOEXEC.BAT : @ . 'taskm'
Task Manager: (c) V1.0 1990,
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'taskm'
.
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'.TMP'.
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, .
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. .
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'.lis'. .
( '.lis')
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TPLAN
===========================================================================
: vitocha
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.
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======================================
||
||
||
||
||
||
||
||
||
||
||
||
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||
|| DOS
||
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||
======================================
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 -
||
============================================
- , .
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8 25 5
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0
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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
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[PE2 FOWF.LIS] .
IV.
" " , :
===================================================
||
||
||
||
|| Pe2 vitocha.dpm -
||
|| WDPM -
||
|| POPM -
||
|| PIPM -
||
|| Pe2 wdpm.lis 'wdpm'
||
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||
|| Pe2 pipm.lis - 'pipm'
||
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||
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||
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||
===================================================
[vitocha.dpm]
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V.
" " , :
===================================================
||
||
||
||
|| Pe2 vitocha.dgm -
||
|| Pe2 vitocha.dtn - .
||
|| WDNM - .
||
|| PONM - .
||
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||
|| Pe2 wdnm.lis - 'wdnm'
||
|| Pe2 ponm.lis - 'ponm'
||
|| Pe2 pinm.lis - 'pinm'
||
|| SNX -
||
|| Pe2 snx.lis - 'snx'
||
|| SGM - ()
||
===================================================
[vitocha.dgn]
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[vitocha.dgn] :
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===================================================
||
||
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||
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===================================================
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. 43.2
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xC yC ,
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X Y
. xC
yC , D xD yD
(. 43.2).
D (. 43.2), ,
C D . . . D
:
1.
:
X C = X A + xC cos AB
(43.1)
YC = YA + xC sin AB
X D = X A + xD cos AB
YD = YA + xD sin AB ;
(43.2)
C = tg
AB
( xC2 + yC2 ) ;
yC
xC
, S AC , S AD C D (. 43.3)
S AD =
D = tg
yD
xD
( xD2 + yD2 )
;
XC = X A + S AC cos ( AB C ) ;
(43.5)
YC = YA + S AC sin ( AB C ) ;
X D = X A + S AC cos ( AB + D ) ;
YD = YA + S AC sin ( AB C ) .
,
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47.1
I
A
B
C
k
P
P
P
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-
= D tg
[g]
J ,m
l ,m
m
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.
D,m
f ,
m
h = h + J
I + f
m
-4.05
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1.54
1.53
2.02
2.02
107.47
87.10
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-4.80
-6.86
-6.58
0.00
0.00
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1.48
2.02
154.80
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b-. - b-p
(. 47.1). , .
-, . .
- - , . .
.
.
H p = Hi + Sip .tg +Ji I p + f ,
(47.1)
i (i =A, B, C);
Sip ;
f .
. ,
- 0,30 m 1:2000 0,40 m 1:5000.
1
. pi = 2 .
Sip
2.
a, b , .
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, (. 47.2).
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p m . .
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3.
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200 m, 600 m. 1:5000
250 m 1000 m. :
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.
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.
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.
(. 47.4).
, - 0,5 mm, ,
(. 47.4).
:
fh = hi ( H B H A ) ,
(47.2)
fh :
fh = 0, 04m
(47.3)
[ m]
Sik
Sik2
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cm
Hi = H A h + J I .
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48.1
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Hi , m
D , m
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h, m
g
c
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J,m
D, m
J =1
6
100.5
1
-6
95
-10.85
125.61
98.5
H = 136.46
J =1
90.0
2
1
65
2.32
138.78
J = 1.40
90.0
J =1
118.6
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11 h 58 min.
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= c t = c(t + ) = + c S c R ,
(51.1)
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X S ,YS ZS S (
) t X, Y Z:
(51.2)
( X S X ) 2 + ( YS Y ) 2 + ( ZS Z ) 2 .
X 0 , Y0 Z0 , ..
X = X 0 + x,
Y = Y0 + y,
Z = Z0 + z
(51.2) , ,
(51.3)
= a x + b y + c z + 0 ,
a, b c , 0 ,
.
(51.1) (51.3)
a x + b y + c z + d R + f = 0 ,
(51.4)
d = c ;
f = ( c S 0 ) .
S
. . R
x , y z
(). ,
.
4
- .
N X +F =0,
(51.5)
N = A * A , F = A * f , A x , y , z R
(51.4) , A * , f e
f .
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1 , GDOP- Q .
Q=N
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2.
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AB
(, ).
AB
. 51.5
A B ).
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() N , ..
.
:
(51.6)
A (t ) =
B (t ) =
A (t )
B (t )
+ N A f [ A (t ) S (t )]
+ NB f [B (t ) S (t )],
f ,
N e .
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X , Y Z N .
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4.
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- 20 km, 4 .
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51.6),
:
Stop and Go .
,
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. Stop and Go .
, .
,
, GPS
(Real Time Kinematic),
.
GPS- .
GPS-
GPS-
Post Processing. :
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GPS- .
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: WGS84- X , Y Z
B , L H , B L
x y , H () H.
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[20], - , -
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(37).
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. 51.8. (Sokkia)
. 51.9. (Topcon)
. 51.10. (Trimble)
10+1
5+1
24
0.4
0.4
IM\MC (Mb)
, (kg)
0.35
0.4
0.4
24
Clear Track
0.74
10+2
.
Clear Track
.
0.4
5+2
24
/8
10 20+2
5+1
10+2
3+0.5
10+1
1.15
, (kg)
1.15
12
10+1
10+2
0.85
5+2
1.6
SR510
SR520
SR530
m=amm +bppm
Radian IS
Sokkia
Leica
, (kg)
GPS-
51.1
Clear Track.
.
-
-.
.
24
10+1
96/ -
10+1
40
/48;96
10+1.5
3+1
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0,6 / 0,4
Legasy-E/H
5700
Trimble Topcon
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Zephyr (Stealth .).
4 kg
XIV
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, , .
:
1. .
2. ,
. .
3. -
.
4. .
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- ().
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-
.
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 .
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
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 ) ;
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 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 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
r1 =
cc
;
DPA
r2 =
cc
;
DPB
r3 =
. 53.3
cc
.
DPC
1 , 2 , 3 :
12 = r22 + r32 2r2 r3 cos 2
(53.6)
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
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
.
.
.
.
.
. ... .
(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 ;
mo = 22,71cc ;
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)
.
:
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 ;
15,24 = 185,8440g ;
18,20 = 217,5517g ;
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
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)
(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 ;
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)
(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
0,30; 0,050
0,30; 0,070
0,30; 0,080
0,10; 0,30
0,30; 0,150
0,20; 0,120
(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
(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
[ 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
= [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
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
= [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'
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
= [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
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
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
= [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
= [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
[ 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
. 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
[ 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)
(63.2)
i ,k = H + A + 1 + .... + i K .200g ,
(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 = 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
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
( B P X Y . 63.5).
64. -
I, II, III IV
. ,
.
[ 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
-
(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)
(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
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
-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
(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
48
my
48
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
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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=
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,
3
1000
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, 1 : 1000 m = 7 cm.
.
, , . . 66.1
.
66.1
100 hm2
1000
2000
5000
4%
100
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150
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1500 m , 1200 m 950 m.
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(. 66.1) 1 : 2000.
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1 : 2000 (. 66.1)
7. 7.2000
m =
=
= 14 cm.
1000
1000
. 66.1
1, 2 3 - .
. 1 53.7,
mR = 20
1 = mR
= 20
= 113 mm = 11,3m.
1,3.sin 78g 1, 4.sin148g + 1, 0.sin 70g
( 52.17)
m
2
2
S12,1
+ S16,1
20 2
10002 + 13002
sin 3
(57.13), m = 75
ms
1
=
, [ s ] = 1800 m
s
4000
n = 12 ,
2
2
2
1 1800 75 1800
M =
+
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XIX
71.
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4.
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PT PS.
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3. 5,
5 ,
. 4
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. .
: ,
. , = 800 mm,
1:4,
P 1
800
=
=
= 200 mm.
4
4
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.
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71.2). , . 1
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5 .
. 71.2
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.
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-
()
.
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:
n
2 P = yi ( xi 1 xi +1 ) ;
. 72.1
(72.1)
i =1
n
2 P = xi ( yi +1 yi 1 ) .
i =1
. .
, , .
(72.1), , :
2 = y1 ( x5 x2 ) + y2 ( x1 x3 ) + y3 ( x2 x1 ) + y4 ( x3 x5 ) + y5 ( x4 x1 );
(72.2)
2 = x1 ( y2 y5 ) + x2 ( y3 y1 ) + x3 ( y4 y2 ) + x4 ( y5 y3 ) + x5 ( y1 y4 ).
, y
, .
, , .
: x
,
. .
mP , ,
1
M P = m Si2 2,i ,
(72.3)
2
m ,
Si 2,i .
72.1
Y
X
y
x
m
m
m
m
1
8426220,47
4702110,25
120,47
10,25
2
8426130,55
4702255,60
30,55
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4702400,75
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5
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72.2
y
x
xi . ( yi +1 yi 1 )
yi . ( xi 1 xi +1 )
m
m
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1
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2
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5
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60185,5380
1
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1
P = = 44863,70 m2
2
. . 72.1 (. 72.1).
.
72.1 . (72.1) .
,
( . 5) ( . 1).
,
, .
xi . yi +1 yy 1 yi . ( xi 1 xi +1 )
:
1) , ;
2)
.
-. :
. 72.1 1, 2, 3 1,
3, 4, 5, .
(. 72.2)
. 72.3.
. 72.2
. 72.3
,
, , ,
, (65) (
), .
.
73.
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- (. 73.1).
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3.3.
3.4, ,
3.5,
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.
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,
,
. O1 O2
,
. 73.1a
(73.1)
P = k ( O2 O1 ) = k n ,
e - ,
, n .
1:1 k0 = 10 mm2 . ,
.
, k0
106 k . : 1 : 5000
k=
2
0
= 10
50002
6
= 250 m2 .
10
10
. ,
k. ,
, . ,
.
.
n0 ,
:
n0 = P .
(73.2)
k
n= 2 1 - -
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n 0 3 5 .
. . ,
. ()
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,
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O2
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:
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, - 200 cm2 .
n '+ n ''
.
2
,
( 1, 2, 3 4 . 73.2), a b ,
.
f = ncp n0 ,
(73.4)
n =
(73.3)
,
, 0
. (73.2),
.
f
:
f = 3 0.68 + 0.028
(73.5)
. 73.2
n)
f e - f ,
f
V=
n .
(73.6)
n cp
V
n = n + V , (73.1).
,
( 73.1).
: , 1: 1000
( k = 10 m2 ) (. 73.2). 73.1.
73.1
O1
1
2
3
4
a
b
1680
0946
1842
2116
2985
3184
12753
O2 n = O2 O1 O1
O2 n = O2 O1
1848
1260
2107
2275
3473
3787
14750
168
314
265
159
488
603
1997
7115
2249
7986
1385
6731
3429
28895
7284
2566
8248
1546
7216
4031
30891
169
317
262
161
485
602
1996
n =
n + n
2
168,5
315
263
160,0
486,5
602,5
1996,5
n = n + V
0,3
0,6
0,5
0.3
0,8
1,0
-3,5
168,8
316,1
264,0
160,3
487,3
603,5
2000,0
P = kn (m2)
1688
3161
2640
1603
4873
6035
2000 m2.
-2000,0
f = 3 0.68 + 0.028
f = 3,5
n ) = 6
() .
PLACOM SOKKIA/ (. 73.3). 6-
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Ni 025, Ni 030, Ni 050.
, - 80 m.
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(74.2)
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[ D] km.
.
57.
:
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74.1
(, )
1:1000
1:1000
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1:500
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.
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.
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(75.3)
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L .
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159.7733
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144.8478
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194.3677
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210.3503
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258.3621
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288.0944
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50.6246
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5) BP = 0 10.
6) IPos := NR [ I ]
7) J 1, BP
1.
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1.
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) . 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
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55
9
50
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55
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51
2
433
1
51
2
S
428.527
620.243
441.836
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511.270
416.284
428.543
412.380
412.391
407.623
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511.284
418.342
418.348
804.182
416.313
367.542
367.554
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444.578
448.376
444.582
448.382
441.819
620.237
795.496
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1
3
5
7
7
9
11
13
14
16
18
19
22
23
25
27
NT
433
51
101
70
91
9
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50
55
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63
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1
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20
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53
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61
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51
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50.3692
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159.7733
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246.7582
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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 ,
, .
-.
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( NP, . ND),
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( , ) ND ( ,
), , .
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( 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].
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 (
) ,
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
. - .
. - .
.
.
.
. - . -
- . .
,
, . 1