,,,,,,,,,
1,, ( ),,,,,, 3S( GPS RS GIS),,,,,,,,,,,, 2002,,,,,,,,,,,,,,,,,,
2,?,, 2004. 7. 31
1,,,,,,,,,,, :,,,,,,,,,,!!,,,, 2004 5
1 1 1 1 1. 1 1 1. 2 3 1. 3 4 6 2. 1 6 2. 2 8 2. 3 12 2. 4 19 2. 5 20 2. 6 22 2. 7 24 2. 8 31 42 3. 1 42 3. 2 45 3. 3 48 3. 4 51 3. 5 55 3. 6 58 62 4. 1 62 4. 2 65 4. 3 81 4. 4 88
2 4. 5 90 103 5. 1 103 5. 2 104 5. 3 115 5. 4 123 5. 5 132 5. 6 137 5. 7 154 5. 8 158 5. 9 162 5. 10 166 172 6. 1 172 6. 2 181 6. 3 195 6. 4 204 6. 5 210 6. 6 ( GPS) 219 226 7. 1 226 7. 2 230 7. 3 235 7. 4 239 248 8. 1 248 8. 2 252 8. 3 257 8. 4 260 267 9. 1 267 9. 2 274 9. 3 278
3 282 10. 1 282 10. 2 283 10. 3 285 10. 4 288 10. 5 291 10. 6 293 299 11. 1 299 11. 2 300 11. 3 304 11. 4 308 11. 5 313 318 12. 1 318 12. 2 320 12. 3 325 12. 4 331 12. 5 335 342 13. 1 342 13. 2 345 13. 3 347 353 14. 1 353 14. 2 355 14. 3 362 14. 4 369
1 1. 1,,,,, : 1.,,,,,, : 2.,,, : ; ;, 3.,,,,,, ( GIS),, 21
2 4.,, : 5.,,, 20 80,, 80,,,,,,,,,,,,,,,,,,,,, ( GIS),
3,, ( GPS) ( RS) ( GIS),, ;, ;,,, 1. 2,,,,,,,, GPS-RTK,,,, :, ; ( ),,, ( DTM),, ( GIS) : ; ;,,, 20 50, 20 70,,, :,,
4, 20 80,,, 20 70, 80 1983,,,,,,,,,,,, ;,, 20 90, RTK( Real Time Kinematic), ( ) GPS GPS,, GPS,,, 20 km,, RTK RTK GPS, GPS 1. 3,,,,, ;,,,,,
5,,, :,,,,,,,,,,,,,,
6 2. 1,, 8 848. 13 m, 11 022m,,, 71%, 29%, : ;,,, ( 2-1 ),,, ( ), 2-1,,,,,, ( 2-2),,,,
7 2-2 ( 2-3 ) ;,,,, a f : f = a - b a,, 2-1 2-3 2-1 a / m f 1800 6 375 653 1334. 0 1841 6 377 397. 155 1299. 152 812 8 1880 6 378 249 1293. 459 1909 6 378 388 1297. 0 1940 6 378 245 1298. 3 1975 1975 6 378 140 1298. 257 IUGG 16 1980 1979 6 378 137 1298. 257 IUGG 17 WGS-84 1984 6 378 137 1298. 257 223 563 ( DMA) : IUGG( International Union of Geodesy and Geophysics),,, :
8 R = 1 ( a + a + b) 6 371km 3 2. 2,, ( ), ( ), ( ) ( ), 1. ( B, L, H), 2-4, P,, L,, 0 180 ;, 0180 2-4 P, B,, 090 ;, 0 90 P H,,,, P P, P ( ) L B,
9 2. O, X, X Y, Z, O-XYZ,, P OP x y z 2-5 2-5, : : e e 2 = a2 - b 2 a N = 1 - e 2 sin 2 B, : x P y P z P = ( N + H) cosbcosl = ( N + H) cosbsinl ( 2-1) = [ N( 1 - e 2 ) + H] sinb a 2 L = arctan y x B = arctan z + Ne2 sinb x 2 + y 2 ( 2-2) H = x 2 + y 2 cosb - N ( 2-2) B, tanb 1 = x 2 z, B 2 + y B 1 N 1 sinb 1, ( 2-2), B 3. WGS-84 WGS-84 ( GPS), WGS-
10 84 1979 17 ( 2-1), WGS-84 ; Z BIH1984. 0 ( CIP) ; X BIH1984. 0 CIP ; Y X Z, X Y Z 4.,, :, X,, ; Y,, ; ( 2-6), X Y, 2-6, -, - 2. 3 ( 100km 2 ),,,,, x y,,,,,, 2-7, xoy, AOB, ( x O, y O ) O, A P ( A P, B P ), ( x P, y P ) :
11 x P = x O + A P cos- B P sin y P = y O + A P sin+ B P cos, x O y O ( 2-3), P ( x P, y P ), ( A P, B P ) : A P = ( x P - x O ) cos+ ( y P - y O ) sin B P = - ( x P - x O ) sin+ ( y P - y O ) cos ( 2-4), 2-7, 2-8, P, P P, P, P,, : ; ; 2-8,,,,,,, 1949,, 1954 1980 1954, ( 2-1), 1942, 1954 1954 1942,, 1972 1982,, 1980
12, 60km, 1975 16 ( 2-1 ),,, 1980, 1954, 2. 3 1.,,,,,,,,,, ( ), : x = F 1 ( L, B) y = F 2 ( L, B) ( 2-5), L B, x y, ( 2-5),,,,,,,,,,,,, 2.,,, 1 ),
13,, 2-9 2-9, ( ),,,,,,,,,,,, 2 ), ( ),,,,,,,,, :
14,,,, -( Gauss-kr ger),, ( UTM), 3.,, ( ), :, ;,,,,,,,,, ( ),,,,,, 1. -,, 150 1825 1830, 1912,,, - 2-10,, ( ),,,, : 2.,, ( 1 ),,, ( 2 ),,, ( 3 ),,
15 3., O, X, X ; Y, Y, ( 2-11 ) 2-10 2-11 4.,,,,,, 63, 6 3( 2-12 ) 2-12 6 3 6 : 0, 6, 1, 2, 3,, 60,, 11 6, 13 23 N L 0 : L 0 = 6N - 3 ( 2-6) 3 : 6 1. 5, 3, 1, 2, 3,, 120 22 3, 24
16 45 n l 0 : l 0 = 3n ( 2-7) 5.,, X, Y Y, X 500km, Y 500km( 2-13),, 2-13, P X P = 3 275 611. 188m; Y P = - 376 543. 211m, 19, P : x P = 3 275 611. 188m, y P = 19 123 456. 789m 6.,, S,, R, = S + y2 m 2R 2 S ( 2-8) ( 2-8), S y m ( ), S, : S = - S = y2 m 2R 2 S ( 2-9) ( 2-9),, ( 2-9) : y m S S = y 2 m 2R 2 ( 2-10) 10 160km, 2-2, 110 000, 3 1. 5 ( )
17 2-2 y m / km 10 20 30 45 50 100 150 160 S/ S 1 / 810 000 1 /200 000 1 /90 000 1 / 40 000 1 /32 000 1 /8 100 1 /3 600 1 /3 170 7. 2-14( a) AB, Q A B ABB 1 A 1 : ABB 1 A 1 : : P ; R 360 = P R 2 ( 2-11),,, 2-14 ( b), a b,, AB, 2-14,, a b a b, ( ), 1 2, = 1, 2 + 2, 1 = 1 ( 2-12) 2 2 P aa 1 b 1 b, : ( 2-12) : P = 1 2 ( y 1 + y 2 ) ( x 2 - x 1 ) = y m ( x 2 - x 1 ) ( 2-13) = y m ( x 2R 2 2 - x 1 ) ( 2-14) ( 2-14), AB
18, y m = 280km, x 2 - x 1 = 5km, R 6 371km, = 4, 2-15 : = + 1, 2-1, 3 ( 2-15),, ( ) ( ),, 2-15 ( UTM ),,,,,,, ( Universal Transverse Mercator Projection), UTM 1938, 1945, UTM ( 2-16 ) 1 0. 999 6,,,, m 0 = 0. 999 6 UTM 0. 999 6, B = 0, l = 3 0. 001 (, 180km 1 40) ; ; ; UTM 60, 6, 180W 174 W 1, 1, 2, 3,, 60 11 000 000 80 80 : y = y + 500 000 ( ), x = 10 000 000 - x ( ) y = 500 000 - y( ), x = x ( )
19 2-16 UTM,,, UTM 2. 4,,,, H,,,,, 2-17,,,, 2-17,,,,,,,,
20 2-17,,,, 1950 1956, 1956, 1956 1959, 1956 1952 1979, 1985 1988 1 1 1985 1956 72. 289m, 1985 72. 260m,,,, 2-18, H A H B A B, H A H B, h AB A B,, h AB = H B - H A = H B - H A 2-18 2. 5,,,,,, R = 6 371km 2-19, AB, S,, R A AC, t A, AC
21 2-19 AB, S: : S = AC - AB = t - s S = R AC = t = Rtan AB = S = R 1 3 3 + 2 15 5 +,, = S, : R S = 1 3 S 3 R 2 S S = 1 3 S 2 R 2 ( 2-16) S = 10km, S S = 1 1 217 700, : 10km,,,, : = P ( 2-17) R 2, P, R, 1, = 1806060 / 206 265 P = 100 km 2, = 0. 51, 100 km 2,, 2-19, BC BC = h,
22 ( R + h) 2 = R 2 + t 2 t 2 h = 2R + h S t, h 2R, : h = S2 2R ( 2-18), h S = 1km, h = 8cm,,,, 100 km 2,,,, 2. 6,, 1.,,, 2. ( X ), X 3., 1., :, ;, ( 2-20 ), L C P : P = ( L P - L C ) sinb P = LsinB ( 2-19), L P B P P ( 2-19 ), L,,, = L;,, = 0 2.,,
23, :, ;,,,,,,,, 0 360 1. :, A 2. :, 3. :, A m,, 2-21, A A m 2-20 2-21 :,, A = A m + ( 2-20) A = + ( 2-21) = A m + - ( 2-22), 2-22, P 1 P 2 P 1 P 2, 12 P 1 P 2, 2 1 P 2 P 1 12 21 12, 21
24, 180, 12 = 21 180 ( 2-23) 2-22 2. 7,,,,,, 2-23 1500 2-24 12 000, ;,,, 2-24,,, :, ;, ;, 1.,
25 2-23 2-24
26 : ( 1 ) 1 d, D, : d D = 1 M ( 2-24), M M, ; M, 1500 11 000 12 000 : 1500 11 000 12 000 15 000 110 000 ; 125 000 150 000 1100 000 ; 1250 000 1500 000 11 000 000 ( 2 ),, 2-2512 000, 2cm 2-25,,,, 1 /10, 1 /100, ( ),, 2-26 1 /100 2-26 2.,,,,, 0. 1mm,
27,,, 0. 1mm 0. 1mm 2-3 2-3 1500 11 000 12 000 15 000 110 000 / m 0. 05 0. 1 0. 2 0. 5 1. 0, : ( 1 ),, ( 2 ),,, 2-4 1500, 11 000, 12 000 ( GB/ T7929-1995) 2-4 1500 11 000 12 000 1500 11 000 12 000 1 3 12 2 13 3 14 a. b. 4 a. 15 a. b. b. 5 16 9
28 1500 11 000 12 000 1500 11 000 12 000 6 17 a. b. 7 18 8 19 9 20 10 1. 2. 21 1. 2. 3. 11 22 : 1., 7. 3 2.,,,,,, 3.
29,,, 1.,,,, 10cm 5mm, 10cm, 2-27 11 000,,,,,,,,, 2.,, 11 110,, 2-28 15, 109 00, 36 00,,,, 1,, 3988 3 988km( ), 89 90, 39, 19321, 19, 321, 19 179km ( 321km - 500 km = - 179km),,,, ( 2-29 ) ( ) ( 2-30 )
30
31 2-28 15 2-29 2-30 2. 8, : ;
32 ( 1100 15 000), 1100,,, ( ),,, ;, ( ) 1. 20 70 80 20 70, 1100, 150 120 110 70 80 125 120, 150 125 110, 110 15 12. 5 11 15 000 2-5 2-5 1100 6 4 4 150 3 2 A, B, C, D J-51-A 1100 6 4 16 125 1 30 1 [ 1], [ 2],, [ 16] J-51-[ 2] 1100 6 4 144 110 30 20 1, 2,, 144 J-51-5 110 30 20 4 15 15 10 A, B, C, D J-51-5-B 110 30 20 64 11 3 45 2 30 ( 1), ( 2),, ( 64) J-51-5-( 24) 15 15 10 4 12. 5 7 30 5 1, 2, 3, 4 J-51-5-B-4 11 3 45 2 30 4 15 000 1 52. 5 1 15 a, b, c, d J-51-5-( 24) -b 1 ) 1100 1100 1100 2-31 1100 1100 6 4, 60 76, 12 4 76 88, 24 4 60, 1100, 4, 88 22, ( ) A, B, C,, V 180, 6, 60, ( ) 1, 2, 3,, 60, 88Z
33 2-31 1100, 1100, 4 6, N S, N 39 54 30, 122 28 25, 1100 120 12436 40, 1100 J-51,, NP-47, 48; NP-49, 50, 51, 52 2-32 1100 2 ) 150, 125, 110 1100
34 2-32 1100 1100 2 2, 4 150 ; A B C D 150 J-51-A, 2-33 2-33 150, 125, 110 1100 4 4, 16 125, [ 1 ], [ 2 ],, [ 16] 125 J-51-[ 2 ], 2-33 1100 12 12, 144 110, l, 2, 3,, 144 110 J-51-5, 2-33
35 3 ) 15, 12. 5, 11 2-34 110, 2-34 15, 125, 11 110 4 15, A B C D 110, 15 J-5l-5-B 15 4 12. 5, l 2 3 4 15 12. 5, J-5l-5-B-4 110 8 8, 64 11, ( 1 ), ( 2), ( 3),, ( 64) ; 2 30, 3 45, 110. J-51-5 -( 24) 4 ) 15 000 15 000 11 11 4 15 000 ( 2-35) 1 15, l 52. 5 11 a b c d 15 000 J-5l-5-( 24) -b 2-35 15 000
36 2-5 2., 1992 ( GB/ T 13989-92), 1993 7 1 ( 1 ) 1100 15 000 1100, 1100,, ( ) ( ), 1100 J50 150 15 000 1100, 1100,, 1100,, 2-36 2-36 150 15 000 2-6 2-6 1500 000 1250 000 1100 000 150 000 125 000 110 000 15 000 B C D E F G H 2-7 1100 15 000 2-37 2-7 1100 150 125 110 15 12. 5 11 15000 6 3 1 30 30 15 7 30 4 2 1 20 10 5 2 30 3 45 1 52. 5 1 15
37 1100 150 125 110 15 12. 5 11 15000 1 2 4 12 24 48 96 192 1 2 4 12 24 48 96 192 1 4 16 144 576 2304 9216 36864 1 4 36 144 576 2304 9216 1 9 36 144 576 2304 1 4 16 64 256 1 4 16 64 1 4 16 1 4 2-37 1100 15 000
38 2-1 150 ( 2-38) J50B001002 2-2 125 ( 2-39) J50C003003 2-3 110 ( 2-40) 45J50D010010 2-38 150 2-39 125 2-40 110 15 000
39 2-4 15 ( 2-40) 135 J50 E017016 2-5 12. 5 ( 2-40) J50F042002 2-6 11 ( 2-40) J50G093004 2-7 15 000 ( 2-40 ) 1100 15 000 J50H192192 ( 2 ), 1100 : a = [ /4 ] + 1 b = [ /6 ] + 31 : [ ] ; a 1100 ; b 1100 ; ; 2-8 114 33 45, 39 22 30, a = [ 39 22 30 /4 ] + 1 = 10 ( J) b = [ 114 33 45 /6] + 31 = 50 1100 J50, 1100 : c = 4 / - [ ( /4 ) / ] d = [ ( /6 ) / ] + 1 : ( ) ; [ ] ; c 1100 ; d 1100 ; ; ; ; 2-9 114 33 45, 39 22 30, 11 11 J50G015010 = 30 2, = 3 45 c = 4 /2 30 - [ ( 39 22 30 /4 ) /2 30 ] = 015 d = [ ( 114 33 45 /6 ) /3 45 ] + 1 = 010 1100,
40 ( GB/ T 13989-92),, 2-31 1100, 2-37, 2-382- 392-40,, ( ) 40cm40cm 40cm50cm 50cm50cm2-8 2-8 cm 2 /km 2 15 000 15 000 4040 4 1 12 000 5050 1 4 11 000 5050 0. 25 16 1500 5050 0. 0625 64 : 1., x, y, 15 000 km ; 12 000 11 000 0. 1km; 1500 0. 01km11 000 x = 83 500m y = 15 500m, 83. 5-15. 5 2.,,, 2-41( a), 15 3., 2-41 ( b), A-4 4. 15 000, 15 000 15 000, 2-41 ( c ) 15 000 32-56,, 2-41( d), 32-56---
41 2-41
42 3. 1,,,,,,,,,,, : 1.,,,, 1mm, 2.,,, 3,,,, 3.,,,,,,,,,,
43 1.,,,,, 30m 30. 004m, 0. 004m,,,,, 2.,,,, ( ),,,,,,,,,,, 3., 4.,,,,,,,,,,,,,,,,, ( ),,, ( ) ;, ( ),,,,, X, n, l 1, l 2,, l n, ( ) 1, 2,, n,
44 i = X - l i, i = 1, 2,, n ( 3-1),,,,,,, 358, ( 180 ),, ( 3-1) ( ),, d= 3 k, k/ n( n = 358 ), k /n 3-1, 3-1 ( 3-1), ( k / n) ( d ),,, 1 3-1 d k k /n k k/ n k k/ n 0 3 45 0. 126 46 0. 128 91 0. 254 3 6 40 0. 112 41 0. 115 81 0. 226 6 9 33 0. 092 33 0. 092 66 0. 184 9 12 23 0. 064 21 0. 059 44 0. 123 12 15 17 0. 047 16 0. 045 33 0. 092 15 18 13 0. 036 13 0. 036 26 0. 073 18 21 6 0. 017 5 0. 014 11 0. 031 21 24 4 0. 011 2 0. 006 6 0. 017 24 0 0 0 0 0 0 181 0. 505 177 0. 495 358 1. 000 3-1, : ( 1 ), ; ( 2 ), ; ( 3 ) ; ( 4 ),, : 1 + lim n n, [ ] 2 + + n = lim n [ ] = 0 ( 3-2) n
45 3-1 358,,,, ( n ), d, 3-1, P n,, : f( ) = 1 e - 2 2 2 2 ( 3-3), = 3. 141 6, e = 2. 718 3,, 2 :, : 2 2 1 + 2 2 + + 2 n [ 2 ] = n lim = lim n n n = lim n [ 2 ] n = lim n [ ] n ( 3-4) ( 3-5) ( 3-5),,,, ( 3-3),,, 3. 2,,,
46, 2,,,,,,, m, 3-1 m = 2 1 + 2 2 + + 2 n n = [ ] n ( 3-6) 10, ( ),, 3-2 3-2 2 2 1 180 00 03-3 9 180 00 00 0 0 2 180 00 02-2 4 179 59 59 + 1 1 3 179 59 58 + 2 4 180 00 07-7 49 4 179 59 56 + 4 16 180 00 02-2 4 5 180 00 01-1 1 180 00 01-1 1 6 180 00 00 0 0 179 59 59 + 1 1 7 180 00 04-4 16 179 59 52 + 8 64 8 179 59 57 + 3 9 180 00 00 0 0 9 179 59 58 + 2 4 179 59 57 + 3 9 10 180 00 03-3 9 180 00 01-1 1 24 72 24 130 m 1 = 2 = 2 10. 7 m = 2 = 3. 6 2 10, m 2 m 1, ( - 7, + 8 ),,,,, 3-3, = 0, f( ), 1 2m
47 m,,,, ; m,,, 3-2 3-2,, 200m 40m, 2cm,,,, ( ),, 0. 02 /200 = 1 /10 000, 0. 02 /40 = 1 /2 000, ( 3-1 ) :,,,,, d: P( ) = f( ) d= 1 2 m e - 2 2m2 d ( 3-7) ( 3-7), k, : P ( < km) = + km - km 1 2m e - 2 2m2 d ( 3-8) k = 1, k = 2, k = 3 ( 3-8 ), 2 3 : P( m) = 0. 683 = 68. 3 %
48 P ( 2m) = 0. 954 = 95. 4% P ( 3m) = 0. 997 = 99. 7%, 2 5 %, 3 0. 3%, 2,, 2,,, 2 = 2m ( 3-9) 3. 3, n, l 1, l 2,, l n x,, : x = l 1 + l 2 + + l n n = [ l] n ( 3-10), : X, l 1, l 2,, l n, 1, 2,, n,, n, : 1 = X - l 1 2 = X - l 2 n = X - l n [ ] = X - [ l] n n ( 4 ),, [ ], n lim n [ ] = 0 n ( 3-11) ( 3-12),,,,,, ( v) : v 1 = x - l 1 v 2 = x - l 2 ( 3-13) v n = x - l n
49, ( 3-10), [ v] = nx - [ l] [ v] = n [ l] n - [ l] = 0 ( 3-14),, ( 3-5),,, m, ( 3-6) X i,, ( 180 ), X, i,, ( 3-6), x, v i ; x X, x X, v i i ( 3-6), ( ) : m = [ vv] n - 1 ( 3-15) ( 3-15) ( 3-6), [ vv] [ ], ( n-1) n :, n ;,, ( n - 1), n ( n - 1 ) ( 3-15) ( 3-1) ( 3-13 ) :, 1 = X - l 1, v 1 = x - l 1 2 = X - l 2, v 2 = x - l 2 n = X - l n, v n = x - l n 1 = v 1 + ( X - x) 2 = v 2 + ( X - x) n = v n + ( X - x), [ v] = 0, [ ] = n( X - x) X - x = [ ] n
50, [ v] = 0 : ( X - x) 2 = [ ] 2 n 2 [ ] = [ vv] + n( X - x) 2 = 2 1 + 2 2 + + 2 n + n 2 2( 1 2 + 1 3 + + n 2 n - 1 n ), i j ( ji), ( 4 ), lim n 1 2 + 1 3 + + n n - 1 n n,, n,, ( X - x) 2 = [ ] n 2 [ ] = [ vv] + [ ] n [ ] = [ vv] n n - 1, ( 3-6) ( 3-15) ( 3-15) 3-2, 6,, 3-3,, l 0, l i, : = 0 l i = l 0 + l i ( 3-16) x = l 0 + [ l] n ( 3-17) 3-3 l / m l / cm v/ cm vv/ mm x, m 1 120. 031 + 3. 1-1. 4 1. 96 2 120. 025 + 2. 5-0. 8 0. 64 3 119. 983-1. 7 + 3. 4 11. 56 4 120. 047 + 4. 7-3. 0 9. 00 5 120. 040 + 4. 0-2. 3 5. 29 6 119. 976-2. 4 + 4. 1 16. 81 x = l 0 + [ l] n = 120. 017m m = [ vv] n - 1 = 3. 0cm ( l 0 = 120. 000) 10. 2 0. 0 45. 26
51 3. 4 ( ),,,,,, ( ),,, : 1., D n, d 1, d 2,, d n, D = d 1 + d 2 + + d n, D d 1, d 2,, d n, : Z = x 1 + x 2 + + x n 2., 11 000 d, D = 1 000d, D d : Z = mx 3., :, l i x = 1 n ( l 1 + l 2 + + l n ) = 1 n l 1 + 1 n l 2 + + 1 n l n ( ),,, : 4. Z = k 1 x 1 + k 2 x 2 + + k n x n, c, a b, a = c sin, b = ccos : Z = f( x 1, x 2,, x n ) ( 3-18),,, 3-3, a b, P,
52 P = a b ( 3-19) 3-3 a b a b a b, P,,, ( 3-19) a b : dp = P a da + P b db dp = bda + a db ( 3-20) : ( 3-20) P = b a + a b ( 3-21) ( 3-21) 3-3, : b a a b, P, a b, a b n, : : n: [ P P ] P 1 P 2 = b+ a a 1 b1 = b+ a a 2 b2 P n = b a n + a bn = b 2 [ a a ] + a 2 [ b b ] + 2 ab[ a b ] ( 3-22) [ P P ] [ = b 2 a a ] [ + a 2 b b ] + 2a b [ a b ] n n n n ( 3-23), ( 4 ), lim n [ a b ] = 0 n
53, ( 3-23) : [ P P ] n, ( 3-24) : P : [ = b 2 a a ] [ + a 2 b b ] n n m 2 P = b 2 m 2 a + a 2 m 2 b ( 3-24) :, x 1, x 2,, x n m n, Z x i m P = b 2 m 2 a + a 2 m 2 b ( 3-25) Z = f( x 1, x 2,, x n ) ( 3-26) ( ), m 1, m 2,, i, Z Z, ( 3-26), d,, Z = f x1 + f x2 + + f xn x 1 x 2 x n f x i ( i = 1, 2,, n),, m Z = f x 1 2 m 2 1 + f x 2 2 m 2 2 + + f x n 2 m 2 n ( 3-27) ( 3-27),, 3-3, : Z = k 1 x 1 + k 2 x 2 + + k n x n ( 3-28), k 1, k 2,, k n, x 1, x 2,, x n, m 1, m 2,, m n, : f f f = k 1, = k 2,, = k n x 1 x 2 x n m Z = k 2 1 m 2 1 + k 2 2m 2 2 + + k 2 nm 2 n ( 3-29) n, ( 3-18) ( 3-29), m x = 1 n 2 m 2 1 + 1 n 2 m 2 2 + + 1 n 2 m 2 n,, m 1 = m 2 = = m n = m, m : m x = m n = [ vv] n( n - 1) ( 3-30)
54, 1, n, 3-3,, : m x = m n = 3. 0 = 1. 2 ( cm) ( 3-31) 6, 1 3. 0cm, : 0. 03 120 = 1 4 000 6 1. 2cm, : 3-4 0. 012 120 = 1 10 000 ( 3-32) ( 3-33) ( ) D x y, A B D m m D, m x m y :,, : x = Dcos y = Dsin d x = cos dd - Dsin d d y = sindd + Dcos d, : ( 3-34) ( 3-35) m 2 m x = cos 2 m 2 D + ( Dsin ) 2 2 ( 3-36) m 2 m y = sin 2 m 2 D + ( Dcos ) 2 2 A B : M AB = m 2 x + m 2 y = m 2 D + D m 2 ( 3-37),,,, A B : ( 3-36) ( 3-37 ), : m x D = 360. 440m 0. 030m, = 60 24 30 16 = 0. 028mm, m y = 0. 030mm, M AB = 0. 041mm
55 3. 5, n ( ),,,,,,,,,, ( m ),, P, : P i = C m 2 i ( 3-38), C 1, m 0 ( 0 ), : : P i = m2 0 m 2 i ( 3-39) m i = m 0 1 P i ( 3-40) m 0, m, N : ( 3-39), N : m ( N ) = m N ( 3-41) P m 2 ( N ) = Nm2 = N ( 3-42), 1km m 0, L k m : m H = m 0 L ( 3-43) ( 3-39), L k m : P H = m2 0 m 2 0 L = 1 L ( 3-44), L 1, L 2,, L n, m 1, m 2,, m n,
56 ( 3-38) P 1, P 2,, P n, : : x = P 1 L 1 + P 2 L 2 + + P n L n = [ PL] P 1 + P 2 + + P n [ P],, : ( 3-45) L i = L 0 + L i ( 3-46) x = L 0 + [ PL] [ P] ( 3-47) n, x, v 1 = x - L 1 v 2 = x - L 2 ( 3-48) v n = x - L n : x,, : [ Pvv] = [ P( x - L) 2 ] = min ( 3-49) d[ Pvv] dx = 2 [ P( x - L) ] = 0 [ P] x - [ PL] = 0 x = [ PL] [ P] ( 3-45), : ( 3-50) [ P v] = [ P ( x - L) ] = [ P ] x - [ P L] = 0 ( 3-51) ( 3-50) :, : x = P 1 [ P ] L 1 + P 2 [ P ] L 2 + + P n [ P ] L n m x = P 1 [ P] 2 m 2 1 + P 2 [ P] 2 m 2 2 + + P n [ P ] 2 m 2 n ( 3-39), m 2 i = m2 0 P i ( m 0 ), m x = m 0 P 1 [ P] 2 + P 2 [ P] 2 + + P n [ P] 2 m x = m 0 [ P ] ( 3-39), : ( 3-52) P x = [ P] ( 3-53)
57, ( 3-39) m 2 0 = P i m 2 i ( 3-54) n, m 2 0 = P 1 m 2 1 m 2 0 = P 2 m 2 2, m 2 0 m 2 0 = [ Pm2 ] n = P n m 2 n = [ Pmm] n i m i, : v i m 0 = [ P ] n ( 3-55), x X, i, ( 3-15), : 3-5 m 0 = [ P vv] n - 1 ( 3-56) 3, 2 4 6, ( 3-4 ), 3-4 L L( ) P PL( ) v( ) Pv( ) 1 2 40 20 14 4 2 8 + 4 + 8 2 4 40 20 17 7 4 28 + 1 + 4 3 6 40 20 20 10 6 60-2 - 12 L 0 = 40 20 10 12 96 0 x = 40 20 10 + 96 12 = 40 20 18 [ Pvv] = 60, m 0 = 60 3-1 = 5. 5 P x = 12, m x = 5. 5 12 = 1. 6
58 3. 6, ( ) 3-4, A H A, L 1 L 2 L 3 L 4 L 5, B C D,,,,,,,, 3-4 t x 1, x 2,, x t, n L 1, L 2,, L n, p 1, p 2,, p n, L 1 + v 1 = a 1 x 1 + b 1 x 2 + + t 1 x t + d 1 L 2 + v 2 = a 2 x 1 + b 2 x 2 + + t 2 x t + d 2 ( 3-57) L n + v n = a n x 1 + b n x 2 + + t n x t + d n, d i L i, l i = d i - L i ( 3-58) : v 1 = a 1 x 1 + b 1 x 2 + + t 1 x t + l 1 v 2 = a 2 x 1 + b 2 x 2 + + t 2 x t + l 2 ( 3-59), a i, b i, c i, l i v n = a n x 1 + b n x 2 + + t n x t + l n [ pvv] = min x 1, x 2,, x t,,
59 [ pvv] x 1, x 2,, x t,, x 1, x 2,, x t [ pvv] x 1, x 2,, x t : [ pvv] v 1 v 2 v n = 2p 1 v 1 + 2 p 2 v 2 + + 2p n v n x 1 x 1 x 1 x 1 [ pvv] x 2 = 2p 1 v 1 v 1 x 2 + 2 p 2 v 2 v 2 x 2 + + 2p n v n v n x 2 ( 3-60) [ pvv] x t = 2p 1 v 1 v 1 x t + 2 p 2 v 2 v 2 x t + + 2p n v n v n x t ( 3-59) v i x 1 = a i, v i x 2 = b i,, v i x t = t i ( i = 1, 2,, n) ( 3-60),, 2 : p 1 a 1 v 1 + p 2 a 2 v 2 + + p n a n v n = [ pa v] = 0 p 1 b 1 v 1 + p 2 b 2 v 2 + + p n b n v n = [ pbv] = 0 p 1 t 1 v 1 + p 2 t 2 v 2 + + p n t n v n = [ ptv] = 0 ( 3-61) t, ( 3-59) n, n v t x n + t, ( 3-59) ( 3-61), : [ pa a ] x 1 + [ pab] x 2 + + [ pa t] x t + [ pa l] = 0 [ pa b] x 1 + [ pbb] x 2 + + [ pbt] x t + [ pbl] = 0 ( 3-62) [ pa t] x 1 + [ pbt] x 2 + + [ ptt] x t + [ ptl] = 0,, ( 3-59) v, v [ pvv] = min v, : m = [ pvv] n - t ( 3-63) 3-4, H A = 237. 483m, B C D X 1 X 2 X 3, : L 1 = 5. 835m, S 1 = 3. 5km L 2 = 3. 782m, S 2 = 2. 7km L 3 = 9. 640m, S 3 = 4. 0km
60 L 4 = 7. 384m, S 4 = 3. 0km L 5 = 2. 270m, S 5 = 2. 5km : L 1 + v 1 = X 1 - H A L 2 + v 2 = - X 1 + X 2 L 3 + v 3 = X 2 - H A L 4 + v 4 = X 2 - X 3 L 5 + v 5 = X 3 - H A, : v 1 = X 1 - ( H A + L 1 ) v 2 = - X 1 + X 2 + - L 2 v 3 = X 2 - ( H A + L 3 ) v 4 = X 2 - X 3 - L 4 v 5 = X 3 - ( H A + L 5 ),, X 0 1 = H A + L 1 X 1 = X 0 1 + x 1 X 0 2 = H A + L 3 X 2 = X 0 2 + x 2 X 0 3 = H A + L 5 X 3 = X 0 3 + x 3 v 1 = x 1 v 2 = - x 1 + x 2 + 23 v 3 = + x 2 v 4 = x 2 - x 3-14 v 5 = + x 3 10km, p i = 10 S i, : p 1 = 2. 9, p 2 = 3. 7, p 3 = 2. 5, p 4 = 3. 3 p 5 = 4. 0: 6. 6x 1-3. 7x 2-85. 1 = 0-3. 7x 1 + 9. 5x 2-3. 3x 3 + 38. 9 = 0-3. 3x 2 + 7. 3x 3 + 46. 2 = 0 x 1 = 11. 75mm, X 1 = 243. 329 8m x 2 = - 2. 04mm, X 2 = 247. 121 0m x 3 = - 7. 25mm, X 3 = 239. 745 8m x 1 x 2 x 3 : v 1 = 11. 8mm, v 2 = 9. 2 mm, v 3 = - 2. 0 mm v 4 = - 8. 8mm v 5 = - 7. 2 mm
61, : ( 3-63) : m = y 1 = L 1 + v 1 = 5. 846 8m y 2 = L 2 + v 2 = 3. 791 2m y 3 = L 3 + v 3 = 9. 638 0m y 4 = L 4 + v 4 = 7. 375 2m y 5 = L 5 + v 5 = 2. 262 8m 357. 16 5-3 = 13. 4mm
62 4. 1,, 4-1, A H A, B H B A B h AB, B H B : B H B = H A + h AB 4-1 h AB : A B, A B, A B, A, a, ; B, b, A B : B H B : h AB = a - b ( 4-1)
63 H B = H A + ( a - b) h AB, a b, h AB, B A ; a b, h AB, B A, h AB h, h AB A B ; h B A B A, h AB = - h BA 4-1, B H i ( ) : H i = H A + a H B = H A + ( a - b) = H i - b ( 4-2),,,, 4-1 A B,,,,,, 4-2, A B h AB,, A1 h A1 12 h 12, nb h nb, 4-2, 1, 2, 3,, n h AB : h AB = h A1 + h 12 + + h nb, h A1 = a 1 - b 1 h 12 = a 2 - b 2 h n B = a n + 1 - b n + 1 1, 2,, n n h AB = ( a 1 - b 1 ) + ( a 2 - b 2 ) + + ( a n + 1 - b n + 1 )
64 n + 1 = 1 n + 1 ( a - b) = 1 n + 1 a - 1 b ( 4-3), h AB ( 4-3), h AB,, ( ) A B,,,,, IN IM ( 4-3 ) 4-3, 4-3, A B : h AB = EA - FB, IM IN, MA NB, EA FB ME NF p 1 p 2 ( ) ME NF : h AB = ( MA - p 1 ) - ( NB - p 2 ),, IMIN,, f 1 f 2 ( ) MM NN, 1. h AB = ( a + f 1 - p 1 ) - ( b + f 2 - p 2 ) ( 4-4) 4-4, I R, S, t, p 2-12 p = S2 2R ( 4-5)
65 4-4 2. R = R, K R R, K 1, K ( 4-5), f = S2 2 R K = K S2 2R ( 4-6), K,,, K = 0. 11 r,, K < 1, r, : ( 4-4) : r = p - f = ( 1 - K) S 2 2R ( 4-7) h = ( a - b) - ( r 1 - r 2 ) ( 4-8) K = 0. 11, S = 100m, R = 6 371km, r = 0. 7 mms 1 S 2, r 1 r 2, S 1 S 2, ( r 1 - r 2 ) 4. 2,,, 4-1 D S, D,05 1 3 10 S3 S10,, S05 S1,
66 4-1 DS05 DS1 DS3 DS10 0. 5mm 1mm 3mm 10mm 4-5 S3 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. 4-5 S3 1 2, 3 4, 5,,,,,,,, 6, 7, 8,,,, 4-5 9, 10, ( ) 11 12,, 13,, 14 15, 4-6, 1 2 34 5 6 7 CC 1,,,,,
67 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. 4-6, ;,,,,,, : V = 20 ( 4-9) DS3, 4-6 7,,, ( ),,,,, 4-7( a),, ( ) (, 1, 2, 3 ),, 4-7( b),,, 4-7,,, :, ;, (
68, ) ; ( ),, ;,,, 1., ( 4-8 ( a ) ),,,, 2mm, 4-8 ( b), O, O, LL 1,,, 4-8,, 4-9,,,, 4-9
69 ( 2mm), ( ), 2mm,, 4-10, R( mm), ( ) : = 2 ( ) ( 4-10) R 4-10 ( 4-10) R, R,,,, 6 30, 10 20, 10 /2mm 20 /2 mm,, 4-11, A, B C B C, A, 4-11 2., 4-12,,,, O, ( O ) L L 1,, 5 /2 mm 10 /
70 4-12,,,, 4-13 N3, 0. 3 mm 4-14 S1, 5mm, 0. 05 mm, S1 5mm 4-15 N3, 100, 10 mm, 0. 1 mm, 0. 01mm10, 1mm, 5mm,,,, 10mm, 5 mm;, 0mm, 5mm 4-15,, a, a 148 149, 5mm, 0,, 148, 6. 50mm,
71 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. ; 16. 4-13 N3 4-14 S1 6. 50 mm - 5 mm, a : a = 148cm + 6. 50mm - 5mm a = 148. 650cm - 5mm, ( ) 5mm,,,
72 4-15,,,,,,, 4-16 DSZ2, 4-17 DSZ3-1 1. 4-18,,, :,, A, f = s ( 4-11),, B, 2.,, DSZ3 4-19( a),,
73 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. 4-16 DSZ2 1. ; 2. ; 3. ; 4.. 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. 4-17 DSZ3-1 4-18 B C, A, 4-19( b), ( P ),, 4-20,,, =
74 4-19 4-20 ( 1), 4-19 ( a),,, :, 4-21,,,, B ( 4-22 ),, 4-22, 4-21 ( ) ADSZ3,, = 4,,, 2 2, 2, 4, = 4,,
75 4-21 ( 2) 4-22 ( 3) 3.,, 4-23( a) P ;,,,,, ( 4-23( b) ) 4-24,,,,,,, 4-23 4-24
76, 3 4m,,,,,,, 1cm,,, 4-25 4-25 3m, ( ), ( ),, 4 687 mm 4 787mm, (, 4-26 ( a) ),,,,,,, (, 4-26 ( b) ) 30cm, 2 3cm,,,,,, 10mm 5mm 10mm 4-27( a),, 0 300cm,,
77 300 600cm,,,, 5mm 4-27 ( b ),, 5mm,,,,, 0. 1 5. 9m, 5mm, 2 4-26 4-27 1.,,,,,,,,,,,,,
78, 2., 4-28, 1 2 3,, ( ) 1 2,, 1 2, 4-28 ( a),, 4-28( b) 4-28 3.,,,, 4., ( ),, 5.,, ( ),,, 4-29,,,,, 4-30 N3, 14 865( 1. 486 5m) 4-31 S1, 198 15( 1. 981 5m)
79 4-29 4-30 N3 4-31 S1 1., ( ),,, :, Leica NA2002
80 NA3003 ( 4-32 ) ;, DiNi10 DiNi20 ;, DL-101C DL-102C 4-32 DNA03 NA2002, 2. 4-33 NA2002 4 4-33,, CCD, 6. 5mm, 256 25m, 256
81, 3. ( ), ( ),,, ( h) ( d), ( d h), 50 000,,,,, d,, 80 %, h 0, d 4.,, Wild Ni2002 10 10-6 m / m,, ( ), 4-34, ;, 1. 35m, 4. 05m 1. 8m, 100m 4-34 ( ),,, : ; 4. 3,, :,,
82,,,,,,,,,,,,,,,,,, 4-2 4-2 A B h H 1 2 3 4 5 A 0 347 46. 215 1 1 631-1 284 1 0 306 2 2 624-2 318 2 0 833 3 1 516-0 683 3 1 528 4 0 501 + 1 027 4 2 368 B 0 694 + 1 674 44. 631, 4-3,, 4-3,
83 4-3 /m /m /m /mm /mm / mm S3 65 3. 0 6. 0 2. 0 3. 0 3. 0 S3 80 5. 0 10. 0 3. 0 5. 0 5. 0 : 1 ), ; 2 ), ; 3 ), ; 4 ), ; ( ) ( ),, 4-4 ( 1 ) ( 8), 1. : ( 9) = ( 4 ) + K - ( 7) ( 10) = ( 3) + K - ( 8 ) ( 11) = ( 10) - ( 9) ( 10) ( 9), ( 11 ) K 4-4, 5 K = 4 787, 6 K = 4 687 ( 16) = ( 3) - ( 4) ( 17) = ( 8) - ( 7) ( 16), ( 17), ( 16) ( 17) ( 4-4 ( 16 ) ( 17) 100 ), ( 11), : ( 11) = ( 16 ) 100 - ( 17) ( 12 ) = ( 1) - ( 2) ( 13 ) = ( 5) - ( 6) ( 14 ) = ( 12) - ( 13 ) ( 15 ) = ( 14) + ( 15 ) ( 12), ( 13), ( 14), ( 15) 5. 6
84 2. 4-4 ( ) 2001 8 2 8 05 : : d d K + ( 1) ( 5) ( 3) ( 8) ( 10) ( 2) ( 6) ( 4) ( 7) ( 9) ( 12) ( 13) - ( 16) ( 17) ( 11) ( 14) ( 15) 1 571 0739 5 1 384 6 171 0 1 1 197 0363 6 0551 5 239-1 374 376 - + 0833 + 0932 + 1 + 0832. 5-0. 2-0. 2 2 121 2 196 6 1 934 6 621 0 2 1 747 1 821 5 2 008 6 796-1 374 375 - - 0074-0175 + 1-0074. 5-0. 1-0. 3 1 914 2 055 5 1 726 6 513 0 3 1 539 1 678 6 1 866 6 554-1 375 377 - - 0140-0041 + 1-0140. 5-0. 2-0. 5 1 965 2 141 6 1 832 6 519 0 4 1 700 1 874 5 2 007 6 793 + 1 265 267 - - 0175-0274 - 1-0174. 5-0. 2-0. 7 0089 0124 5 0054 4 842-1 5 0020 0050 6 0087 4 775-1 69 74 - - 0033 + 0067 0-0033. 0-0. 5-1. 2 : ( 3) - ( 4) = ( 16) = h {( 3) + K} - ( 8) = ( 10 ) ( 8) - ( 7) = ( 17) = h {( 4) + K} - ( 7) = ( 9)
85 h = 1 2 ( h + h ) h h, h : ( 15) = ( 12) - ( 13) = ( 12 ) + ( 13),,,, 1 cm ( 1 ),, ( 2), 2mm,, ( 1) ( 2), 4-5, ;,,,, ( 3), ( 3 ),,,, ( 4), ( 5) ( 6) ( 4 ),,, ( 7 ) ( 5 ),,, ( 8) 4-5 ( 1) ( 8), ( 9 ) ( 18),, : : ( 9) = ( 1) - ( 2 ) ( 10 ) = ( 5) - ( 6) ( 11 ) = ( 9) - ( 10) ( 12 ) = ( 11) + ( 12 ) ( 14) = ( 3) + K - ( 8 ) K ( N3 K = 3. 015 5 m)
86 ( 13) = ( 4) + K - ( 7) ( 15) = ( 3) - ( 4) ( 16) = ( 8) - ( 7) ( 17) = ( 14 ) - ( 13) = ( 15 ) - ( 16) ( 18) = 1 2 { ( 15 ) + ( 16) } 4-5 N3, S1 Ni004,,, 4-5 200 d d + K ( ) ( ) ( ) ( 1) ( 5) ( 3) ( 8) ( 14) ( 2) ( 6) ( 4) ( 7) ( 13) ( 9) ( 10) - ( 15) ( 16) ( 17) ( 11) ( 12) h - ( 18) 2 406 1 809 31 219. 83 521. 38 0 1 1 986 1 391 32 160. 06 461. 63-2 420 418 - + 059. 77 + 059. 75 + 2 + 2 + 2 h + 059. 760 1 800 1 639 32 157. 40 458. 95 0 2 1 351 1 189 31 141. 40 442. 92 + 3 449 450 - + 016. 00-016. 03-3 - 1 + 1 h + 016. 015 1 825 1 962 31 160. 32 461. 88-1 3 1 383 1 523 32 174. 27 475. 82 0 442 439 - - 013. 94-013. 94-1 + 3 + 4 h - 013. 945 1 728 1 884 32 150. 81 452. 36 0 4 1 285 1 439 31 166. 19 467. 74 0 443 445 - - 015. 38-015. 38 0-2 + 2 h - 015. 380
87 d d ( ) ( ).... -.. -. 688. 36 1 894. 57 641. 92 1 848. 11 1 754 1 752 - + 046. 44 + 046. 46 h + 046. 450 + K ( ) 4-6 4-6 0. 5cm 1cm / m / m / m / m / mm / mm / mm / mm / mm S05 35 0. 5 1. 5 0. 5 0. 4 1. 5 3. 0 0. 7 2 K S1 50 1. 0 3. 0 0. 3 0. 6 1. 5 3. 0 1. 0 4 K S05 60, : ( 1 ) : ; ( 2 ) : ;,, : ( 1 ), ; ; ( 2 ),, ( 3), 3
88 ( 4 ),, ( 5 ),,, 2, ( 6 ),, 2,, 2, 4. 4 1.,, i, i, 4-35 A B, S A S B, x A x B, B A : h AB = ( a - x A ) - ( b - x B ) = ( a - b) - ( x A - x B ) x = Stani h AB = ( a - b) - ( S A - S B ) tani = ( a - b) - ( S A - S B ) h = ( a - b) - i ( S A - S B ) i ( 4-12) 4-35 i x A = x B, S A = S B,,,,, i i,, i
89,, 2.,,,,, 1., = 20 /2mm, 100m, 0. 5, 5mm,,,,, 2.,, i, 3.,,,, 4.,,,,,,,,,,, 1.,,,,,,, :, ;,,, : ;, ;, 2.,,
90, 0. 3m, 3.,, 4. 5,,,,,, 4-36 4-36 1. : ;,,,,,
91 2. : ;,,,,,, : 1. ( 1 ),,, 4-37 V, L,,, L, V, 4-37 ( a) 180 ( 4-37( b) ), V, V,,,, L 4-37 ( b) L 2,,, 2 4-37
92 ( 2 ), 180,, ;,, ( 3 ),, 4-38,,,, l V, 4-39 ( a), V, 4-39( b),,,, 180,,,,, 4-38 4-39 2. ( 1 )
93,,,,,,,,,, ;,, ( 2 ), 4-40 ( a) A,, A A, ; A, 4-40 ( b),, ( 3 ),,, 4-40 ( b) A,, A,,, 4-40 3.,, i,, i i = 0,,, ( 1 ) i i, : A B, A B h AB h AB i, ( 4-12) h AB i = h AB - ( S A - S B )
94 h AB i = h AB - ( S A - S B ) i h AB - ( S i A - S B ) = h AB - ( S A - S B ) i = h AB - h AB ( 4-13) ( S A - S B ) - ( S A - S B ), S A = S B, h AB i h AB, ( 4-13) : S A - S B = - ( S A - S B ), ( 2 ) i = i = h AB - h AB ( 4-14) S A - S B h AB - h AB ( 4-15) 2( S A - S B ) A B,, A B,, 4-41( a) h AB,, B, 4-41( b), 4-41 i h AB i, ( 4-13) i = h AB - h AB ( 4-16) S A - S B, i 15 ; i 20, A, i i : x A x A = i S A,, B, A a 2 : a 2 = a 2 - x A a 2,,
95, ( ) ( 4-42),, ( ), a 2,, 4-42 ( 3 ) 4-43( a) AB A, A B h AB AB B, 4-46( b), A B h AB ;, S AB h AB = a 2 - b 2 = S A - S B = - ( S A - S B ) 4-43 i ( 4-15) i: i = h AB - h AB ( 4-17) 2S AB,, B, A : x A = i S A : A, B : a 2 = a 2 - x A
96 x B = i S B : b 1 = b 1 - x B B, A : A, B : a 2 b 1 = a 2 - x A = b 1 - x B, B, A a 2, A, B b 1, ( 4 ),,,, i i, i i 4-44, P, V, R ; P V R AB P, V, AC P, AB AC, AB AC, AC AC 1, AC 1 V AE AB i, i,, 4-47, i 4-44 i
97 C 1 C 2 BC, C 1 EBE, : i, tani = BE AB BE = C 1 C 2 BC 1 = BC 1 sin = ABtan tani = ABtan sin = tan sin AB i = i = ( 4-18) 8,, = 4 i < 1, ( 4-18) : = i 14, i, i, i + ( 4-44, ) ;, i - ( ), : i, i = - i, h AB = i S - i S h AB = i ( S + S ),,,,, i +, -, i,, ( ),,,,,,, :
98,,,,, :, i,,, ;, i, i, 4-45,,,,,, 4-45 ( 1), :, i, 4-46( a),,,, ;, i, 4-46 ( b),,,, 4-46 ( 2),, 4-47,, A B,,,,,,, A B,,,,, 4-48
99 4-47 ;, 4-48( c) ( d) ( e), ( 4-48( d) ), i > : ( 4-51( e) ), i = 0, 0; ( 4-48 ( c) ), i <,, 2mm,,,, i,,, i,, i 4-48 1. : ( ),
100,, A B,,,,, ( ) ( ), A B ;,,, 2. A B, AB 100 m, A B ( ), AB, ( 1 2 ) AB, A B h AB, ; 3, ( ), A B h AB ; 3, ( ), A B h AB ; 3, ; 1, ( ), A B h AB ; 1, ( ), A B h AB,,, h AB h AB h AB h AB h AB,, 5mm,,,, 1.,, 4-49, a < 8 mm, a,,, 4-49 2.,,,,,
101, 50 m,,, 90,, 3. : ; ; ; : ( 1 ),, 0. 5 mm,, 4-50, 103cm, 0. 2 mm,,, 4-50 ( 2 ), 1. 0 mm,,, ( 3 ) 4 687 mm 4 787mm,, :, 20m, ( ), ( )
102,, 180, K ( 4 ),,,,, :,, 1m, A 1, A 2, z : 4-51 z = A 2 - A 1 4-51
103 5. 1,,,, 0 360 5-1, AOC OA OC, AOC, A 1 B 1 C 1, AOC 5-1, A 1 B 1 C 1 OA OC OB 1 OB 1 O ( ), OB 1, OA a, OC b, b a, A 1 B 1 C 1 = b - a ( 5-1) 5-1
104,,,, 0 90 ( ),, Z, 0 180,, 5-2 5-2,, ( ),,, 90, 5. 2 5-3,,,,, ( ) ( 5-3),,,,,,,,,,
105 5-3,, D, J, DJ07DJ1 DJ2 DJ6 DJ15 DJ6 6, J6, 5-4 J6 5-5 J2 5-6 T3, 0. 7 1. ( 1 ),, ( 2 ), ( ) ( 3 ),,, J6 1, J2 20,
106 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. ; 16. ; 17. ; 18. ; 19. ; 20. ; 21. ; 22. 5-4 J6 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. 5-5 J2
107 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. ; 16. ; 17. ; 18. ; 19. ; 20. ; 21. 5-6 WildT3, T3 4 ( 8 ) 1 5-7 J6,,,,, ( ),,,,,,,,,,,, 5-8 5-9,, 0 ( 5-8( a) ) 90 ( 5-9( a) ) 2., 5-10
108 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. 5-7 5-8 ( ) 5-9 ( ) J6 : ( 1 ) J6, 1 1, 1 5-11, ( H), ( V), 60, 1, 10, 10, 1, 0. 1, 6 0,
109 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. ; 16. ; 17. ; 18. ; 19. ; 20. ; 21. ; 22. ; 23. 5-10 J6
110, J6 5-11 214 54 42 79 05 30 ( 2 ) J2, ( ) 180,,,,,, T2 5-12( a) ( b) T2, ( a) 285 51 55. 0, ( b) 94 22 44. 0 5-12 T2 ( 3 ),, ( 5-13),
111,,,,, ( 5-13 ) ; 1 2,,,,,,,,,,, JGJ2 5-14 JGJ2, ( a ) 174 02 00. 0, ( b) 91 17 16. 0 5-13 5-14 JGJ2, 20 60,, 1. 5-15 DT5, 5-16 ET-02
112 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. ; 16. ; 17. ; 18. ; 19. BDC21; 20. ; 21. ; 22. ; 23. ; 24. ; 25. ; 26. ; 27. ; 28. ; 29. ; 30. ; 31. ; 32. ; 33. ; 34. 5-15 DT5 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. ; 16. ; 17. ; 18. ; 19. ; 20. ; 21. ; 22. ; 23. 5-16 ET-02
113 2. 5-17 16, ( ), 5-17 ( ) ( ), ( ) 0, ( ) 1, 5-1,, 5-17 5-1 0 1 2 3 0000 0001 0010 0011 4 5 6 7 0100 0101 0110 0111 8 9 10 11 1000 1001 1010 1011 12 13 14 15 1100 1101 1110 1111 5-18,,,,, 0,, 1 5-18 1001 s, s n, : s = 2 n = 360 s ( 5-2), 5-17 22. 5,,,
114 5-18, 3. 5-19( a),,, a, 5-19 ( b),,,,,, ( ) 5-19 d, w,, : w = dcot ( 5-3) ( 5-2),, 5-19( a),,
115,,,,,,,,,, 5. 3 ;, 1.,,,,,,,,,,,,,,,,,,,, ;,,,,, 90,, 3mm 2.,,, 5-20, 1mm :,,, (, ),, (, ),,
116 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. 5-20, ( ),,,,,, 5-21 5-21,,,, ;,,, 2,
117 1. 5-22, B, BA BC, B, : ( 1 ) C, c ( 2 ), A, a, : ( 3 ), A, a ( 4 ) C, c, : = a - c ( 5-4) = a - c ( 5-5) 5-22,,, DJ6, 40, : 5-2 = 1 2 ( + ) ( 5-6) 5-2 C 0 20 45 125 14 15 A 125 35 00 B 125 14 20 C 180 21 15 125 14 25 A 305 35 40
118 2. 5-23 O, O A B C D, : 5-23 : 0 00 ( ), ( ) A, B C D, 3, A,,, A D C B A,, 5-3 J6,, ( 3 5 ) 12 0024, 0 00 00, 6, A ( 12 ),,,, J2,,,,, J2, 2C ( J6 ), : 2C = L - ( R 180 ) ( 5-7)
119 5-3 J6 J6 1 2 3 4 5 6 7 8 9 12 18 A 0 01 06 180 01 18 0 00 00 0 00 00 0 00 00 B 91 54 06 271 54 00 91 52 54 91 52 48 91 52 45 42 C 153 32 48 333 32 48 153 31 36 153 31 33 153 31 33 30 D 214 06 12 34 06 06 214 05 00 214 04 54 214 05 00 04 48 A 0 01 18 180 01 18 24 30 A 90 01 18 270 01 24 0 00 00 0 00 00 B 181 54 00 01 54 18 91 52 36 91 52 42 48 C 243 32 54 63 33 06 153 31 30 153 31 33 36 D 304 06 36 124 06 18 214 05 12 214 05 00 04 48 A 90 01 30 270 01 36, L, R, 180 180
120 2 C, 2C, 2C ( ) 2C,, 1 2 ( L + R 180 ),,,, 0 00 00,,, 5-4 5-4 ( ) 2C DJ1 1 6 9 6 DJ2 3 8 13 9 DJ6 18 24, 1. ( ),,,,,,, 90,,,,, : ( 1 ),, = - ; ( 2 ),, = - J6 ( ), 5-24,, L ; R,
121 5-24: = 90- L = R - 270, : ( 5-8) = 1 2 ( + ) = 1 2 [ ( R - L) - 180 ] ( 5-9) +, ; -, 5-24 2.,, 90, x, x, x, x ;,, x, x 5-9 5-24,, 90, 90 + x;, L x, :, : : = 90 - ( L - x) ( 5-10) = ( R - x) - 270 ( 5-11) = 1 2 [ ( 90- L + x) + ( R - 270- x) ] = 1 2 [ ( R - L) - 180 ] ( 5-12)
122 ( 5-12),, x = 1 2 [ ( L + R) - 360 ] ( 5-13) ( 5-13) 3., : ( 1 ) :,, (, ;,, ),, L,, R ( 2 ),, 17, - 17, + 17,, L R,,,,,, J6 25, 5-5, 5-9 5-5 /m / m 59 20 30 30 39 30 4. 10 15 30 39 45 300 40 00 30 40 00 71 44 12 18 15 48 No. 4 1. 43 4. 40 12 18 16 00 288 16 12 18 16 12 124 03 42-34 03 42 3. 82 18-34 03 24 235 56 54-34 03 06
123 4.,,,,,,, J2,,,,, 5-25( a),, 5-25( b), O, A ;,, A, A O,,, O A,, 5-25 5. 4,
124 1.,,,,,,,,,,, ( 1 ) 5-26, O, O, O O,, M, M, OCO M, MM, MMOC5-26 : OC = OO sinoo C = OO R sinoo C OOe, OO 0, OO C M, = e R sin( M + ) ( 5-14) 5-26, R, M M 5-26 M = M + ( 5-14) M ( 5-14),
125 sin( M + ) = - sin( 180+ M + ), 180 ( ),, ( 180 ),, DJ2, DJ6,,, ( 2 ) :, 5-27AO, c, A, A A,, a a A A a Oa = x c c A RtOaa RtOAA RtA a O sinx c = aa Oa a a = AA AA= OAsinc Oa= OAcos ( 5-15) x c c, x c = c cos ( 5-15) ( 5-16) 5-27 c,,,
126 c ( ), ( ),, x c ( 5-16), x c,, x c = 0, x c = c, + - x c,, L, L, L = L - x c ( 5-17), R, R,, R = R + x c ( 5-18) A = 1 2 ( L + R ) ( 5-19), c,,,,,, ( 5-17) ( 5-18) R = L 180 L - R 180= 2 x c ( 5-20) ( 5-16),, cos 1, x c c, ( 5-20) L - R 180= 2c ( 5-21),, 2c, 2c 2c, 2c, 2c, 2c J2 13, 2c,, 2 c J2 16, J6 20, ( 3 ), i, i 5-28H ( H 1 H 1 ), h H, HOh H 1 H 1 i A 1 A 1, HOh i AOh, A, a A hoa = x i i
127 5-28 Rta ho sinx i = a h ao RtAa h RtAa O, x i i, a h = Aa tani ao = Aa / tan x i = itan ( 5-22) i,,,,, i ( ), i ( ), x i x i,, x i ; = 0, x i = 0,, x i,, L, L, L = L - x i, R, R,, R = R+ x i A = 1 2 ( L + R ),, : L = L - x i - x c
128 R = L 180, ( 4 ) R = R + x i + x c L - R 180= 2( x c + x i ) = 2 c cos + itan ( 5-23),,,,, 5-29, OT, P, OT V, P, P P O 1 O 2 TOT,, V,, P, O 1 O 2 V ON, 5-29 OR, i v, R NON, N R P N R, N OR = RtR RO RtN NO RtR N O, V i v, sini v = R R OR R R = N N N N = ONsinV OR= ON cos ( 5-22), A x v : 2. i v = Vcos ( 5-24) x v = Vcostan ( 5-25) 5-30, O, O, (
129 ), ( ), e 5-30 = - ( 1 + 2 ) 2 = - 1 = esin s 1 esin( + ), + O O s 2 5-30 d= - = 1 + 2 = e sin sin( + - ) ( 5-26) s 2, O O e d, d d, ( 5-26), m 2 = s 1 m 2 = [ d d ] 2 d 2 2 e 2 sinsin( + - ) 2 = 2 e2 20 0 s 1 2 s 2 2 2 d s 2 sin 2 + sin2 ( + ) sinsin( + - 2 ) d s 1 s 2 s 2 2 2 sin 2 d= 0 2 sin 2 ( + ) d= 0 2 sinsin( + ) d= cos 0 m 2 = 2 e2 2 s 2 1 + - 2 cos s 2 2 s 1 s 2
130 2 = 2 e2 2 s 1 + s 2 2-2s 1 s 2 cos = 2 e2 s 2 1 s 2 2 2 AB 2 s s 2 1 s 2 2 m = e 2 s AB ( 5-27) s 1 s 2 ( 5-27), s AB, 180, s AB = s 1 + s 2 ; s 1 s 2,,,, 3. 5-31, A B, A B, 5-31, A A, A + 1 = A B + 2 = B = B - A = B + 2 - A - 1 = + 2-1 1 = e 1 sin 1 ( 5-28) s 1 2 = e 2 sin 2 ( 5-29) s 2 - = 1-2 = e 1 sin 1 - e 2 sin 2 ( 5-30) s 1 s 2 5-31 A, A e 1,, 1, A : ( 5-28), m 2 A = [ 1 1 ] 2 d
131 m 2 A = e 2 2 1 2 s 2 1 0 sin 2 1 2 d 2 0 e 2 = 2 1 2 sin 2 1 d 1 = s1 2 2 0 sin 2 1 d 1 e 2 m 2 A = 2 1 2s 2 1, ( 5-29), ( 5-31) : m 2 B e 2 = 2 2 2 s 2 2 m = m 2 A + m 2 B = 1 2 e 2 1 s 2 1 + e2 2 s 2 2 ( 5-32) ( 5-32), s 1 s 2,,,,, e,,,,,,,, 4. :,,, : d= p v, p (, ), v, 20 10, p = 10, v = 25, d= 10 = 0. 4 25, d k, d= k v,,, k = 1. 5; ( J2 ) 2 8km, k = 3 J6
132, 1 /10, 6,, 5.,,,,,,,,,,,,,,,, J6 m 1 = 6,, : m 1 = m 1 2 = 62 = 8. 5, : m = m 1 2 = 62 = 8. 5, : m = m 2 = 62 2 = 12 2, 24, : m 1d = m 1 2 = 62 = 8. 5 2, 17 5. 5,,, 5-32, : VV( ) HH( ) CC LL, : ( 1 ) ; ( 2 ), ; ( 3 ),
133 5-32,,,, ( 1 ) ( 2),,, ;,,,, : ; ; ;,,, ;,,,, 1.,,, 180 ( ),,,
134 5-33,,, 5-33( a) 180,, 5-33 ( b) 2, 2 5-33( b), LL, LLVV,,, 5-33 ( c),, 5-33( d), 5-33 2.,,,, ( 5-34),, 3. c, x c = c, x c, x i = 0, : A,, ( 180 ) 2 c : 2c = L - R 180 c, J2 8, J6 10,,, R: R = R+ c = 1 2 ( L+ R 180 )
135 5-34, R A, (, ),, A 4., 5-35, P ( 30 ), m 1 ( 5-35 ( a) ), P, m 2 ( 5-35 ( b) ) m 1 m 2, ;,,,,, i,,, i, i, m 1 m 2 m P, Pm i : i = m 1 m 2 Pm 1 2 ( 5-33),,, m 1 m m 2 m P J2, i 15 ; J6, i 20,, m 1 m 2 m,,, P, P,,,,, :, ;,,,,,,
136, 5-35 5.,,,, :,, L R, ( 5-13) x, x,,,,, R, x, R( 5-24) : R= R - x R,,,, x, x, ; x,, x,,, 6. ( ) 5-36
137, 5-37 5-37 ( a), 5-37( b) :, ( 1. 3m), A, 180, A, ; B,, AB, A (, 1. 3m 1. 0m), 5-37 A, 180, A, ; A B,, A B, K( 5-37 ),,,,,,, 5-36 5-37 5. 6,, : ( )
138 1.,,,,,, 30m 100N,,,, : l t = l + l + l( t - t 0 ) ( 5-34), l t t ( m) ; l, ( m) ; l t 0 ;, 11. 610-6 12. 510-6 m /( m ) ; t 0,, 20; t, l,,, 2. 3, ( 1 ),,, 5-38, n, q, : D = nl + q ( 5-35) 5-38,,,, 1 AB 327. 47m, 327. 35m, :
139 K = D - D D = 0. 12 327. 47 = 1 2 700 K 1 /3 000 1 /1 000, ( 2 ),,,,,, 5-39,, AB L, A B h, :, D h D = L 2 - h 2 D = L + D h, 5-40 5-39 5-40 D h = D - L = ( L 2 - h 2 ) 1 2 - L = L 1 - D h = L 1 - = - h 2 2L - 1 8 h 2 L 2 1 2 h 2 2L 2 - h 4 L 3-1 1 8 - h 4 L 4 - - 1 h L,, :, 3. D h = - h 2 2 L D = Lcos ( 5-36),,,,,,,
140 : 5-40, L, D ( 1 ) D l = L l l ( 5-37), l ; l, ; D l ( 2 ) D t = L ( t - t 0 ) ( 5-38), t 0 ; t ; D t ( 3 ), h A B D h = D - L = - h 2 2L ( 5-39) D = L + D l + D t + D h ( 5-40),, 4.,,,, ( 1 ),,,, 0. 1m,, ( 2 ),,, 30m, 0. 4 m, 1 /11 250,, ( 3 ),, 1, 1 /80 000 10,,,, ( 4 ), p, l p : l p = pl EA
141 : E, 210 7 N /cm 2 ; A 70N, 10-4,, ( 5 ),,,,, : : L f = - q2 l 3 24p : L = L f cos 2, L f L ; q ; l ; p ;,,,, ( 6 ),, ( 7 ),,, 1.,,, ( ),,, ( ),,,,,,,,,, 1 /300 1 /200 2. ( 1 ) L 1 L 2 ( 5-41 ), R,, L 2, 5-41
142 5-41, R,, L 1 : S f 1 = l p S= f 1 p l, l, pl L 2, p ( l L 1 L 2 p p = b a ), p p, a, b, p, 1 b - 1 a 1 a = 1 f 2 = f 2 - b bf 2 p p = f 2 - b f 2 1 p = f 2 - b pf 2 S= f 1 ( f 2 - b) pf 2 5-41, S : l S = f 1( f 2 - b) pf 2 l + f 1 + ( 5-41)
143 b = b + b, b S b ( 5-41 ) S = f 1 ( f 2 - b - b) pf 2 l + f 1 + = f 1 ( f 2 - b ) pf 2 l - c = - K = f 1 ( f 2 - b ) pf 2 f 1 b l + f 1 pf 2 + f 1 b l + f 1 pf 2 + S = Kl + c ( 5-42), b l S,,, K = 100, f 1 b l f 1 pf 2 +, c, ( 5-42 ) : ( 2 ) S = Kl = 100l 5-42, B A,,,,,,, : ; 5-42 AB S ( 5-42 ), A, B, M G Q ( ), M G MQM= GQG= QMM= 90-1 2
144 QGG= 90+ 1 2 1 2 ( 17 11. 5 ), QMM QGG 5-42 : V + V 1 = V cos+ V 1 cos= ( V 1, V + V 1 l, V + V 1 l 0, : ( 5-42), NQ : l 0 D = Kl 0 S cos, = lcos = Klcos + V 1 ) cos S = Klcos 2 ( 5-43) i v : 1. h = Stan+ i - v,, t, c, A B D, 5-43, A, B, D : D = 1 2 ct ( 5-44) 5-43,
145 : : :, :, ;,,,,, 3010 4 km /s,,,,, ( 5km), ( GaAs),,,,,, : 3 km ; ;, ;,,, ;,, ( ),,, m D = A + BD D = 1 km, m D 1km,, : m D 5mm, : 5mm < m D 10mm m D = A + BD, A, mm ; B, mm / km ; D, km 2. t, ( 5-44) 5-44 :,,,, ( ),, ( ),,
146 t t, ( t), T ( ),,,,,,,,, T,, ( ) ( ) n, t = nt( 5-44) D = 1 2 cnt l = 1 2 ct, T, D = nl ( 5-45) 5-44,, l, l ( 0. 1m) n, D,, ( ),,,, 3. ( 1 ) D 5-45,, ( ) ( ),
147 5-45, 5-46 5-46 5-46, : : = N2+ = 2N + 2 ( 5-46) D = ( N + ) ( 5-47) 2, N, ; ; = /2, u = 2, D = u( N + ) ( 5-48) ( 5-48) u,, u = 2, N,, D ( 2 ) N ( 5-48), u D, N = 0,, D = u = un,,, 2
148 u = 2 = c 2f, c = 310 5 km / s, ( ), 5-6 ( 10-3, m /2< 1 /1 000) ( 5-6 ),,,, ( ), ( ), 12, 5-6 15MHz 1. 5MHz 150kHz 15kHz 1. 5kHz 10m 100m 1km 10km 100km 1cm 10cm 1m 10m 100m, f 1, u 1 f 2, u 2 :, K = u 2 u 1 = f 1 f 2, = c 2f 1 ; = c 2f 2, ( 5-48 ) D = u 1 ( N 1 + N 1 ) D = u 2 ( N 2 + N 2 ) N 1 + N 1 = u 2 u 1 ( N 2 + N 2 ) = K( N 2 + N 2 ) ( 5-49) D < u 2, N 2 = 0N 1, N 1 1,, N 1 = KN 2 N 1, K N 2 ( 3 ), : = D +, D, 5-47,, A,, B,,,,
149 1. ; 2. ; 3. ; 4. 5-47, = d + = D + ( 5-50), d 2d,,, = ( 5-50 ) D - d = D - d = -, D - d 2( D - d), D - d 4.,,,,,, 5-48( a) ( b) 5-48 ( b), 5-48 ( c), ADB ADC BDC, L i P i, L i BDC P 1, P 1 ADC P 2, P 2 ADB P 3, P 3 ABC P r L i ABC P r L r, L r L i,,, : Q r = 6. 5n ( 5-51), n ; 3 90 ; Q r, = 2, n1, Q r 3,, 5-49
150 5-48 5-49 5. 5-50 ND3000, 6.,,,,, 1, 2 4,,,,,,,
151 5-50 ND3000, ( ),, 5m,, 7.,, : ; ;, ( ) ( ), ( 10 km ),,, Wild DJ20 ( 1 ) 5-51,,, D 0 - d D,,, : k = D - ( D 0 - d),,,,,
152,,, ( ), 5-51 ( 2 ),,, f, f, : f = f - f R = f f, D, km, R mm / km ( 5-52) D R = RD ( 5-53),,,,,, ( 3 ) ( t P e) ( ),,,, : D = 1 2 V t V = c n, c, ; n
153 D = 1 2 c n t ( 5-54), ( t = + 12, P = 1 013 hpa) n r,, n,, nn r ( 5-54) n, D = - 1 2 ct n = - n 2 1 2 c n t n n = - D n n D, D t P, D, ( 5-55) D t P D tp = - D n - n r n r = D - D ( 5-55) = D n r - n ( n r - n) D ( 5-56) n r ( t = 0, P = 1 013 hpa, e = 0 %, 0. 03 % ) n g, : n g = 1 + 2 876. 04 + 48. 864 + 2, :,, 1 273. 16 : 0. 680 10-7 ( 5-57) 4 n = 1 + n g - 1 1 + t P 1 013-5. 510-8 e ( 5-58) 1 + t, ( ),, n = 1 + n g - 1 1 + t P 1 013 ( t = + 15, P = 1 013 hpa), n r, n g n r = 1. 000 279 n ( 5-56) ( 5-59), D tp = 279-0. 29P 1 + 0. 0037t ( 5-59) D ( 5-60), t ; P hpa ( ) ; D km ; D tp mm : D= D+ D t P,,,
154 ( 4 ), : D = D + K + D R + D tp h, : D h = - h 2 2D -, h S = D + D h, : ( 5 ) : h 4 8 D 3 ( 5-61) S = D cos ( 5-62) S = - S H R ( 5-63) H, ( 5-62 ) S ; ( 5-61) S 5. 7 ( 5-64), : m 2 D = m c c D = N c 2nf + 2 c 2nf + K ( 5-64) 2 + m n n 2 + m f f 2 D 2 + 2 m 2 + m 2 K ( 5-65) 4, ( = c f ), m c, m n, m f, m, m K, :, m A, : m 2 D = m c c 2 + m n n 2 + m f f 2 D 2 + 2 m 2 + m 2 K + m 2 A ( 5-66) 4 ( 5-66), : D,, ;,,,,,,, : m D = ( A + BD) ( 5-67), A, mm ; B, mm / km ; D,
155 km 1. c 0, 1975 c 0 = 299792458 1. 2( m / s), m c 0 = 410-9,, c 0 2. n c = c 0, n,,, n t p e, 1km, 1 0. 95mm; 1hPa 0. 27mm; 1hPa 0. 04mm n, n, ( t p e) ;, 3. f : ;,,,,, m f ( 0. 5 f 1. 0)10-6, 10-4,,,,, 1.,,,,,,
156 ( 1 ),,,,, 1, ( 2 ),, 5-52 u 1 u 2 2, u 0,,, 5-52,, ( 3 ),,,,, 2.,, D, L a, L i, L r
157 t = 2L a + L r, 1 = L i ( 2L a + L r - L i ) 2D, ( t - 1 ) 2,,,,,, ( ),,, 5-53, E 1, E 2,, e 1 e 2,, : E 1 E 2 = e 1 cos( t + ) = e 2 cos t E 1 E 2 E k, e k, E 2, E k E k,, = e k cos( t + ) = e k cos cos t - e k sin sin t E k = E 1 + E 2 = e 1 cos( t + ) + e 2 cos t = ( e 1 cos+ e 2 ) cos t - e 1 sin sin t tan = e k cos = e 1 cos+ e 2 e k sin = e 1 sin e 1 sin e 1 cos+ e 2 = sin cos+ k, k = e 2 e 1 5-53, : = - = - arctan sin cos+ k ( 5-68) ( 5-68) 5-54,,, 2 E 2, E 1,,, ( 2 )
158 5-53 5-54 ( 5-68) 5-53, k, e 2, k,,, ;,,,,,,, 5. 8,,,,,,,,,, ; ;,,,,,,,,,, 200 300m
159,,,,,, 1., : (, ), 20m, 20m, 50 100m, 5-55,, 1 u ( u 40 ), 1, 2, 3, 4,, 40,,, 5-55 2. D 01 0 1 ; v 0 1 D 01 ; d ( 5-56) ; K ; D i z ( i = 1, 2,, 40) ; V i ; i D iz ; A ; 0 5-56
160 5-56 : : D 01 + v 01 = D 1 z + V 1 + K + Asin( 0 + 1 ) D 01 + v 01 + d = D 2z + V 2 + K + Asin( 0 + 2 ) D 01 + v 01 + 39d = D 4 0z + V 4 0 + K + Asin( 0 + 4 0 ) V 1 = ( v 01 - K) - Asin( 0 + 1 ) + ( D 01 - D 1z ) V 2 = ( v 01 - K) - Asin( 0 + 2 ) + ( D 01 + d - D 2 z ) V 40 = ( v 01 - K) - Asin( 0 + 40 ) + ( D 01 + 39d - D 40 z ) 1 = D 1z 360 2 2 = 1 + d 360= 1 + 2 3 = 1 + d + d 360 = 1 + 2 2 40 = 1 + 39 ( 5-69) ) d, = d 360 ( 2 1 = 0 + 1 X = Acos 1 Y = Asin 1,,, X Y A = X 2 + Y 2 1 = arctan Y X A 1, 1. v i = Asin[ 1 + ( i - 1) ] ( 1 ), A B, AB 200m, AB C,
161 5-57 A B C, 5-57 ( 2 ) A C B, A D AC D AB ; C D AC D CB ; B D AB D CB ( 3 ) D AB D AC D CB, K = D AB - ( D AC + D CB ), 2., K, R ( ),,, 21, 0, 1, 2, 3, 4, 5, 6, : D 01 D 02 D 03 D 04 D 05 D 06 D 12 D 13 D 14 D 15 D 16 D 23 D 24 D 25 D 26 D 34 D 35 D 36 D 45 D 46, 21 D 01 D 56 21 ; v 01 v 5 6 21 ; D 01 D 56 21 D 56 D 0 1 + v 01 + K + D 01 R = D 01 D 0 2 + v 02 + K + D 02 R = D 02 : D 5 6 + v 56 + K + D 56 R = D 56 v 01 = - K - D 01 R + l 01 v 02 = - K - D 02 R + l 02 ( 5-70), l 01 R v 56 = - K - D 56 R + l 56 l 5 6, l 01 = D 01 D 01 K
162 5. 9, 5-58 NTS-355, 5, 2 mm + 2ppmD( D ),,,, 1. ( ), 5-59, 360, 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. ; 16. ; 17. ; 18. ; 19. ; 20. ; 21. ; 22. ; 23. CE-203 5-58 NTS-355 2.,,,
163 5-59, 3, 0. 1 OPTON 5-60, 1, 6 4,, 7 2 ;, 4, ( ),, ( ) L ( ) T, ( ) 1. ; 2. ; 3. ; 4. ; 5. ; 6. ; 7. 5-60 L, T, ( ) : Z = Z L + L V = V L + L ( 5-71)
164 H = H L + T/ tanz = H L + TcotZ = H L + TtanV ( 5-72), Z ( ) ; Z L ( ) ( L ) ; V L ( ) ; V ( ) ; H ( ) ; H L ( ) 3., :,, ;, ;,, 4.,,, ; ; ; ( 1 ) 5-61, S 1 S 2, h A1 h A2, P 1 P 2 C h 12 : C = S 2 1 + S 2 2-2S 1 S 2 cos h 12 = h A2 - h A1 ( 5-73) 5-61 ( 2 ),, 5-62,,,,, : H 1 = h 1 + h 2 h 2 = Ssinz 1 ( cotz 2 - cotz 1 ) ( 5-74)
165 5-62, 5-63 TPS110,, :,, CCD,,,,,,,,, 5-63 TCA2003
166 5. 10,,,,, ( ),, 5-64, A B h AB, A, B I A i, B M, B v, IM IN, A B S, 5-64 h AB : A H A, B : h AB = Stan+ i - v ( 5-75) H B = H A + h AB = H A + Stan+ i - v ( 5-76) 5-64,, Stan,, Stan A ( + ), B, i v, D, A B : h AB = Dsin+ i - v ( 5-77), ;,,
167 1.,, A B,,,,,,,,,,,,,,,, ( ) 2. 5-65, S 0 A B A, ib, v, R A B PE AF P A PCPEP, PN P PN PM,, N, A P N 5-65
168 5-65, A B : h 12 = BF = MC + CE + EF - MN - NB ( 5-78), EF i; NB v; CE MN CE = 1 2R S2 0 MN = 1 2R S2 0, R PNN R = K, R K MN = K 2R S2 0 A B S 0 R ( S 0 = 10km, S 0 5), PC OM, PCM90, PCM ( 5-78) MC : MC = S 0 tan ( 5-78), A B : 1 - K 2R h 12 = S 0 tan+ 1 2 R S2 0 + i - = S 0 tan+ 1 - K 2R S2 0 K 2R S2 0 + i - v = C, C, : - v h 12 = S 0 tan+ CS 2 0 + i - v ( 5-79) ( 5-79), i v, S 0, d : h = Dsin+ ( 1 - K) D2 2R cos2 + i - v ( 5-80), h,, D, K, i, v 3. 5-66, H A H B A B ( ), H m = 1 2 ( H A + H B ), mm S 0 ( 10km ), S 0 5-66 : S 0 S = R + H m R = 1 + H m R S 0 = S( 1 + H m R ) ( 5-81)
169 5-66 S 0, y m S S d : S = d( 1 - y 2 m 2R 2 ) ( 5-82) A B ( 5-82) ( 5-81), 4. S 0 ( 5-81) ( 5-79), h 12, CS 2, S 0 S 5. ( 5-82) ( 5-84),, h = dtan ( 5-85) : = d( 1 + H 2 m R - ym ) ( 5-83) 2R 2 = Stan 12 ( 1 + H m R ) + CS2 + i - v ( 5-84) h 12 = dtan+ Cd 2 + i - v + dtan ( H 2 m R - ym ) 2R 2 = dtan+ Cd 2 + i - v + h ( H 2 m R - ym ) ( 5-85) 2R 2 h 12 = h ( H m R - 2 y m 2R 2 ) ( 5-86) h 1 2 = dtan+ Cd 2 + i - v + h 12 ( 5-87)
170 ( 5-87) d ( 5-86) H m R, H m, H m R H m = 1 000 m, h = 100m, H m R 0. 02m,,, y m = 300km, h = 100m, y 2 m 2R 2 0. 11 m 0. 1m, y2 m h 2R 2 0. 04m,, ( 5-87) h 12 H m hy m 6., A B 12, B A 21 ( 5-87 ) A B : B A : h 12 h 21 = dtan 12 + i 1 - v 2 + C 1 2 d 2 + h 1 2 = dtan 21 + i 2 - v 1 + C 2 1 d 2 + h 2 1, i 1, v 1 i 2, v 2 A B ; C 1 2 C 2 1 A B B A,, K, C 12 h 12 h 2 1 : : h 12( ) = dtan 1 2 ( 12-21 ) + 1 2 ( i 1 + v 1 ) - h 12 = H m R - 2 ym 2R 2 h h= dtan 1 2 ( 12-21 ) = C 21, 1 2 ( i 2 + v 2 ) + h 12 ( 5-88),,,, ;,,, 1mm,, 1mm,,
171,,,, K,,,, K,,,, 10 16, K 0. 08 0. 14,,, 400m,,,,,,, ; ;,,,, m 2. 0, 2 km,, m 1. 5, 3. 5km, ; 1. 2km
172 6. 1,,,,,,,,,,,,,,,,,,,,,,,, ; ;,,, ;,,,,,,,,,, GPS( Global Positioning System) 1.,, ( ) ( ),,,, ( 6-1 ), ( 6-2),
173 6-1 6-2 2.,,,, (, ), ( ), ( ),,,,, 3. ; ; 4., ( ),,,,,,,,,, 6-3, 20 25km,,, 13 km,, 8km, 2 6km15 20km 2, 110 00015 000, 1500 12 000,,
174 6-3, 6-1 6-2 6-1 ( km) ( ) DJ1 DJ2 DJ6 ( ) 9 1. 0 1 / 120 000 12 - - 3. 5 5 1. 8 1 /80 000 6 9-7. 0 2 2. 5 1 /45 000 4 6-9. 0 1 5. 0 1 /20 000-2 6 15. 0 0. 5 10. 0 1 /10 000-1 2 30. 0
175 6-2 ( km) ( km) ( ) ( mm) DJ1 DJ2 DJ6 ( ) 15 3 1. 5 18 8 12-3 n 1 /60 000 10 1. 6 2. 5 18 4 6-5 n 1 /40 000 3. 6 0. 3 5 15-2 4 10 n 1 /14 000 2. 4 0. 2 8 15-1 3 16 n 1 /10 000 1. 5 0. 12 12 15-1 2 24 n 1 /6 000 : n 10km 2,,,,,,,,, 5. GPS GPS GPS 20 80, ( GPS), GPS GPS GPS, A B C D E GPS, ( GPS) A 27 B 818, ( GPS) A 6-4,,,,,,,, 6-5,,,,, 6-3,,,,
176 6-4 ( GPS) A, 6-3 / mm / km / mm / mm 1 2 400 4 R 4 L 3 6 45 12 R 12 L 5 10 15 20 R 20 L 10 20 8 40 L : R, km; L, km,
177 6-5, GPS,,,,,,,,,,,,,,, ;, ;, :, ;,,,,, 6-6 6-10
178 6-6 6-7 ( ; ),,,,, ( ), ( )
179 6-8 6-9 6-10 ( GPS), 1. 6-11, AB AB, B, ( 6-11( a) ), BC BC : ( 6-11( b) ), BC BC : ( 6-1) ( 6-2) : BC = AB + - 180 ( 6-1) BC = AB - + 180 ( 6-2) = 180 ( 6-3) ( 6-3),, +,, - 360, 360,, 360
180 6-11 2. 6-12, A, B, A ( x A, y A ) A B S AB AB, B ( x B, y B ), 6-12 6-12, ( 6-4) : x B = x A + x AB ( 6-4) y B = y B + y AB x AB y AB, x AB y AB = S AB cos AB = S AB sin AB ( 6-5) x B = x A + S AB cos AB ( 6-6) y B = y B + S AB sin AB, 6-12, A B ( x A, y A ) ( x B, y B ), AB AB S AB :
181 AB = arctan y AB ( 6-7) x AB S AB = y AB = x AB = x 2 AB sin AB cos AB, x AB = x B - x A, y AB = y B - y A ( 6-8) S AB, + y 2 AB ( 6-8), ( 6-7) y AB x AB, R, 0 90,, R,, 6-4 6-4 y AB x AB + + AB = R + - AB = 180 - R - - AB = 180+ R - + AB = 360 - R 6. 2,,,, 1. 6-13( a),, 2. 6-13( b),,,,, 3. 6-13( c),,,,
182 4. 6-13( d), 5. 6-13( e),,,,,,,,, 6-13 1. 2, 6-2, ;,, 3. 5 5. 0,,,,,,,,, 2.,,,
183,, 3.,, 4., 6-14, i, i - 1 i + 1,, i i + 1,, i + 1, i, i - 1 i + 2,,,, 6-14,,,,,,,,,,,,,,,, ( ), ( ),
184 1. 6-15, : MA MA, ( 6-3), ( 6-5) ( 6-4) P 2, P 3,, P n + 1 6-15 2. 6-16, A B, P 2, P 3,, P n, i ( i = 1, 2,, n + 1), S i j, 6-16 B, x B y B, x B y B, f x f y, f x f y = x B - x B ( 6-9) = y B - y B,,, : : v x = - f x ij SS ij v y = - f y ij SS ij x i j y i j = x ij + v xij ( 6-10) ( 6-11) = y ij + v yij, ( 6-4 ) P 2, P 3,, B( P n + 1 )
185,, B,, f S S, k, k = 1 S f S ( 6-12), f S = f 2 x + f 2 y 3. 6-17, B, MA BN B N,, BN 6-17 BN, f, f = BN - B N ( 6-13), f, v i, i, : v i = - f n + 1 ( 6-14) i, : v i = f n + 1 ( 6-15),,,, m 2 n + 1, f = 2 n + 1m ( 6-16) 6-5
186 6-5 S x y x y M ( ) ( ) / m / m / m / m / m A( P 1 ) P 2 P 3 P 4 P 5 B( P 6 ) N + 7 99 01 00 + 7 167 45 36 + 7 123 11 24 + 7 189 20 36 + 7 179 59 18 + 7 129 27 24 888 45 18 237 59 30 157 00 37 225. 85 144 46 20 139. 03 87 57 51 172. 57 97 18 34 100. 07 97 17 59 102. 48 46 45 30 = 740. 00 n - 0 = - 191 14 00 + 4-207. 91 + 2-113. 57 + 3 + 6. 13 + 2-12. 73 + 2-13. 02 = - 341. 10 f S = f x = - 0. 13 m f y = + 0. 12 m - 4 + 88. 21-2 + 80. 20-3 + 172. 46-1 + 99. 26-2 + 101. 65 = + 541. 78 f 2 x + f 2 y = 0. 18 m 2 507. 69 1 215. 63 2 299. 82 1 303. 80 2 186. 27 1 383. 98 2 192. 43 1 556. 41 2 179. 72 1 655. 66 2 166. 72 1 757. 29 x B - x A = - 340. 97 m y B - y A = + 541. 66 m f = - 42 ; f = 406 = 97 ; K = f S 0. 18 = S 740. 00 = 1 4 100 < 1 4 000 4. 6-18,,,, 6-18
187 v i : f = [ ] n 1 - ( n - 2) 180 ( 6-17) v i = - f n ( 6-18),,, ( 6-19) : f x f y = [ x] n 1 = [ y] n 1, x i y i ( 6-19),,,, 5., :,,,,,, 6-19, A( x A, y A ) B( x B, y B ), S AB AB AB ; i S i i S i ; ( x i, y i ) ( x i, y i ) A1 A1,,, AB x AB y AB S AB AB 6-19, Q, : A1 S A1 = S A2 = = S Ai = = S AB = Q ( 6-20) S A1 S A2 S Ai S AB - A1 = A2 - A2 = = Ai - Ai = = AB - AB = ( 6-21) x Ai = x i - x A = S Ai cos Ai ; y Ai = y i - y A = S Ai sin Ai, ( 6-20) ( 6-21),
188 Q 1 x Ai y Ai = Qcos, Q 2 = Qsin, = QS Ai cos( Ai + ) = QS Ai ( cos Ai cos- sin Ai sin ) = QS Ai sin( Ai + ) = QS Ai ( sin Ai cos+ cos Ai sin ) x Ai y Ai i B, ( 6-22 ) : x AB y AB = Q 1 x Ai - Q 2 y Ai = Q 1 y Ai + Q 2 x = Q 1 x AB - Q 2 y AB = Q 1 y AB + Q 2 x AB Ai ( 6-22), x AB y AB, x AB y AB Q 1 Q 1 Q 2 = x AB x ( x AB ) 2 = x AB y ( x AB ) 2 + y AB y AB + ( y AB ) 2 - y AB x AB + ( y AB ) 2 Q 1 Q 2 ( 6-22), x i = x A + Q 1 ( x i - x A ) - Q 2 ( y i - y A ) y i = y A + Q 1 ( y i - y A ) + Q 2 ( x i - x A ) k, Q 2, ( 6-23) ( 6-24) k = 1 S AB f S, f S = S AB - S AB, S AB S AB ( 6-8) 6-6 ( 6-25) 6-6 A 1 175 21 42 2 191 05 34 3 168 42 12 4 220 16 41 5 146 17 44 B x y x / m / m / m /m 220. 179 87 27 10 197. 917 82 48 51 217. 634 93 54 25 186. 208 82 36 37 222. 716 122 53 18 157. 812 89 11 02 + 9. 785 + 219. 961 + 24. 757 + 196. 362-14. 829 + 217. 128 + 23. 950 + 184. 661-120. 936 + 187. 021 + 2. 234 + 156. 796 y / m x / m y / m 5 264. 106 5 004. 762 5 273. 891 5 224. 723 5 269. 981 5 224. 868 5 298. 648 5 421. 085 5 291. 246 5 421. 644 5 283. 819 5 638. 213 5 272. 560 5 638. 480 5 307. 769 5 822. 874 5 293. 226 5 823. 542 5 186. 833 6 009. 895 5 168. 982 6 008. 390 5 189. 067 6 166. 691 5 168. 430 6 165. 205 Q 1 = 0. 999 868 67 Q 2 = 0. 017 769 46
189 D AB = 1 164. 380m; D AB = 1 164. 350m; f D = D AB - D AB = - 0. 03 m; k = f D 1 = D AB 38 800 < 1 14 300 6. 6-20, A B C, A B B C C, J, : 6-20 ( 1 ) ( JJ ) Z 1 Z 2 Z 3 1 2 3, n 1 n 2 n 3, 1 2 3 P 1 = C 1 n 1 P 2 = C 1 P n 3 = C 1 ( C 1 2 n 3 : ), JJ J J = P 1 1 + P 2 2 + P 3 3 ( 6-26) P 1 + P 2 + P 3, JJ,,,