Антропова Н.А., Садыков Т.Д. Геодезическое обеспечение нефтегазопроводов и газонефтехранилищ
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2. Ɋɟɲɢɬɟ ɨɛɪɚɬɧɭɸ ɝɟɨɞɟɡɢɱɟɫɤɭɸ ɡɚɞɚɱɭ, ɟɫɥɢ ɢɡɜɟɫɬɧɵ ɤɨɨɪ-
ɞɢɧɚɬɵ ɧɚɱɚɥɚ ɢ ɤɨɧɰɚ ɨɬɪɟɡɤɚ ɋD:
ɏ
D
= 1056 ɦ
ɏ
ɋ
= 2361 ɦ
ɍ
D
= 4625 ɦ
ɍ
ɋ
= 5364 ɦ
3. Ɋɟɲɢɬɟ ɨɛɪɚɬɧɭɸ ɝɟɨɞɟɡɢɱɟɫɤɭɸ ɡɚɞɚɱɭ, ɟɫɥɢ ɢɡɜɟɫɬɧɵ ɤɨɨɪ-
ɞɢɧɚɬɵ ɧɚɱɚɥɚ ɢ ɤɨɧɰɚ ɨɬɪɟɡɤɚ ɋD:
ɏ
D
= 3127 ɦ
ɏ
ɋ
= 2084 ɦ
ɍ
D
= 4235 ɦ
ɍ
ɋ
= 6257 ɦ
8.3. Ɉɬɜɟɬɵ ɤ ɡɚɞɚɧɢɹɦ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɜɵɩɨɥ-
ɧɟɧɢɹ
1. Ⱥɥɝɨɪɢɬɦ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɩɪɟɞɫɬɚɜɥɟɧ ɜ ɬɚɛɥ. 8.2.
Ɍɚɛɥɢɰɚ 8.2
ʋ ɞɟɣɫɬɜɢɹ Ɉɛɨɡɧɚɟɧɢɟ Ɋɟɲɟɧɢɟ Ɋɟɡɭɥɶɬɚɬ
1 ɏ
D
ɂɫɯ. ɞɚɧɧɵɟ 1056 ɦ
2 ɏ
ɋ
ɂɫɯ. ɞɚɧɧɵɟ 2361ɦ
5
X
ɏ
D
–
ɏ
ɋ
-1305
3 ɍ
D
ɂɫɯ. ɞɚɧɧɵɟ 4625
4 ɍ
ɋ
ɂɫɯ. ɞɚɧɧɵɟ 5364
6
Y
ɍ
D
–
ɍ
ɋ
-739
7
0,56628
8
29,52216
9 ɱɟɬɜɟɪɬɶ
ɩɨ ɡɧɚɤɚɦ
X,
X
ɉɨ ɫɬɨɪɨɧɚɦ
ɫɜɟɬɚ ɘɁ
10
92,72631099 209,5221629
11
ɩɨ ɱɟɬɜɟɪɬɢ
209
31’20”
209 31’
12 S
CD
1499,72
13 S
CD
1499,72
14 S
CD
1499,72
151
2.
Ⱥɥɝɨɪɢɬɦ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɩɪɟɞɫɬɚɜɥɟɧ ɜ ɬɚɛɥ. 8.3
Ɍɚɛɥɢɰɚ 8.3
ʋ ɞɟɣɫɬɜɢɹ Ɉɛɨɡɧɚɟɧɢɟ Ɋɟɲɟɧɢɟ Ɋɟɡɭɥɶɬɚɬ
1 ɏ
D
ɂɫɯ. ɞɚɧɧɵɟ 1056 ɦ
2 ɏ
ɋ
ɂɫɯ. ɞɚɧɧɵɟ 2361ɦ
5
X
ɏ
D
–ɏ
ɋ
-1305
3 ɍ
D
ɂɫɯ. ɞɚɧɧɵɟ 4625
4 ɍ
ɋ
ɂɫɯ. ɞɚɧɧɵɟ 5364
6
Y
ɍ
D
–ɍ
ɋ
-739
7
0,56628
8
29,52216
9 ɱɟɬɜɟɪɬɶ
ɩɨ ɡɧɚɤɚɦ
X,
X
ɉɨ ɫɬɨɪɨɧɚɦ
ɫɜɟɬɚ ɘɁ
10
92,72631099 209,5221629
11
ɩɨ ɱɟɬɜɟɪɬɢ
209
31’20”
209
31’
12 S
CD
1499,72
13 S
CD
1499,72
14 S
CD
1499,72
3.
Ⱥɥɝɨɪɢɬɦ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɩɪɟɞɫɬɚɜɥɟɧ ɜ ɬɚɛɥ. 8.4
Ɍɚɛɥɢɰɚ 8.4
ʋ ɞɟɣɫɬɜɢɹ Ɉɛɨɡɧɚɟɧɢɟ Ɋɟɲɟɧɢɟ Ɋɟɡɭɥɶɬɚɬ
1 ɏ
D
ɂɫɯ. ɞɚɧɧɵɟ 3127 ɦ
2 ɏ
ɋ
ɂɫɯ. ɞɚɧɧɵɟ 2084ɦ
5
X
ɏ
D
–ɏ
ɋ
1043
3 ɍ
D
ɂɫɯ. ɞɚɧɧɵɟ 4235
4 ɍ
ɋ
ɂɫɯ. ɞɚɧɧɵɟ 6257
6
Y
ɍ
D
–ɍ
ɋ
-2022
7
-1,93864
8
-62,71414
9 ɱɟɬɜɟɪɬɶ
ɩɨ ɡɧɚɤɚɦ
X,
X
ɉɨ ɫɬɨɪɨɧɚɦ
ɫɜɟɬɚ ɋɁ
152
10
92,72631099 297,2858565
11
ɩɨ ɱɟɬɜɟɪɬɢ
297
17’09”
297
17’
12 S
CD
2275,16
13 S
CD
2275,16
14 S
CD
2275,16
153
8.4. Ɋɚɫɱɟɬɧɨ-ɝɪɚɮɢɱɟɫɤɚɹ ɪɚɛɨɬɚ «Ɋɟɲɟɧɢɟ ɨɛɪɚɬɧɨɣ
ɝɟɨɞɟɡɢɱɟɫɤɨɣ ɡɚɞɚɱɢ»
Ɋɟɲɢɬɟ ɨɛɪɚɬɧɭɸ ɝɟɨɞɟɡɢɱɟɫɤɭɸ ɡɚɞɚɱɭ. ȼɚɪɢɚɧɬɵ ɢɫɯɨɞɧɵɯ ɞɚɧ-
ɧɵɯ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ. 8.4. ɇɨɦɟɪ ɜɚɪɢɚɧɬɚ ɭɤɚɡɵɜɚɟɬ ɩɪɟɩɨɞɚɜɚɬɟɥɶ.
Ɋɟɡɭɥɶɬɚɬɵ ɜɵɱɢɫɥɟɧɢɣ ɨɮɨɪɦɢɬɟ ɜ ɜɢɞɟ ɬɚɛɥɢɰɵ ɧɚ ɝɪɚɮɢɱɟ-
ɫɤɨɦ ɥɢɫɬɟ, ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɨɮɨɪɦɥɟɧɧɵɣ ɪɚɦɤɨɣ ɲɢɪɢɧɨɣ ɩɨ 0,5 ɫɦ
ɨɬ ɤɪɚɹ ɥɢɫɬɚ ɢ ɲɬɚɦɩɨɦ, ɩɪɢɧɹɬɵɦ ɧɚ ɤɚɮɟɞɪɟ ɌɏɇȽ (ɉɪɢɥɨɠɟɧɢɟ 1).
Ɍɢɬɭɥɶɧɵɣ ɥɢɫɬ ɜɵɩɨɥɧɢɬɟ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɪɟɛɨɜɚɧɢɹɦɢ ɫɬɚɧ-
ɞɚɪɬɚ Ɍɉɍ (ɉɪɢɥɨɠɟɧɢɟ 2).
ȼɫɟ ɩɨɞɩɢɫɢ ɜɵɩɨɥɧɹɣɬɟ ɱɟɪɬɟɠɧɵɦ ɲɪɢɮɬɨɦ. ɇɟɛɪɟɠɧɨ ɜɵɩɨɥ-
ɧɟɧɧɵɟ ɪɚɛɨɬɵ ɧɟ ɩɪɢɧɢɦɚɸɬɫɹ.
ɆȺɌȿɊɂȺɅɕ Ʉ ɋȾȺɑȿ
1.
Ɍɢɬɭɥɶɧɵɣ ɥɢɫɬ.
2.
Ƚɪɚɮɢɱɟɫɤɢɣ ɥɢɫɬ ɫ ɪɟɡɭɥɶɬɚɬɚɦɢ ɜɵɱɢɫɥɟɧɢɣ.
154
ɉɊɂɅɈɀȿɇɂȿ 1. ɈȻɊȺɁȿɐ ȽɊȺɎɂɑȿɋɄɈȽɈ ɅɂɋɌȺ
ɎɈɊɆȺɌȺ Ⱥ4 ȾɅə ȼɕɉɈɅɇȿɇɂə ɊȺɋɑȿɌɇɈ-
ȽɊȺɎɂɑȿɋɄɂɏ ɊȺȻɈɌ
155
ɉɊɂɅɈɀȿɇɂȿ 2. ɌɂɌɍɅɖɇɕɃ ɅɂɋɌ
ɎȿȾȿɊȺɅɖɇɈȿ ȺȽȿɇɌɋɌȼɈ ɉɈ ɈȻɊȺɁɈȼȺɇɂɘ
Ƚɨɫɭɞɚɪɫɬɜɟɧɧɨɟ ɨɛɪɚɡɨɜɚɬɟɥɶɧɨɟ ɭɱɪɟɠɞɟɧɢɟ ɜɵɫɲɟɝɨ ɩɪɨɮɟɫɫɢɨɧɚɥɶɧɨɝɨ ɨɛɪɚɡɨɜɚɧɢɹ
«ɌɈɆɋɄɂɃ ɉɈɅɂɌȿɏɇɂɑȿɋɄɂɃ ɍɇɂȼȿɊɋɂɌȿɌ»
ɂɇɋɌɂɌɍɌ ɉɊɂɊɈȾɇɕɏ ɊȿɋɍɊɋɈȼ
Ʉɚɮɟɞɪɚ ɬɪɚɧɫɩɨɪɬɚ ɢ ɯɪɚɧɟɧɢɹ ɧɟɮɬɢ ɢ ɝɚɡɚ
Ɋɚɫɱɟɬɧɨ-ɝɪɚɮɢɱɟɫɤɚɹ ɪɚɛɨɬɚ ʋ 4
ɉɨɫɬɪɨɟɧɢɟ ɩɪɨɮɢɥɹ ɦɟɫɬɧɨɫɬɢ
ɩɨ ɬɨɩɨɝɪɚɮɢɱɟɫɤɨɣ ɤɚɪɬɟ
ȼɚɪɢɚɧɬ 1
ɂɫɩɨɥɧɢɬɟɥɶ Ɏɚɦɢɥɢɹ ɂ.Ɉ.
ɋɬɭɞɟɧɬ ɝɪɭɩɩɵ 2Ȼ01 ɩɨɞɩɢɫɶ
Ɋɭɤɨɜɨɞɢɬɟɥɶ Ɏɚɦɢɥɢɹ ɂ.Ɉ.
Ⱦɨɰɟɧɬ ɤɚɮɟɞɪɵ ɌɏɇȽ ɩɨɞɩɢɫɶ
156
Ɍɨɦɫɤ 2010
ɉɊɂɅɈɀȿɇɂȿ 3. ɋɏȿɆȺ ȼɁȺɂɆɈɋȼəɁɂ ȺɁɂɆɍɌɈȼ ɂ
ɊɍɆȻɈȼ
ɉɊɂɅɈɀȿɇɂȿ 4. ɁɇȺɄɂ ɉɊɂɊȺɓȿɇɂɃ ɄɈɈɊȾɂɇȺɌ
ɉɈ ɑȿɌȼȿɊɌəɆ
Ɂɧɚɤɢ ɩɪɢɪɚɳɟɧɢɣ ɩɨ ɨɫɢ ɏ
Ɂɧɚɤɢ ɩɪɢɪɚɳɟɧɢɣ ɩɨ ɨɫɢ ɍ
157
ɉɊɂɅɈɀȿɇɂȿ 5. ȿȾɂɇɂɐɕ ɂɁɆȿɊȿɇɂɃ, ɉɊɂɆȿɇəȿ-
Ɇɕȿ ȼ ȽȿɈȾȿɁɂɂ
Ɇɟɪɵ ɞɥɢɧɵ (ɥɢɧɟɣɧɵɟ)
1 ɤɢɥɨɦɟɬɪ (ɤɦ) = 1 000 ɦɟɬɪɨɜ (ɦ);
1 ɦɟɬɪ (ɦ) = 10 ɞɟɰɢɦɟɬɪɚɦ (ɞɦ) = 100 ɫɚɧɬɢɦɟɬɪɚɦ (ɫɦ);
1 ɞɟɰɢɦɟɬɪ (ɞɦ) = 10 ɫɚɧɬɢɦɟɬɪɚɦ (ɫɦ) = 0,1 ɦɟɬɪɚ (ɦ);
1 ɫɚɧɬɢɦɟɬɪ (ɫɦ) = 10 ɦɢɥɥɢɦɟɬɪɚɦ (ɦɦ) = 0,01 ɦɟɬɪɚ (ɦ);
1 ɦɢɥɥɢɦɟɬɪ (ɦɦ) = 0,001 ɦɟɬɪɚ (ɦ).
Ɇɟɪɵ ɩɥɨɳɚɞɢ
1 ɤɜ. ɤɢɥɨɦɟɬɪ (ɤɦ
2
) = 1 000 000 ɤɜ. ɦɟɬɪɨɜ (ɦ
2
);
1 ɤɜ. ɦɟɬɪ (ɦ
2
) = 100 ɤɜ. ɞɟɰɢɦɟɬɪɚɦ (ɞɦ
2
)
= 10 000 ɤɜ. ɫɚɧɬɢɦɟɬɪɨɜ (ɫɦ
2
);
1 ɝɟɤɬɚɪ (ɝɚ) = 10 000 ɤɜ. ɦɟɬɪɨɜ (ɦ
2
);
1 ɞɟɰɢɦɟɬɪɚɦ ɤɜ. (ɞɦ
2
) = 0,01 ɤɜ. ɦɟɬɪɚ (
ɦ2
);
1 ɫɚɧɬɢɦɟɬɪɨɜ ɤɜ. (ɫɦ
2
) = 0,000 1 ɤɜ. ɦɟɬɪɚ (ɦ
2
);
1 ɫɚɧɬɢɦɟɬɪɨɜ ɤɜ. (ɦɦ
2
) = 0,000 001 ɤɜ. ɦɟɬɪɚ (ɦ
2
).
Ɇɟɪɵ ɨɛɴɺɦɚ
1 ɤɭɛ. ɦɟɬɪ (ɦ
3
) = 1 000 ɤɭɛ. ɞɟɰɢɦɟɬɪɨɜ (ɞɦ
3
)
= 1 000 000 ɤɭɛ. ɫɚɧɬɢɦɟɬɪɨɜ (ɫɦ
3
);
1 ɤɭɛ. ɞɟɰɢɦɟɬɪ (ɞɦ
3
) = 1 000 ɤɭɛ. ɫɚɧɬɢɦɟɬɪɨɜ (ɫɦ
3
);
1 ɥɢɬɪ (ɥ) = 1 ɤɭɛ.ɞɟɰɢɦɟɬɪɭ (ɞɦ
3
).
Ɇɟɪɚ ɦɚɫɫɵ
1 ɬɨɧɧɚ (ɬ) = 1 000 ɤɢɥɨɝɪɚɦɦɨɜ (ɤɝ);
1 ɰɟɧɬɧɟɪ (ɰ) = 100 ɤɢɥɨɝɪɚɦɦɚɦ (ɤɝ);
1 ɤɢɥɨɝɪɚɦɦ (ɤɝ) = 1 000 ɝɪɚɦɦɨɜ (ɝ);
1 ɝɪɚɦɦ (ɝ) = 0,001 ɤɢɥɨɝɪɚɦɦɚɦ (ɤɝ) = 1 000 ɦɢɥɥɢɝɪɚɦɦɨɜ (ɦɝ).
ɍɝɥɨɜɵɟ ɟɞɢɧɢɰɵ
1 ɝɪɚɞɭɫ (10) = 1/360 ɱɚɫɬɶ ɨɤɪɭɠɧɨɫɬɢ = 60 ɦɢɧɭɬɚɦ (')
= 3600 ɫɟɤɭɧɞɚɦ (") = 1
ɨ
00'00";
1 ɦɢɧɭɬɚ (') = 1/60 ɱɚɫɬɶ ɝɪɚɞɭɫɚ = 60 ɫɟɤɭɧɞɚɦ (") = 0
ɨ
01'00";
1 ɫɟɤɭɧɞɚ (") = 1/3600 ɱɚɫɬɶ ɝɪɚɞɭɫɚ = 1/60 ɱɚɫɬɶ ɦɢɧɭɬɵ = 00
ɨ
0'01";
1 ɝɪɚɞ (
g
) = 1/400 ɱɚɫɬɶ ɨɤɪɭɠɧɨɫɬɢ =100 ɞɟɫ.ɦɢɧɭɬɚɦ (
c
)
=10000 ɞɟɫ.ɫɟɤɭɧɞɚɦ (
ɫɫ
) = 1
g
00
c
00
ɫɫ
;
1 ɞɟɫ.ɦɢɧɭɬɚ (
c
) = 0,01 ɝɪɚɞɚ = 100 ɞɟɫ.ɫɟɤɭɧɞɚɦ (
ɫɫ
) = 0
g
01
c
00
ɫɫ
;
1 ɞɟɫ.ɫɟɤɭɧɞɚ (
ɫɫ
) = 0,0001 ɝɪɚɞɚ = 0,01 ɞɟɫ.ɦɢɧɭɬɵ = 0
g
00
c
01
ɫɫ
.
158
ɉɊɂɅɈɀȿɇɂȿ 6. ɄɊȺɌɇɕȿ ɂ ȾɈɅɖɇɕȿ ɉɊɂɋɌȺȼɄɂ
Ʉ ȿȾɂɇɂɐȺɆ ɎɂɁɂɑȿɋɄɂɏ ȼȿɅɂɑɂɇ
Ɍɚɛɥɢɰɚ
Ʉɪɚɬɧɨɫɬɶ ɢ ɞɨɥɶɧɨɫɬɶ
ɨɛɨɡɧɚɱɟɧɢɟ
ɇɚɢɦ.
ɩɪɢɫɬɚɜɨɤ
ɋɨɤɪɚɳɟɧɧɵɟ
ɪɭɫɫɤɨɟ ɦɟɠɞɭ-
ɧɚɪɨɞ-
ɧɨɟ
1 000 000 000 000 = 10
12
Ɍɟɪɚ Ɍ Ɍ
1 000 000 000 = 10
9
Ƚɢɝɚ Ƚ G
1 000 000 = 10
6
Ɇɟɝɚ ɦ Ɇ
1 000 = 10
3
ɤɢɥɨ ɤ ɤ
100 = 10
2
ɝɟɤ- ɝ h
10 = 10
1
ɞɟɤɚ ɞɚ da
0,1 = 10
-1
ɞɟɰɢ ɞ d
0,01 = 10
-2
ɫɚɧ- ɫ ɫ
0,001 = 10
-3
ɦɢɥ- ɦ m
0,000 001 = 10
-6
ɦɢɤ- ɦɤ μ
0,000 000001 = 10
-9
ɧɚɧɨ ɧ n
0,000 000 000 001 =10
-12
ɩɢɤɨ ɩ p
0,000 000 000 000 001 =10
-15
ɮɟɦ- ɮ f
0,000 000 000 000 000 001 =10
-18
ɚɬɬɨ ɚ Į
159
ɉɊɂɅɈɀȿɇɂȿ 7. Ⱥɧɚɥɢɬɢɱɟɫɤɢɣ ɫɩɨɫɨɛ (ɜɵɜɨɞ ɮɨɪɦɭɥɵ)
ɉɭɫɬɶ ɢɡɜɟɫɬɧɵ ɩɪɹɦɨɭɝɨɥɶɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɜɟɪɲɢɧ ɬɪɟɭɝɨɥɶɧɢɤɚ
1–2–3 (ɪɢɫ. 1). Ɉɩɭɫɬɢɜ ɢɡ ɟɝɨ ɜɟɪɲɢɧ ɩɟɪɩɟɧɞɢɤɭɥɹɪɵ ɧɚ ɨɫɶ Ɉɭ, ɩɥɨ-
ɳɚɞɶ ɬɪɟɭɝɨɥɶɧɢɤɚ S ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
IIIIII
SSSS
,
ɝɞɟ S
I
, S
II
, S
III
– ɩɥɨɳɚɞɢ ɬɪɚɩɟɰɢɣ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ I – (1'–1–2–2'),
II – (2'–2–3–3') ɢ III – (1'–1–3–3').
ɉɥɨɳɚɞɢ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɬɪɚɩɟɰɢɣ ɨɩɪɟɞɟɥɹɸɬɫɹ ɤɚɤ:
1221
2
1
yyxxS
I
;
2332
2
1
yyxxS
II
;
1331
2
1
yyxxS
I
.
Ɍɨɝɞɚ ɭɞɜɨɟɧɧɚɹ ɢɫɤɨɦɚɹ ɩɥɨɳɚɞɶ ɬɪɟɭɝɨɥɶɧɢɤɚ 1–2–3 ɛɭɞɟɬ ɪɚɜ-
ɧɚ:
133123321221
2 yyxxyyxxyyxxS
ɢɥɢ (10)
313123321221
2 yyxxyyxxyyxxS
.
ɉɨɫɥɟ ɪɚɫɤɪɵɬɢɹ ɫɤɨɛɨɤ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɝɪɭɩɩɢɪɨɜɤɢ ɱɥɟɧɨɜ
ɭɪɚɜɧɟɧɢɹ ɢ ɜɵɧɟɫɟɧɢɹ ɡɚ ɫɤɨɛɤɢ ɨɛɳɢɯ ɡɧɚɦɟɧɚɬɟɥɟɣ ɩɨɥɭɱɢɦ
21313121
2 yyxyyyyxS
ɢɥɢ
123312231
2 xxyxxyxxyS
.
ȼ ɨɛɳɟɦ ɜɢɞɟ
11
3
1
2
1
¦
ii
i
i
i
yyxS
ɢɥɢ
11
3
1
2
1
¦
ii
i
i
i
xxyS
. (11)
Ɍɨɝɞɚ ɞɥɹ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ ɫ ɱɢɫɥɨɦ ɜɟɪɲɢɧ ɩ ɩɪɢ ɢɯ ɨɰɢɮɪɨɜɤɟ ɩɨ
ɯɨɞɭ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ ɮɨɪɦɭɥɵ ɨɛɳɟɝɨ ɜɢɞɚ ɡɚɩɢɲɭɬɫɹ ɬɚɤ:
(12)
;
2
1
11
1
¦
ii
n
i
i
yyxS
,
2
1
11
1
¦
ii
n
i
i
yxyS
160