Антропова Н.А., Садыков Т.Д. Геодезическое обеспечение нефтегазопроводов и газонефтехранилищ

Подождите немного. Документ загружается.

Ɋɢɫ. 5.7. ȼɟɪɬɢɤɚɥɶɧɵɣ ɩɪɨɮɢɥɶ ɦɟɫɬɧɨɫɬɢ ɩɨ ɥɢɧɢɢ Ⱥȼ

Ɂɚɞɚɱɚ 5.20. ɇɚ ɤɚɪɬɟ ɦɚɫɲɬɚɛɚ 1:25000 ɩɨɫɬɪɨɣɬɟ ɥɢɧɢɸ ɫ ɭɤɥɨ-

ɧɨɦ ɧɟ ɛɨɥɟɟ 1,5 ɦɟɠɞɭ ɬɨɱɤɚɦɢ Ⱥ ɢ ȼ (ɪɢɫ. 5.8). ȼɵɫɨɬɚ ɫɟɱɟɧɢɹ ɪɟɥɶ-

ɟɮɚ 5 ɦ.

ɑɬɨɛɵ ɩɪɨɜɟɫɬɢ ɧɚ ɤɚɪɬɟ ɥɢɧɢɸ ɦɟɫɬɧɨɫɬɢ ɫ ɡɚɞɚɧ-

ɧɵɦ ɭɤɥɨɧɨɦ, ɛɟɪɭɬ ɩɨ ɦɚɫɲɬɚɛɭ ɡɚɥɨɠɟɧɢɣ ɜ ɪɚɫɬɜɨɪ

ɰɢɪɤɭɥɹ ɜɟɥɢɱɢɧɭ ɡɚɥɨɠɟɧɢɹ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɡɚɞɚɧ-

ɧɨɦɭ ɭɝɥɭ ɧɚɤɥɨɧɚ ɢɥɢ ɭɤɥɨɧɭ, ɢ ɨɬ ɧɚɱɚɥɶɧɨɣ ɬɨɱɤɢ ɩɨ-

ɫɥɟɞɨɜɚɬɟɥɶɧɨ ɡɚɫɟɤɚɸɬ ɷɬɢɦ ɪɚɫɬɜɨɪɨɦ ɫɨɫɟɞɧɢɟ ɝɨɪɢɡɨɧɬɚɥɢ ɩɪɢ ɭɫɥɨ-

ɜɢɢ, ɱɬɨ ɢɯ ɨɬɦɟɬɤɢ ɨɬɥɢɱɚɸɬɫɹ ɧɚ ɜɵɫɨɬɭ ɫɟɱɟɧɢɹ. ɋɨɟɞɢɧɹɹ

ɲɨɦ ɬɨɱɤɢ ɭɤɨɥɨɜ ɰɢɪɤɭɥɟɦ, ɩɨɥɭɱɚɸɬ ɥɨɦɚɧɭɸ ɥɢɧɢɸ, ɢɦɟɸɳɭɸ ɨɞɢɧ

ɢ ɬɨɬ ɠɟ ɡɚɞɚɧɧɵɣ ɭɤɥɨɧ.

Ɋɟɲɟɧɢɟ. Ɋɚɫɫɱɢɬɚɟɦ ɡɚɥɨɠɟɧɢɟ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɞɚɧɧɨɦɭ ɭɝɥɭ

ɧɚɤɥɨɧɚ:

ȼɵɪɚɡɢɦ ɡɚɥɨɠɟɧɢɟ ɜ ɦɚɫɲɬɚɛɟ ɩɥɚɧɚ

ȼɟɥɢɱɢɧɭ ɡɚɥɨɠɟɧɢɹ d' ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɬɚɤɠɟ ɩɨ ɝɪɚɮɢɤɭ ɡɚɥɨɠɟɧɢɣ.

Ɋɚɫɬɜɨɪɨɦ ɰɢɪɤɭɥɹ, ɪɚɜɧɵɦ ɡɚɥɨɠɟɧɢɸ d' = 8 ɦɦ, ɢɡ ɬɨɱɤɢ Ⱥ ɡɚɫɟ-

ɤɚɸɬ ɫɨɫɟɞɧɸɸ ɝɨɪɢɡɨɧɬɚɥɶ ɢ ɩɨɥɭɱɚɸɬ ɬɨɱɤɭ 1; ɢɡ ɬɨɱɤɢ 1 ɬɟɦ ɠɟ ɪɚɫ-

ɬɜɨɪɨɦ ɡɚɫɟɤɚɸɬ ɫɥɟɞɭɸɳɭɸ ɝɨɪɢɡɨɧɬɚɥɶ, ɩɨɥɭɱɚɹ ɬɨɱɤɭ 2; ɞɚɥɟɟ ɩɟɪɟ-

ɫɟɤɚɟɦ ɪɭɱɟɣ ɩɨɞ ɩɪɹɦɵɦ ɭɝɥɨɦ ɞɨ ɬɨɱɤɢ 3 ɢ ɬ. ɞ. ɋɨɟɞɢɧɢɜ ɩɨɥɭɱɟɧ-

ɧɵɟ ɬɨɱɤɢ, ɩɪɨɜɨɞɢɦ ɥɢɧɢɸ ɫ ɡɚɞɚɧɧɵɦ ɭɤɥɨɧɨɦ.

ȿɫɥɢ ɪɚɫɫɱɢɬɚɧɧɨɟ ɡɚɥɨɠɟɧɢɟ d' ɨɤɚɠɟɬɫɹ ɦɟɧɶɲɟ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠ-

ɞɭ ɞɜɭɦɹ ɫɨɫɟɞɧɢɦɢ ɝɨɪɢɡɨɧɬɚɥɹɦɢ (ɬ. ɟ. ɭɤɥɨɧ ɫɤɚɬɚ ɧɚ ɞɚɧɧɨɦ ɭɱɚɫɬɤɟ

ɦɟɧɶɲɟ ɡɚɞɚɧɧɨɝɨ – ɬɨɱɤɢ 4–5), ɬɨ ɭɱɚɫɬɨɤ ɬɪɚɫɫɵ ɩɪɨɜɨɞɹɬ ɩɨ ɤɪɚɬ-

ɱɚɣɲɟɦɭ ɪɚɫɫɬɨɹɧɢɸ ɦɟɠɞɭ ɧɢɦɢ. ɉɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɞɨɪɨɝ ɩɨɫɥɟɞ-

ɧɟɟ ɪɚɫɰɟɧɢɜɚɟɬɫɹ ɤɚɤ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɮɚɤɬɨɪ.

ɋɥɟɞɭɟɬ ɫɤɚɡɚɬɶ, ɱɬɨ ɪɟɲɟɧɢɟ ɞɚɧɧɨɣ ɡɚɞɚɱɢ ɩɨɡɜɨɥɹɟɬ ɧɚɦɟɬɢɬɶ

ɧɟɫɤɨɥɶɤɨ ɜɚɪɢɚɧɬɨɜ ɬɪɚɫɫɵ, ɢɡ ɤɨɬɨɪɵɯ ɜɵɛɢɪɚɟɬɫɹ ɧɚɢɛɨɥɟɟ ɩɪɢɟɦ-

ɥɟɦɵɣ ɫ ɬɟɯɧɢɤɨ-ɷɤɨɧɨɦɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ.

Ɋɢɫ. 5.8. ɋɯɟɦɚ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɬɪɚɫɫɵ ɫ ɡɚɞɚɧɧɵɦ ɭɤɥɨɧɨɦ

Ɂɚɞɚɱɚ 5.21. Ɉɩɪɟɞɟɥɢɬɟ ɝɪɚɧɢɰɭ ɜɨɞɨɫɛɨɪɧɨɝɨ ɛɚɫɫɟɣɧɚ ɞɥɹ ɬɨɱ-

ɤɢ Ⱥ (ɪɢɫ. 5.9).

ȼɨɞɨɫɛɨɪɧɨɣ ɩɥɨɳɚɞɶɸ, ɢɥɢ ɛɚɫɫɟɣɧɨɦ, ɧɚɡɵɜɚɟɬɫɹ ɭɱɚ-

ɫɬɨɤ ɡɟɦɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɫ ɤɨɬɨɪɨɣ ɜɨɞɚ, ɩɨɫɬɭɩɚɹ ɢɯ

ɚɬɦɨɫɮɟɪɵ, ɫɬɟɤɚɟɬ ɩɨ ɫɤɥɨɧɚɦ ɜ ɨɞɧɭ ɬɨɱɤɭ ɜɨɞɨɬɨɤɚ

(ɪɟɤɢ, ɥɨɳɢɧɵ, ɨɜɪɚɝɚ ɢ ɬ. ɞ.). ɉɪɢ ɷɬɨɦ ɩɪɢɧɢɦɚɸɬ, ɱɬɨ

ɩɨɫɬɭɩɚɸɳɚɹ ɜɨɞɚ ɧɟ ɩɨɝɥɨɳɚɟɬɫɹ ɝɪɭɧɬɨɦ, ɚ ɷɜɚɤɭɢɪɭ-

ɟɬɫɹ ɩɨ ɩɨɜɟɪɯɧɨɫɬɢ ɡɟɦɥɢ.

Ʌɢɧɢɹ ɜɨɞɨɫɛɨɪɚ ɩɪɨɯɨɞɢɬ ɩɨ ɬɨɱɤɚɦ ɫ ɧɚɢɛɨɥɶɲɢɦɢ ɨɬɦɟɬɤɚɦɢ,

ɨɤɚɣɦɥɹɹ ɬɭ ɩɨɜɟɪɯɧɨɫɬɶ, ɫ ɤɨɬɨɪɨɣ ɫɬɟɤɚɟɬ ɜɨɞɚ ɜ ɞɚɧɧɭɸ ɱɚɫɬɶ ɜɨɞɨ-

ɬɨɤɚ. Ɉɧɚ ɫɨɜɩɚɞɚɟɬ ɫ ɜɨɞɨɪɚɡɞɟɥɨɦ, ɩɟɪɟɫɟɤɚɹ ɡɚɦɤɧɭɬɵɟ ɝɨɪɢɡɨɧɬɚɥɢ

ɩɨ ɧɨɪɦɚɥɢ ɤ ɧɢɦ ɜ ɬɨɱɤɚɯ ɧɚɢɛɨɥɶɲɟɣ ɤɪɭɬɢɡɧɵ. ȿɫɥɢ ɩɥɨɳɚɞɶ ɜɨɞɨ-

ɫɛɨɪɚ ɨɝɪɚɧɢɱɟɧɚ ɤɚɤɢɦ-ɥɢɛɨ ɧɚɦɟɱɚɟɦɵɦ ɩɨɩɟɪɟɱɧɵɦ ɫɟɱɟɧɢɟɦ. ɇɚ-

ɩɪɢɦɟɪ, ɫɬɜɨɪɨɦ ɩɥɨɬɢɧɵ, ɬɨ ɜɨɞɨɪɚɡɞɟɥɶɧɚɹ ɥɢɧɢɹ ɞɨɥɠɧɚ ɩɨɞɯɨɞɢɬɶ ɤ

ɷɬɨɦɭ ɫɬɜɨɪɭ.

Ɋɟɲɟɧɢɟ. Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɧɢɰɵ ɜɨɞɨɫɛɨɪɧɨɝɨ ɛɚɫɫɟɣɧɚ (ɪɢɫ.

5.9) ɧɟɨɛɯɨɞɢɦɨ ɩɨɞɧɹɬɶɫɹ ɩɨ ɥɢɧɢɹɦ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵɦ ɝɨɪɢɡɨɧɬɚ-

ɥɹɦ, ɞɨ ɛɥɢɠɚɣɲɟɣ ɜɨɞɨɪɚɡɞɟɥɶɧɨɣ ɥɢɧɢɢ. Ⱦɚɥɟɟ ɝɪɚɧɢɰɚ ɩɪɨɞɨɥɠɚɟɬɫɹ

ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɩɨ ɥɢɧɢɹɦ ɜɨɞɨɪɚɡɞɟɥɨɜ ɞɨ ɢɯ ɡɚɦɵɤɚɧɢɹ.

Ƚɪɚɧɢɰɵ ɜɨɞɨɫɛɨɪɧɵɯ ɛɚɫɫɟɣɧɨɜ ɢɫɩɨɥɶɡɭɸɬ ɞɥɹ ɩɨ-

ɫɥɟɞɭɸɳɟɣ ɨɩɪɟɞɟɥɟɧɢɹ ɩɥɨɳɚɞɢ ɛɚɫɫɟɣɧɚ, ɧɟɨɛɯɨɞɢɦɨɣ

ɩɪɢ ɪɚɫɱɟɬɚɯ ɜɨɡɦɨɠɧɵɯ ɩɪɢɬɨɤɨɜ ɜɨɞɵ ɤ ɨɬɜɟɪɫɬɢɹɦ ɜɨ-

ɞɨɩɪɨɩɭɫɤɧɵɯ ɫɢɫɬɟɦ ɩɨɞ ɞɨɪɨɝɚɦɢ, ɩɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ

ɚɷɪɨɞɪɨɦɨɜ ɢ ɞɪ.

Ɂɧɚɹ ɜɨɞɨɫɛɨɪɧɭɸ ɩɥɨɳɚɞɶ, ɫɪɟɞɧɟɝɨɞɨɜɨɟ ɤɨɥɢɱɟɫɬɜɨ ɨɫɚɞɤɨɜ,

ɭɫɥɨɜɢɹ ɢɫɩɚɪɟɧɢɹ ɢ ɜɩɢɬɵɜɚɧɢɹ ɜɥɚɝɢ ɩɨɱɜɨɣ, ɦɨɠɧɨ ɩɨɞɫɱɢɬɚɬɶ

ɦɨɳɧɨɫɬɶ ɜɨɞɧɨɝɨ ɩɨɬɨɤɚ, ɤɨɬɨɪɚɹ ɧɟɨɛɯɨɞɢɦɚ ɞɥɹ ɪɚɫɱɟɬɚ ɦɨɫɬɨɜ,

ɩɥɨɳɚɞɨɤ ɞɚɦɛ ɢ ɞɪɭɝɢɯ ɝɢɞɪɨɬɟɯɧɢɱɟɫɤɢɯ ɫɨɨɪɭɠɟɧɢɣ.



Ɋɢɫ. 5.9. ɋɯɟɦɚ ɨɩɪɟɞɟɥɟɧɢɹ ɝɪɚɧɢɰɵ ɜɨɞɨɫɛɨɪɧɨɣ

ɩɥɨɳɚɞɢ ɢ ɩɥɨɳɚɞɢ ɡɚɬɨɩɥɟɧɢɹ

Ɂɚɞɚɱɚ 5.22. Ɉɩɪɟɞɟɥɢɬɟ ɝɪɚɧɢɰɭ ɡɨɧɵ ɡɚɬɨɩɥɟɧɢɹ ɩɨ ɤɚɪɬɟ.

ȼɵɩɨɥɧɹɸɬ ɩɪɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɩɥɨɬɢɧ ɥɢɛɨ ɞɪɭɝɢɯ

ɝɢɞɪɨɬɟɯɧɢɱɟɫɤɢɯ ɫɨɨɪɭɠɟɧɢɣ, ɩɪɟɞɫɬɚɜɥɹɸɳɢɯ ɫɨɛɨɣ

ɩɪɟɩɹɬɫɬɜɢɟ ɞɥɹ ɫɜɨɛɨɞɧɨɝɨ ɬɨɤɚ ɜɨɞɵ. Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ

ɡɨɧɵ ɡɚɬɨɩɥɟɧɢɹ ɢɫɯɨɞɧɨɣ ɜɟɥɢɱɢɧɨɣ ɹɜɥɹɟɬɫɹ ɚɛɫɨɥɸɬ-

ɧɚɹ ɜɵɫɨɬɚ ɩɥɨɬɢɧɵ ɢɥɢ ɩɨɞɩɨɪɧɨɝɨ ɫɨɨɪɭɠɟɧɢɹ, ɧɚ

ɬɚɤɠɟ ɩɨɥɨɠɟɧɢɟ ɫɚɦɨɣ ɩɥɨɬɢɧɵ (ɬɨɱɤɢ 1-2 ɧɚ ɪɢɫ. 5.9) ɧɚ ɦɟɫɬɧɨɫɬɢ.

Ⱥɛɫɨɥɸɬɧɚɹ ɜɵɫɨɬɚ ɩɥɨɬɢɧɵ ɡɚɞɚɟɬ ɚɛɫɨɥɸɬɧɭɸ ɜɵɫɨɬɭ ɝɨɪɢɡɨɧɬɚɥɢ

(ɪɢɫ. 5.9), ɤɨɬɨɪɭɸ ɫɪɚɜɧɢɬɟɥɶɧɨ ɥɟɝɤɨ ɩɪɨɜɟɫɬɢ ɦɟɠɞɭ ɝɨɪɢɡɨɧɬɚɥɹɦɢ,

ɢɦɟɸɳɢɦɢɫɹ ɧɚ ɤɚɪɬɟ.

Ƚɪɚɧɢɰɚ ɡɨɧɵ ɡɚɬɨɩɥɟɧɢɹ ɩɨɤɚɡɵɜɚɟɬ ɧɚ ɤɚɪɬɟ ɦɟɫɬɧɨɫɬɶ, ɩɨɤɪɵɜɚɸ-

ɳɭɸɫɹ ɜɨɞɨɣ ɩɨɫɥɟ ɫɬɪɨɢɬɟɥɶɫɬɜɚ ɩɥɨɬɢɧɵ, ɱɬɨ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɩɪɢɧɹ-

ɬɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɩɪɟɞɭɩɪɟɞɢɬɟɥɶɧɵɯ ɦɟɪ. Ʉɪɨɦɟ ɬɨɝɨ, ɢɫɩɨɥɶɡɨɜɚ-

ɧɢɟ ɝɨɪɢɡɨɧɬɚɥɟɣ ɤɚɪɬɵ ɢ ɨɬɦɟɬɤɢ ɜɨɞɧɨɝɨ ɡɟɪɤɚɥɚ ɩɨɡɜɨɥɹɟɬ ɪɟɲɢɬɶ

ɡɚɞɚɱɭ ɨ ɺɦɤɨɫɬɢ ɜɨɞɨɯɪɚɧɢɥɢɳɚ.

Ɂɚɞɚɱɚ 5.23. Ɉɩɪɟɞɟɥɢɬɟ ɨɛɴɺɦ ɯɨɥɦɚ, ɨɝɪɚɧɢɱɟɧɧɨɝɨ ɭɬɨɥɳɺɧ-

ɧɨɣ ɝɨɪɢɡɨɧɬɚɥɶɸ ɫ ɜɟɪɲɢɧɨɣ ɝ. Ʉɧɨɪɪɟɧ (ɪɢɫ. 5.11, ɜɵɫɨɬɚ 875 ɦ ɜ ɤɜ.

0881), ɟɫɥɢ S

, S

ɢ S

ɪɚɜɧɵ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ 52812,5 ɦ

, 162187,5 ɦ

270625 ɦ

Ɉɛɴɟɦ ɩɨɪɨɞ, ɡɚɤɥɸɱɟɧɧɵɯ ɜ ɯɨɥɦɟ (ɪɢɫ. 5.10), ɦɨɠɟɬ

ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧ ɤɚɤ ɫɭɦɦɚ ɨɛɴɟɦɨɜ, ɡɚɤɥɸɱɟɧɧɵɯ ɦɟ-

ɠɞɭ ɫɨɫɟɞɧɢɦɢ ɝɨɪɢɡɨɧɬɚɥɹɦɢ. Ɉɛɴɟɦ ɤɚɠɞɨɝɨ ɩɨɹɫɚ

ɨɩɪɟɞɟɥɢɬɫɹ ɩɨ ɩɪɢɛɥɢɠɟɧɧɨɣ ɮɨɪɦɭɥɟ ɨɛɴɟɦɚ ɭɫɟɱɟɧ-

ɧɨɝɨ ɤɨɧɭɫɚ:

ɞɥɹ I ɩɨɹɫɚ



;

ɞɥɹ II ɩɨɹɫɚ



,

ɝɞɟ h – ɜɵɫɨɬɚ ɫɟɱɟɧɢɹ ɪɟɥɶɟɮɚ; S

ɢ S

i+1

– ɩɥɨɳɚɞɢ

ɧɢɠɧɟɝɨ ɢ ɜɟɪɯɧɟɝɨ ɨɫɧɨɜɚɧɢɣ ɩɨɹɫɚ, ɨɝɪɚɧɢɱɟɧɧɵɟ

ɝɨɪɢɡɨɧɬɚɥɹɦɢ; ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɧɟ-

ɨɛɯɨɞɢɦɨɣ ɬɨɱɧɨɫɬɢ ɨɩɪɟɞɟɥɹɸɬɫɹ

ɝɪɚɮɢɱɟɫɤɢ ɥɢɛɨ ɫ ɩɨɦɨɳɶɸ ɩɥɚɧɢ-

ɦɟɬɪɚ (ɉɪɢɥɨɠɟɧɢɟ).

ȿɫɥɢ ɜɟɪɯɧɢɣ ɫɥɨɣ ɯɨɥɦɚ ɢɦɟɟɬ ɮɨɪɦɭ ɤɭɩɨɥɚ, ɬɨ ɟɝɨ ɨɛɴɺɦ ɨɩɪɟɞɟɥɢɬ-

ɫɹ ɩɨ ɩɪɢɛɥɢɠɺɧɧɨɣ ɮɨɪɦɭɥɟ

Ɋɢɫ. 5.10.

ɋɯɟɦɚ ɨɩɪɟɞɟɥɟɧɢɹ

ɨɛɴɺɦɨɜ ɡɟɦɥɹɧɵɯ ɬɟɥ

hSV

ȼȼ

ɝɞɟ

– ɩɥɨɳɚɞɶ ɨɫɧɨɜɚɧɢɹ ɜɟɪɯɧɟɝɨ ɫɥɨɹ; h' – ɪɚɡɧɨɫɬɶ ɨɬɦɟɬɨɤ

ɝɨɪɢɡɨɧɬɚɥɢ ɨɫɧɨɜɚɧɢɹ ɜɟɪɯɧɟɝɨ ɫɥɨɹ ɢ ɜɟɪɲɢɧɵ ɯɨɥɦɚ.

Ɉɛɳɢɣ ɨɛɴɺɦ ɯɨɥɦɚ

Ɋɟɲɟɧɢɟ.

1 ɩɨɹɫ: .

2 ɩɨɹɫ:

3 ɩɨɹɫ:

Ɉɛɳɢɣ ɨɛɴɺɦ ɯɨɥɦɚ .

Ɋɢɫ. 5.11. Ɉɩɪɟɞɟɥɟɧɢɟ ɨɛɴɺɦɚ ɯɨɥɦɚ (ɮɪɚɝɦɟɧɬ ɤɚɪɬɵ ɭɦɟɧɶɲɟɧ)

Ɂɚɞɚɱɚ 5.23

. Ɉɩɪɟɞɟɥɢɬɟ ɩɥɨɳɚɞɶ ɩɨɥɢɝɨɧɚ ɩɨ ɤɨɨɪɞɢɧɚɬɚɦ ɟɝɨ

ɜɟɪɲɢɧ (ɬɚɛɥ. 2).

Ɍɚɛɥɢɰɚ 5.1

ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ

Ɍ 1 2 3 4

X, ɦ

Y, ɦ

2156,847

4600,212

1921,315

4563,842

1541,242

4781,747

1756,211

4763,226

ɋɭɳɟɫɬɜɭɟɬ ɧɟɫɤɨɥɶɤɨ ɫɩɨɫɨɛɨɜ ɨɩɪɟɞɟɥɟɧɢɹ

ɩɥɨɳɚɞɟɣ ɭɱɚɫɬɤɨɜ. ȼɵɛɨɪ ɫɩɨɫɨɛɚ ɡɚɜɢɫɢɬ ɨɬ ɮɨɪɦɵ

ɝɪɚɧɢɰ ɭɱɚɫɬɤɚ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɬɟɯɧɢɱɟɫɤɢɯ ɫɪɟɞɫɬɜ ɢ

ɧɟɨɛɯɨɞɢɦɨɣ ɬɨɱɧɨɫɬɢ ɨɩɪɟɞɟɥɟɧɢɹ ɩɥɨɳɚɞɢ.

ȿɫɥɢ ɢɡɜɟɫɬɧɵ ɩɪɹɦɨɭɝɨɥɶɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɭɱɚ-

ɫɬɤɚ, ɜɟɪɲɢɧɵ ɤɨɬɨɪɨɝɨ ɨɛɨɡɧɚɱɟɧɵ ɩɨ ɯɨɞɭ ɞɜɢɠɟɧɢɹ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ

(ɪɢɫ. 1), ɬɨ ɜɵɱɢɫɥɟɧɢɟ ɩɥɨɳɚɞɢ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ ɩɨ ɤɨɨɪɞɢɧɚɬɚɦ ɟɝɨ

ɜɟɪɲɢɧ ɫɥɟɞɭɟɬ ɜɵɩɨɥɧɹɬɶ ɞɥɹ ɤɨɧɬɪɨɥɹ ɞɜɚ ɪɚɡɚ ɩɨ ɮɨɪɦɭɥɚɦ (5.1) ɢ

(5.2) (ɚɧɚɥɢɬɢɱɟɫɤɢɣ ɫɩɨɫɨɛ):







yyxS

(5.1)

ɢɥɢ







xxyS

. (5.2)

ɉɨɩɨɜ ȼ.ɇ., ɑɟɤɚɥɢɧ ɋ.ɂ. Ƚɟɨɞɟɡɢɹ: ɍɱɟɛɧɢɤ ɞɥɹ ɜɭɡɨɜ. – Ɇ.: «Ɇɢɪ ɝɨɪɧɨɣ

ɤɧɢɝɢ», ɂɡɞɚɬɟɥɶɫɬɜɨ Ɇɨɫɤɨɜɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɝɨɪɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ, ɢɡɞɚ-

ɬɟɥɶɫɬɜɨ «Ƚɨɪɧɚɹ ɤɧɢɝɚ», 2007. – 722 ɫ.: ɢɥ.

ȼ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɫɥɭɱɚɟ ɬɨɱ-

ɧɨɫɬɶ ɜɵɱɢɫɥɟɧɢɹ ɩɥɨɳɚɞɢ ɨɩɪɟɞɟ-

ɟɬɫɹ ɥɢɲɶ ɩɨɝɪɟɲɧɨɫɬɹɦɢ ɭɝɥɨɜɵɯ ɢ

ɥɢɧɟɣɧɵɯ ɢɡɦɟɪɟɧɢɣ ɧɚ ɦɟɫɬɧɨɫɬɢ.

Ɍɚɤ, ɩɪɢ ɢɡɦɟɪɟɧɢɢ ɭɝɥɨɜ ɫ ɬɨɱɧɨɫɬɶɸ

1´ ɢ ɞɥɢɧ ɥɢɧɢɣ ɫ ɬɨɱɧɨɫɬɶɸ 1:2000

ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɨɩɪɟɞɟɥɟ-

ɧɢɹ ɩɥɨɳɚɞɢ ɫɨɫɬɚɜɢɬ ɩɪɢɦɟɪɧɨ

1:1500.

Ɋɟɲɟɧɢɟ.

S = 0,5 [ɯ

(ɭ

– ɭ

) + ɯ

(ɭ

– ɭ

) + ɯ

(ɭ

– ɭ

) + ɯ

(ɭ

– ɭ

)] = 0,5

[2156,847(4563,842 – 4763,226) + 1921,315(4781,747 – 4600,212) +

1541,242 (4763,226 – 4563,842) + 1756,211(4600,212 – 4781,747)] =

0,5[2156,847 (–199,384) + 1921,315 (181,535) + 1541,242(199,384) +

1756,211 (–181,535)] = 46384,816 ɦ

S = 0,5 [ɭ

(ɯ

– ɯ

) + ɭ

(ɯ

– ɯ

) + ɭ

(ɯ

– ɯ

) + ɭ

(ɯ

– ɯ

)] = 0,5

[4600,212(1921,315 – 1756,211) + 4563,842(1541,242 – 2156,847) +

4781,747 (1756,211 – 1921,315) + 4763,226(2156,847 – 1541,242)] =

0,5[4600,212 (165,104) + 4563,842 (–615,605) + 4781,747(–165,104) +

4763,226(615,605)] = 46384,816 ɦ

ȼɵɲɟɩɪɢɜɟɞɺɧɧɵɟ ɜɵɱɢɫɥɟɧɢɹ ɭɞɨɛɧɟɟ ɩɪɨɜɨɞɢɬɶ ɜ ɬɚɛɥɢɱɧɨɣ

ɮɨɪɦɟ (ɬɚɛɥ. 3).

Ɍɚɛɥɢɰɚ 3

ȼɵɱɢɫɥɟɧɢɟ ɩɥɨɳɚɞɢ ɩɨ ɤɨɨɪɞɢɧɚɬɚɦ

Ʉɨɨɪɞɢɧɚɬɵ

1 2 3 4 5 6 7

1 2156,84

4600,21

–199,384 –165,104 –430040,78 –759513,40

2 1921,31

4563,84

181,535 615,605 348785,92 2809523,95

3 1541,24

4781,74

199,384 165,104 307298,99 789485,56

Ɋɢɫ. 5.12. Ⱥɧɚɥɢɬɢɱɟɫɤɢɣ

ɫɩɨɫɨɛ ɨɩɪɟɞɟɥɟɧɢɹ ɩɥɨɳɚɞɢ ɮɢɝɭ-

ɪɵ

4 1756,21

4763,22

–181,535 –615,605 –318813,76 2932265,74

Ɂɚɞɚɱɚ 5.24. Ɋɚɫɫɱɢɬɚɣɬɟ ɩɥɨɳɚɞɶ ɩɨɥɢɝɨɧɚ ɩɨ ɤɨɨɪɞɢɧɚɬɚɦ ɬɨ-

ɱɟɤ ɢ ɩɪɢɪɚɳɟɧɢɹɦ ɤɨɨɪɞɢɧɚɬ (ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ. 4) ɢ

ɜɵɪɚɡɢɬɟ ɟɟ ɜ ɝɚ (1ɝɚ = 10000 ɦ

Ɍɚɛɥɢɰɚ 4

Ɏɪɚɝɦɟɧɬ ɜɟɞɨɦɨɫɬɢ ɜɵɱɢɫɥɟɧɢɹ ɤɨɨɪɞɢɧɚɬ

ɬɨɱɟɤ

ɂɫɩɪɚɜɥɟɧ-

ɧɵɟ

ɩɪɢɪɚɳɟɧɢɹ,

Ʉɨɨɪɞɢɧɚɬɵ,

±ǻɯ ±ǻɭ ±ɯ ±ɭ

+8328,1 +774

+141,63 +172,00

+8469,75 +7917,84

–

55,02 +133,19

+8414,73 +8051,03

–

112,19 –31,00

+8302,54 +8020,03

–

64,54 –66,83

+8238,00 +7953,20

+8,33 –110,09

+8246,33 +7843,11

+81,79 –97,27

+8328,12 +7745,84

ɇɚ ɩɪɚɤɬɢɤɟ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɩɥɨɳɚɞɟɣ ɩɨɥɢɝɨɧɚ

ɭɞɨɛɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɮɨɪɦɭɥɵ, ɜ ɤɨɬɨɪɵɟ ɧɚɪɹɞɭ ɫ ɤɨ-

ɨɪɞɢɧɚɬɚɦɢ ɬɨɱɟɤ ɜɯɨɞɹɬ ɩɪɢɪɚɳɟɧɢɹ ɤɨɨɪɞɢɧɚɬ. ɗɬɨ

ɩɨɡɜɨɥɹɟɬ ɜɟɫɬɢ ɜɵɱɢɫɥɟɧɢɹ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɜ ɜɟɞɨ-

ɦɨɫɬɢ ɜɵɱɢɫɥɟɧɢɹ ɤɨɨɪɞɢɧɚɬ, ɜ ɤɨɬɨɪɨɣ ɢɦɟɸɬɫɹ ɜɫɟ

ɷɥɟɦɟɧɬɵ, ɜɯɨɞɹɳɢɟ ɜ ɮɨɪɦɭɥɭ.

ɇɚ ɨɫɧɨɜɟ (ɮɨɪɦɭɥɚ 10 ɉɪɢɥ. 6) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɨɛɳɟɦ ɜɢɞɟ:

 

1 ii

yyxxS 



ɉɨɫɤɨɥɶɤɭ



iii

yyy ' 

1

, ɬɨ