Учет ветра в математической модели судна с целью оценки его

ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 7, ʋ3, 2004 ɝ.
ɫɬɪ.375-380
ɍɱɟɬ ɜɟɬɪɚ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫɭɞɧɚ ɫ ɰɟɥɶɸ ɨɰɟɧɤɢ
ɟɝɨ ɜɥɢɹɧɢɹ ɧɚ ɦɚɧɟɜɪɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
Ƚ.ɂ. Ɇɚɪɬɸɤ1, ɘ.ɂ. ɘɞɢɧ2, Ⱥ.ɘ. ɘɞɢɧ2
1
ɈȺɈ Ɇɭɪɦɚɧɫɤɨɟ ɦɨɪɫɤɨɟ ɩɚɪɨɯɨɞɫɬɜɨ
2
ɋɭɞɨɜɨɞɢɬɟɥɶɫɤɢɣ ɮɚɤɭɥɶɬɟɬ ɆȽɌɍ, ɤɚɮɟɞɪɚ ɫɭɞɨɜɨɠɞɟɧɢɹ
Ⱥɧɧɨɬɚɰɢɹ. Ⱦɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɞɜɢɠɟɧɢɹ ɫɭɞɧɚ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɫɥɨɠɧɵɯ ɦɚɧɟɜɪɨɜ ɜ ɪɟɚɥɶɧɵɯ
ɭɫɥɨɜɢɹɯ ɩɥɚɜɚɧɢɹ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɫɭɞɧɚ ɬɪɟɛɭɟɬɫɹ ɜɜɟɫɬɢ ɩɚɪɚɦɟɬɪɵ, ɨɩɪɟɞɟɥɹɸɳɢɟ ɜɥɢɹɧɢɟ
ɜɧɟɲɧɢɯ ɮɚɤɬɨɪɨɜ, ɨɞɧɢɦ ɢɡ ɤɨɬɨɪɵɯ ɹɜɥɹɟɬɫɹ ɜɟɬɟɪ. ȼ ɫɬɚɬɶɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɩɨɫɨɛ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ
ɨɩɢɫɚɧɢɹ ɜɥɢɹɧɢɹ ɜɟɬɪɚ ɧɚ ɦɚɧɟɜɪɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫɭɞɧɚ.
Abstract. The mathematical model of the ship’s movement while carrying out the complex manouvring under
real sailing conditions needs some parameters taking into account the influence of the external factors, namely
wind. The method of mathematical description of the wind influence on the ship manouvring characteristics has
been given in the paper.
1. ȼɜɟɞɟɧɢɟ
ȼɥɢɹɧɢɟ ɜɟɬɪɚ ɧɚ ɩɚɪɚɦɟɬɪɵ ɦɚɧɟɜɪɢɪɨɜɚɧɢɹ ɫɭɞɧɚ ɫɭɳɟɫɬɜɟɧɧɨ ɢ ɨɫɨɛɟɧɧɨ ɡɚɦɟɬɧɨ, ɟɫɥɢ
ɨɬɧɨɲɟɧɢɟ ɫɤɨɪɨɫɬɢ ɜɟɬɪɚ X$ ɤ ɫɤɨɪɨɫɬɢ ɫɭɞɧɚ X ɞɨɫɬɢɝɚɟɬ ɡɧɚɱɟɧɢɣ, ɡɧɚɱɢɬɟɥɶɧɨ ɩɪɟɜɵɲɚɸɳɢɯ 1.
ɉɨɫɥɟɞɫɬɜɢɹ ɜɨɡɞɟɣɫɬɜɢɹ ɜɟɬɪɚ ɧɚ ɞɜɢɠɭɳɟɟɫɹ ɫɭɞɧɨ ɦɨɝɭɬ ɛɵɬɶ ɬɪɭɞɧɨ ɩɪɨɝɧɨɡɢɪɭɟɦɵɦɢ, ɟɫɥɢ
ɫɭɞɨɜɨɞɢɬɟɥɶ ɩɥɨɯɨ ɩɪɟɞɫɬɚɜɥɹɟɬ, ɨɬ ɱɟɝɨ ɡɚɜɢɫɢɬ ɯɚɪɚɤɬɟɪ ɩɨɜɟɞɟɧɢɹ ɫɭɞɧɚ ɜ ɪɟɡɭɥɶɬɚɬɟ
ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ. ɍɱɢɬɵɜɚɹ, ɱɬɨ ɲɜɚɪɬɨɜɧɵɟ ɨɩɟɪɚɰɢɢ ɨɛɵɱɧɨ ɜɵɩɨɥɧɹɸɬɫɹ ɧɚ ɦɚɥɵɯ
ɫɤɨɪɨɫɬɹɯ, ɬ.ɟ. ɨɬɧɨɲɟɧɢɟ X$X ɞɨɫɬɚɬɨɱɧɨ ɜɟɥɢɤɨ, ɩɪɢ ɷɬɨɦ ɜɨɡɦɨɠɧɵ ɱɚɫɬɵɟ ɩɟɪɟɯɨɞɧɵɟ ɪɟɠɢɦɵ
ɞɜɢɠɟɧɢɹ ɢ ɞɜɢɠɟɧɢɹ ɩɪɢ ɧɟɪɚɛɨɬɚɸɳɟɦ ɞɜɢɠɢɬɟɥɟ ɢɥɢ ɞɜɢɠɟɧɢɟ ɡɚɞɧɢɦ ɯɨɞɨɦ, ɪɟɡɤɨ ɜɨɡɪɚɫɬɚɟɬ
ɡɧɚɱɢɦɨɫɬɶ ɡɧɚɧɢɹ ɫɭɞɨɜɨɞɢɬɟɥɟɦ ɤɚɤ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɫɨɛɫɬɜɟɧɧɨɝɨ ɫɭɞɧɚ, ɬɚɤ ɢ ɨɛɳɢɯ
ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ɜɨɡɞɟɣɫɬɜɢɹ ɜɟɬɪɚ ɧɚ ɭɩɪɚɜɥɹɟɦɨɫɬɶ ɫɭɞɧɚ. ȼ ɷɬɨɣ ɫɜɹɡɢ ɩɪɨɜɟɞɟɦ ɚɧɚɥɢɡ ɫɭɳɟɫɬɜɭɸɳɢɯ
ɞɨɫɬɚɬɨɱɧɨ ɞɟɬɚɥɶɧɨ ɪɚɡɪɚɛɨɬɚɧɧɵɯ ɫɩɨɫɨɛɨɜ ɭɱɟɬɚ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ ɧɚ ɫɭɞɧɨ ɫ ɰɟɥɶɸ
ɜɵɛɨɪɚ ɨɞɧɨɝɨ ɢɡ ɧɢɯ ɞɥɹ ɞɚɥɶɧɟɣɲɟɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɜ ɦɨɞɟɥɶɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɚɯ, ɚ ɬɚɤɠɟ ɪɚɫɫɦɨɬɪɢɦ
ɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɭɫɥɨɜɢɹɦ ɜɵɩɨɥɧɟɧɢɹ ɲɜɚɪɬɨɜɧɨɣ ɨɩɟɪɚɰɢɢ ɧɟɤɨɬɨɪɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɩɨɜɟɞɟɧɢɹ ɫɭɞɧɚ ɜ
ɩɪɨɰɟɫɫɟ ɜɵɩɨɥɧɟɧɢɹ ɷɬɨɝɨ ɫɥɨɠɧɨɝɨ ɦɚɧɟɜɪɚ (ɤɚɤ ɢɡɜɟɫɬɧɨ, ɤɥɚɫɫɢɱɟɫɤɢ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɭɩɪɚɜɥɹɟɦɨɫɬɶ
ɫɭɞɧɚ ɩɪɢ ɞɜɢɠɟɧɢɢ ɧɚ ɩɪɹɦɨɦ ɤɭɪɫɟ). ȼ ɱɚɫɬɧɨɫɬɢ, ɜ ɤɨɧɬɟɤɫɬɟ ɪɟɲɚɟɦɨɣ ɡɚɞɚɱɢ ɜɟɫɶɦɚ ɫɭɳɟɫɬɜɟɧɧɨ
ɡɧɚɬɶ ɯɚɪɚɤɬɟɪ ɩɨɜɟɞɟɧɢɹ ɲɜɚɪɬɭɸɳɟɝɨɫɹ ɫɭɞɧɚ ɩɪɢ ɟɝɨ ɞɜɢɠɟɧɢɢ ɜ ɜɵɲɟɭɤɚɡɚɧɧɵɯ ɪɟɠɢɦɚɯ (ɦɚɥɚɹ
ɫɤɨɪɨɫɬɶ, ɞɜɢɠɟɧɢɟ ɩɨ ɢɧɟɪɰɢɢ, ɞɜɢɠɟɧɢɟ ɧɚ ɩɟɪɟɯɨɞɧɵɯ ɪɟɠɢɦɚɯ, ɞɜɢɠɟɧɢɟ ɡɚɞɧɢɦ ɯɨɞɨɦ).
ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜɚɠɧɵɦ ɜ ɢɡɭɱɟɧɢɢ ɜɥɢɹɧɢɹ ɜɟɬɪɚ ɹɜɥɹɟɬɫɹ ɩɪɨɰɟɫɫ ɞɜɢɠɟɧɢɹ ɫɭɞɧɚ ɫ
ɨɫɬɚɧɨɜɥɟɧɧɵɦɢ ɦɚɲɢɧɚɦɢ ɜ ɩɟɪɢɨɞ, ɤɨɝɞɚ ɫɤɨɪɨɫɬɶ ɟɝɨ ɞɪɟɣɮɚ ɫɬɚɧɟɬ ɩɨɫɬɨɹɧɧɨɣ. ɇɨ ɩɪɟɠɞɟ, ɱɟɦ ɞɪɟɣɮ
ɫɭɞɧɚ ɫ ɨɫɬɚɧɨɜɥɟɧɧɵɦɢ ɦɚɲɢɧɚɦɢ ɞɨɫɬɢɝɚɟɬ ɫɜɨɟɝɨ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ, ɜ ɬɟɱɟɧɢɟ ɧɟɤɨɬɨɪɨɝɨ
ɩɟɪɢɨɞɚ ɜɪɟɦɟɧɢ ɨɫɧɨɜɧɵɟ ɩɚɪɚɦɟɬɪɵ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɟ ɢ ɨɩɪɟɞɟɥɹɸɳɢɟ ɯɚɪɚɤɬɟɪ ɩɪɨɬɟɤɚɧɢɹ ɩɪɨɰɟɫɫɚ,
ɦɟɧɹɸɬ ɫɜɨɢ ɡɧɚɱɟɧɢɹ. ɋɭɞɨɜɨɞɢɬɟɥɶ, ɜɵɩɨɥɧɹɸɳɢɣ ɲɜɚɪɬɨɜɧɭɸ ɨɩɟɪɚɰɢɸ, ɨɛɹɡɚɧ ɩɪɟɞɫɬɚɜɥɹɬɶ
ɞɢɧɚɦɢɤɭ ɩɨɜɟɞɟɧɢɹ ɫɭɞɧɚ ɜɨ ɜɪɟɦɹ ɞɪɟɣɮɚ ɫ ɩɟɪɟɦɟɧɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ɞɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɩɪɨɝɧɨɡɢɪɨɜɚɬɶ
ɧɚɩɪɚɜɥɟɧɢɟ ɩɪɨɬɟɤɚɧɢɹ ɩɪɨɰɟɫɫɚ ɞɥɹ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɢ ɫɜɨɟɜɪɟɦɟɧɧɨɝɨ ɢɡɦɟɧɟɧɢɹ ɟɝɨ ɩɚɪɚɦɟɬɪɨɜ.
Ʉɪɨɦɟ ɬɨɝɨ, ɨɞɧɨɜɪɟɦɟɧɧɨɟ ɜɨɡɞɟɣɫɬɜɢɟ ɧɚ ɫɭɞɧɨ ɧɟɫɤɨɥɶɤɢɯ ɜɧɟɲɧɢɯ ɮɚɤɬɨɪɨɜ (ɜɟɬɟɪ, ɬɟɱɟɧɢɟ,
ɜɨɥɧɟɧɢɟ, ɦɟɥɤɨɜɨɞɶɟ) ɦɨɠɟɬ ɩɪɢɜɟɫɬɢ ɤ ɧɟɩɪɟɞɫɤɚɡɭɟɦɨɦɭ ɩɨɜɟɞɟɧɢɸ ɫɭɞɧɚ ɢ, ɤɚɤ ɫɥɟɞɫɬɜɢɟ, ɩɨɬɟɪɟ
ɭɩɪɚɜɥɟɧɢɹ. ɑɬɨɛɵ ɢɫɤɥɸɱɢɬɶ ɢɥɢ, ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ, ɫɭɳɟɫɬɜɟɧɧɨ ɫɧɢɡɢɬɶ ɜɟɪɨɹɬɧɨɫɬɶ ɜɨɡɧɢɤɧɨɜɟɧɢɹ
ɩɨɞɨɛɧɨɣ ɫɢɬɭɚɰɢɢ, ɫɭɞɨɜɨɞɢɬɟɥɸ ɧɟɨɛɯɨɞɢɦɨ ɢɦɟɬɶ ɜɫɸ ɜɨɡɦɨɠɧɭɸ ɢɧɮɨɪɦɚɰɢɸ ɨ ɡɚɤɨɧɨɦɟɪɧɨɫɬɹɯ
ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ ɧɚ ɫɭɞɧɨ ɫ ɭɱɟɬɨɦ ɟɝɨ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɨɫɨɛɟɧɧɨɫɬɟɣ, ɜɤɥɸɱɚɹ ɜɩɨɥɧɟ
ɜɟɪɨɹɬɧɨɟ ɤɨɦɩɥɟɤɫɧɨɟ ɜɨɡɞɟɣɫɬɜɢɟ ɩɪɢ ɨɩɪɟɞɟɥɟɧɧɨɦ ɫɨɱɟɬɚɧɢɢ ɜɵɲɟɭɤɚɡɚɧɧɵɯ ɜɧɟɲɧɢɯ ɮɚɤɬɨɪɨɜ.
ɍɱɢɬɵɜɚɹ, ɱɬɨ ɛɨɥɶɲɢɧɫɬɜɨ ɤɪɭɩɧɨɬɨɧɧɚɠɧɵɯ ɫɭɞɨɜ, ɩɨ ɪɨɞɭ ɫɜɨɟɣ ɞɟɹɬɟɥɶɧɨɫɬɢ ɜɵɩɨɥɧɹɸɳɢɯ ɫɥɨɠɧɵɟ
ɦɚɧɟɜɪɵ ɜ ɬɹɠɟɥɵɯ ɝɢɞɪɨɦɟɬɟɨɪɨɥɨɝɢɱɟɫɤɢɯ ɭɫɥɨɜɢɹɯ, ɫɧɚɛɠɟɧɵ ɫɪɟɞɫɬɜɚɦɢ ɚɤɬɢɜɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ (ɋȺɍ),
ɨɩɪɟɞɟɥɟɧɧɵɣ ɫɦɵɫɥ ɢɦɟɟɬ ɢɡɭɱɟɧɢɟ ɜɨɩɪɨɫɚ ɨɛ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɷɬɢɯ ɫɪɟɞɫɬɜ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɭɩɪɚɜɥɹɟɦɨɫɬɢ
ɫɭɞɧɚ ɜɨ ɜɪɟɦɹ ɩɪɨɜɟɞɟɧɢɹ ɲɜɚɪɬɨɜɧɨɣ ɨɩɟɪɚɰɢɢ ɩɪɢ ɧɚɥɢɱɢɢ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ.
ɇɟɨɛɯɨɞɢɦɨ ɩɪɢɡɧɚɬɶ, ɱɬɨ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɞɪɭɝɢɦ ɜɧɟɲɧɢɦ ɮɚɤɬɨɪɚɦ, ɩɪɢɫɭɬɫɬɜɭɸɳɢɦ ɜ ɪɚɣɨɧɟ
ɜɵɩɨɥɧɹɟɦɨɣ ɲɜɚɪɬɨɜɧɨɣ ɨɩɟɪɚɰɢɢ, ɜɟɬɟɪ ɹɜɥɹɟɬɫɹ ɨɫɧɨɜɧɵɦ, ɬɚɤ ɤɚɤ, ɧɚɩɪɢɦɟɪ, ɜɥɢɹɧɢɟ ɦɟɥɤɨɜɨɞɶɹ ɩɪɢ
ɞɜɢɠɟɧɢɢ ɫɭɞɧɚ ɧɚ ɦɚɥɵɯ ɫɤɨɪɨɫɬɹɯ ɛɭɞɟɬ ɧɟ ɫɬɨɥɶ ɫɭɳɟɫɬɜɟɧɧɨ, ɚ ɜɨɥɧɟɧɢɟ ɫ "ɞɨɩɭɫɬɢɦɨɣ" ɛɚɥɥɶɧɨɫɬɶɸ,
ɧɨɪɦɚɬɢɜɧɨ ɭɫɬɚɧɨɜɥɟɧɧɨɣ ɞɥɹ ɞɚɧɧɨɝɨ ɜɢɞɚ ɦɚɧɟɜɪɢɪɨɜɚɧɢɹ (ɤɚɤ ɩɪɚɜɢɥɨ, 5 ɛɚɥɥɨɜ ɩɨ ɲɤɚɥɟ Ȼɨɮɨɪɬɚ),
375
Ɇɚɪɬɸɤ Ƚ.ɂ. ɢ ɞɪ. ɍɱɟɬ ɜɟɬɪɚ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫɭɞɧɚ…
ɬɚɤɠɟ ɧɟ ɨɤɚɡɵɜɚɟɬ ɩɪɟɢɦɭɳɟɫɬɜɟɧɧɨɝɨ ɜɥɢɹɧɢɹ ɧɚ ɦɚɧɟɜɪɟɧɧɵɟ ɤɚɱɟɫɬɜɚ ɫɭɞɧɚ. Ɉɞɧɚɤɨ ɫɩɪɚɜɟɞɥɢɜɨɫɬɢ
ɪɚɞɢ ɧɚɞɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɧɢ ɦɟɥɤɨɜɨɞɶɟ, ɧɢ ɜɨɥɧɟɧɢɟ ɧɟɥɶɡɹ ɫɛɪɚɫɵɜɚɬɶ ɫɨ ɫɱɟɬɨɜ, ɬɚɤ ɤɚɤ ɜ ɫɨɜɨɤɭɩɧɨɫɬɢ ɫ
ɜɟɬɪɨɜɵɦ ɜɨɡɞɟɣɫɬɜɢɟɦ ɨɧɢ ɦɨɝɭɬ ɩɪɢɞɚɬɶ ɨɩɪɟɞɟɥɟɧɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɯɚɪɚɤɬɟɪɭ ɩɨɜɟɞɟɧɢɹ ɫɭɞɧɚ.
2. Ɉɩɪɟɞɟɥɟɧɢɟ ɨɫɧɨɜɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɜɟɬɪɚ
Ⱦɥɹ ɞɚɥɶɧɟɣɲɟɝɨ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɲɜɚɪɬɨɜɧɨɣ ɨɩɟɪɚɰɢɢ ɜ ɭɫɥɨɜɢɹɯ ɜɟɬɪɨɜɨɝɨ
ɜɨɡɞɟɣɫɬɜɢɹ, ɧɟɨɛɯɨɞɢɦɨ ɩɪɟɠɞɟ ɜɫɟɝɨ ɨɩɪɟɞɟɥɢɬɶɫɹ ɫ ɨɫɧɨɜɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɦɢ
ɜɟɬɪɨɜɨɣ ɩɨɬɨɤ, ɜ ɤɨɬɨɪɨɦ ɛɭɞɟɬ ɧɚɯɨɞɢɬɶɫɹ ɫɭɞɧɨ. Ʉ ɨɫɧɨɜɧɵɦ ɩɚɪɚɦɟɬɪɚɦ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɨɬɧɨɫɹɬɫɹ
ɫɤɨɪɨɫɬɶ ɢ ɧɚɩɪɚɜɥɟɧɢɟ ɜɟɬɪɚ. ɂɯ ɡɧɚɱɟɧɢɹ ɜ ɩɪɨɰɟɫɫɟ ɜɵɩɨɥɧɟɧɢɹ ɲɜɚɪɬɨɜɧɨɣ ɨɩɟɪɚɰɢɢ ɦɟɧɹɸɬɫɹ, ɤɚɤ
ɡɚ ɫɱɟɬ ɢɡɦɟɧɟɧɢɹ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɩɨɥɨɠɟɧɢɹ ɫɭɞɧɚ, ɬɚɤ ɢ ɡɚ ɫɱɟɬ ɫɥɭɱɚɣɧɨɝɨ ɯɚɪɚɤɬɟɪɚ ɩɪɨɰɟɫɫɚ, ɤɚɤɢɦ
ɹɜɥɹɟɬɫɹ ɜɟɬɪɨɜɨɣ ɩɨɬɨɤ.
Ⱦɥɹ ɭɞɨɛɫɬɜɚ ɪɚɫɱɟɬɨɜ ɫɤɨɪɨɫɬɢ ɜɟɬɪɚ ɟɟ ɜɟɥɢɱɢɧɚ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɧɨɣ
ɮɭɧɤɰɢɟɣ ɜɪɟɦɟɧɢ. ɋɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɫɤɨɪɨɫɬɢ ɜɟɬɪɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɛɚɥɥɚ ɜɟɬɪɚ ɩɨ
ɢɡɜɟɫɬɧɨɣ ɲɤɚɥɟ Ȼɨɮɨɪɬɚ ɧɚ ɫɬɚɧɞɚɪɬɧɨɣ ɜɵɫɨɬɟ ɧɚɞ ɩɨɜɟɪɯɧɨɫɬɶɸ ɦɨɪɹ (z = 6 ɦ). ȼɟɥɢɱɢɧɚ
ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɣ ɫɤɨɪɨɫɬɢ ɜɟɬɪɚ X$ (ɦ/ɫ) ɜ ɩɪɟɞɟɥɚɯ ɧɚɞɜɨɞɧɨɣ ɱɚɫɬɢ ɫɭɞɧɚ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɨ
ɚɩɩɪɨɤɫɢɦɚɰɢɨɧɧɨɣ ɮɨɪɦɭɥɟ, ɩɪɟɞɫɬɚɜɥɟɧɧɨɣ ɜ ɪɚɛɨɬɟ ȼ.Ƚ. ɉɚɜɥɟɧɤɨ (1979)
X$ = [0,17(zA – d)]0,14 (1,36Ȼ + 0,108Ȼ2),
(1)
ɝɞɟ zA – ɚɩɩɥɢɤɚɬɚ ɰɟɧɬɪɚ ɩɚɪɭɫɧɨɫɬɢ; d – ɫɪɟɞɧɹɹ ɨɫɚɞɤɚ; Ȼ – ɛɚɥɥɶɧɨɫɬɶ ɜɟɬɪɚ ɩɨ ɲɤɚɥɟ Ȼɨɮɨɪɬɚ. Ʉɪɨɦɟ
ɮɨɪɦɭɥɵ (1), ɜ ɪɚɫɱɟɬɚɯ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɚ ɮɨɪɦɭɥɚ Ⱦ.Ʌ. Ʌɚɣɯɬɦɚɧɚ (Ⱦɟɜɧɢɧ, 1983)
X$ = 0,1248XȻ (ln zA + 6,22),
(2)
ɝɞɟ XȻ – ɫɤɨɪɨɫɬɶ ɜɟɬɪɚ ɩɨ ɲɤɚɥɟ Ȼɨɮɨɪɬɚ.
3. ɋɢɥɵ ɢ ɦɨɦɟɧɬ ɜɟɬɪɨɜɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ
ɋɢɥɵ ɢ ɦɨɦɟɧɬ, ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɫɭɞɧɨ ɫɨ ɫɬɨɪɨɧɵ ɜɟɬɪɚ, ɡɚɜɢɫɹɬ ɨɬ ɫɤɨɪɨɫɬɢ ɜɟɬɪɚ, ɫɤɨɪɨɫɬɢ
ɫɭɞɧɚ, ɨɬ ɩɥɨɳɚɞɢ ɢ ɤɨɧɮɢɝɭɪɚɰɢɢ ɟɝɨ ɧɚɞɫɬɪɨɟɤ ɢ ɪɭɛɨɤ, ɚ ɬɚɤɠɟ ɭɝɥɚ ɦɟɠɞɭ ɞɢɚɦɟɬɪɚɥɶɧɨɣ
ɩɥɨɫɤɨɫɬɶɸ (Ⱦɉ) ɫɭɞɧɚ ɢ ɧɚɩɪɚɜɥɟɧɢɟɦ ɜɟɬɪɨɜɨɝɨ ɩɨɬɨɤɚ (ɤɭɪɫɨɜɨɣ ɭɝɨɥ ɜɟɬɪɚ qA ɢɡɦɟɪɹɟɬɫɹ ɜ
ɩɨɥɭɤɪɭɝɨɜɨɣ ɫɢɫɬɟɦɟ ɨɬ 0q (ɜɟɬɟɪ ɜ ɧɨɫ) ɞɨ 180q (ɜɟɬɟɪ ɜ ɤɨɪɦɭ)). ȼ ɨɛɳɟɦ ɜɢɞɟ ɫɢɥɵ ɢ ɦɨɦɟɧɬ
ɜɟɬɪɨɜɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ ɜ ɫɜɹɡɚɧɧɨɣ ɫ ɫɭɞɧɨɦ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ:
FAX = 0,5CAX UȺXR2SM;
FAY = 0,5CAY UȺXR2SȾɉ;
MAZ = 0,5CAM UȺXR2SȾɉL,
(3)
(4)
(5)
ɝɞɟ FAX, FAY, MAZ – ɬɚɧɝɟɧɰɢɚɥɶɧɚɹ, ɧɨɪɦɚɥɶɧɚɹ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɟ ɫɢɥɵ ɢ ɦɨɦɟɧɬ; CAX, CAY, CAM –
ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɬɚɧɝɟɧɰɢɚɥɶɧɨɣ, ɧɨɪɦɚɥɶɧɨɣ ɫɢɥ ɢ ɦɨɦɟɧɬɚ; U$ – ɩɥɨɬɧɨɫɬɶ ɜɨɡɞɭɯɚ
(1,226 ɤɝ/ɦ3); XR – ɫɤɨɪɨɫɬɶ ɤɚɠɭɳɟɝɨɫɹ ɜɟɬɪɚ; SM, SȾɉ – ɩɥɨɳɚɞɶ ɩɪɨɟɤɰɢɢ ɧɚɞɜɨɞɧɨɣ ɱɚɫɬɢ ɤɨɪɩɭɫɚ
ɫɭɞɧɚ, ɧɚɞɫɬɪɨɟɤ ɢ ɪɭɛɨɤ ɧɚ ɩɥɨɫɤɨɫɬɶ ɦɢɞɟɥɶ-ɲɩɚɧɝɨɭɬɚ ɢ ɞɢɚɦɟɬɪɚɥɶɧɭɸ ɩɥɨɫɤɨɫɬɶ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.
Ⱦɥɹ ɨɰɟɧɤɢ ɯɚɪɚɤɬɟɪɚ ɞɜɢɠɟɧɢɹ ɫɭɞɧɚ ɜ ɭɫɥɨɜɢɹɯ ɜɟɬɪɨɜɨɣ ɧɚɝɪɭɡɤɢ ɫɤɨɪɨɫɬɶ X$ ɢ ɧɚɩɪɚɜɥɟɧɢɟ
qA ɢɫɬɢɧɧɨɝɨ ɜɟɬɪɚ ɜ ɞɚɥɶɧɟɣɲɟɦ ɛɭɞɟɦ ɡɚɞɚɜɚɬɶ ɜ ɤɨɨɪɞɢɧɚɬɚɯ, ɫɜɹɡɚɧɧɵɯ ɫ Ɂɟɦɥɟɣ. ɉɚɪɚɦɟɬɪɵ
ɤɚɠɭɳɟɝɨɫɹ ɜɟɬɪɚ (XR, qR) ɜ ɤɨɨɪɞɢɧɚɬɚɯ, ɫɜɹɡɚɧɧɵɯ ɫ ɫɭɞɧɨɦ, ɨɩɪɟɞɟɥɹɸɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ
XR = [XA2 + X2 + 2XAX cos(qA – \ + E)]0,5;
qR = arccos[(X + XA cos(qA – \ + E))/XR] – E,
(6)
(7)
ɝɞɟ X, \ – ɫɤɨɪɨɫɬɶ ɢ ɤɭɪɫ ɫɭɞɧɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ; E – ɭɝɨɥ ɞɪɟɣɮɚ ɫɭɞɧɚ.
ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɨɬɫɭɬɫɬɜɭɸɬ ɤɚɤɢɟ-ɥɢɛɨ ɚɞɟɤɜɚɬɧɵɟ (ɩɨ ɫɨɨɬɜɟɬɫɬɜɢɸ ɪɟɡɭɥɶɬɚɬɨɜ ɦɨɞɟɥɶɧɨɦɭ
ɷɤɫɩɟɪɢɦɟɧɬɭ ɜ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɬɪɭɛɟ) ɫɩɨɫɨɛɵ ɨɩɪɟɞɟɥɟɧɢɹ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɜ
ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɧɚɩɪɚɜɥɟɧɢɹ ɜɨɡɞɭɲɧɨɝɨ ɩɨɬɨɤɚ ɨɬɧɨɫɢɬɟɥɶɧɨ Ⱦɉ ɫɭɞɧɚ. Ɉɞɧɚɤɨ ɛɨɥɶɲɚɹ ɱɚɫɬɶ ɩɨɞɨɛɧɵɯ
ɢɫɩɵɬɚɧɢɣ ɩɪɨɜɨɞɢɥɚɫɶ ɫ ɦɨɞɟɥɹɦɢ ɤɨɧɤɪɟɬɧɵɯ ɫɭɞɨɜ. Ʉɪɨɦɟ ɬɨɝɨ, ɩɪɢ ɩɪɨɜɟɞɟɧɢɢ ɦɨɞɟɥɶɧɵɯ ɢɫɩɵɬɚɧɢɣ
ɤɚɤ ɜ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɬɪɭɛɟ, ɬɚɤ ɢ ɜ ɨɩɵɬɨɜɵɯ ɛɚɫɫɟɣɧɚɯ ɧɟ ɭɞɚɟɬɫɹ ɦɨɞɟɥɢɪɨɜɚɬɶ ɪɚɡɧɨɫɤɨɪɨɫɬɧɨɣ ɩɨ
ɭɪɨɜɧɸ ɩɨɬɨɤ, ɬ.ɟ. ɢɦɟɸɳɢɣ ɦɟɫɬɨ ɜ ɪɟɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɷɮɮɟɤɬ ɩɨɞɫɬɢɥɚɸɳɟɣ ɜɨɞɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɧɚ
ɦɨɞɟɥɶɧɵɯ ɢɫɩɵɬɚɧɢɹɯ ɨɬɫɭɬɫɬɜɭɟɬ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɡɚɜɵɲɟɧɢɸ ɡɧɚɱɟɧɢɣ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ.
ɍɤɚɡɚɧɧɨɟ ɧɟɫɨɨɬɜɟɬɫɬɜɢɟ Ⱥ.Ⱦ. Ƚɨɮɦɚɧ (1988) ɪɟɤɨɦɟɧɞɭɟɬ ɭɱɢɬɵɜɚɬɶ ɜ ɩɪɚɤɬɢɱɟɫɤɢɯ ɪɚɫɱɟɬɚɯ
ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ. ȼɟɥɢɱɢɧɚ ɩɨɩɪɚɜɤɢ ɡɚɜɢɫɢɬ ɨɬ ɤɨɧɤɪɟɬɧɵɯ ɪɚɡɦɟɪɨɜ ɫɭɞɧɚ, ɚ ɢɦɟɧɧɨ
GɋX,Y,M = 0,433(SȾɉ/L)0,267.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, CAxɧ = GɋXCAXɦ , ɚɧɚɥɨɝɢɱɧɨ ɢ ɞɥɹ CAY, CAM.
376
(8)
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 7, ʋ3, 2004 ɝ.
ɫɬɪ.375-380
ɇɚɢɛɨɥɟɟ ɤɪɭɩɧɵɟ ɫɟɪɢɢ ɦɨɞɟɥɶɧɵɯ ɢɫɩɵɬɚɧɢɣ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɫɭɞɨɜ ɛɵɥɢ
ɩɪɨɜɟɞɟɧɵ ɂ.ȼ. Ƚɢɪɫɨɦ ɢ Ⱥ.Ɇ. ɋɚɪɢɛɚɧɨɦ (1939), Shearer K.D.A. and Linn W.M. (1960).
ɍɤɚɡɚɧɧɵɟ ɢ ɪɹɞ ɞɪɭɝɢɯ ɢɫɩɵɬɚɧɢɣ ɩɪɨɜɨɞɢɥɢɫɶ ɫ ɫɭɞɚɦɢ, ɢɦɟɸɳɢɦɢ ɪɚɡɧɨɨɛɪɚɡɧɵɟ
ɚɪɯɢɬɟɤɬɭɪɧɵɟ ɮɨɪɦɵ ɧɚɞɜɨɞɧɨɣ ɱɚɫɬɢ. Ɋɟɡɭɥɶɬɚɬɵ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɪɟɞɫɬɚɜɥɹɥɢɫɶ ɜ ɝɪɚɮɢɱɟɫɤɨɣ ɮɨɪɦɟ
ɜ ɜɢɞɟ ɝɪɚɮɢɤɨɜ ɡɚɜɢɫɢɦɨɫɬɟɣ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ (CAX, CAY, CAM) ɨɬ ɧɚɩɪɚɜɥɟɧɢɹ
ɜɨɡɞɭɲɧɨɝɨ ɩɨɬɨɤɚ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ Ⱦɉ ɫɭɞɧɚ, ɬ.ɟ. ɜ ɜɢɞɟ ɮɭɧɤɰɢɣ CAX (qR), CAY (qR), CAM (qR). ɉɪɢ ɷɬɨɦ
ɛɵɥɢ ɩɪɟɞɩɪɢɧɹɬɵ ɩɨɩɵɬɤɢ ɤɚɤ-ɬɨ ɫɢɫɬɟɦɚɬɢɡɢɪɨɜɚɬɶ ɪɟɡɭɥɶɬɚɬɵ ɦɨɞɟɥɶɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɞɥɹ
ɞɚɥɶɧɟɣɲɟɝɨ ɩɪɢɛɥɢɠɟɧɧɨɝɨ ɨɩɪɟɞɟɥɟɧɢɹ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɫɭɞɨɜ (Martin, 1980). Ȼɵɥɢ
ɨɩɪɟɞɟɥɟɧɵ ɝɪɚɧɢɰɵ, ɜ ɪɚɦɤɚɯ ɤɨɬɨɪɵɯ ɧɚɯɨɞɹɬɫɹ ɡɧɚɱɟɧɢɹ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɜ
ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɤɭɪɫɨɜɨɝɨ ɭɝɥɚ ɤɚɠɭɳɟɝɨɫɹ ɜɟɬɪɚ. ȼ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɡɧɚɱɢɦɵɦ ɦɨɦɟɧɬɨɦ ɹɜɥɹɟɬɫɹ ɬɨ, ɱɬɨ
ɛɵɥɚ ɭɫɬɚɧɨɜɥɟɧɚ ɨɛɳɚɹ ɡɚɤɨɧɨɦɟɪɧɨɫɬɶ ɜ ɯɚɪɚɤɬɟɪɟ ɢɡɦɟɧɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ CAX, CAY, CAM ɜ
ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ qR, ɛɟɡ ɭɱɟɬɚ ɚɪɯɢɬɟɤɬɭɪɧɵɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɫɭɞɨɜ. ȼɟɪɯɧɢɟ ɢ ɧɢɠɧɢɟ ɩɪɟɞɟɥɶɧɵɟ
ɡɧɚɱɟɧɢɹ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɞɥɹ ɫɭɞɨɜ, ɢɦɟɸɳɢɯ ɪɚɡɥɢɱɧɭɸ ɚɪɯɢɬɟɤɬɭɪɧɭɸ ɮɨɪɦɭ
ɧɚɞɜɨɞɧɨɣ ɱɚɫɬɢ, ɨɬɥɢɱɚɥɢɫɶ ɧɚ 15-30 %, ɩɪɢɱɟɦ ɮɚɤɬɨɪɨɦ, ɜ ɨɫɧɨɜɧɨɦ ɨɩɪɟɞɟɥɹɸɳɢɦ ɜɟɥɢɱɢɧɭ
ɪɚɫɯɨɠɞɟɧɢɹ, ɹɜɥɹɟɬɫɹ ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ ɫɪɟɞɧɹɹ ɜɵɫɨɬɚ ɧɚɞɜɨɞɧɨɝɨ ɛɨɪɬɚ SȾɉ/L2 (ɦɚɤɫɢɦɭɦ ɡɧɚɱɟɧɢɣ
ɤɨɷɮɮɢɰɢɟɧɬɨɜ CAX, CAY, CAM ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɚɢɛɨɥɶɲɢɦ ɡɧɚɱɟɧɢɹɦ SȾɉ/L2).
4. Ɋɚɫɱɟɬɧɵɟ ɡɚɜɢɫɢɦɨɫɬɢ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ
Ɍɚɤ ɤɚɤ ɝɪɚɮɢɱɟɫɤɚɹ ɮɨɪɦɚ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɡɚɜɢɫɢɦɨɫɬɟɣ CAX (qR), CAY (qR), CAM (qR) ɧɟɭɞɨɛɧɚ ɞɥɹ
ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɨɞɟɥɹɯ, ɪɚɡɥɢɱɧɵɦɢ ɚɜɬɨɪɚɦɢ ɛɵɥɢ ɪɚɡɪɚɛɨɬɚɧɵ ɪɚɫɱɟɬɧɵɟ ɮɨɪɦɭɥɵ,
ɢɦɟɸɳɢɟ ɨɩɪɟɞɟɥɟɧɧɭɸ ɫɬɟɩɟɧɶ ɨɛɴɟɤɬɢɜɧɨɫɬɢ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɪɚɡɥɢɱɧɵɦ ɬɢɩɚɦ ɫɭɞɨɜ,
ɩɪɟɢɦɭɳɟɫɬɜɟɧɧɨ ɪɚɡɞɟɥɟɧɧɵɯ ɧɚ ɞɜɚ ɤɥɚɫɫɚ: ɪɟɱɧɵɟ ɢ ɦɨɪɫɤɢɟ.
Ɍɚɤɢɟ ɮɨɪɦɭɥɵ ɛɵɥɢ, ɧɚɩɪɢɦɟɪ, ɩɪɟɞɥɨɠɟɧɵ Ʉ.Ʉ. Ɏɟɞɹɟɜɫɤɢɦ (Ɏɟɞɹɟɜɫɤɢɣ, ɋɨɛɨɥɟɜ, 1963)
CAY = 1,2 sin qR;
CAM = 1,2 [0,25 – (qR/2S)] sin qR.
(9)
(10)
Ⱦɚɧɧɵɟ ɮɨɪɦɭɥɵ ɧɟ ɭɱɢɬɵɜɚɸɬ ɚɪɯɢɬɟɤɬɭɪɧɵɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɤɨɧɤɪɟɬɧɨɝɨ ɫɭɞɧɚ, ɚ ɥɢɲɶ ɨɬɪɚɠɚɸɬ ɨɛɳɭɸ
ɡɚɤɨɧɨɦɟɪɧɨɫɬɶ ɢɡɦɟɧɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ CAY, CAM ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɤɭɪɫɨɜɨɝɨ ɭɝɥɚ ɤɚɠɭɳɟɝɨɫɹ ɜɟɬɪɚ qR.
ɑɬɨɛɵ ɱɚɫɬɢɱɧɨ ɭɫɬɪɚɧɢɬɶ ɭɤɚɡɚɧɧɵɣ ɧɟɞɨɫɬɚɬɨɤ, Ɋ.ə. ɉɟɪɲɢɰ ɩɪɟɞɥɨɠɢɥ ɧɟɫɤɨɥɶɤɨ ɢɧɵɟ
ɡɚɜɢɫɢɦɨɫɬɢ (ȼɨɣɬɤɭɧɫɤɢɣ ɢ ɞɪ., 1973)
CAY = 1,05 sin qR;
(11)
CAM = 1,05 [0,25 + CxA – (qR/2S)] sin qR,
(12)
ɝɞɟ CxA = xA /L (xA – ɚɛɫɰɢɫɫɚ ɰɟɧɬɪɚ ɩɚɪɭɫɧɨɫɬɢ).
ɉɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɬɚɧɝɟɧɰɢɚɥɶɧɨɣ ɫɢɥɵ ɞɚɜɥɟɧɢɹ ɜɟɬɪɚ,
ɛɨɥɶɲɢɧɫɬɜɨ ɢɫɫɥɟɞɨɜɚɬɟɥɟɣ ɨɬɞɚɸɬ ɩɪɟɞɩɨɱɬɟɧɢɟ ɮɨɪɦɭɥɟ, ɩɨɥɭɱɟɧɧɨɣ Ⱥ.Ⱦ. Ƚɨɮɦɚɧɨɦ (1988)
CAX = [(0,6SMɛ + 0,25SMɧ + 0,6SMɤ)/SȾɉ] tg(S/2 – qR),
(13)
ɝɞɟ SMɛ, SMɧ, SMɤ – ɩɥɨɳɚɞɢ ɩɪɨɟɤɰɢɣ ɧɚ ɩɥɨɫɤɨɫɬɶ ɦɢɞɟɥɶ-ɲɩɚɧɝɨɭɬɚ ɧɚɞɜɨɞɧɨɣ ɱɚɫɬɢ ɤɨɪɩɭɫɚ, ɧɨɫɨɜɨɣ
ɢ ɤɨɪɦɨɜɨɣ ɧɚɞɫɬɪɨɟɤ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.
ɍɱɢɬɵɜɚɹ ɨɫɨɛɟɧɧɨɫɬɢ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɵ, ɧɟɥɶɡɹ ɧɟ ɨɬɦɟɬɢɬɶ ɜɵɪɚɠɟɧɢɟ, ɩɨɥɭɱɟɧɧɨɟ
Ⱥ.ɉ. Ɍɭɦɚɲɢɤɨɦ ɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɤɪɭɩɧɨɬɨɧɧɚɠɧɵɦ ɬɚɧɤɟɪɚɦ
CAX = 0,03 + 0,08cos qR.
(14)
Ⱦɥɹ ɞɚɥɶɧɟɣɲɟɝɨ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɬɚɧɤɟɪɚ ɭɤɚɡɚɧɧɵɯ ɡɚɜɢɫɢɦɨɫɬɟɣ
ɩɪɨɜɟɞɟɦ ɢɯ ɫɪɚɜɧɢɬɟɥɶɧɵɣ ɚɧɚɥɢɡ, ɜɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ ɪɟɡɭɥɶɬɚɬɚɦɢ ɷɤɫɩɟɪɢɦɟɧɬɚ ɫ ɦɨɞɟɥɶɸ ɫɭɞɧɚ,
ɤɨɬɨɪɨɟ ɩɨ ɚɪɯɢɬɟɤɬɭɪɧɵɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ ɜ ɨɫɧɨɜɧɨɦ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɬɢɩɨɜɨɦɭ ɬɚɧɤɟɪɭ (ɤɨɪɦɨɜɚɹ
ɧɚɞɫɬɪɨɣɤɚ, ɛɚɤ, ɛɨɥɶɲɚɹ ɩɨ ɩɪɨɬɹɠɟɧɧɨɫɬɢ ɢ ɫɜɨɛɨɞɧɚɹ ɨɬ ɫɩɥɨɲɧɵɯ ɤɨɧɫɬɪɭɤɰɢɣ ɩɚɥɭɛɚ). Ʉɪɨɦɟ
ɩɪɟɞɫɬɚɜɥɟɧɧɵɯ ɜɵɲɟ ɡɚɜɢɫɢɦɨɫɬɟɣ, ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɬɚɤɠɟ ɚɩɩɪɨɤɫɢɦɚɰɢɹɦɢ, ɩɨɥɭɱɟɧɧɵɦɢ:
1) Ⱥ.Ⱦ. Ƚɨɮɦɚɧɨɦ (1988) ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɫɟɪɢɣɧɵɯ ɢɫɩɵɬɚɧɢɣ, ɩɪɨɜɟɞɟɧɧɵɯ Ⱥ.ȼ. ɋɟɦɟɧɨɜɨɣ-Ɍɹɧ-ɒɚɧɫɤɨɣ
CAY = (CAYɛSȾɉɛ + CAYɧSȾɉɧ + CAYɤSȾɉɤ)/SȾɉ;
CAɆ = (CAɆɛSȾɉɛ + CAɆɧSȾɉɧ + CAɆɤSȾɉɤ)/SȾɉ,
(15)
(16)
ɝɞɟ SȾɉɛ, SȾɉɧ, SȾɉɤ – ɩɥɨɳɚɞɢ ɩɪɨɟɤɰɢɣ ɧɚ Ⱦɉ ɧɚɞɜɨɞɧɨɝɨ ɛɨɪɬɚ, ɧɨɫɨɜɨɣ ɢ ɤɨɪɦɨɜɨɣ ɧɚɞɫɬɪɨɟɤ,
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ. ȼɯɨɞɹɳɢɟ ɜ (15), (16) ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɧɨɪɦɚɥɶɧɨɣ ɫɢɥɵ ɢ ɦɨɦɟɧɬɚ
ɞɚɜɥɟɧɢɹ ɜɟɬɪɚ ɧɚ ɧɚɞɜɨɞɧɵɣ ɛɨɪɬ, ɧɨɫɨɜɭɸ ɢ ɤɨɪɦɨɜɭɸ ɧɚɞɫɬɪɨɣɤɢ ɫɭɞɧɚ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɮɨɪɦɭɥɚɦ:
CAYɛ = (0,812H/B – 0,0322L/B + 1,16) sin qR – (1,16H/B – 0,037) sin 3qR;
377
(17)
Ɇɚɪɬɸɤ Ƚ.ɂ. ɢ ɞɪ. ɍɱɟɬ ɜɟɬɪɚ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫɭɞɧɚ…
CAMɛ = (0,202H/B – 0,0075L/B + 0,08) sin 2qR – (0,025H/B – 0,0016L/B + 0,02) sin 4qR;
CAYɧ = 0,55 – 0,013B/H + (1,24 – 0,4lɧ/B – 0,03B/hɧ) sin[2(qR° – 2,3 + 9,6lɧ/B + 1,47B/hɧ)];
CAmɧ = CAYɧCLɧ;
CAYɤ = [1,96 + 0,16h2/h1 + (0,02 h2/h1 – 0,31)/(h1/B – 0,02 h2/h1 + 0,2)] sin qR –
– (0,85 h1/B + 0,211) sin 2qR;
CAMɤ = CAYɤ{CLɤ – (lɤ/L) [0,2 + (1,05 – 0,30lɤ/B) sin 2(qR° + 10)]},
(18)
(19)
(20)
(21)
(22)
ɡɞɟɫɶ H – ɜɵɫɨɬɚ ɧɚɞɜɨɞɧɨɝɨ ɛɨɪɬɚ ɫɭɞɧɚ; lɧ – ɞɥɢɧɚ ɧɨɫɨɜɨɣ ɧɚɞɫɬɪɨɣɤɢ; hɧ – ɜɵɫɨɬɚ ɧɨɫɨɜɨɣ
ɧɚɞɫɬɪɨɣɤɢ;CLɧ = Lɧ/L – ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɰɟɧɬɪɚ ɩɚɪɭɫɧɨɫɬɢ ɧɨɫɨɜɨɣ ɧɚɞɫɬɪɨɣɤɢ ɞɨ
ɩɥɨɫɤɨɫɬɢ ɦɢɞɟɥɶ-ɲɩɚɧɝɨɭɬɚ; lɤ – ɞɥɢɧɚ ɤɨɪɦɨɜɨɣ ɧɚɞɫɬɪɨɣɤɢ; h1 – ɜɵɫɨɬɚ ɧɢɠɧɟɝɨ ɹɪɭɫɚ ɤɨɪɦɨɜɨɣ
ɧɚɞɫɬɪɨɣɤɢ; h2 – ɜɵɫɨɬɚ ɜɬɨɪɨɝɨ ɹɪɭɫɚ ɤɨɪɦɨɜɨɣ ɧɚɞɫɬɪɨɣɤɢ; CLɤ = Lɤ/L – ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɨɬ
ɰɟɧɬɪɚ ɩɚɪɭɫɧɨɫɬɢ ɤɨɪɦɨɜɨɣ ɧɚɞɫɬɪɨɣɤɢ ɞɨ ɩɥɨɫɤɨɫɬɢ ɦɢɞɟɥɶ-ɲɩɚɧɝɨɭɬɚ; qR° – qR ɜ ɝɪɚɞɭɫɚɯ.
2) Ɋ.ə. ɉɟɪɲɢɰɟɦ ɢ ɂ.ɉ. Ɇɟɥɤɨɡɟɪɨɜɨɣ ɩɨ ɦɚɬɟɪɢɚɥɚɦ ɂ.ɉ. Ɇɟɥɤɨɡɟɪɨɜɨɣ (ɋɩɪɚɜɨɱɧɢɤ..., 1985):
CAY = (1,0 – 28,0CSȾɉɤɡ2)[1,0 +CSȾɉ6(1,12 – 65,0CH2)](7,0CH + 0,62) sin qR +
+ h sin 3qR/[1,0 +CSȾɉ6(1,12 – 65,0CH2)]6;
CAM = (CH + 0,04) sin 2qR – 0,25CH sin 4qR + 1,4CxA sin[1,5(90 – _ qR – 90_)] –
–CH(CSȾɉ6 +CSȾɉɧ)k[1,0 + sin(4qR – 90)];
ɟɫɥɢ ɧɚɞɫɬɪɨɣɤɢ ɪɚɡɧɟɫɟɧɵ ɩɨ ɞɥɢɧɟ, ɬɨ
CAMp = CAM [1,0 +Cl(SȾɉɦɧ /SȾɉɛɧ)(0,02 qR – 1,8) sign CAM].
(23)
(24)
(25)
Ɂɞɟɫɶ CH = H/L – ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɜɵɫɨɬɚ ɧɚɞɜɨɞɧɨɝɨ ɛɨɪɬɚ; CSȾɉɤɡ = SȾɉɤɡ/SȾɉ – ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɩɥɨɳɚɞɶ
ɩɚɪɭɫɧɨɫɬɢ ɧɨɫɨɜɨɝɨ ɤɨɡɵɪɶɤɚ; CS6Ⱦɉ = (SȾɉɧ+ SȾɉɤ)/SȾɉ – ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɫɭɦɦɚɪɧɚɹ ɩɥɨɳɚɞɶ ɩɚɪɭɫɧɨɫɬɢ
ɧɨɫɨɜɨɣ ɢ ɤɨɪɦɨɜɨɣ ɧɚɞɫɬɪɨɟɤ;Cl = l/L – ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɜɧɭɬɪɟɧɧɢɦɢ ɫɬɟɧɤɚɦɢ
ɪɚɡɧɟɫɟɧɧɵɯ ɩɨ ɞɥɢɧɟ ɧɚɞɫɬɪɨɟɤ.
Ɂɧɚɱɟɧɢɟ ɩɚɪɚɦɟɬɪɚ h, ɜɯɨɞɹɳɟɝɨ ɜ ɜɵɪɚɠɟɧɢɟ (23), ɨɩɪɟɞɟɥɹɟɬɫɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɟɥɢɱɢɧɵCH:
ɟɫɥɢ 0,005 ”CH ” 0,1, ɬɨ
h = 0,53CH2 – 5,7CH + 0,03,
(26)
ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ h = 0.
Ʉɨɷɮɮɢɰɢɟɧɬ k ɜ ɮɨɪɦɭɥɟ (24) ɡɚɜɢɫɢɬ ɨɬ ɤɭɪɫɨɜɨɝɨ ɭɝɥɚ ɤɚɠɭɳɟɝɨɫɹ ɜɟɬɪɚ qR, ɚ ɢɦɟɧɧɨ, ɩɪɢ
qR ɦɟɧɶɲɟ 90q k = 1, ɩɪɢ qR ɛɨɥɶɲɟ 90q k = 0.
3) ɂɲɟɪɜɭɞɨɦ (1973), ɜ ɜɢɞɟ ɪɟɝɪɟɫɫɢɜɧɵɯ ɭɪɚɜɧɟɧɢɣ, ɚɩɩɪɨɤɫɢɦɢɪɭɸɳɢɯ ɝɪɚɮɢɱɟɫɤɢɟ ɪɟɡɭɥɶɬɚɬɵ 45
ɨɩɵɬɨɜ, ɩɪɨɜɟɞɟɧɧɵɯ ɫ ɦɨɪɫɤɢɦɢ ɫɭɞɚɦɢ ɪɚɡɥɢɱɧɨɣ ɚɪɯɢɬɟɤɬɭɪɵ
CAX = A0 + A12SȾɉ /Lmax2 + A22SM /B2 + A3Lmax /B + A4PȾɉ /Lmax + A5lA/Lmax + A6M;
CAY = B0 + B12SȾɉ /Lmax2 + B22SM /B2 + B3Lmax /B + B4PȾɉ /Lmax + B5lA/Lmax + B6SȾɉ6/SȾɉ;
CAM = C0 + C12SȾɉ /Lmax2 + C22SM /B2 + C3Lmax /B + C4PȾɉ /Lmax + C5lA/Lmax.
(27)
(28)
(29)
ȼ ɩɪɟɞɫɬɚɜɥɟɧɧɵɯ ɜɵɪɚɠɟɧɢɹɯ Lmax – ɦɚɤɫɢɦɚɥɶɧɚɹ ɞɥɢɧɚ ɫɭɞɧɚ; PȾɉ – ɩɟɪɢɦɟɬɪ ɩɥɨɳɚɞɢ ɩɪɨɟɤɰɢɢ SȾɉ
ɛɟɡ ɭɱɟɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɧɤɢɯ ɜɵɫɬɭɩɚɸɳɢɯ ɱɚɫɬɟɣ (ɦɚɱɬɵ, ɜɟɧɬɢɥɹɬɨɪɵ, ɫɬɪɟɥɵ ɢ ɬ.ɩ.); lA – ɪɚɫɫɬɨɹɧɢɟ
ɨɬ ɧɨɫɨɜɨɣ ɨɤɨɧɟɱɧɨɫɬɢ ɫɭɞɧɚ ɞɨ ɟɝɨ ɰɟɧɬɪɚ ɩɚɪɭɫɧɨɫɬɢ. ɑɢɫɥɨɜɵɟ ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ
ɪɟɝɪɟɫɫɢɜɧɵɯ ɭɪɚɜɧɟɧɢɣ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɬɚɛɥ. 1.
4) ȼ.Ƚ. ɉɚɜɥɟɧɤɨ (1979), ɩɨ ɭɠɟ ɭɩɨɦɹɧɭɬɵɦ ɦɚɬɟɪɢɚɥɚɦ Ⱥ.ȼ. ɋɟɦɟɧɨɜɨɣ-Ɍɹɧ-ɒɚɧɫɤɨɣ
CAY = asin qR;
CAM = N0sin qR + N1sin2qR – N2sin4qR,
(30)
(31)
ɝɞɟ
a = 0,735 + 1,12 Hc/B;
N0 = xA/L(0,735 + 1,12 Hc/B);
N1 = 0,089 + 0,153Hc/B – 0,0095L/B;
N2 = 0,079Hc/B – 0,013.
(32)
(33)
(34)
(35)
ȼ ɮɨɪɦɭɥɚɯ (32-35) Hc – ɜɨɡɜɵɲɟɧɢɟ ɜɟɪɯɧɟɣ ɩɚɥɭɛɵ ɧɚɞɫɬɪɨɣɤɢ ɧɚɞ ɜɚɬɟɪɥɢɧɢɟɣ.
ɉɪɢɜɟɞɟɧɧɵɟ ɡɞɟɫɶ ɚɧɚɥɢɬɢɱɟɫɤɢɟ ɡɚɜɢɫɢɦɨɫɬɢ, ɩɨɥɭɱɟɧɧɵɟ ɜ ɪɟɡɭɥɶɬɚɬɟ ɫɥɨɠɧɵɯ
ɷɤɫɩɟɪɢɦɟɧɬɨɜ, ɬɟɦ ɧɟ ɦɟɧɟɟ ɧɟ ɞɚɸɬ ɨɞɧɨɡɧɚɱɧɨɝɨ ɨɬɜɟɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɞɥɹ ɚɧɚɥɢɡɚ
ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɜɥɢɹɧɢɹ ɧɚ ɦɚɧɟɜɪɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɤɨɧɤɪɟɬɧɨɝɨ ɫɭɞɧɚ, ɜ ɱɚɫɬɧɨɫɬɢ, ɬɚɧɤɟɪɚ.
378
ȼɟɫɬɧɢɤ ɆȽɌɍ, ɬɨɦ 7, ʋ3, 2004 ɝ.
ɫɬɪ.375-380
ɂɡ ɪɢɫ. 1 ɜɢɞɧɨ, ɧɚɫɤɨɥɶɤɨ ɫɭɳɟɫɬɜɟɧɧɨ ɪɚɫɯɨɞɹɬɫɹ ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ
ɩɪɢ ɪɚɫɱɟɬɟ ɟɝɨ ɪɚɡɥɢɱɧɵɦɢ ɫɩɨɫɨɛɚɦɢ.
Ⱥɧɚɥɨɝɢɱɧɭɸ ɤɚɪɬɢɧɭ ɦɨɠɧɨ ɧɚɛɥɸɞɚɬɶ ɢ ɩɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɪɟɡɭɥɶɬɚɬɨɜ ɪɚɫɱɟɬɚ ɡɧɚɱɟɧɢɣ
ɤɨɷɮɮɢɰɢɟɧɬɚ ɩɪɨɞɨɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɢɥɵ, ɢ ɬɨɥɶɤɨ ɪɚɫɱɟɬ ɩɨɩɟɪɟɱɧɨɣ
ɫɨɫɬɚɜɥɹɸɳɟɣ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɫɢɥɵ ɩɪɢɜɟɞɟɧɧɵɦɢ ɫɩɨɫɨɛɚɦɢ ɞɚɟɬ ɫɪɚɜɧɢɬɟɥɶɧɨ ɛɥɢɡɤɢɟ ɪɟɡɭɥɶɬɚɬɵ.
Ɍɚɛɥɢɰɚ 1
qR, ɝɪɚɞ.
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
Ⱥ0
ȼ0
ɋ0
2,152
1,714
0,096
0,0596
1,818
0,176
0,1106
1,965
0,225
0,2258
2,333
0,329
0,2017
1,726
1,164
0,1759
0,913
1,163
0,1925
0,457
0,916
0,2133
0,341
0,844
0,1827
0,355
0,889
0,2627
0,601
0,799
0,2102
0,651
0,797
0,1567
0,564
0,996
0,0801
-0,142
1,014
-0,0189
-0,677
0,784
0,0256
-0,723
0,536
0,0552
-2,148
0,251
0,0881
-2,707
0,125
0,0851
-2,529
Ⱥ1
ȼ1
ɋ1
-5,0
-3,33
0,22
0,061
-3,97
0,71
0,204
-4,81
1,38
0,245
-5,99
1,82
0,457
-6,54
1,26
0,573
-4,68
0,96
0,480
-2,88
0,53
0,315
-0,91
0,55
0,254
1,29
2,54
3,58
3,64
3,14
2,56
3,97
3,76
Ⱥ2
ȼ2
ɋ2
0,243
0,145
0,211
0,243
0,247
0,189
0,121
0,101
0,069
0,082
0,138
0,155
-0,0195
0,151
-0,0258
0,184
-0,0311
0,191
-0,0488
0,166
-0,0422
0,176
-0,0381
0,106
-0,0306
-0,175
0,046
-0,0122
-0,174
Ⱥ3
ȼ3
ɋ3
-0,164
-0,121
-0,143
-0,154
0,023
-0,190
0,043
0,0067
-0,173
0,0118
-0,104
0,0115
-0,068
0,0081
-0,031
0,0053
0,047
0,0101
0,069
0,0100
0,064
-0,029
0,0109
0,081
-0,022
0,0091
0,126
-0,012
0,0025
0,128
379
Ⱥ4
ȼ4
ɋ4
Ⱥ5
ȼ5
ɋ5
0,348
-0,242
0,482
-0,177
0,346
-0,247
-0,372
0,0335
-0,582
0,0497
-0,748
-0,212
0,0740
-0,700
-0,280
0,1128
-0,529
-0,209
0,0889
-0,475
-0,163
0,0689
0,0366
-
-0,074
-0,170
-0,29
-0,380
-0,59
-0,472
-0,95
-0,523
-0,88
-0,546
-0,65
-0,526
-0,54
-0,443
-0,66
-0,508
-0,55
-0,492
-0,55
-0,457
-0,66
-0,396
-0,69
-0,420
-0,53
-0,463
-0,476
1,27
-0,415
1,81
-0,220
1,55
Ⱥ6
ȼ6
0,033
0,041
0,042
0,048
0,052
0,043
0,032
0,018
-0,020
-0,031
-0,024
0,34
-0,028
0,44
-0,032
0,38
-0,032
0,27
-0,027
-
Ɇɚɪɬɸɤ Ƚ.ɂ. ɢ ɞɪ. ɍɱɟɬ ɜɟɬɪɚ ɜ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ ɫɭɞɧɚ…
Ɋɢɫ. 1. Ɂɚɜɢɫɢɦɨɫɬɶ ɤɨɷɮɮɢɰɢɟɧɬɚ
ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ CAM ɨɬ ɤɭɪɫɨɜɨɝɨ ɭɝɥɚ
ɤɚɠɭɳɟɝɨɫɹ ɜɟɬɪɚ qR, ɪɚɫɫɱɢɬɚɧɧɚɹ ɩɨ ɮɨɪɦɭɥɚɦ:
1 – Ƚ.ȼ. ɋɨɛɨɥɟɜɚ; 2 – ɂɲɟɪɜɭɞɚ; 3 –
Ɋ.ə. ɉɟɪɲɢɰɚ; 4 – Ⱥ.Ⱦ. Ƚɨɮɦɚɧɚ; 5 – ɩɨ ɞɚɧɧɵɦ
ɐɇɂɂ ɢɦ. ɚɤɚɞ. Ⱥ.ɇ. Ʉɪɵɥɨɜɚ
Ɋɢɫ. 2. Ɋɚɫɱɟɬɧɵɟ ɡɚɜɢɫɢɦɨɫɬɢ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ
ɤɨɷɮɮɢɰɢɟɧɬɨɜ CAX (1,2); CAY (3,4); CAM (5,6) ɨɬ
ɤɭɪɫɨɜɨɝɨ ɭɝɥɚ ɤɚɠɭɳɟɝɨɫɹ ɜɟɬɪɚ qR ɞɥɹ ɬɚɧɤɟɪɚ
"ɋɚɪɚɬɨɜ" ɜ ɛɚɥɥɚɫɬɟ (2, 3, 5) ɢ ɜ ɝɪɭɡɭ (1, 4, 6)
ɋɪɟɞɢ ɦɨɞɟɥɟɣ ɫɭɞɨɜ, ɫ ɤɨɬɨɪɵɦɢ ɩɪɨɜɨɞɢɥ ɢɫɩɵɬɚɧɢɹ ɂɲɟɪɜɭɞ, ɛɵɥɢ ɫɭɞɚ, ɚɪɯɢɬɟɤɬɭɪɧɵɟ
ɨɫɨɛɟɧɧɨɫɬɢ ɤɨɬɨɪɵɯ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɡɹɬɨɦɭ ɧɚɦɢ ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɣ ɬɢɩɭ ɫɭɞɧɚ, ɩɨɷɬɨɦɭ ɜ ɤɚɱɟɫɬɜɟ
ɩɟɪɜɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ ɜ ɫɜɨɢɯ ɢɫɫɥɟɞɨɜɚɧɢɹɯ ɦɵ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɪɟɡɭɥɶɬɚɬɚɦɢ ɭɤɚɡɚɧɧɵɯ ɢɫɩɵɬɚɧɢɣ.
Ɋɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɚ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɞɥɹ ɬɚɧɤɟɪɚ "ɋɚɪɚɬɨɜ" ɜ ɛɚɥɥɚɫɬɟ ɢ ɜ ɝɪɭɡɭ ɫ
ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɫɩɨɫɨɛɚ, ɩɪɟɞɥɨɠɟɧɧɨɝɨ ɜ ɪɚɛɨɬɟ (Isherwood, 1973), ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 2.
5. Ɂɚɤɥɸɱɟɧɢɟ
ɉɨɫɤɨɥɶɤɭ ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɢɦɟɸɬɫɹ ɞɚɧɧɵɟ ɩɪɨɞɭɜɨɤ ɥɢɲɶ ɦɨɞɟɥɟɣ ɫɭɞɨɜ ɧɚɢɛɨɥɟɟ
ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɯ ɚɪɯɢɬɟɤɬɭɪɧɵɯ ɬɢɩɨɜ, ɦɵ ɧɟ ɦɨɠɟɦ ɫ ɜɵɫɨɤɨɣ ɫɬɟɩɟɧɶɸ ɜɟɪɨɹɬɧɨɫɬɢ ɭɬɜɟɪɠɞɚɬɶ, ɱɬɨ
ɜɵɛɪɚɧɧɵɣ ɧɚɦɢ ɫɩɨɫɨɛ ɨɩɪɟɞɟɥɟɧɢɹ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɹɜɥɹɟɬɫɹ ɭɧɢɜɟɪɫɚɥɶɧɵɦ ɢ, ɱɬɨ
ɫɚɦɨɟ ɝɥɚɜɧɨɟ, ɚɞɟɤɜɚɬɧɨ ɨɬɪɚɠɚɟɬ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ ɜɟɬɪɨɜɨɝɨ ɜɨɡɞɟɣɫɬɜɢɹ ɧɚ ɤɨɧɤɪɟɬɧɨɟ ɫɭɞɧɨ. ɂ ɜ ɬɨ
ɠɟ ɜɪɟɦɹ ɦɵ ɜɵɛɢɪɚɟɦ ɧɚɢɛɨɥɟɟ ɛɥɢɡɤɭɸ ɩɨ ɚɪɯɢɬɟɤɬɭɪɟ ɤ ɫɨɜɪɟɦɟɧɧɨɦɭ ɬɚɧɤɟɪɭ ɦɨɞɟɥɶ ɢ ɜ
ɞɚɥɶɧɟɣɲɟɦ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɪɟɡɭɥɶɬɚɬɚɦɢ ɷɤɫɩɟɪɢɦɟɧɬɚ, ɩɪɨɜɟɞɟɧɧɨɝɨ ɫ ɧɟɸ ɜ ɚɷɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɬɪɭɛɟ,
ɨɫɬɚɜɥɹɹ ɡɚ ɫɨɛɨɣ ɩɪɚɜɨ ɧɟɤɨɬɨɪɨɝɨ ɭɬɨɱɧɟɧɢɹ ɪɟɡɭɥɶɬɚɬɨɜ ɦɨɞɟɥɶɧɨɝɨ ɷɤɫɩɟɪɢɦɟɧɬɚ ɫ ɭɱɟɬɨɦ ɧɚɬɭɪɧɵɯ
ɧɚɛɥɸɞɟɧɢɣ ɧɚ ɤɨɧɤɪɟɬɧɨɦ ɫɭɞɧɟ.
Ʌɢɬɟɪɚɬɭɪɚ
Isherwood R. Wind resistance of merchant ships. TRINA, v.115, p.327-335, 1973.
Martin L.L. Ship manoeuvring and control in wind. SNAME Tr., v.88, p.257-281, 1980.
Shearer K.D.A., Linn W.M. Wind tunnel test on models of merchant ships. NE Coast Inst. of Engrs. and
Shipbuilders, v.76, part 5, 1960.
ȼɨɣɬɤɭɧɫɤɢɣ ə.ɂ., ɉɟɪɲɢɰ Ɋ.ə., Ɍɢɬɨɜ ɂ.Ⱥ. ɋɩɪɚɜɨɱɧɢɤ ɩɨ ɬɟɨɪɢɢ ɤɨɪɚɛɥɹ. Ʌ., ɋɭɞɨɫɬɪɨɟɧɢɟ, 1973.
Ƚɢɪɫ ɂ.ȼ., ɋɚɪɢɛɚɧ Ⱥ.Ɇ. Ⱥɷɪɨɞɢɧɚɦɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɪɟɱɧɵɯ ɫɭɞɨɜ. ɋɭɞɨɫɬɪɨɟɧɢɟ, ʋ 9, 1939.
Ƚɨɮɦɚɧ Ⱥ.Ⱦ. Ⱦɜɢɠɢɬɟɥɶɧɨ-ɪɭɥɟɜɨɣ ɤɨɦɩɥɟɤɫ ɢ ɦɚɧɟɜɪɢɪɨɜɚɧɢɟ ɫɭɞɧɚ: ɋɩɪɚɜɨɱɧɢɤ. Ʌ., ɋɭɞɨɫɬɪɨɟɧɢɟ,
c.360, 1988.
Ⱦɟɜɧɢɧ ɋ.ɂ. Ⱥɷɪɨɝɢɞɪɨɦɟɯɚɧɢɤɚ ɩɥɨɯɨɨɛɬɟɤɚɟɦɵɯ ɤɨɧɫɬɪɭɤɰɢɣ: ɋɩɪɚɜɨɱɧɢɤ. Ʌ., ɋɭɞɨɫɬɪɨɟɧɢɟ, c.320,
1983.
ɉɚɜɥɟɧɤɨ ȼ.Ƚ. Ɇɚɧɟɜɪɟɧɧɵɟ ɤɚɱɟɫɬɜɚ ɪɟɱɧɵɯ ɫɭɞɨɜ (ɍɩɪɚɜɥɹɟɦɨɫɬɶ ɫɭɞɨɜ ɢ ɫɨɫɬɚɜɨɜ): ɍɱɟɛ. ɩɨɫɨɛɢɟ
ɞɥɹ ɢɧ-ɬɨɜ ɜɨɞɧ. ɬɪɚɧɫɩ. Ɇ., Ɍɪɚɧɫɩɨɪɬ, c.184, 1979.
ɋɩɪɚɜɨɱɧɢɤ ɩɨ ɬɟɨɪɢɢ ɤɨɪɚɛɥɹ: ɍɩɪɚɜɥɹɟɦɨɫɬɶ ɜɨɞɨɢɡɦɟɳɚɸɳɢɯ ɫɭɞɨɜ. Ƚɢɞɪɨɞɢɧɚɦɢɤɚ ɫɭɞɨɜ ɫ
ɞɢɧɚɦɢɱɟɫɤɢɦɢ ɩɪɢɧɰɢɩɚɦɢ ɩɨɞɞɟɪɠɚɧɢɹ. ȼ 3-ɯ ɬ. ɉɨɞ ɪɟɞ. ə.ɂ. ȼɨɣɬɤɭɧɫɤɨɝɨ. Ʌ.,
ɋɭɞɨɫɬɪɨɟɧɢɟ, ɬ.3, c.544, 1985.
Ɏɟɞɹɟɜɫɤɢɣ Ʉ.Ʉ., ɋɨɛɨɥɟɜ Ƚ.ȼ. ɍɩɪɚɜɥɹɟɦɨɫɬɶ ɤɨɪɚɛɥɹ. Ʌ., ɋɭɞɩɪɨɦɝɢɡ, 1963.
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