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Файл:Элементы теории образования электрического тока в грунтовых и водных средах (проводниках второго рода). Монография
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ɜɫɟɯ ɫɤɨɪɨɫɬɟɣ ɦɟɠɞɭ ɧɭɥɟɦ ɢ ɜɟɥɢɱɢɧɨɣ
ȿ
7
10
ɦ/ɫ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɱɢɫɥɨ ɡɚɪɹ
ɠɟɧɧɵɯ ɱɚɫɬɢɰ, ɩɪɟɜɪɚɳɚɸɳɢɯ ɱɚɫɬɶ ɫɜɨɟɣ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɜ ɬɟɩɥɨɜɭɸ
,
ɜɤɨɧɟɱɧɨɦɫɱɟɬɟ, ɧɚ ɩɨɥɨɠɢɬɟɥɶɧɨɦ ɷɥɟɤɬɪɨɞɟ, ɜɵɪɚɠɚɟɬɫɹ ɱɢɫɥɨɦ ɟɞɢɧɢɱ
ɢ
ɧɵɯ ɡɚɪɹɞɨɜ, ɩɨɥɭɱɟɧɧɵɯ ɩɪɢ ɷɥɟɤɬɪɨɥɢɡɟ. Ʉɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ, ɫɨɨɛɳɚɟɦɚɹ
ɥɸɛɨɣ ɱɚɫɬɢɰɟ ɩɪɢ ɟɟ ɭɫɤɨɪɟɧɢɢ ɧɚ ɩɭɬɢ ɨɬ ɨɞɧɨɝɨ ɷɥɟɤɬɪɨɞɚ ɤ ɞɪɭɝɨɦɭ ɪɚɜɧɚ
,
ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɫɢɥɟ
ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɨɞɢɧ ɷɥɟɦɟɧɬɚɪɧɵɣ ɡɚɪɹɞ
.
-
-
ɉɨɫɬɚɧɨɜɤɚ ɡɚɞɚɱɢ
. ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɪɚɫɱɟɬ ɷɥɟɤɬɪɢɱɟ
ɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɢ ɭɫɬɚɧɨɜɥɟɧɢɟ ɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɪɚɜɧɨɜɟɫɢɹ ɩɨ ɜɟɥɢɱɢɧɟ
ɫɬɨɪ
ɫɬɨɪɨɧɧɟɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɩɨɥɹ
ɜ ɫɢɫɬɟɦɟ ɤɚɬɨɞɧɨɣ ɡɚɳɢɬɵ
ɗɣɧɲɬɟɣɧ ɢ Ʌɚɭɛ ɜ ɫɜɨɟɣ ɡɧɚɦɟɧɢɬɨɣ ɪɚɛɨɬɟ, ɧɚɩɢɫɚɧɧɨɣ ɜ
.
1908 ɝ.,
ɩɨɤɚ
ɡɚɥɢ, ɱɬɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɟ ɦɟɠɞɭ ɦɚɬɟɪɢɟɣ (ɫɪɟɞɨɣ) ɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɦ ɩɨɥɟɦ
,
ɨɛɭɫɥɨɜɥɢɜɚɟɬɫɹ ɢɫɤɥɸɱɢɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɵɦɢ ɱɚɫɬɢɰɚɦɢ
ɧɟɡɚɜɢɫɢɦɨ ɪɚɫɩɪɟ
ɞɟɥɟɧɧɵɦɢ ɜ ɬɟɥɟ ɢɥɢ ɫɜɹɡɚɧɧɵɦɢ ɜ ɞɢɩɨɥɢ. ɉɨɷɬɨɦɭ ɫɢɥɚ, ɞɟɣɫɬɜɭɸɳɚɹ ɜ
,
ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɧɚ ɷɥɟɦɟɧɬ ɨɛɴɟɦɚ ɦɚɬɟɪɢɢ
,
ɩɨɧɞɟɪɨɦɨɬɨɪɧɵɯ ɫɢɥ
ɤɨɬɨɪɵɟ ɞɟɣɫɬɜɭɸɬ ɜ ɷɬɨɦ ɩɨɥɟ ɧɚ ɜɫɟ ɧɚɯɨɞɹɳɢɟɫɹ ɜ
ɞɚɧɧɨɦ ɷɥɟɦɟɧɬɟ ɨɛɴɟɦɚ ɷɥɟɤɬɪɢɱɟɫɤɢɟ ɢ ɦɚɝɧɢɬɧɵɟ ɷɥɟɦɟɧɬɚɪɧɵɟ ɱɚɫɬɢɰɵ
ɩɨɬɟɧɰɢɚɥɶɧɨɦ ɷɥɟɤɬɪɢɱɟɫɤɨɦ ɩɨɥɟ ɩɪɨɹɜɥɹɸɬɫɹ ɬɨɥɶɤɨ ɫɢɥɵ
,
ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɡɚɪɹɞɨɦ
ɚɬɚɤɠɟɫɢɥɵ, ɢɫɩɵɬɵɜɚɟɦɵɟ ɞɢɩɨɥɹɦɢ ɩɨɥɹɪɢɡɨɜɚɧ
ɹɜɥɹɟɬɫɹ ɪɟɡɭɥɶɬɢɪɭɸɳɟɣ
.
ȼ
,
ɢɫɩɵɬɵɜɚɟɦɵɟ
-
-
-
-
ɧɨɝɨ ɜɟɳɟɫɬɜɚ. ɉɪɨɢɡɜɟɞɟɧɢɟ ɫɢɥɵ, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɷɥɟɦɟɧɬɚɪɧɵɣ ɡɚɪɹɞ, ɧɚ
ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɷɥɟɤɬɪɨɞɚɦɢ ɩɨɥɭɱɚɟɬɫɹ ɜɫɟɝɞɚ ɨɞɢɧɚɤɨɜɵɦ ɢ ɞɚɟɬ ɷɧɟɪɝɢɸ
ɩɟɪɟɞɚɜɚɟɦɭɸ ɡɚɪɹɞɭ, ɤɨɬɨɪɚɹ ɨɫɬɚɟɬɫɹ ɜɫɟɝɞɚ ɩɨɫɬɨɹɧɧɨɣ ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɪɚɫ
ɫɬɨɹɧɢɹ ɦɟɠɞɭ ɷɥɟɤɬɪɨɞɚɦɢ. ɗɧɟɪɝɢɹ, ɫɨɨɛɳɚɟɦɚɹ ɷɥɟɦɟɧɬɚɪɧɨɦɭ ɡɚɪɹɞɭ, ɧɟ
ɡɚɜɢɫɢɬ ɢ ɨɬ ɜɟɥɢɱɢɧɵ ɫɢɥɵ ɬɨɤɚ
.
ȼɵɫɨɤɨ ɨɰɟɧɢɜɚɹ ɫɩɪɚɜɟɞɥɢɜɨɫɬɶ ɮɨɪɦɭɥ Ɇɚɤɫɜɟɥɥɚ ɜ ɫɚɦɨɦ ɨɛɳɟɦ ɫɥɭ
ɱɚɟ ɢ ɩɪɨɢɡɜɟɞɹ ɩɪɨɫɬɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ
,
ɜɟɤɬɨɪɚ ɉɨɣɧɬɢɧɝɚ
ɉɨɥɢɜɚɧɨɜ ɩɨɤɚɡɚɥ
()() ()()
:
111
[33],
ɜɡɹɜ ɩɪɨɢɡɜɨɞɧɭɸ ɩɨ ɜɪɟɦɟɧɢ ɨɬ
222
.///)/1(///
ct=tc=ctt
∂∂∂⋅∂∂∂⋅−∂∂⋅
ɉHEEHHE
(97)
,
-
-
ȼɟɤɬɨɪ ɉɨɣɧɬɢɧɝɚ, ɞɟɥɟɧɧɵɣ ɧɚ
2
ɫ
,
ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɭɸ
ɩɥɨɬɧɨɫɬɶ ɢɦɩɭɥɶɫɚ
(∂ɉ/∂ t)/ɫ2 = ∂ (mu)/∂
t.
ɉɪɟɞɫɬɚɜɥɹɹ ɩɥɨɬɧɨɫɬɶ ɩɟɪɟɧɨɫɚ ɩɨɬɨɤɚ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɯ ɱɚɫɬɢɰ ɜ ɫɢɫɬɟ
ɦɟ ɷɥɟɤɬɪɨɞ-ɝɪɭɧɬɨɜɵɣ ɷɥɟɤɬɪɨɥɢɬ ɜ ɜɢɞɟ ɜɟɤɬɨɪɚ ɉɨɣɧɬɢɧɝɚ, ɦɵ
ɉ
/ɫ2 = mu
ɤɚɤ ɨɛɴɟɦɧɭɸ ɩɥɨɬɧɨɫɬɶ ɫɢɥɵ
[8–12]
ɜɵɹɜɢ
-
-
ɥɢ ɡɚɤɨɧɨɦɟɪɧɨɫɬɶ ɩɪɟɜɪɚɳɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹɩɨɞ
ɜɨɡɞɟɣɫɬɜɢɟɦ ɢɡɦɟɧɟɧɢɹ ɭɪɨɜɧɹ ɩɨɫɬɨɹɧɧɨɣ ɢɥɢ ɜɵɩɪɹɦɥɟɧɧɨɣ ɗȾɋ
2
sin
ɝɞɟ z
ɝɢɢ; ij
ɥɟɧɢɟ
=
z
εμ
g
–
ɤɚɠɭɳɟɟɫɹ ɫɨɩɪɨɬɢɜɥɟɧɢɟ; Į
–
ɭɝɨɥ ɩɪɟɥɨɦɥɟɧɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ
; g –
ɨɛɳɚɹ ɩɪɨɜɨɞɢɦɨɫɬɶ
=ϕ
gRz
//cos –
++
ɞɥɹ ɩɨɥɨɠɢɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɵɯ ɢɨɧɨɜ
;
R
–
ɭɝɨɥ ɨɬɪɚɠɟɧɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪ
α−εμ
R
g
gRz
//cos =ϕ –
,cos
ϕ=⋅
; R –
ɨɦɢɱɟɫɤɨɟ ɫɨɩɪɨɬɢɜ
ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɫɢɫɬɟɦɟ
;
:
(98)
-
-
;
=ϕ
gRz
//cos –
−−
ɞɥɹ ɨɬɪɢɰɚɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɵɯ ɢɨɧɨɜ
.
Ⱥɧɚɥɢɡ ɮɨɪɦɭɥɵ ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨ ɫɭɦɦɚ ɭɝɥɨɜ ɩɪɟɥɨɦɥɟɧɢɹ ɩɨɥɨɠɢɬɟɥɶɧɨ
ɢ ɨɬɪɢɰɚɬɟɥɶɧɨ ɡɚɪɹɠɟɧɧɵɯ ɢɨɧɨɜ ɜɫɟɝɞɚ ɫɨɫɬɚɜɥɹɟɬ ɭɝɨɥ ɪɚɜɧɵɣ
90°.
ɉɨɫɥɟɞɭɸɳɢɣ ɚɧɚɥɢɡ ɩɨɤɚɡɚɥ, ɱɬɨ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɡɚɠɢɦɚɯ ɷɥɟɤɬɪɨɞɨɜ ɟɫɬɶ
,
ɪɚɡɧɨɫɬɶ ɩɚɞɟɧɢɣ ɧɚɩɪɹɠɟɧɢɣ
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɨɬ ɬɨɤɨɜ ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɪɚɡ
ɞɟɥɶɧɨ ɚɧɢɨɧɨɜ ɢ ɤɚɬɢɨɧɨɜ. ɉɨɷɬɨɦɭ ɩɪɢ ɨɞɧɨɦ ɢ ɬɨɦ ɠɟ ɢɡɦɟɪɹɟɦɨɦ ɧɚɩɪɹ
ɠɟɧɢɢ ɫɨɫɬɚɜɥɹɸɳɢɟ ɩɚɞɟɧɢɹ ɧɚɩɪɹɠɟɧɢɣ ɦɨɝɭɬ ɪɟɡɤɨ ɨɬɥɢɱɚɬɶɫɹ ɨɬ ɨɞɧɨɣ
,
ɫɢɫɬɟɦɵ ɤ ɞɪɭɝɨɣ
ɬɭɬ ɧɟ ɜɫɩɨɦɧɢɬɶ ɜɵɫɤɚɡɵɜɚɧɢɟ ɬɜɨɪɰɨɜ ɧɶɸɬɨɧɨɜɫɤɨɣ ɦɟɯɚɧɢɤɢ
ɪɹɬɶ, ɬɪɭɞɧɟɟ ɡɧɚɬɶ, ɱɬɨ ɬɵ ɢɡɦɟɪɹɟɲɶ
ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɤɪɢɬɟɪɢɟɦ ɩɪɨɰɟɫɫɚ ɨɧɢ ɛɵɬɶ ɧɟ ɦɨɝɭɬ. Ʉɚɤ
: «
Ʌɟɝɤɨ ɢɡɦɟ
».
Ɂɞɟɫɶ ɧɟɥɶɡɹ ɫɦɟɲɢɜɚɬɶ ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɫ ɧɚɩɪɹɠɟɧɢɟɦ. ȼɩɟɪɜɨɦ
,
ɫɥɭɱɚɟ
ɟɫɥɢ ɟɫɬɶ ɬɨɤ ɱɟɪɟɡ ɭɱɚɫɬɨɤ ɰɟɩɢ, ɬɨ ɧɚ ɷɬɨɦ ɭɱɚɫɬɤɟ ɩɚɞɚɟɬ ɧɚɩɪɹɠɟ
ɧɢɟ. ȼɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ, ɟɫɥɢ ɟɫɬɶ ɧɚɩɪɹɠɟɧɢɟ (ɩɨɥɟ) ɢɫɬɨɱɧɢɤɚ, ɬɨ ɜ ɩɪɨɜɨɞɧɢɤɟ
-
-
-
-
ɩɨɹɜɥɹɟɬɫɹ ɬɨɤ
.
112
ɇɟɨɛɯɨɞɢɦɨ ɡɚɦɟɬɢɬɶ, ɱɬɨ ɦɵ ɧɚ ɡɚɠɢɦɚɯ ɷɥɟɤɬɪɨɞɨɜ ɢɡɦɟɪɹɟɦ ɪɚɡɧɨɫɬɶ
ɩɚɞɟɧɢɣ ɧɚɩɪɹɠɟɧɢɣ
ɪɚɡɧɨɫɬɟɣ ɜ ɨɬɞɟɥɶɧɨɫɬɢ ɧɟɜɨɡɦɨɠɧɨ
,
ɧɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɩɪɨɫɥɟɞɢɬɶ ɢɡɦɟɧɟɧɢɟ ɫɥɚɝɚɸɳɢɯ
.
ȿɫɥɢ ɢɡɦɟɪɹɬɶ ɱɢɫɥɨ ɷɥɟɦɟɧɬɚɪɧɵɯ ɡɚɪɹɞɨɜ, ɩɟɪɟɧɨɫɢɦɵɯ ɡɚ ɫɟɤɭɧɞɭ, ɚ
–
ɗȾɋ
ɩɪɢ ɨɩɪɟɞɟɥɟɧɧɨɣ ɦɨɳɧɨɫɬɢ
ɜ ɞɠɨɭɥɹɯ ɧɚ ɷɥɟɦɟɧɬɚɪɧɵɣ ɡɚɪɹɞ, ɬɨ ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɜɟɥɢɱɢɧɭ ɬɨɤɚ
:
19 18
1,65 10 6,25 10PU I
=⋅ ⋅ ⋅⋅ ⋅
/ 1,6510 6,2510IPU
=⋅⋅⋅⋅
−
19 18
−
; (99)
.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɝɟɧɟɪɢɪɭɟɦɚɹ ɷɧɟɪɝɢɹ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɥɟɤɬɪɨɞɧɨɣ ɰɟɩɢ
ɨɤɚɡɚɥɚɫɶ ɫɜɹɡɚɧɧɨɣ ɫ ɷɧɟɪɝɢɟɣ ɢ ɤɨɥɢɱɟɫɬɜɨɦ ɞɜɢɠɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɦɢɤɪɨ
ɱɚɫɬɢɰ ɢɨɧɨɜ, ɞɜɢɠɭɳɢɯɫɹ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ. ɉɪɢ ɷɬɨɦ ɥɟɝɤɨ
ɡɚɦɟɬɢɬɶ
,
ɱɬɨ I·E
≥
I·U.
Ʉɚɤ ɭɠɟ ɨɬɦɟɱɚɥɨɫɶ, ɱɬɨɛɵ ɩɨɞɞɟɪɠɢɜɚɬɶ ɩɨɫɬɨɹɧɧɵɣ ɬɨɤ, ɧɟɨɛɯɨɞɢɦɨ
-
,
ɧɚɥɢɱɢɟ ɫɬɨɪɨɧɧɟɣ ɗȾɋ ɧɟɷɥɟɤɬɪɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɪɨɢɫɯɨɠɞɟɧɢɹ
ɪɚɛɨɬɨɣ ɤɨɬɨ
ɪɨɣ ɤɨɦɩɟɧɫɢɪɭɟɬɫɹ ɡɚɬɪɚɬɚ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ, ɜɵɞɟɥɹɸɳɟɣɫɹ ɜ ɮɨɪɦɟ
.
ɞɠɨɭɥɟɜɨɣ ɬɟɩɥɨɬɵ
ɥɚɞɚɟɬ ɩɨɬɟɧɰɢɚɥɨɦ (ɮɨɪɦɭɥɚ
Ɇɟɬɨɞɢɤɚ ɢɫɫɥɟɞɨɜɚɧɢɹ
ɷɥɟɤɬɪɨɞɧɚɹ ɫɢɫɬɟɦɚ ɫ ɝɪɭɧɬɨɜɵɦ ɷɥɟɤɬɪɨɥɢɬɨɦ
ɦɟɬɪɵ ɷɥɟɤɬɪɨɞɨɜ ɢ ɜɨɞɧɨɣ ɫɪɟɞɵ, ɜɫɬɪɟɱɚɸɳɢɟɫɹ ɜ ɬɟɯɧɢɤɟ
ɂɫɫɥɟɞɨɜɚɧɢɹ ɩɪɨɜɨɞɢɥɢɫɶ ɜ ɧɟɫɤɨɥɶɤɨ ɷɬɚɩɨɜ
ɂɡɦɟɪɹɥɢɫɶ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ, ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɢ ɚɤɬɢɜɧɚɹ ɦɨɳ
1.
ɉɪɢɧɢɦɚɹ ɜɨ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɜ ɩɨɥɟ ɩɨɫɬɨɹɧɧɵɯ ɬɨɤɨɜȿɨɛ
(96),
ɫɬɨɪ
jE=Q
ȺɄ
Ɋ
ɞɥɹ ɡɚɦɤɧɭɬɨɝɨ ɩɪɨɜɨɞɧɢɤɚ ɩɨɥɭɱɢɦ
ɫɬɨɪ
ȺɄ
ɫɬɨɪ
ȺɄ
./ɢɥɢ;
jP=EjE=
:
(100)
. Ⱦɥɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ ɜɵɛɪɚɧɚ
,
ɜ ɤɨɬɨɪɨɣ ɧɚɢɛɨɥɶɲɢɟ ɩɚɪɚ
, –
ɤɚɬɨɞɧɚɹ ɡɚɳɢɬɚ
:
ɧɨɫɬɶ. ɉɨɤɚɡɚɧɢɹ ɩɪɢɛɨɪɨɜ ɢ ɪɚɫɱɟɬɧɵɟ ɞɚɧɧɵɟ ɡɚɧɨɫɢɥɢɫɶ ɜ ɬɚɛɥɢɰɭ ɞɥɹ ɮɢɤ
ɫɢɪɨɜɚɧɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɨɬ
U
min
ɞɨ
U
max
(
ɬɚɛɥ
. 6).
-
-
-
.
-
-
113
Ⱦɚɧɧɵɟ ɩɪɹɦɵɯ ɢɡɦɟɪɟɧɢɣ ɜ ɪɟɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɤɚɬɨɞɧɨɣ ɡɚɳɢɬɵ
Ɍɚɛɥɢɰɚ 6
ɇɚɩɪɹɠɟɧɢɟ U
Ɍɨɤ
I
, Ⱥ 3 5 8 10 12
+
Ɇɨɳɧɨɫɬɶ Ɋ
2.
ɉɨ ɮɨɪɦɭɥɟ
, ȼ 5 10 15 18 25
, ȼɬ·c
w
(100)
43,75 118,75 250 325 550
ɨɩɪɟɞɟɥɹɥɚɫɶ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɫɬɨɪɨɧɧɟɝɨ ɩɨɥɹ
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɨɩɪɟɞɟɥɹɥɚɫɶ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɩɨɥɹ
E
ɫɬɨɪ
ȺɄ
, ȿ
ɇɚɩɪɹɠɟɧɧɨɫɬɶ ɩɨɥɹ
ɫɬɨɪ
E
=
Ɋ/I
AK
14,58 –9,58 –5,75 1,66
23,75 –13,75 –6,875 2,00
(ȼ)
Ɋɚɫɱɟɬɧɚɹ ɬɚɛɥɢɰɚ
ɇɚɩɪɹɠɟɧɧɨɫɬɶ ɩɨɥɹ
ȿ
ȺɄ
= U
ɫɬɨɪ
E
–
AK
ȿ
(
ɬɚɛɥ
ȺɄ
, I
ȺɄ
–
Ɍɨɤ, ɨɛɪɚɡɨɜɚɧɧɵɣ
ɤɚɬɢɨɧɚɦɢ
I
–
. 7).
= ȿȺɄ/Z
ɫɬɨɪ
E
Ɍɚɛɥɢɰɚ 7
=
Z
U
,
AK
I
+
31,25 –16,25 –8,66 1,87
32,40 –14,40 –8,00 1,80
46,00 –21,00 –10,00 2,08
3.
ɉɨ ɮɨɪɦɭɥɟ
ɤɚɬɢɨɧɚɦɢ (ɬɚɛɥ
4.
Ɉɩɪɟɞɟɥɟɧ ɪɚɫɱɟɬɧɵɣ ɬɨɤ ɜ ɫɢɫɬɟɦɟ ɩɨ ɮɨɪɦɭɥɟ
UPI
w
5.
ɉɨɫɥɟ ɩɪɹɦɵɯ ɢɡɦɟɪɟɧɢɣ ɢ ɪɚɫɱɟɬɨɜ ɜ ɪɟɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɫɪɚɜɧɢɜɚɥɢɫɶ
. 7).
ȿ
ȺɄ
/Z = I
Ɋɚɫɱɟɬɧɵɣ ɬɨɤ ɜ ɫɢɫɬɟɦɟ ɩɨ ɮɨɪɦɭɥɟ (99)
−
⋅⋅⋅⋅=
ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɜɟɥɢɱɢɧɚ ɬɨɤɚ, ɨɛɪɚɡɨɜɚɧɧɨɝɨ
–
1819
A,1025,61065,1/
8,75 11,875 16,66 18 22
(99) (
ɬɚɛɥ
. 8).
ɬɟɨɪɟɬɢɱɟɫɤɢɟ ɪɚɫɱɟɬɧɵɟ ɞɚɧɧɵɟ ɫ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ
Ɍɚɛɥɢɰɚ 8
,
ɩɨɥɭɱɟɧɧɵ
-
ɦɢ ɪɚɧɟɟ ɜ ɦɧɨɝɨɮɚɤɬɨɪɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɹɯ ɚɜɬɨɪɚ
114
[1, 8, 11, 15, 16] (
ɬɚɛɥ
. 9, 10).
Ɋɚɫɱɟɬɧɚɹ ɬɚɛɥɢɰɚ ɩɨ ɮɨɪɦɭɥɟ (98)
Z
Z
Ɍɚɛɥɢɰɚ 9
ɍɪɨɜɟɧɶ
ɇɚɩɪɹɠɟɧɢɹ, ȼ
Ɉɛɳɚɹ ɩɪɨɜɨɞɢɦɨɫɬɶ ɫɢɫɬɟɦɵ
5 4,86 0,5824 0,8085 54° 36° 90°
10 4,75 0,65 0,7519 50° 41° 91°
15 3,9 0,69 0,7239 46° 44° 90°
18 3,25 0,74 0,6618 42°20´ 49° 91°20´
25 3,8 0,75 0,6818 42° 47° 89°
Ɋɚɫɱɟɬɧɚɹ ɬɚɛɥɢɰɚ ɩɪɨɜɨɞɢɦɨɫɬɟɣ: ɨɛɳɟɣ ɩɪɨɜɨɞɢɦɨɫɬɢ ɜ ɫɢɫɬɟɦɟ,
R
g
=
2
=
R
, Ɉɦ
P
w
cos / /zRg
2
I
+
1
−
ϕ
=
+
ɚɧɢɨɧɨɜ ɢ ɤɚɬɢɨɧɨɜ
ɉɪɨɜɨɞɢɦɨɫɬɶ ɚɧɢɨɧɨɜ
+
1
=
cos / /zRg
ϕ
=
−
1
−
, Ɉɦg
+
ij
−
ɉɪɨɜɨɞɢɦɨɫɬɶ ɤɚɬɢɨɧɨɜ
+
1
=
r
−
ij
–
, Ɉɦg
−
ij
+
Ɍɚɛɥɢɰɚ 10
1
−
+
ij
–
1,75 0,6 1,15
1,187 0,5 0,67
1,11 0,53 0,58
1 0,55 0,44
0,88 0,48 0,4
Ⱥɧɚɥɢɡ ɬɚɛɥ
ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɭɪɨɜɧɹ ɩɪɢɥɨɠɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɤ ɷɥɟɤɬɪɨɥɢɬɚɦ ɩɪɨ
1.
. 6–10
ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɫɞɟɥɚɬɶ ɫɥɟɞɭɸɳɢɟ ɜɵɜɨɞɵ
:
ɢɫɯɨɞɹɬ ɫɥɨɠɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɫɬɨɪɨɧɧɟɝɨ ɩɨɥɹ, ɱɬɨ ɨɛɭɫɥɨɜɥɟ
ɧɨ ɪɚɡɥɢɱɢɟɦ ɩɪɨɰɟɫɫɨɜ, ɩɪɨɢɫɯɨɞɹɳɢɯ ɧɚ ɚɧɨɞɟ ɢ ɤɚɬɨɞɟ
Ⱦɜɢɠɟɧɢɟ ɡɚɪɹɞɨɜ ɨɬ ɚɧɨɞɚ ɤ ɤɚɬɨɞɭ I
2.
ɷɥɟɤɬɪɨɧɧɨɝɨ ɬɨɤɚ
ɧɨɫɚ ɢɨɧɧɨɝɨ ɬɨɤɚ I
.
ɗɥɟɤɬɪɢɱɟɫɤɢɣ ɬɨɤ ɨɬ ɤɚɬɨɞɚ ɤ ɚɧɨɞɭ ɹɜɥɹɟɬɫɹ ɦɟɪɨɣ ɩɟɪɟ
.
Ⱥɦɩɟɪɦɟɬɪ (ɬɚɛɥ
–
. 6)
ɠɟɧɢɟɦ ɡɚɪɹɞɨɜ ɨɬ ɚɧɨɞɚ ɤ ɤɚɬɨɞɭ, ɩɨɷɬɨɦɭ ɬɨɤ
+
ɹɜɥɹɟɬɫɹ ɦɟɪɨɣ ɩɟɪɟɧɨɫɚ ɬɨɥɶɤɨ
ɮɢɤɫɢɪɭɟɬ ɬɨɤ, ɨɛɪɚɡɨɜɚɧɧɵɣ ɞɜɢ
I
ɢɡɦɟɧɹɟɬɫɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ
–
.
-
-
-
-
ɬɚɛɥ
. 7,
ɚɬɨɤI
ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɚɛɥ
+
. 6.
115
3.
Ɍɨɤ, ɪɚɫɫɱɢɬɚɧɧɵɣ ɩɨ ɮɨɪɦɭɥɟ
(99)
ɢ ɩɪɟɞɫɬɚɜɥɹɸɳɢɣ ɫɨɛɨɣ ɦɟɪɭ ɩɟ
ɪɟɧɨɫɚ ɫɭɦɦɚɪɧɨɝɨ ɡɚɪɹɞɚ ɚɧɢɨɧɨɜ ɢ ɤɚɬɢɨɧɨɜ, ɩɪɨɬɢɜɨɩɨɥɹɪɧɵɯ ɢ ɜɫɬɪɟɱɧɨ
,
ɞɜɢɠɭɳɢɯɫɹ
ɩɨɡɜɨɥɹɟɬ ɨɰɟɧɢɬɶ ɪɟɡɭɥɶɬɚɬ ɢɫɫɥɟɞɨɜɚɧɢɹ ɩɨ ɮɨɪɦɭɥɟ I
=
I
+
I
+
–
-
.
Ⱦɚɧɧɵɟ I
ɧɵɟ ɢɡɦɟɧɟɧɢɹ ɬɨɤɚ I
4.
ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ
+
. 6,
I
–
.
Ƚɥɭɛɨɤɢɣ ɚɧɚɥɢɡ ɮɨɪɦɭɥɵ
ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ
(98)
ɢ ɩɪɢɜɟɞɟɧɧɵɟ ɡɞɟɫɶ ɢɫɫɥɟɞɨɜɚɧɢɹ ɩɨ
. 7,
ɜɬɚɛɥ
. 8
ɩɪɢɜɟɞɟɧɵ ɞɚɧ
ɡɜɨɥɹɸɬ ɫ ɩɨɦɨɳɶɸ ɩɪɹɦɵɯ ɢɡɦɟɪɟɧɢɣ ɪɚɫɫɱɢɬɚɬɶ ɩɪɨɜɨɞɢɦɨɫɬɢ ɩɪɚɤɬɢɱɟɫɤɢ
ɜ ɥɸɛɵɯ ɷɥɟɤɬɪɨɥɢɬɚɯ ɢ ɪɚɫɬɜɨɪɚɯ
.
7.3. Ɉɛ ɚɧɚɥɨɝɢɢ ɩɟɪɟɞɚɱɢ ɫɜɟɬɨɜɨɣ ɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ,
ɩɨɤɚɡɚɬɟɥɹ ɩɪɟɥɨɦɥɟɧɢɹ (ɨɬ ɋɧɟɥɥɢɭɫɚ – ɤ ɗɣɧɲɬɟɣɧɭ)
ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɷɧɟɪɝɢɹ ɢ ɫɜɟɬ ɢɦɟɸɬ ɚɧɚɥɨɝɢɱɧɵɟ ɫɜɨɣɫɬɜɚ: ɨɬɪɚɠɟ
ɧɢɹ, ɩɪɟɥɨɦɥɟɧɢɹ, ɩɨɝɥɨɳɟɧɢɹ
,
ɝɟɧɟɪɢɪɭɟɬɫɹ
ɩɨɬɪɟɛɥɹɟɬɫɹ, ɩɟɪɟɞɚɺɬɫɹ, ɬɟɪɹɟɬɫɹ, ɩɪɟɨɛɪɚɡɨɜɵɜɚɟɬɫɹ. ȼɵɹɜɥɹɹ
ɚɧɚɥɨɝɢɸ ɡɚɤɨɧɨɜ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɫɜɟɬɚ
[5].
ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɷɧɟɪɝɢɹ, ɚɧɟɦɨɳɧɨɫɬɶ
(
ɡɚɤɨɧ ɋɧɟɥɥɢɭɫɚ ɢ Ⱦɟɤɚɪɬɚ
) [2]
ɢ
-
-
-
(
ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ
[3, 9]
ɢ ɢɫɩɨɥɶɡɭɹ ɟɟ ɜɨ ɜɫɟɯ ɫɥɭɱɚɹɯ ɛɟɡ ɪɚɡɛɨɪɚ, ɦɵ ɦɨɠɟɦ ɨɱɟɧɶ ɫɤɨɪɨ ɩɪɢɣɬɢ
ɤ ɨɲɢɛɨɱɧɵɦ ɜɵɜɨɞɚɦ
ɷɥɟɤɬɪɢɱɟɫɬɜɚ ɢ ɦɚɝɧɟɬɢɡɦɚ
ɸɬɫɹ ɤɚɤ ɞɟɣɫɬɜɢɬɟɥɶɧɵɟ ɧɟɤɨɦɩɥɟɤɫɧɵɟ ɱɢɫɥɚ
ɭɪɚɜɧɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ ɢ ɩɨɬɨɤ ɍɦɨɜɚ–ɉɨɣɧɬɢɧɝɚ
.
ɋɨɝɥɚɫɧɨ ɤɥɚɫɫɢɱɟɫɤɨɣ ɮɟɧɨɦɟɧɨɥɨɝɢɱɟɫɤɨɣ ɬɟɨɪɢɢ
εμ,
ɭɫɪɟɞɧɟɧɧɵɟ ɜɨ ɜɪɟɦɟɧɧɨɦ ɫɦɵɫɥɟ, ɩɪɢɧɢɦɚ
[7; 33].
Ɉɞɧɚɤɨ ɩɪɢ ɜɡɚɢɦɨɞɟɣ
ɫɬɜɢɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɢ ɫɜɟɬɨɜɨɝɨ ɢɡɥɭɱɟɧɢɹ ɫ ɜɟɳɟɫɬɜɨɦ, ɜɨɫɩɪɢɧɢɦɚɸ
ɳɢɦ ɷɬɨ ɢɡɥɭɱɟɧɢɟ, ɩɪɨɬɟɤɚɸɬ ɛɵɫɬɪɨɩɟɪɟɦɟɧɧɵɟ ɜɨ ɜɪɟɦɟɧɢ ɩɪɨɰɟɫɫɵ, ɡɚɜɢ
ɫɹɳɢɟ ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɱɚɫɬɢɰ ɢ ɦɧɨɠɟɫɬɜɚ ɞɪɭɝɢɯ ɮɚɤɬɨɪɨɜ. ɗɬɢ ɩɪɨɰɟɫɫɵ
ɫɨɩɪɨɜɨɠɞɚɸɬɫɹ ɢɡɦɟɧɟɧɢɹɦɢ ɷɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɢ
ɩɥɨɬɧɨɫɬɢ ɬɨɤɚ (ɩɨɬɨɤɚ
),
,
ɨɛɪɚɡɨɜɚɧɢɟɦ ɞɜɨɣɧɨɝɨ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɫɥɨɹ ɢ ɬ.ɞ. ɉɪɢ ɷɬɨɦ ɫɭɳɧɨɫɬɶ ɹɜɥɟɧɢɣ
ɩɪɢ ɜɨɡɞɟɣɫɬɜɢɢ ɫɜɟɬɚ ɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ ɧɚ ɜɟɳɟɫɬɜɨ ɧɚɢɛɨɥɟɟ ɩɨɥ
ɧɨ ɨɬɪɚɠɚɸɬ ɡɚɤɨɧɵ ɋɧɟɥɥɢɭɫɚ ɢ Ɇɚɤɫɜɟɥɥɚ. Ɂɧɚɦɟɧɢɬɨɟ ɫɨɨɬɧɨɲɟɧɢɟ ɋɧɟɥ
)
-
-
-
-
-
-
116
ɥɢɭɫɚ
ϕ
α sin/sin
n=
ɹɜɥɹɟɬɫɹ «ɧɟɨɬɴɟɦɥɟɦɵɦ ɩɨɤɚɡɚɬɟɥɟɦ ɫɜɨɣɫɬɜ ɜɟɳɟɫɬɜɚ
:
ɬɟɦɩɟɪɚɬɭɪɵ ɩɥɚɜɥɟɧɢɹ
».
Ɉɞɧɚɤɨ ɡɚɤɨɧ ɋɧɟɥɥɢɭɫɚ ɧɟ ɭɱɢɬɵɜɚɟɬ ɢɡɦɟɧɟɧɢɹ
ɩɪɨɢɫɯɨɞɹɳɢɟ ɜ ɜɟɳɟɫɬɜɟ ɩɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɢɡɥɭɱɟɧɢɹ (ɨɧɢ ɞɥɹ ɥɭɱɚ ɫɜɟɬɚ ɧɟ
ɡɧɚɱɢɬɟɥɶɧɵ
) [14],
ɚ ɡɚɤɨɧ Ɇɚɤɫɜɟɥɥɚ
εμ= /
cc
1
ɧɟ ɪɚɫɤɪɵɜɚɟɬ ɩɪɟɜɪɚɳɟɧɢɣ
ɩɚɪɚɦɟɬɪɨɜ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɩɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɗȾɋ ɩɨɫɬɨɹɧɧɨɝɨ
ɬɨɤɚ
[14].
ɭɪɚɜɧɟɧɢɟ
ɝɪɚɧɢɰɭ ɪɚɡɞɟɥɚ ɮɚɡ
ɉɨɣɧɬɢɧɝɚ
ɝɞɟ
Z –
ɧɢɹ ɷɧɟɪɝɢɢ
ɋ ɰɟɥɶɸ ɜɵɹɜɥɟɧɢɹ ɷɬɢɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɩɪɢɜɟɞɟɦ ɜɵɹɜɥɟɧɧɨɟ ɧɚɦɢ
(85),
ɩɪɟɞɫɬɚɜɥɹɹ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ ɱɟɪɟɡ
,
ɧɚɩɪɢɦɟɪ
«
ɦɟɬɚɥɥ–ɝɪɭɧɬ
»,
ɜɜɢɞɟɜɟɤɬɨɪɚɍɦɨɜɚ
[14, 18]:
2
α−εμ
=
Z ⋅
ɤɚɠɭɳɟɟɫɹ ɫɨɩɪɨɬɢɜɥɟɧɢɟ
; g –
ɨɛɳɚɹ ɩɪɨɜɨɞɢɦɨɫɬɶ ɚɧɢɨɧɨɜ ɢ ɤɚɬɢɨɧɨɜ
; R –
sin
,
R
g
εμ
ɨɦɢɱɟɫɤɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ; Į
; εμ –
–
ɭɝɨɥ ɩɚɞɟ
ɞɢɷɥɟɤɬɪɢɱɟ
,
-
–
-
-
ɫɤɚɹ ɢ ɦɚɝɧɢɬɧɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ
.
Ɋɟɲɢɦ ɭɪɚɜɧɟɧɢɟ ɫɨɜɦɟɫɬɧɨ ɫ ɩɪɢɧɹɬɵɦ ɜɵɪɚɠɟɧɢɟɦ ɜ ɩɪɚɤɬɢɱɟɫɤɨɣ
,
ɷɥɟɤɬɪɨɬɟɯɧɢɤɟ
ɩɪɟɞɫɬɚɜɥɹɸɳɢɦ ɫɨɛɨɣ ɤɨɦɩɥɟɤɫɧɨɟ (ɤɚɠɭɳɟɟɫɹ) ɫɨɩɪɨɬɢɜɥɟ
ɧɢɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫɨɟɞɢɧɟɧɧɨɝɨ ɚɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɫ ɺɦɤɨɫɬɧɵɦ
(
ɪɚɡɞɟɥɶɧɨ ɢ ɫ ɢɧɞɭɤɬɢɜɧɵɦ
),
ɱɬɨ ɢɦɟɟɬ ɦɟɫɬɨ ɩɪɢ ɩɨɥɧɨɦ ɢɥɢ ɱɚɫɬɢɱɧɨɦ ɩɪɟ
ɜɪɚɳɟɧɢɢ ɩɚɪɚɦɟɬɪɨɜ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ, ɧɚɩɪɢɦɟɪ, ɷɥɟɤɬɪɨɥɢɬɨɜ
ɬɨɝɞɚ ɢɦɟɟɦ
:
+=
g
sin
εμ
xRZ
2
α−εμ
22
.
⋅
;
R
=
Z
°
®
°
¯
=
Z
°
®
°
¯
2
α−εμ
sin
εμ
g
−=
xRZ
⋅
;
R
22
.
ɉɪɢɪɚɜɧɢɜɚɹ ɩɨɨɱɟɪɟɞɧɨ ɩɪɚɜɵɟ ɱɚɫɬɢ ɢ ɨɫɜɨɛɨɠɞɚɹɫɶ ɨɬ ɤɜɚɞɪɚɬɧɵɯ
ɤɨɪɧɟɣ
,
ɪɚɡɞɟɥɢɦ ɨɛɟ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɣ ɧɚ
R
222
;/1))/(sin(
RxRg +=εμα−εμ ./1))/(sin(
2
ɢɩɨɥɭɱɢɦ
222
RxRg −=εμα−εμ
-
-
,
117
Ɂɚɦɟɧɢɜ ɨɬɧɨɲɟɧɢɟ ɪɟɚɤɬɢɜɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɤ ɚɤɬɢɜɧɨɦɭ ɱɟɪɟɡ
ɩɨɥɭɱɢɦ
tgij,
22
;1))/(sin(
ϕ+=εμα−εμ tgRg .1))/(sin(
ɍɱɢɬɵɜɚɹ ɩɪɢɧɹɬɨɟ ɨɛɨɡɧɚɱɟɧɢɟ
1/R = g,
22
ɩɨɥɭɱɢɦ
)./(sintg
εμα±=ϕ (93')
22
ϕ+=εμα−εμ tgRg
ɇɟɬɪɭɞɧɨ ɡɚɦɟɬɢɬɶ, ɱɬɨ ɷɬɨ ɜɵɪɚɠɟɧɢɟ ɭɱɢɬɵɜɚɟɬ ɢɡɦɟɧɟɧɢɹ, ɩɪɨɢɫɯɨɞɹ
ɳɢɟ ɜ ɜɟɳɟɫɬɜɟ, ɢ ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɡɚɤɨɧɚ ɋɧɟɥɥɢɭɫɚ ɜɟɥɢɱɢɧɨɣ
ɋɧɟɥɥɢɭɫɚ ɦɨɠɧɨ ɬɨɬɱɚɫ ɠɟ ɩɨɥɭɱɢɬɶ ɢɡ ɜɵɪɚɠɟɧɢɹ
ɱɟɪɟɡ ɩɚɪɚɦɟɬɪɵ
ZɢR,
ɩɪɟɧɟɛɪɟɝɚɹ ɩɪɟɜɪɚɳɟɧɢɹɦɢ ɩɚɪɚɦɟɬɪɨɜ ɩɨɞ ɜɨɡɞɟɣɫɬ
,
ɟɫɥɢ ɩɪɟɞɫɬɚɜɢɬɶ
1/cos ij.
ɜɢɟɦ ɜɧɟɲɧɟɝɨ ɢɫɬɨɱɧɢɤɚ. Ɍɨɝɞɚ
22
ȼɵɪɚɠɟɧɢɟ
(93’)
ɭɱɢɬɵɜɚɟɬ ɜɨɡɦɨɠɧɵɟ ɢɡɦɟɧɟɧɢɹ ɜ ɡɚɦɤɧɭɬɨɣ ɷɥɟɤɬɪɨɞ
ɧɨɣ ɫɢɫɬɟɦɟ ɤɚɤ ɜ ɢɫɬɨɱɧɢɤɟ ɫ ɪɟɡɭɥɶɬɢɪɭɸɳɢɦ ɩɨɥɟɦ
εμα−=g
22
),/(sin1Z
ɝɞɟ
()
Z/R = cos ij, g = 1/R
εμ=ϕαεμα−=ϕ
ȿ
,
ɪɟɡ
.
.sin/sin,/sin1cos
ɬɚɤ ɢ ɜ ɜɟɳɟɫɬɜɟ
Ɂɚɤɨɧ
cos
-
ij
-
-
.
Ⱦɥɹ ɛɨɥɶɲɟɣ ɧɚɝɥɹɞɧɨɫɬɢ ɩɪɢɜɟɞɺɦ ɞɜɟ ɝɪɚɮɢɱɟɫɤɢɟ ɡɚɜɢɫɢɦɨɫɬɢ ɩɨ ɜɵɪɚɠɟ
ɧɢɸ
(
ɪɢɫ
(93):
sin
. 20, ɛ).
2
()
εμ=α f
ɩɪɢ ij
= const (
ɪɢɫ
. 20, ɚ)
a
2
ɢ
tg
ɛ
()
εμ=ϕ f
ɩɪɢ Į
2
tg
ij
= const
ij
= 60
˚
ij
= 45
˚
ij
= 30
˚
Ɉ Ɉ
Ɋɢɫ
. 20.
Ɍɟɨɪɟɬɢɱɟɫɤɢɟ ɡɚɜɢɫɢɦɨɫɬɢ
: a –
sin
2
; ɛ –
()
εμ=α f
tg
2
()
εμ=ϕ f
-
118
Ʉɚɤ ɜɢɞɢɦ (ɪɢɫ
ϕ
α
/
ϕ
. 20, ɚ),
ɩɚɪɚɦɟɬɪ
sin
2
α
ɢɦɟɟɬ ɥɢɧɟɣɧɭɸ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬ
ɩɚɪɚɦɟɬɪɚ
εμ,
ɚɡɚɜɢɫɢɦɨɫɬɶ
2
ϕ
tg
ɨɬ ɬɨɝɨ ɠɟ ɩɚɪɚɦɟɬɪɚ
εμ (
ɪɢɫ
. 20, ɛ)
ɩɪɟɞ
ɫɬɚɜɥɹɟɬɫɹ ɪɚɜɧɨɫɬɨɪɨɧɧɟɣ ɝɢɩɟɪɛɨɥɨɣ, ɚɫɢɦɩɬɨɬɚɦɢ ɤɨɬɨɪɨɣ ɹɜɥɹɸɬɫɹ ɨɫɢ ɤɨ
ɨɪɞɢɧɚɬ
[14, ɫ. 75–85].
Ɂɚɤɨɧ ɋɧɟɥɥɢɭɫɚ ɩɨ ɫɜɨɟɣ ɫɭɬɢ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɨɤɚɡɚɬɟɥɶ ɩɪɟɥɨɦɥɟ
ɧɢɹ ɥɭɱɚ ɫɜɟɬɚ ɩɪɢ ɩɟɪɟɯɨɞɟ ɢɡ ɨɞɧɨɣ ɫɪɟɞɵ ɜ ɞɪɭɝɭɸ, ɬɨɱɧɟɟ ɫɤɚɡɚɬɶ, ɨɧ ɹɜɥɹ
ɟɬɫɹ ɩɨɤɚɡɚɬɟɥɟɦ ɩɪɟɥɨɦɥɟɧɢɹ ɜɟɳɟɫɬɜɚ ɬɨɥɶɤɨ ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɨɡɞɭɯɚ. ȼɬɚɛ
ɥɢɰɟ ɜ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɩɪɟɞɫɬɚɜɥɟɧɵ ɩɨɤɚɡɚɬɟɥɢ ɪɹɞɚ ɜɟɳɟɫɬɜ
ɉɨɤɚɡɚɬɟɥɢ ɩɪɟɥɨɦɥɟɧɢɹ ɜɟɳɟɫɬɜ
ȼɟɳɟɫɬɜɨ
ɋɬɟɤɥɨ
Ⱥɥɦɚɡ
ɉɥɚɜɥɟɧɵɣ ɤɜɚɪɰ
1,5–1,9
2,42
1,46
ɉɨɤɚɡɚɬɟɥɶ
ɩɪɟɥɨɦɥɟɧɢɹ
ȼɟɳɟɫɬɜɨ
Ƚɥɢɰɟɪɢɧ
ɗɬɢɥɨɜɵɣ ɫɩɢɪɬ
Ɉɥɟɢɧɨɜɚɹ ɤɢɫɥɨɬɚ
1,47
1,36
1,46
.
ɉɨɤɚɡɚɬɟɥɶ
ɩɪɟɥɨɦɥɟɧɢɹ
-
-
-
-
-
Ʉɪɢɫɬɚɥɥɢɱɟɫɤɢɣ ɤɜɚɪɰ
Ɂɚɤɨɧ ɋɧɟɥɥɢɭɫɚ ɨɩɪɟɞɟɥɹɟɬ ɩɨɫɬɨɹɧɫɬɜɨ ɜɟɥɢɱɢɧɵ
1,54
ȼɨɞɚ
1,33
sin
sin
ɞɥɹ ɜɫɟɯ ɭɝ
ɥɨɜ ɩɚɞɟɧɢɹ, ɱɬɨ ɜ ɡɧɚɱɢɬɟɥɶɧɨɣ ɫɬɟɩɟɧɢ ɭɩɪɨɳɚɟɬ ɨɩɢɫɚɧɢɟ ɹɜɥɟɧɢɹ ɩɪɟɥɨɦ
ɥɟɧɢɹ ɫɜɟɬɚ. Ⱦɨɫɬɚɬɨɱɧɨ ɡɧɚɬɶ ɩɨɤɚɡɚɬɟɥɢ ɩɪɟɥɨɦɥɟɧɢɹ ɜɚɠɧɟɣɲɢɯ ɫɪɟɞ, ɤɨɬɨ
ɪɵɟ ɦɨɝɭɬ ɩɨɦɟɫɬɢɬɶɫɹ ɧɚ ɨɞɧɨɣ ɫɬɪɚɧɢɰɟ, ɢ ɦɧɨɝɨɱɢɫɥɟɧɧɵɟ ɤɧɢɝɢ, ɡɚɩɨɥɧɟɧ
ɧɵɟ ɝɪɚɮɢɤɚɦɢ ɬɢɩɚ
=
Ɂɚɤɨɧɵ Ɇɚɤɫɜɟɥɥɚ
ɜɨ ɜɟɥɢɱɢɧɵ ɫɢɧɭɫɨɜ ɭɝɥɨɜ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɪɟɞɵ, ɤɨɬɨɪɚɹ ɩɪɢɧɢɦɚɟɬɫɹ ɡɚ
,
ɛɭɞɭɬ ɧɟ ɧɭɠɧɵ
()af
εμ=ϕα sin/sin
.
ɢ
1
εμ= /
cc
ɨɩɪɟɞɟɥɹɸɬ ɩɨɫɬɨɹɧɫɬ
const,
ɢɥɢ ɩɨɫɬɨɹɧɫɬɜɨ ɨɬɧɨɲɟɧɢɹ ɫɤɨɪɨɫɬɟɣ ɪɚɫɩɪɨɫɬɪɚɧɹɸɳɟɣɫɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ
εμ
ɷɧɟɪɝɢɢ ɜ ɫɪɟɞɟ ɫ ɩɨɫɬɨɹɧɧɵɦɢ ɫɜɨɣɫɬɜɚɦɢ
ɭɫɥɨɜɢɹɯ ɨɬɧɨɲɟɧɢɹ ɭɝɥɨɜ Į
/ ij = const,
ɧɚɩɪɢɦɟɪ, ɞɥɹ ɜɫɟɯ ɭɝɥɨɜ ɧɟ ɨɩɪɚɜɞɵ
ɬɨɝɨ ɢɥɢ ɢɧɨɝɨ ɩɪɨɰɟɫɫɚ. ȼɷɬɢɯ
ɜɚɟɬɫɹ. Ɉɞɧɚɤɨ ɞɥɹ ɦɚɥɟɧɶɤɢɯ ɭɝɥɨɜ ɩɚɞɟɧɢɹ ɫɜɟɬɚ ɢɥɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɥɭɱɚ
-
-
-
-
-
-
ɉɨɣɧɬɢɧɝɚ ɨɬɧɨɲɟɧɢɟ ɭɝɥɨɜ Į
/
ij ɩɨɫɬɨɹɧɧɨ ɢ ɪɚɜɧɨ ɨɤɨɥɨ
119
1,5
ɞɥɹ ɫɬɟɤɥɚ ɢ
1,38
ɞɥɹ ɜɨɞɵ. ɉɪɢ ɛɨɥɶɲɢɯ ɭɝɥɚɯ ɩɨɫɬɨɹɧɫɬɜɨ, ɤɚɤ ɢɡɜɟɫɬɧɨ, ɧɚɪɭɲɚɟɬɫɹ, ɢɨɬɧɨ
-
ɲɟɧɢɟ ɫɢɧɭɫɨɜ ɭɝɥɨɜ
ɏɨɬɹ ɞɚɧɧɵɟ ɨ ɩɪɟɥɨɦɥɟɧɢɢ ɫɜɟɬɚ ɛɵɥɢ ɯɨɪɨɲɨ ɢɡɜɟɫɬɧɵ ɟɳɟ ɉɬɨɥɟɦɟɸ ɢ
ɢɫɩɨɥɶɡɨɜɚɥɢɫɶ ɜ ɬɟɱɟɧɢɟ ɰɟɥɨɝɨ ɬɵɫɹɱɟɥɟɬɢɹ
ɞɚɥ ɢɡɹɳɧɭɸ ɮɨɪɦɭɥɢɪɨɜɤɭ ɡɚɜɢɫɢɦɨɫɬɢ ɦɟɠɞɭ ɜɟɥɢɱɢɧɚɦɢ
17
ɫɩɭɫɬɹ
Ɉɬɤɪɵɬɢɟ ɋɧɟɥɥɢɭɫɚ ɢ Ⱦɟɤɚɪɬɚ ɩɨɹɫɧɹɟɬɫɹ ɪɢɫ
Ʌɭɱ ɫɜɟɬɚ ɜɯɨɞɢɬ ɜ ɫɪɟɞɭ ɜ ɬɨɱɤɟ Ɉ, ɝɞɟ ɨɧ ɢ ɩɪɟɥɨɦɥɹɟɬɫɹ. ȼɩɥɨɫɤɨɫɬɢ
ɩɪɨɯɨɠɞɟɧɢɹ ɥɭɱɟɣ ɩɪɨɜɟɞɟɧɚ ɨɤɪɭɠɧɨɫɬɶ ɫ ɰɟɧɬɪɨɦ ɜ ɬɨɱɤɟ Ɉ
ɜɟɞɟɧɚ ɧɨɪɦɚɥɶ ɄɈ. Ⱦɥɢɧɵ ɞɭɝ
sin
Į
/ sin
ɛɨɥɶɲɢɯ ɭɝɥɚɯ
ɨɬɧɨɲɟɧɢɹ ɩɨɥɭɯɨɪɞ
ɯɨɪɞɵ ɢ ɞɭɝɢ ɩɨɱɬɢ ɨɞɢɧɚɤɨɜɵ
ɥɟɬ Ⱦɟɤɚɪɬ ɨɩɭɛɥɢɤɨɜɚɥ ɡɚɜɢɫɢɦɨɫɬɶ, ɤɨɬɨɪɨɣ ɦɵ ɬɟɩɟɪɶ ɩɨɥɶɡɭɟɦɫɹ
ij
= ȺɄ / MD.
.
sin Į / sin
ij ɜɨɡɪɚɫɬɚɟɬ
.
,
ɥɢɲɶ ɬɨɥɶɤɨ ɜ
1621 ɝ.
sin
Įɢ
sin ij.
. 17.
,
ɝɞɟ ɬɚɤɠɟ ɩɪɨ
ȺɄ
ɢ
MD
ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ ɭɝɥɚɦ Į ɢ ij, ɬ.ɟ
ɗɬɨ ɨɬɧɨɲɟɧɢɟ ɩɨɱɬɢ ɩɨɫɬɨɹɧɧɨ ɩɪɢ ɦɚɥɵɯ, ɧɨ ɧɟ ɩɪɢ
ɉɨɷɬɨɦɭ ɪɚɛɨɬɵ ɋɧɟɥɥɢɭɫɚ ɢ Ⱦɟɤɚɪɬɚ ɫɜɟɥɢɫɶ ɤ ɪɚɫɫɦɨɬɪɟɧɢɸ
AB/CD
ɜɦɟɫɬɨ ɨɬɧɨɲɟɧɢɹ ɞɭɝ
,
ɧɨ ɞɥɹ ɛɨɥɶɲɢɯ ɭɝɥɨɜ ɞɥɢɧɚ ɯɨɪɞ ɢ ɞɭɝ ɫɭɳɟ
AKɢMD.
Ⱦɥɹ ɦɚɥɵɯ ɭɝɥɨɜ
ɋɧɟɥɥɢɭɫ
Ɂɚɬɟɦ
.
-
.
-
ɫɬɜɟɧɧɨ ɨɬɥɢɱɚɟɬɫɹ. ɉɨɷɬɨɦɭ ɨɬɧɨɲɟɧɢɟ ɯɨɪɞ ɢ ɞɭɝ ɢɡɦɟɧɹɟɬɫɹ ɩɨ-ɪɚɡɧɨɦɭ. Ɍɚ
ɤɢɦ ɨɛɪɚɡɨɦ, ɨɬɧɨɲɟɧɢɟ
AO ɢ OD
ɟɫɬɶ ɪɚɞɢɭɫ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɨɤɪɭɠɧɨɫɬɢ, ɬɨ
sin
sin
ɝɞɟ
n –
ɩɨɤɚɡɚɬɟɥɶ ɩɪɟɥɨɦɥɟɧɢɹ
ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɫɢɧɭɫɨɜ ɭɝɥɨɜ Į ɢ ij ɜɦɟɫɬɨ ɫɚɦɢɯ ɭɝɥɨɜ Į ɢ ij ɩɨɡɜɨɥɢɥɨ
ɪɟɲɢɬɶ ɡɚɞɚɱɭ ɩɨɞɛɨɪɚ ɬɚɤɨɣ ɮɭɧɤɰɢɢ
ɩɪɢ ɛɨɥɶɲɢɯ ɭɝɥɚɯ
ɥɨɦɥɟɧɢɹ ɩɪɢ ɦɚɥɵɯ ɭɝɥɚɯ ɩɚɞɟɧɢɹ ɢ ɩɪɢ ɛɨɥɶɲɢɯ ɞɥɹ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɫɪɟɞɵ
.
ɩɨɱɬɢ ɪɚɜɧɵ
ɡɧɚɱɟɧɢɹ
.
Ⱦɥɹ ɞɪɭɝɢɯ ɤɚɤɢɯ-ɥɢɛɨ ɜɟɳɟɫɬɜ ɨɬɧɨɲɟɧɢɟ
Ⱦɥɹ ɥɸɛɨɝɨ ɜɟɳɟɫɬɜɚ ɷɬɨ ɨɬɧɨɲɟɧɢɟ ɹɜɥɹɟɬɫɹ ɧɟɨɬɴɟɦɥɟɦɵɦ ɫɜɨɣɫɬ
,
AB/AO = sin Į,
ɚɨɬɧɨɲɟɧɢɹ
CD/OD = sin ij.
ɉɨɫɤɨɥɶɤɭ
:
α
ϕ
/
AOAB
/
ODCD
AB
==
,
ɩɨɷɬɨɦɭ
CD
sin
sin
α
ϕ
,
n=
.
,
ɤɨɬɨɪɚɹ ɨɫɬɚɜɚɥɚɫɶ ɛɵ ɩɨɫɬɨɹɧɧɨɣ ɤɚɤ
ɬɚɤ ɢ ɩɪɢ ɦɚɥɵɯ. Ɉɬɧɨɲɟɧɢɟ ɫɢɧɭɫɨɜ ɭɝɥɨɜ ɩɚɞɟɧɢɹ ɢ ɩɪɟ
α
sin
sin
ɢɦɟɟɬ ɞɪɭɝɢɟ
ϕ
-
-
-
ɜɨɦ
–
ɬɚɤɢɦ ɤɚɤ ɟɝɨ ɬɟɦɩɟɪɚɬɭɪɚ ɤɢɩɟɧɢɹ ɢɥɢ ɩɥɚɜɥɟɧɢɹ
120
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