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. ɇɟɭɤɚɡɚɧɧɵɟ ɩɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɪɚɡɦɟɪɨɜ: ɨɬɜɟɪɫɬɢɣ - ɇ4, ɜɚ-

ɥɨɜ- h 4, ɨɫɬɚɥɶɧɵɯ + (IT 4)/2.

2. Ɇɚɪɤɢɪɨɜɚɬɶ: m = 3, α = 20° , ɤɥ.ȼ, ωt = 2° 26', Pz = 5 68, Ɋ6Ɇ5Ʉ5.

ɉɪɢɥɨɠɟɧɢɟ 3.

ɉɪɢɦɟɪ ɪɚɫɱɟɬɚ ɩɪɨɮɢɥɹ ɡɭɛɶɟɜ ɢ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ

ɩɚɪɚɦɟɬɪɨɜ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɩɨɞ ɲɟɜɟɪ

Ɋɚɫɫɱɢɬɚɬɶ ɢ ɫɩɪɨɟɤɬɢɪɨɜɚɬɶ ɱɟɪɜɹɱɧɭɸ ɮɪɟɡɭ ɞɥɹ ɧɚɪɟɡɚɧɢɹ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ m = 3 ɦɦ, α = 20° , z = 40, h*a = , h*f = ,25; β = 0° , x = 0, ɫɬɟɩɟɧɢ ɬɨɱ-

ɧɨɫɬɢ 7 ɢ ɜɢɞɚ ɫɨɩɪɹɠɟɧɢɹ ȼ ɩɨ ȽɈɋɌ 643-8 , ɧɚɯɨɞɹɳɟɝɨɫɹ ɜ ɡɚɰɟɩɥɟɧɢɢ ɫ

ɤɨɥɟɫɨɦ z2 = 20, ɯ2 = 0

Ɋɚɫɱɟɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɫɨɩɪɹɠɟɧɧɵɯ ɡɭɛ-

ɱɚɬɵɯ ɤɨɥɟɫ

. ( . ) d =

m z

3 40

= 20;

mz2

3 20

= 60.

cosβ

cos0°

( .2) α

= arctg

tgα

= arctg

tg20°

= 20° ; m

= 3

cosβ

cos0°

cosβ

cos0°

( .3) db

= d cosα t

= 20 cos20° = 2,763;

= d cosα t

= 60 cos20° = 56,38 .

( .4)α tw

= α t

= 20° ;

Y = 0.

( .5)invα tw = invα t +

2(x + x2 )

tgα ;α tw

= α t

= 20° .

z + z2

( .6)α w = α = 20° .

( .8) aw = [0,5 m(z + z2 ) cosα t ] (cosα tw cosβ)=

= [0,5 3 (40 + 20)cos20°] cos20° cos0° = 90.

8. ( . 0)

= (h* + x −

y) 3 = ( + 0− 0) 3= 3;

(h*

+ x

−

y) 3 = ( + 0 − 0) 3= 3.

( . ) da

= d + 2m = 20 + 2 3= 26; da

= d

2 + 2m = 60 + 2 3= 66.

0. ( . 2) h

= (2h*

+ c −

y)3 = (2 + 0,25 − 0) 3= 6,75.

. ( . 4) = hf

= h − ha

= 6,75 −

3 =

3,75; hf

= 3,75.

2. ( . 5) df = da

− 2h = 26 − 2 6,75= 2,5;

= da

− 2h = 66 − 2 6,75= 52,5.

3. ( . 6) Sn

= 0,5

π m − ECS

= 0,5 π 3 − 0, 2 = 4,592; Sn

= 4,6 2.

( . 7) ρa = 0,5

da2

− db2 = 0,5

262 − 2,7632 = 28, 09.

( . 8) ρ p = aw sinαtw − 0,5

90 sin 20° − 0,5 66

da2

− db2

− 56,38 =

= 3,627.

( . 9) L = 0,5(

da2

− db2 +

da2

− db2

)− aw sinα tw =

= 0,5( 262 − 2,7632 + 662 − 56,38 2 )− 90 sin 20° = 4,482.

7. ( .20) L = 0, 5 msinα tw = 0, 5 3sin 20° = ,3 6.

8. ( .22) ε = L +0, 5Lπ m sinσ cosα =

= ( 4,482 + ,3 6)π 3 sin90° cos20° = ,67.

ɒɟɜɢɧɝɨɜɚɧɢɟ ɜɨɡɦɨɠɧɨ.

Ɋɚɫɱɟɬ ɪɚɡɦɟɪɨɜ ɩɪɨɮɢɥɹ ɢ ɤɨɧɫɬɪɭɤɬɢɜɧɨ-ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɩɚɪɚ-

ɦɟɬɪɨɜ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɩɨɞ ɲɟɜɟɪ

. dao = 80; dɨɬɜ = 32; L = 25; i = 1; z0 = 0; γ = 0° ; αɜ = 9° ;

K = π dao tgαɜ = 3, 4 80 tg9° = 3,98. ɉɪɢɧɢɦɚɸ Ʉ = 4° ; Ʉ = 6. z0 0

αɛɨɤ = arctg(tgαɜ sinα wo )= arctg(tg9,04° sin 20°)= 3, ° .

ȼɟɥɢɱɢɧɚ ɡɚɞɧɟɝɨ ɭɝɥɚ ɧɚ ɛɨɤɨɜɨɣ ɪɟɠɭɳɟɣ ɤɪɨɦɤɟ ɞɨɫɬɚɬɨɱɧɚɹ.

2.	Ɍ.ɤ. df	< db	, ɬɨ (2.62) α wo	= arccos	df	= arccos	2,5	= 3,9° ;
2.	Ɍ.ɤ. df	< db	, ɬɨ (2.62) α wo	= arccos		= arccos		= 3,9° ;
				min	db		2,763
					db		2,763
3,9° < 20° . ɋɥɟɞɨɜɚɬɟɥɶɧɨ, α wo = 20° .
3.	(2.65)	S = 0,0 7 m + 0,08 = 0,0 7 3+ 0,08; ɩɪɢɧɢɦɚɟɦ S = 0, 4;

(2.66) δ = S = 0, 4 = 0,07.

4.(2.67) Pb = π m cosα = π 3 cos20° = 8,856.

	Pb	8,856
5. (2.68) Pwo =		=		= 9,425.
	cosα wo		cos20°

(2.69) β wo

= arcsin

sin β cosα

= arcsin

sin 0°cos20°

= 0°.

cosα wo

cos20°

(2.70) α wto

= arctg

tgα wo

= arctg

tg20°

20° .

cosβw

cos0°

(2.7 ) d

d cosα

20 cos20°

= 20.

cosα wto

cos20°

(2.72) Sw

Sn +

= dw

+ invα t − invα wto =

d cosβ

4,592

+ 0, 4

+ inv20° − inv20° = 4,732.

cos0°

0. (2.73) Sno = Pwo − Sw = 9,425 – 4,732 = 4,693.

. (2.74) hno

− df

20 − 2,5

= 3,75.

2. (2.75) h0 = h + 0,3 m =6,75 + 0,3 3= 7,65/

3. (2.76) hy

= hno − [(0,5dw

sinα wto − ρ p

− δ ) sinα wto ]=

=3,75 − [(0,5 20 sin20° − 3,627 − 0,07) sin20°]=

=,674≈ ,67.

(2.77) C =

,67

,78;

coaα wo

cos20°

a = δ + 0,05 = 0,07 + 0,05 = 0, 2;

b = c –

0, 2

tg(α wo − 5°) = ,78 –

tg(20° − 5°)= ,33;

0, m

0, 3

= 0,43 ;

− sin20°

− sinα wo

ɉɪɢɧɢɦɚɟɦ rɝ= 0,5; ɬ.ɤ. b > 0,5, ɬɨ ɩɪɢɧɢɦɚɟɦ ɮɨɪɦɭ ɭɫɢɤɚ ȼ.

4. ɉɪɨɜɟɪɤɚ ɜɟɥɢɱɢɧɵ ɭɬɨɥɳɟɧɢɹ ɭ ɝɨɥɨɜɤɢ ɡɭɛɚ ɮɪɟɡɵ ɧɚ ɜɨɡɦɨɠ-

ɧɨɫɬɶ ɱɪɟɡɦɟɪɧɨɝɨ ɩɨɞɪɟɡɚɧɢɹ ɧɨɠɤɢ ɡɭɛɚ ɤɨɥɟɫɚ

(2.78) hɤ = hno − rɝ − sin α wo = 3,75 − [0,5( − sin 20°)]= 3,4

(2.79) rB = (0,5db )2 + (ρ p + δ )2 = (0,5 2,763)2 + ( 3,627 + 0,07)2 =

=58,02 ;

(2.80) α B = arccos

2,763

= arccos

= 3,65305° ;

2 rɜ

58,02

6,042

λ = arccos

0,5dw − hɤ

= arccos

0,5 20 −

3,4

= 2,7067° = 0,22 773 ɪɚɞ;

58,02

(2.8 ) ϕ = λ + invα wto − invα B

= 0,22 7737+ inv20° − inv 3,65305° =

= 0,2320635;

(2.82) e

= 0,5d

−h

tgλ

ϕ−h

tgα

− 0,5 d

wto

= [(0,5 20 − 3,4)tg0,22 7737]− (0,5 20 0,2320635 − 3,4 tg20°)= 0,075; (2.83) e = et cosα wto cosβw = 0,075 cos20° cos0° = 0,07.

Ⱦɨɥɠɧɨ ɛɵɬɶ a < e; a = 0, 2, e = 0,07. ɉɪɢɧɢɦɚɟɦ a = e = 0,07.

Ɍɨɝɞɚ b = ,78 – 0,07 = ,5. Ⱦɥɹ ɭɦɟɧɶɲɟɧɢɹ ɬɪɭɞɧɨɫɬɟɣ ɢɡɝɨɬɨɜɥɟɧɢɹ tg 5°

ɢɧɫɬɪɭɦɟɧɬɚ ɥɭɱɲɟ ɩɪɢɧɹɬɶ ɜɚɪɢɚɧɬ ɨɮɨɪɦɥɟɧɢɹ ɭɫɢɤɚ – δ ɩɨ ɪɢɫ. 2.5. Ɂɞɟɫɶ c = ,78, h y = ,67, a = 0,07, rɝ= 0,05.

5. (2.84) hf

= 0,075 m + 0,35 = 0,075 3 + 0,35 = 0,57; ɩɪɢɧɢɦɚɸ

= 0,6; f = 0,05 m = 0,05 3= 0, 5.

(2.85)

αɮɨ = α wo + 0° = 20° + 0° = 30° ;

(2.86)

dA = da − 2hf = 26 − 2 0,6= 24,8;

(2.87)

αA

= arccos

dw cosα wo

20 cos20°

= 25,37 8° ;

24,8

(2.88)

αɮA = arccos

dw cosαɮɨ

= arccos

cos30°

= 33,62 °

24,8

(2.89) hɮɨ =

d (invα wo − invαA − invαɮɨ + invαɮȺ )

+ hno =

2(tg30° − tg20°)

= 20(inv20° − inv25,37 8° − inv30° + inv33,62 °)+

( ) 3,75= 5,964; 2 tg30° − tg20°

(2.90) αɚɨɫɧ

d cosα

20 cos20$

= arccos

26,49854

= d

(

+ invα

− invα

) =

ɨɫɧ

(2.9 )

ɨɫɧ

4,732

= 26(

+ inv20° − inv26,49854°) = 2,303

(2.92)SA = dA

4,732

+invα w

−invα A

= 24,8

+inv20°−inv25,37 8° =

2,862;

(2.93) αaɮ

= arccos

cosαɮɨ

= arccos

20 cos30°

= 94,433 4° ;

(2.94) Sɚɮ = da

+ invαɮɚ

− invαɚɮ =

2,862

= 26

+inv33,62 °−inv34,433 4° = 2,075:

27,8

(2.95) q =

Saɨɫɧ

− Sɚɮ

2,303

− 2,075

= 0, 4;

q < f ɧɚ 0,036 ɦɦ. ɉɨɷɬɨɦɭɩɪɢɧɢɦɚɟɦ αɮɨ = 35° , hɮɨ= 6 ɦɦ.

(2.8) rH = 0,3 m = 0,3 3 = 0,9.
6.	(2. 3) hao = hf = 3,75.
7.	(2. 4) D t = dao - 2 hao - 0,4 k = 80 - 2 3,75 - 0,4 5,5 = 70,3.
8.	(2. 5) ωt = arcsin	m i	= arcsin	3	= 2,44579 ° = 2° 26'45".

		Dt		70,3

ɇɚɩɪɚɜɥɟɧɢɟ ɜɢɧɬɨɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɢ – ɩɪɚɜɨɟ.

9. (2. 6) Hɤ = h0	+	K + K	+ 2 = 7,65 +	4 + 6	+ = 3,05.

	2		2

ɉɪɢɧɢɦɚɟɦ ɇɤ = 4. 20.Θ = 30° .

2 .

(2. 7) r = π (dao −2Hɤ ) / 0 z0 = 3, 4(80 -2 8) / 0 0 = ,38, ɩɪɢɧɢɦɚɸ r

= ,5

22.

ɇɚɩɪɚɜɥɟɧɢɟ ɫɬɪɭɠɟɱɧɨɣ ɤɚɧɚɜɤɢ ɧɨɪɦɚɥɶɧɨɟ

ɤ ɱɟɪɜɹɱɧɨɣ ɧɚɪɟɡɤɟ, ɬ.ɟ.

ɥɟɜɨɟ ɢ (2. 8) ω ɤ =ωt = 2°26'.

(2. 9)

= π Dɤ

3, 4 70,3

= 5 68.

tgωɤ

tg2°26'

23.

(2. 20) Dwo =dao −2hno −0,4 k =80−2 3,75−0,4 5,5= 70,3

70,3

24.

tg2,44579 ° =2°26'45"

(2. 2 ) ω=arctg

tgωt =arctg

70,3

Dwo

25.

(2. 22)

Pwo i

9,725

= 9,433.

cosω

cos2,44579 °

26.(2. 23) ψ = β + ωt = 0° + 2°26'= 2° 26'

27.ɉɪɨɮɢɥɢɪɨɜɚɧɢɟ ɧɚ ɨɫɧɨɜɟ ɤɨɧɜɨɥɸɬɧɨɝɨ ɱɟɪɜɹɤɚ ɢ ɩɨɷɬɨɦɭ ɧɚ ɪɚɛɨɱɟɦ ɱɟɪɬɟɠɟ ɩɪɨɮɢɥɶ ɡɭɛɶɟɜ ɩɨɤɚɡɵɜɚɟɬɫɹ ɬɨɥɶɤɨ ɜ ɧɨɪɦɚɥɶɧɨɦ ɫɟɱɟɧɢɢ ɤ ɜɢɧɬɨ-

ɜɨɣ ɥɢɧɢɢ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ.

28.(2. 24) Pto = π m = π 3= 9,425.

29.(2. 25) Sto = Sno + 2 tgα wo (hao − hno )= 4,693 + 2 tg20° (3,75 − 3,75)= =4,693

30. (2. 26) Poc.o =	Pwo	9,425		= 9,433.
		=
	cosω		cos2,44579 °

3 . (Ɍɚɛɥ.2.3) d = 50; l = 5; (Ɍɚɛɥ.2.4) bn = 8C ; C = 34,8 H 2; R = 0,9+0,3 ; L = 25; (2.30) lɲ = 0,3 L = 0,3 25 = 40

dɜ = dɨɬɜ + 2 = 32 + 2 = 34

Ɋɚɛɨɱɢɣ ɱɟɪɬɟɠ ɱɟɪɜɹɱɧɨɣ ɮɪɟɡɵ ɩɨɞ ɲɟɜɟɪ ɩɨɤɚɡɚɧ ɧɚ ɪɢɫ.ɉ 3. .

Ʉ ɮɪɟɡɚɦ ɩɪɟɞɴɹɜɥɹɸɬɫɹ ɫɥɟɞɭɸɳɢɟ ɬɟɯɧɢɱɟɫɤɢɟ ɬɪɟɛɨɜɚɧɢɹ.

. HRCɷ 64...66.

2.ɇɚ ɜɫɟɯ ɩɨɜɟɪɯɧɨɫɬɹɯ ɮɪɟɡ ɧɟ ɞɨɥɠɧɨ ɛɵɬɶ ɬɪɟɳɢɧ, ɡɚɭɫɟɧɰɟɜ ɢ ɫɥɟɞɨɜ ɤɨɪɪɨɡɢɢ.

3.ɇɟɩɨɥɧɵɟ ɜɢɬɤɢ ɩɪɢɬɭɩɢɬɶ ɞɨ ɬɨɥɳɢɧɵ ɜɟɪɯɧɟɣ ɱɚɫɬɢ ɡɭɛɚ ɧɟ ɦɟɧɟɟ 0,5

ɦɨɞɭɥɹ.

4.ɉɪɹɦɨɥɢɧɟɣɧɨɫɬɶ ɢ ɧɚɤɥɨɧ ɥɢɧɢɢ ɩɟɪɟɫɟɱɟɧɢɹ ɩɟɪɟɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɢ ɩɥɨɫɤɨɫɬɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɨɫɢ ɮɪɟɡɵ, ɧɚ ɪɚɛɨɱɟɣ ɜɵɫɨɬɟ ɡɭɛɚ ≤ 0,04.

5.ɇɚɤɨɩɥɟɧɧɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɨɤɪɭɠɧɨɝɨ ɲɚɝɚ ɫɬɪɭɠɟɱɧɵɯ ɤɚɧɚɜɨɤ ≤ 0,08.

6.Ɉɬɤɥɨɧɟɧɢɟ ɩɟɪɟɞɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɨɬ ɧɨɦɢɧɚɥɶɧɨɝɨ ɪɚɫɩɨɥɨɠɟɧɢɹ, ɨɬɧɟ-

ɫɟɧɧɨɟ ɤ 00 ɦɦ ɞɥɢɧɵ ɪɚɛɨɱɟɣ ɱɚɫɬɢ ɮɪɟɡɵ ≤ ± 0, .

7.ɉɨɝɪɟɲɧɨɫɬɶ ɡɚɰɟɩɥɟɧɢɹ ɨɬ ɡɭɛɚ ɤ ɡɭɛɭ ≤ 0,0 2.

8.ɉɨɝɪɟɲɧɨɫɬɶ ɡɚɰɟɩɥɟɧɢɹ ≤ 0,022.

9.ɉɪɟɞɟɥɶɧɨɟ ɨɬɤɥɨɧɟɧɢɟ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜɟɪɫɬɢɹ 32ɇ6 ɞɨɥɠɧɨ ɛɵɬɶ ɜɵ-

ɞɟɪɠɚɧɨ ɧɚ 24 ɦɦ ɞɥɢɧɵ ɤɚɠɞɨɝɨ ɩɨɫɚɞɨɱɧɨɝɨ ɩɨɹɫɤɚ.

0. Ⱦɨɩɭɫɤɚɟɦɨɟ ɫɦɟɳɟɧɢɟ ɲɩɨɧɨɱɧɨɝɨ ɩɚɡɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɩɨɫɚɞɨɱɧɨɝɨ ɨɬɜ. 32ɇ6 ≤ 0,09.

. ɇɟɭɤɚɡɚɧɧɵɟ ɩɪɟɞɟɥɶɧɵɟ ɨɬɤɥɨɧɟɧɢɹ ɪɚɡɦɟɪɨɜ: ɨɬɜɟɪɫɬɢɣ - ɩɨ ɇ 4, ɜɚ-

ɥɨɜ - h 4, ɨɫɬɚɥɶɧɵɯ + (IT 4)/2.

2. Ɇɚɪɤɢɪɨɜɚɬɶ: m =3, α = 20° , ɤɥ.ȼ, ωt = 2° 26' Pz = 5 68, P6M5K5.

ɉɪɢɥɨɠɟɧɢɟ 4.

ɉɪɢɦɟɪ ɪɚɫɱɟɬɚ ɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɞɨɥɛɹɤɚ ɞɥɹ ɧɚɪɟɡɚɧɢɹ ɡɭɛɶɟɜ ɤɨɥɟɫ

Ɋɚɫɫɱɢɬɚɬɶ ɢ ɫɩɪɨɟɤɬɢɪɨɜɚɬɶ ɞɨɥɛɹɤ ɞɥɹ ɧɚɪɟɡɚɧɢɹ ɡɭɛɶɟɜ ɤɨɥɟɫɚ ɫ ɩɚ-

ɪɚɦɟɬɪɚɦɢ: α = 20° , m= 3 ɦɦ, z = 25, h*a = , h*l = 2, h*f = ,25; β = 22° , x =0; 7

ɫɬ. ɬɨɱɧɨɫɬɢ ɫ ɫɨɩɪɹɠɟɧɢɟɦ «ɋ» ɩɨ ȽɈɋɌ 6-443-8 , ɧɚɯɨɞɹɳɟɝɨɫɹ ɜ ɡɚɰɟɩ-

ɥɟɧɢɢ ɫ ɡɭɛɱɚɬɵɦ ɤɨɥɟɫɨɦ m = 3 ɦɦ, z2 = 75, ɯ2 = 0 ɬɨɣ ɠɟ ɫɬɟɩɟɧɢ ɬɨɱɧɨɫɬɢ.

Ɉɩɪɟɞɟɥɟɧɢɟ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɡɭɛɱɚɬɵɯ

ɤɨɥɟɫ

. ( . ) d

3 25

= 80,89; d

mz2

3 75

= 242,67.

cosβ

cos22°

cosβ

cos22°

2. ( .2) α t

= arctg

tgα

= arctg

tg20°

= 2 ,4327° ;

cos22°

cosβ

mt = m cosβ = 3 cos22° = 3,2356.

3.( .3) db = d cosα t = 80,890 cos2 ,4327° = 75,296;

db2 = d2 cosα t = 242,67 cos2 ,4327° = 225,889.

4.( .4) x = x2 = 0 :α tw = α t = 2 ,4327° .

5.	( .8) aw = [0,5 m (z + z2 ) cosα t ] (cosα tw cosβ)=
	= [0,5 3 (25 + 75) cos2 ,4327°] (cos2 ,4327° cos22°)= 6 ,78.
6.	( .9)	ɭ = 0.
7.	( . ) da = d + 2(h*a + x −		y) m = 80,89 + 2( + 0 − 0) 3 = 86,89;
	da	= d2 + 2(h*a + x2 −	y) m = 242,67 + 2( + 0 − 0) 3= 248,67.
		2

8.( . 2) h =(2h*a + c* − y) m = (2 + 0,25 − 0) 3= 6,75.

9.( . 5) df = da − 2h = 86,89 − 2 6,75= 73,39;

df	2	= da	− 2h = 248,67 − 2 67 = 235, 7.
	2		2
0. ( . 6)		Sn = 0,5 π m + 2 x m tgα − Ecs = 0,5 π 3 + 2 0 tg20° − 0,07 =
= 4,642;

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