Cálculo para obtenção de curvas de nível

Segmento 12:

1 (-90,000; 25,000; 41,630)

2 (0,000; -100,000; 39,500)

x² = (90)² + (-125)² x²= 8100 + 15625 154,029m

Desnível 41,630 – 39,500 = 2,130m

154,029 - 2,130

X - 0,630 x = 45,558m C.N. = 41m

154,029 - 2,130

X - 1,630 x = 47,272m C.N. = 40m

Segmento 23:

2 (0,000; -100,000; 39,500)

3 (95,000; -35,000; 37,300)

x² = (95)² + (65)² x²= 9025 + 4225 115,109m

Desnível 39,500 – 37,300 = 2,200m

115,109 - 2200

X - 0,500 x = 26,161m C.N. = 39m

115,109 - 2,200

X - 1,500 x = 78,483m C.N. = 38m

Segmento 34:

3 (95,000; -35,000; 37,300)

4 (172,000; -98,000; 36,500)

x² = (77)² + (63)² x²= 5929 + 3969 99,489m

Desnível 37,300 – 36,500 = 0,800m

99,489 - 0,800

X - 0,300 x = 37,308 C.N. = 37m

Segmento 45:

4 (172,000; -98,000; 36,500)

5 (233,000; 50,000; 34,800)

x² = (61)² + (148)² x²= 3721 + 21904 160,078m

Desnível 36,500 – 34,800 = 1,700m

160,078 - 1,700

X - 0,500 x = 47,082m C.N. = 36m

160,078 - 1,700

X - 1,500 x = 141,245m C.N. = 35m

Segmento 56:

5 (233,000; 50,000; 34,800)

6 (190,000; 160,000; 36,350)

x ² = (-43)² + (110)² x²= 1849 + 12100 118,106m

Desnível 36,350 – 34,800 = 1,550m

118,106 - 1,550

X - 0,350 x = 26,669m C.N. = 36m

118,106 - 1,550

X - 1,350 x = 102,867m C.N. = 35m

Segmento 67:

6 (190,000; 160,000; 36,350)

7 (60,000; 120,000; 39,500)

x ² = (-130)² + (-40)² x²= 16900 + 1600 136,015m

Desnível 39,500 – 36,350 = 3,150m

136,015 - 3,150

X - 0,500 x = 21,59m C.N. = 37m

136,015 - 3,150

X - 1,500 x = 64,769m C.N. = 38m

136,015 - 3,150

X - 2,500 x=107,948 C.N. = 39m

Segmento 78:

7 (60,000; 120,000; 39,500)

8 (30,500; 130,000; 39,200)

x² = (-29,5)² + (10)² x²= 870,25 + 100 31,149m

Desnível 39,500 – 39,200= 0,300m

Não há curva de nível.

Segmento 81:

8 (30,500; 130,000; 39,200)

1 (-90,000; 25,000; 41,630)

x² = (-120,500)² + (-105)² x²= 14520,25 + 11025 159,829m

Desnível 41,630 – 39,200 = 2,430m

159,829 - 2,430

X - 0,630 x = 41,437m C.N. = 41m

159,829 - 2,430

X - 1,630 x = 107,210m C.N. = 40m

Segmento 1E:

1 (-90,000; 25,000; 41,630)

E (25,000; 30,000; 39,900)

x ² = (115)² + (5)² x²= 13225 + 25 115,109m

Desnível 41,630 – 39,900 = 1,730m

115,109- 1,730

X - 0,630 x = 41,418m C.N. = 41m

115,109 - 1,730

X - 1,630 x = 108,455m C.N. = 40m

Segmento 2E:

2 (0,000; -100,000; 39,500)

E (25,000; 30,000; 39,900)

x²=(25)² + (130)² x²= 625 + 16900 132,382m

Desnível 39,900 - 39,500 = 0,400m

Não há curva de nível.

Segmento 3E:

3 (95,000; -35,000; 37,300)

E (25,000; 30,000; 39,900)

x² = (-70)² + (65)² x²= 4900 + 4225 95,525m

Desnível 39,900 - 37,300 = 2,600m

95,525 - 2,600

X - 0,900 x = 33,066m C.N. = 39m

95,525 - 2,600

X - 1,900 x = 69,806m C.N. = 38m

Segmento 4E:

4 (172,000; -98,000; 36,500)

E (25,000; 30,000; 39,900)

x² = (-147)² + (128)² x² = 21609 + 16384 194,918m

Desnível 39,900 - 37,300 = 3,400m

194,918 - 3,400

X - 0,900 x= 51,596m C.N. = 39m

194,918 - 3,400

X - 1,900 x = 108,925m C.N. = 38m

194,918 - 3,400

X - 2,900 x = 166,253m C.N. = 37m

Segmento 5E:

5 (233,000; 50,000; 34,800)

E (25,000; 30,000; 39,900)

x² = (-208)² + (-20)² x²= 43264 + 400 208,959m

Desnível 39,900 - 34,800 = 5,100m

208,959 - 5,100

X - 0,900 x = 36,875m C.N. = 39m

208,959 - 5,100

X - 1,900 x = 77,847m C.N. = 38m

208,959 - 5,100

X - 2,900 x = 118,820m C.N. = 37m

208,959 - 5,100

X - 3,900 x = 159,792 C.N. = 36m

208,959 - 5,100

X - 4,900 x = 200,764 C.N. = 35m

Segmento 6E:

6 (190,000; 160,000; 36,350)

E (25,000; 30,000; 39,900)

x ² = (-165)² + (-130)² x²= 27225 + 16900 210,059m

Desnível 39,900 - 36,350 = 3,550m

210,059 - 3,550

X - 0,900 x = 53,254m C.N. = 39m

210,059 - 3,550

X - 1,900 x = 112,426m C.N. = 38m

210,059 - 3,550

X - 2,900 x = 171,597m C.N. = 37m

Segmento 7E:

7 (60,000; 120,000; 39,500)

E (25,000; 30,000; 39,900)

x² = (-35)² + (-90)² x²= 1225 + 8100 96,566m

Desnível 39,900 - 39,500 = 0,400m

Não há curva de nível

Segmento 8E:

8 (30,500; 130,000; 39,200)

E (25,000; 30,000; 39,900)

x² = (-5,500)² + (-100)² x²= 30,250 + 10000 100,151m

Desnível 39,900 - 39,200 = 0,700m

Não há curva de nível

Calculo de área através de triangulos

Formula: A =

Triangulo E12

A=

A = 7412,514m²

Triangulo E23

A=

A = 5362,519m²

Triangulo E34

A=

A = 282,110m²

Triangulo E45

A=

A = 14782,120m²

Triangulo E56

A=

A = 11869,985m²

Triangulo E67

A=

A = 5147,234m²

Triangulo E78

A=

A = 1502,507m²

Triangulo E81

A=

A = 5736,355m²

ATOTAL = A1 +A2 + A3 +A4 + A5 + A6 + A7 + A8

ATOTAL = 52095,344 m²

Ângulos do internos polígono.

Obtidos através de AutoCAD.

812 = 95°

123 = 91°

234 = 254°

345 = 73°

456 = 136°

567 = 94°

678 = 216°

781= 121°

Cálculo dos Ângulos internos

1)

Coss= 56°44’8”

Coss= 38°34’42’’

1= 95°20’06’’

2)

Coss= 44°44’3”

Coss= 46°38’23’’

2= 91°22’26’’

3)

Coss= 78°56’30”

Coss= 176°24’12’’

3= 255°20’52’’

4)

Coss= 11°45’42”

Coss= 61°21’07’’

4 = 73°06’49’’

5)

Coss= 71°08’38”

Coss= 62°06’30

5 = 136°15’08’’

6)

Coss= 73°07’00”

Coss= 21°06’15

6 = 94°13’15’’

7)

Coss= 128°24’14”

Coss= 87°33’57

7 = 215°58’11’’

8)

Coss= 74°19’50”

Coss= 45°47’03”

8 = 120°06’53’’

Cálculo da Escala

Epx = Epy =

Epx = Epy =

Epx = Epy =

Usar escala

Cordenadas centrais

Xc=71,500 Yc=30,00