Rumus Perhitungan Poligon Tertutup

Hitungan besar sudut (terhitung)

ᵝn = ᵝ_n.n_-₁ - ᵝ_n.n₊₁

ᵝ1 = ᵝ_1.15- ᵝ_1.₂

= (265°35’25” –86°31’50”) = 179°3’35”

ᵝ2 = ᵝ_2.₁- ᵝ_2.₃

= (329°27’20” –69°52’25” ) = 259°34’55”

ᵝ3 = ᵝ_3.2- ᵝ_3.₄

= (193°1’40” –82°50’35”) = 110°11’5”

ᵝ4 = ᵝ_4.3 - ᵝ_4.5

= (258°30’40” – 14°54’30”) = 243°36’10”

ᵝ5 = ᵝ_5.4 - ᵝ_5.6

= (197°21’20” – 343°44’10”) = 213°17’10”

ᵝ6 = ᵝ_6.5- ᵝ_6.7

= (161°28’25” – 255°33’25”) = 265°55’0”

ᵝ7 = ᵝ_7.6- ᵝ_7.8

= (70°14’45” – 302°31’50”) = 127°44’55”

ᵝ8 = ᵝ_8.7- ᵝ_8.9

= (126°29’55” – 262°39’40”) = 223°50’15”

ᵝ9 = ᵝ_9.8 - ᵝ_9.10

= (86°1’5” – 236°40’35”) = 209°20’30”

ᵝ10 = ᵝ_10.9- ᵝ_10.11

= (60°39’5” – 286°25’30”) = 134°13’35”

ᵝ11 = ᵝ_11.1₀- ᵝ_11.12

= (102°6’35” – 249°33’5”) = 212°33’30”

ᵝ12 = ᵝ_12.11 - ᵝ_12.13

= (75°44’5” – 182°27’35”) = 253°16’30”

ᵝ13 = ᵝ_13.12 - ᵝ_13.14

= (355°13’25” – 177°52’45”) = 177°20’40”

ᵝ14 = ᵝ_14.13 - ᵝ_14.15

= (3°30’0” – 93°47’40”) = 269°44’20”

ᵝ15 = ᵝ_15.14 - ᵝ_15.1

= (268°57’25” – 89°6’0”) = 179°51’25”

∑ βὶ = 3059^o59’45”

Hitungan koreksi salah penutup sudut

= (n+2) x 180 -

= (15+ 2) x 180°– 3059^o59’45”

= 3060^o00’00” – 3059^o59’45”

= 0°00’15”

= 0° 00’ 1”

Hitungan koreksi besar sudut (terkoreksi)

= +

₁ = _1.2 +

= 179°3’35” + 0°0’1” = 179°3’36”

₂_.3 = _2.3 +

=259°34’55” + 0°0’1” = 259°34’56”

₃_.4 = _3.4 +

=110°11’5” + 0°0’1” = 110°11’6”

₄_.5 = _4.5 +

=243°36’10” + 0°0’1” = 243°36’11”

_5.6 = _5.6 +

= 213°17’10” + 0°0’1” = 213°17’11”

_6.7 = _6.7 +

= 265°55’0” + 0°0’1” = 265°55’1”

_7.8 = _7.8 +

=127°44’55” + 0°0’1” = 127°44’56”

_8.9 = _8.9 +

= 223°50’15” + 0°0’1” = 223°50’16”

_9.10 = _9.10 +

= 209°20’30” + 0°0’1” = 209°20’31”

_10.11 = _10.11 +

= 134°13’35” + 0°0’1” = 134°13’36”

_11.12 = _11.12 +

= 212°33’30” + 0°0’1” = 212°33’31”

_12.13 = _12.13 +

= 253°16’30” + 0°0’1” = 253°16’31”

_13.14 = _13.14 +

= 177°20’40” + 0°0’1” = 177°20’41”

_14.15 = _14.15 +

= 269°44’20” + 0°0’1” = 269°44’21”

_15.1 = _15.1₆+

= 179°51’25” + 0°0’1” = 179°51’26”

= 3060°0’0”

Hitungan besar sudut jurusan ( )

Patok utama

___

_1.2 = _awal= terukur

_1.= 86°31’50”

____ ___ ___

_2.3= ( _1.2+ _2.3)- 180

= (86°31’50”+ 259°34’56”) – 180° = 165°5’46”

___ ___ ___

_3.4= ( _2.3+ _3.4)- 180

= (165°5’46”+ 110°11’6”)– 180 = 96°16’52”

___ ___ ___

_4.5= ( _3.4+ _4.5)- 180

= (96°16’52”+ 243°36’11”)– 180 = 159°52’3”

___ ___ ___

_5.6= ( _4.5+ _5.6)- 180

= (159°52’3”+ 213°17’11”)– 180 = 193°9’14”

___ ___ ___

_6.7= ( _5.6+ _6.7)- 180)

= (193°9’14”+ 265°55’1”) -180) = 279°4’15”

___ ___ ___

_7.8 = ( _6.7+ _7.8)- 180

= (279°4’15”+ 127°44’56”) – 180 = 226°48’11”

___ ___ ___

_8.9 = ( _7.8+ _8.9)- 180

= (226°48’11”+ 223°50’16”)– 180 = 270°38’27”

___ ___ ___

_9.10 = ( _8.9+ _9.10)- 180

= (270°38’27”+ 209°20’31”)– 180 = 300°58’58”

___ ___ ___

_10.11= ( _9.10+ _10.11)- 180

= (300°58’58”+ 134°13’36”) – 180 = 254°16’34”

___ ___ ___

_11.12= ( _10.11+ _11.12)- 180

= (254°16’34”+ 212°33’31”)– 180 = 286°50’5”

___ ___ ___

_12.13= ( _11.12+ _12.13)- 180 - 360

= (286°50’5”+ 253°16’31”) – 180 - 360 = 0°6’36”

___ ___ ___

_13.14= ( _12.13+ _13.14) + 180

= (0°6’36”+ 177°20’41”) + 180 = 357°27’17”

___ ___ ___

_14.15 = ( _13.14+ _14.15)- 180 - 360

= (357°27’17”+ 269°44’21”)– 180 - 360 = 87°11’39”

___ ___ ___

_15.1 = ( _14.1₅+ _15.1)- 180

= (87°11’39”+ 179°51’26”) – 180 = 87°3’5”

Hitungan Jarak (m)

d_{ij op}= (Ba – Bb) x COS²m

d_{ij op1.2}= (1467 – 1124) =34,300 m

d_{ij op1.}₁₅= (1848 – 1503) = 34,500 m

d_{ij op2.3}= (1087 – 899) = 18,800 m

d_{ij op2.1}= (1810– 1467) = 34,300 m

d_{ij op3.4}= (1383 – 1142) = 24,100 m

d_{ij op3.2}= (1555 – 1365) =19,000 m

d_{ij op4.5}= (893 – 617) = 27,600 m

d_{ij op4.3}= (924 – 683) =24,100 m

d_{ij op5.6}= (732 – 409) = 32,300 m

d_{ij op5.4}= (1588 – 1313) = 27,500 m

d_{ij op6.7}= (1911 – 1662) = 24,900 m

d_{ij op6.5}= (1856 – 1533) = 32,300 m

d_{ij op7.8}= (399 – 191) = 20,800 m

d_{ij op7.6}= (742 – 493) = 24,900 m

d_{ij op8.9}= (1972 – 1754) = 21,800 m

d_{ij op8.7}= (2228 – 2019) = 20,900 m

d_{ij op9.10}= (1891 – 1667) = 22,400 m

d_{ij op9.8}= (911 – 693) = 21,800 m

d_{ij op10.11}= (990 – 713) = 27,700 m

d_{ij op10.9}= (978 – 754) = 22,400 m

d_{ij op11.12}= (1807 – 1589) = 21,800 m

d_{ij op11.10}= (1558 – 1280) = 27,800 m

d_{ij op12.13}= (990– 713) = 27,700 m

d_{ij op12.11}= (2491– 1883) = 40,900 m

d_{ij op13.14}= (1580 – 1267) = 31,300 m

d_{ij op13.12}= (978 – 563) = 41,500 m

d_{ij op14.15}= (1376 – 1061) = 31,500 m

d_{ij op14.13}= (1150 – 835) = 31,500 m

d_{ij op15.1}= (1378– 1031) = 34,700 m

d_{ij op1}₅_.1₄= (1695 – 1379) = 31,600 m

d_ij= d_{ij op}+ d_{ij uk}

d_ij1.2= 34,300 + 34,200 = 34,250

d_ij2.3=18,900 + 18,800 = 18,850

d_ij3.4= 24,100 + 24,000 = 24,050

d_ij4.5= 27,550 + 27,600 = 27,575

d_ij5.6= 32,300 + 32,200 = 32,250

d_ij6.7= 24,900 + 24,880 = 24,890

d_ij7.8= 20,850 + 20,900 = 20,875

d_ij8.9= 21,800 + 21,800 = 21,800

d_ij9.10= 22,400 + 22,380 = 22,390

d_ij10.11= 27,750+ 27,700 = 27,725

d_ij11.12= 21,800 + 21,850 = 21,825

d_ij12.13= 41,400 + 41,300 = 41,350

d_ij13.14= 31,400 + 31,500 = 31,450

d_ij14.15= 31,550 + 31,550 = 31,550

d_ij15.1= 34,500 + 34,600 = 34,550

Hitungan selisih koordinat ( X dan Y)

_ _

X_n.n+1= d_n.n+1SIN _n.n+1

_ _

X_1.2= d_1.2SIN _1.2

= 34,300x SIN 86°31’50” = 34,179

_ _

X_2.3= d_2.3SIN _2.3

= 18,850 x SIN 165°5’46” = 4,589

_ _

X_3.4= d_3.4SIN _3.4

= 24,050 x SIN 96°16’52” = 23,913

_ _

X_4.5= d_4.5SIN _4.5

= 27,575 x SIN 159°52’3” = 9,553

_ _

X_5.6= d_5.6SIN _5.6

= 32,250 x SIN 193°9’14” = -7,445

_ _

X_6.7= d_6.7SIN _6.7

= 24,890 x SIN 279°4’15” = -24,568

_ _

X_7.8= d_7.8SIN _7.8

= 20,875 x SIN 226°48’11” = -15,258

_ _

X_8.9= d_8.9SIN _8.9

= 21,800 x SIN 270°38’27” = -21,798

_ _

X_9.10= d_9.10SIN _9.10

= 22,390 x SIN 300°58’58” = -19,356

_ _

X_10.11= d_10.11SIN _10.11

= 27,725x SIN 254°16’34” = -26,706

_ _

X_11.12= d_11.12SIN _11.12

= 21,825 x SIN 286°50’5” = -20,872

_ _

X_12.13= d_12.13SIN _12.13

= 41,350 x SIN 0°6’36” = 0,203

_ _

X_13.14= d_13.14SIN _13.14

= 31,450 x SIN 357°27’17” = -1,294

_ _

X_14.15= d_14.15SIN _14.15

= 31,550 x SIN 87°11’39” = 31,517

_ _

X_15.1= d_15.1SIN _15.1

= 34,550 x SIN 87°3’5” = 34,510

= 1,158

_ _

Y_n.n+1= d_n.n+1COS _n.n+1

_ _

Y_1.2= d_1.2COS _1.2

= 34,300x COS 86°31’50” = 2,203

_ _

Y_2.3= d_2.3COS _2.3

= 18,850 x COS 165°5’46” = -18,283

_ _

Y_3.4= d_3.4COS _3.4

= 24,050 x COS 96°16’52” = -2,560

_ _

Y_4.5= d_4.5COS _4.5

= 27,575 x COS 159°52’3” = -25,867

_ _

Y_5.6= d_5.6COS _5.6

= 32,250 x COS 193°9’14” = -31,337

_ _

Y_6.7= d_6.7COS _6.7

= 24,890 x COS 279°4’15” = 3,993

_ _

Y_7.8= d_7.8COS _7.8

= 20,875 x COS 226°48’11” = -14,247

_ _

Y_8.9= d_8.9COS _8.9

= 21,800 x COS 270°38’27” = 0,311

_ _

Y_9.10= d_9.10COS _9.10

= 22,390 x COS 300°58’58” = 11,254

_ _

Y_10.11= d_10.11COS _10.11

= 27,725x COS 254°16’34” = -7,448

_ _

Y_11.12= d_11.12COS _11.12

= 21,825 x COS 286°50’5” = 6,378

_ _

Y_12.13= d_12.13COS _12.13

= 41,350 x COS 0°6’36” = 41,350

_ _

Y_13.14= d_13.14COS _13.14

= 31,450 x COS 357°27’17” = 31,423

_ _

Y_14.15= d_14.15COS _14.15

= 31,550 x COS 87°11’39” = 1,451

_ _

Y_15.1= d_15.1COS _15.1

= 34,550 x COS 87°3’5” = 1,666

= 0,246

Hitungan besar f_x dan f_y

fx = (X_akhir - X_awal) -

fx = (X_akhir– X_awal ) -

= (0,0 ) – (1,158) = -1,158

fy = (Y_akhir - Y_awal) -

fy = (Y_akhir – Y_awal ) -

= (0) – (0,246) = -0,246

Hitungan selisih/koreksi absis dan ordinat (Metode Bowdith)

__ _

_n.n+1 = _n.n+1 + d_n.n+1x f_x

__ _

_1.2 = _1.2 + d_1.2 x f_x

= 34,179+ 34,300 x -1,158 = 34,084

415,380

__ _

_2.3 = _2.3 + d_2.3 x f_x

= 4,589 + 18,850 x –1,158 = 4,536

415,380

__ _

_3.4 = _3.4 + d_3.4 x f_x

= 23,913 + 24,050 x –1,158 = 23,846

415,380

__ _

_4.5 = _4.5 + d_4.5 x f_x

= 9,553+ 27,575 x -1,158 = 9,476

415,380

__ _

_5.6 = _5.6 + d_5.6 x f_x

= -7,445 + 32,250 x -1,158 = -7,545

415,380

__ _

_6.7 = _6.7 + d_6.7 x f_x

= -24,568 + 24,890 x –1,158 = -24,637

415,380

__ _

_7.8 = _7.8 + d_7.8 x f_x

= -15,258 + 20,875 x -1,158 = -15,316

415,380

__ _

_8.9 = _8.9 + d_8.9 x f_x

= -21,798 + 21,800 x -1,158 = -21,859

415,380

__ _

_9.10 = _9.10 + d_9.10 x f_x

= -19,356 + 22,390 x -1,158 = -19,419

415,380

__ _

_10.11 = _10.11 + d_10.11 x f_x

= -26,706 + 27,725 x -1,158 = -26,783

415,380

__ _

_11.12 = _11.12 + d_11.12 x f_x

= -20,872 + 21,825 x -1,158 = -20,933

415,380

__ _

_12.13 = _12.13 + d_12.13 x f_x

= 0,203 + 41,350 x -1,158 = 0,088

415,380

__ _

_13.14 = _13.14 + d_13.14 x f_x

= -1,294 + 31,450 x -1,158 = -1,381

415,380

__ _

_14.15 = _14.15 + d_14.15 x f_x

= 31,517 + 31,550 x -1,158 = 31,429

415,380

__ _

_15.1 = _15.1 + d_15.1₆ x f_x

= 34,510 + 34,550 x -1,158 = 34,414

415,380

__ _

_n.n+1 = _n.n+1 + d_n.n+1x f_y

__ _

_1.2 = _1.2 + d_1.2 x f_y

= 2,203+ 34,300 x -0,246 = 2,183

415,380

__ _

_2.3 = _2.3 + d_2.3 x f_y

= -18,823 + 18,850 x –0,246 = -18,294

415,380

__ _

_3.4 = _3.4 + d_3.4 x f_y

= -2,560 + 24,050 x –0,246 = 23,846

415,380

__ _

_4.5 = _4.5 + d_4.5 x f_y

= -25,867+ 27,575 x -0,246 = -25,884

415,380

__ _

_5.6 = _5.6 + d_5.6 x f_y

= -31,377 + 32,250 x -0,246 = -31,396

415,380

__ _

_6.7 = _6.7 + d_6.7 x f_y

= 3,993 + 24,890 x –0,246 = 3,978

415,380

__ _

_7.8 = _7.8 + d_7.8 x f_y

= -14,247 + 20,875 x -0,246 = -14,259

415,380

__ _

_8.9 = _8.9 + d_8.9 x f_y

= 0,311, + 21,800 x -0,246 = 0,298

415,380

__ _

_9.10 = _9.10 + d_9.10 x f_y

= 11,254 + 22,390 x -0,246 = 11,241

415,380

__ _

_10.11 = _10.11 + d_10.11 x f_y

= -7,448 + 27,725 x -0,246 = -7,465

415,380

__ _

_11.12 = _11.12 + d_11.12 x f_y

= 6,378+ 21,825 x -0,246 = 6,365

415,380

__ _

_12.13 = _12.13 + d_12.13 x f_y

= 41,350 + 41,350 x -0,246 = 41,325

415,380

__ _

_13.14 = _13.14 + d_13.14 x f_y

= 31,423 + 31,450 x -0,246 = 31,405

415,380

__ _

_14.15 = _14.15 + d_14.15 x f_y

= 1,451 + 31,550 x -0,246 = 1,432

415,380

__ _

_15.1 = _15.1₆ + d_15.1₆ x f_y

= 1,666 + 34,550 x -0,246 = 1,645

415,380

Hitungan koordinat definitif

X_n+1= X_n + _n.n+1

X_{1 =}260358

X₂= X₁ + _1.2

= 260358 + 34,084 = 260391,944

___{___}

X₃= X₂ + _2.3

= 260391,944 + 4,536 = 260396,480

___{__}

X₄= X₃ + _3.4

= 260396,480 + 23,846 = 260420,326

X₅= X₄ + _4.5

= 260420,326 + 9,476 = 260429,803

X₆= X₅ + ₅_.₆

= 260429,803 + (-7,545) = 260422,258

___{___}

X₇= X₆ + ₆_.₇

= 260422,258 + (-24,637) = 260397,621

___{___}

X₈= X₇ + _7.8

= 260397,621 + (-15,316) = 260382,305

___{___}

X₉= X₈ + ₈_.₉

= 260382,305 + (-21,859) = 260360,446

___{___}

X₁₀= X₉ + ₉_.₁₀

= 260360,446+ (-19,419) = 260341,028

___{___}

X₁₁= X₁₀ + ₁₀_.₁₁

= 260341,028 + (-26,783) = 260314,244

___{___}

X₁₂= X₁₁ + _11.12

= 260314,244 + (-20,933) = 260293,311

___{___}

X₁₃= X₁₂ + ₁₂_.₁₃

= 260293,311 + 0,088 = 260293,399

___{___}

X₁₄= X₁₃ + ₁₃_.₁₄

= 260293,399 + (-1,381) = 260292,018

___{___}

X₁₅= X₁₄ + ₁₄_.₁₅

= 260292,018 + 31,429 = 260323,446

___{___}

X₁= X₂₂ + ₂₂_.₁

= 260323,446 + 34,414 = 260359

Y_n+1= Y_n + _n.n+1

Y₁= 9618810

Y₂= Y₁ + _1.2

= 9618810 + 2,183 = 9618812,453

_{_}___{__}

Y₃= Y₂ + _2.3

= 9618812,453 + (-18,294) = 9618794,158

___{___}

Y₄= Y₃ + _3.4

= 9618794,158 + (-2,575) = 9618791,584

___{___}

Y₅= Y₄ + _4.5

= 9618791,584 + (-25,884) = 9718765,700

_{_} ___{__}

Y₆= Y₅ + _5.6

= 9718765,700 + (-31,396) = 9618734,305

___{___}

Y₇= Y₆ + _6.7

= 9618734,305 + 3,978 = 9618738,283

___{___}

Y₈= Y₇ + _7.8

= 9618738,283 + (-14,259) = 9618724,024

_{_} ___{__}

Y₉= Y₈ + _8.9

= 9618724,024+ 0,298 = 9618724,322

_{_}___{__}

Y₁₀= Y₉ + _9.10

= 9618724,322 + 11,241 = 9618735,562

___{___}

Y₁₁= Y₁₀ + _10.11

= 9618735,562 + (-7,465) = 9618728,098

___{___}

Y₁₂= Y₁₁ + ₁₁_.₁₂

= 9618728,098 + 6,365 = 9618734,462

_{__} ___{_}

Y₁₃= Y₁₂ + ₁₂_.₁₃

= 9618734,462 + 41,325 = 9618775,788

___{___}

Y₁₄= Y₁₃ + ₁₃_.₁₄

= 9618775,788 + 31,405 = 9618807,192

___{___}

Y₁₅= Y₁₄ + ₁₄_.₁₅

= 9618807,192 +1,432 = 9618808,625

___{___}

Y₁ = Y₁₉ + ₁₉_.₁

= 9618808,625 + 1,645 = 9618810

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