Pengukuran Poligon Tertutup Terikat Koordinat (1)

7/30/2019 Pengukuran Poligon Tertutup Terikat Koordinat (1)

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DATA PENGUKURAN POLIGON TERTUTUP TERIKAT KOORDINAT

299 34 2

51 16 1

0 0 0

136 37 2

0 0 0

128 39 2

0 0 0

99 55 5

0 0 0

117 22 5

0 0 0

263 17 5

0 0 0

42 26 2

BM03B = -21.69972222

P1 = -46.61722222P2 = -38.65055556

P3 = -9.918055556

P4 = -27.36805556

P5 = -173.2847222

BM03 = 47.56611111

= 899.9722222

42.43388889

111.6997222

136.6172222

128.6505556

99.91805556

117.3680556

263.2847222

"

299.5672222

51.26694444

0

136.6172222

0

128.6505556

0.300

1.588

BM03 (G) 1.281B

Baca

Tengah

Tinggi

Pesawat

Nomor / Nama

Titik

Kedudukan

Teropong

Bacaan Sudut Horizontal

3.020B B

1.400

BM03B (A) B

C B

1.461

B B 0.600

0.330

D B 1.280

0.735

1.563

C B0

99.91805556

F B 1.210

1.5510

117.3680556

1.300

Letak

Pesawat

BM03B

(A)

B

C

D

BM03 (G) B 0.780

1.485

E B

E

F

1.560

D B

E B

1.7250

263.2847222

0

42.43388889BM03B (A) B 1.660

0.930BM03

(G)1.400

F B


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n = 7 0.028


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Atas

Bawah

1.561 90 0 0

1.001

3.210 90 0 0

2.830

0.489 88 20 11

0.111

0.463 97 13 2

0.197

0.730 86 52 0

0.470

1.560 88 52 01.000

1.580 91 37 0

1.020

0.880 88 38 0

0.590

1.699 93 0 0

1.403

1.420 89 15 0

1.000

1.930 90 51 21.520

0.900 90 52 1

0.660

1.050 92 9 0

0.810

1.940 89 18 54

1.380

68.30027778

43.38277778

51.34944444

80.08194444

62.63194444

-83.28472222

137.5661111

90

90

88.33638889

97.21722222

86.86666667

88.86666667

37.7681413

56

Nomor /

Nama Titik

BM03 (G)

an Rambu

Jarak Datar

Bacaan Sudut Miring

"

38 B

C

25.92232016

26.1801653

B

55.97809206

BM03B (A)

D

41.99280382

29.51892405

91.61666667

88.63333333

93

55.95542735

E

F

C

D

28.98350336 E

23.99450566

40.99096533

89.25

BM03 (G)

BM03B (A)

F

90.85055556

90.86694444

92.15

89.31555.99199607

23.9662216


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0.143

1.666666667

0.238095238


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60.43277778 31.0841667

56.000000 dag (d1) = 55.99799895 0.9995785

dba (d2) = 37.89203364

38.000000 dcb (d3) = 26.17518939 0.999157177

ddc (d4) = 55.9833771

37.784067 ded (d5) = 29.27559237 0.866025404

dfe (d6) = 41.49594209

26.389248 dgf (d7) = 23.99017876 37.73630944

25.961131

37.7522220155.989045

55.977709

28.991751

29.559434

41.996402

40.995482

23.997253

23.983105

55.995998


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PERHITUNGAN SUDUT DALAM () DAN JARAK DATAR

1. Perhitungan Sudut Dalam ()

A = 51.26694444 - 299.5672222

= -248.3002778 ( ditambah 360)

= 111.6997222

B = 136.6172222

C = 128.6505556

D = 99.91805556

E = 117.3680556

F = 263.2847222

G = 42.43388889

2. Perhitungan Jarak Datar

Rumus Umum :

Jarak Datar = (BA - BB) x 100 x Sin2

V

a.) Jarak Titik A - G (d1)d1 --> Pesawat di Titik A (d1a) :

BA = 1.561

BT = 1.281

BB = 1.001

Sudut V = 90.00000000


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(BA - BB) = 1.561 - 1.001 = 0.56

Sin2

V = Sin2 90.00000000 = 1

d1a = (BA - BB) x 100 x Sin2

V

= 0.56 x 100 x 1= 56

d1 --> Pesawat di Titik G (d1g) :

BA = 1.940

BT = 1.660

BB = 1.380

Sudut V = 89.31500000

(BA - BB) = 1.94 - 1.38 = 0.56

Sin2

V = Sin2 89.31500000 = 0.999857073

d1g = (BA - BB) x 100 x Sin2 V

= 0.56 x 100 x 0.999857073

= 55.99199607

d1 --> Rata-rata :

d1 rata-rata = (d1a + d1g) / 2

56.0000000 + 55.99199607

2

b.) Jarak Titik A - B (d2)

d2 --> Pesawat di Titik A (d2a) :

BA = 3.210

BT = 3.020

BB = 2.830

Sudut V = 90.00000000

(BA - BB) = 3.21 - 2.83 = 0.38

Sin2

V = Sin2 90.00000000 = 1

d2a = (BA - BB) x 100 x Sin2

V

= 0.38 x 100 x 1

= 38

d2 --> Pesawat di Titik B (d2b) :

BA = 0.489

BT = 0.300

BB = 0.111

Sudut V = 88.33638889

(BA - BB) = 0.489 - 0.111 = 0.378

= = 55.99599804


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Sin2

V = Sin2 88.33638889 = 0.999157177

d2b = (BA - BB) x 100 x Sin2

V

= 0.378 x 100 x 0.999157177

= 37.7681413

d2 --> Rata-rata :

d2 rata-rata = (d2a + d2b) / 2

38.0000000 + 37.7681413

2

c.) Jarak Titik B - C (d3)

d3 --> Pesawat di Titik B (d3b) :

BA = 0.463

BT = 0.330

BB = 0.197Sudut V = 97.21722222

(BA - BB) = 0.463 - 0.197 = 0.266

Sin2

V = Sin2 97.21722222 = 0.984216741

d3b = (BA - BB) x 100 x Sin2

V

= 0.266 x 100 x 0.984216741

= 26.1801653

d3 --> Pesawat di Titik C (d3c) :

BA = 0.730

BT = 0.600

BB = 0.470

Sudut V = 86.86666667

(BA - BB) = 0.73 - 0.47 = 0.26

Sin2

V = Sin2 86.86666667 = 0.997012314

d3c = (BA - BB) x 100 x Sin2

V

= 0.26 x 100 x 0.997012314

= 25.92232016

d3 --> Rata-rata :d3 rata-rata = (d3b + d3c) / 2

26.1801653 + 25.92232016

2

= = 37.88407065

= = 26.05124273


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d.) Jarak Titik C - D (d4)

d4 --> Pesawat di Titik C (d4c) :

BA = 1.560

BT = 1.280

BB = 1.000Sudut V = 88.86666667

(BA - BB) = 1.56 - 1 = 0.56

Sin2

V = Sin2 88.86666667 = 0.999608787

d4c = (BA - BB) x 100 x Sin2

V

= 0.56 x 100 x 0.999608787

= 55.97809206

d4 --> Pesawat di Titik D (d4d) :

BA = 1.580

BT = 1.300BB = 1.020

Sudut V = 91.61666667

(BA - BB) = 1.58 - 1.02 = 0.56

Sin2

V = Sin2 91.61666667 = 0.99920406

d4d = (BA - BB) x 100 x Sin2

V

= 0.56 x 100 x 0.99920406

= 55.95542735

d4 --> Rata-rata :

d4 rata-rata = (d4c + d4d) / 2

55.9780921 + 55.95542735

2

e.) Jarak Titik D - E (d5)

d5 --> Pesawat di Titik D (d5d) :

BA = 0.880

BT = 0.735

BB = 0.590

Sudut V = 88.63333333

(BA - BB) = 0.88 - 0.59 = 0.29

Sin2 V = Sin2 88.63333333 = 0.99943115

d5d = (BA - BB) x 100 x Sin2

V

= 0.29 x 100 x 0.99943115

= 28.98350336

= = 55.96675971


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d5 --> Pesawat di Titik E (d5e) :

BA = 1.699

BT = 1.551

BB = 1.403

Sudut V = 93.00000000(BA - BB) = 1.699 - 1.403 = 0.296

Sin2

V = Sin2 93.00000000 = 0.997260948

d5e = (BA - BB) x 100 x Sin2

V

= 0.296 x 100 x 0.997260948

= 29.51892405

d5 --> Rata-rata :

d5 rata-rata = (d5d + d5e) / 2

28.9835034 + 29.51892405

2

f.) Jarak Titik E - F (d6)

d6 --> Pesawat di Titik E (d6e) :

BA = 1.420

BT = 1.210

BB = 1.000

Sudut V = 89.25000000

(BA - BB) = 1.42 - 1 = 0.42

Sin2

V = Sin2 89.25000000 = 0.999828662

d6e = (BA - BB) x 100 x Sin2 V

= 0.42 x 100 x 0.999828662

= 41.99280382

d6 --> Pesawat di Titik F (d6f) :

BA = 1.930

BT = 1.725

BB = 1.520

Sudut V = 90.86694444

(BA - BB) = 1.93 - 1.52 = 0.41

Sin2

V = Sin2 90.86694444 = 0.999771069

d6f = (BA - BB) x 100 x Sin2

V

= 0.41 x 100 x 0.999771069

= 40.99061384

= = 29.2512137


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d6 --> Rata-rata :

d6 rata-rata = (d6e + d6f) / 2

41.9928038 + 40.99061384

2

g.) Jarak Titik F - G (d7)

d7 --> Pesawat di Titik F (d7f) :

BA = 0.900

BT = 0.780

BB = 0.660

Sudut V = 90.86694444

(BA - BB) = 0.9 - 0.66 = 0.24

Sin2

V = Sin2 90.86694444 = 0.999771069

d7f = (BA - BB) x 100 x Sin2

V

= 0.24 x 100 x 0.999771069= 23.99450566

d7 --> Pesawat di Titik G (d7g) :

BA = 1.050

BT = 0.930

BB = 0.810

Sudut V = 92.15000000

(BA - BB) = 1.05 - 0.81 = 0.24

Sin2

V = Sin2 92.15000000 = 0.998592567

d7g = (BA - BB) x 100 x Sin2 V

= 0.24 x 100 x 0.998592567

= 23.9662216

d7 --> Rata-rata :

d7 rata-rata = (d7f + d7g) / 2

23.9945057 + 23.9662216

2= = 23.98036363

= = 41.49170883


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Rekap Hasil Perhitungan Jarak Datar :

d1 = 55.99599804 m

d2 = 37.88407065 m

d3 = 26.05124273 m

d4 = 55.96675971 md5 = 29.25121370 m

d6 = 41.49170883 m

d7 = 23.98036363 m


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PERHITUNGAN KOORDINAT TITIK

Diketahui :

Koordinat Titik A :

XA = 433914.1438

YA = 9220458.1361

Koordinat Titik G :

XG = 433865.4380 48.70579178 433914.1438

YG = 9220485.7680 -27.63189703 9220458.1361

Sudut-Sudut Dalam () :

A = 111.6997222

B = 136.6172222

C = 128.6505556

D = 99.91805556

E = 117.3680556

F = 263.2847222

G = 42.43388889

= 899.9722222

Jumlah Titik Sudut :n = Jumlah Titik Sudut

= 6


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Ukuran Jarak Datar :

d1 = 55.99599804 m

d2 = 37.88407065 m

d3 = 26.05124273 m

d4 = 55.96675971 m

d5 = 29.2512137 m

d6 = 41.49170883 m

d7 = 23.98036363 m

d = 270.6213573 m

Keterangan :

Toleransi KPS = 7"n1 fx2 + fy2

200 di

1. Hitung Sudut Jurusan Awal (ag) dan Sudut Jurusan Akhir (ga)

Sudut Jurusan Awal (ag)

Xg - Xa

Yg - Ya

433865.4380 - 433914.1438

9220485.7680 - 9220458.1361

-48.7058

27.6319

= ArcTan -1.762665615 = -60.43277929

Berada di kuadran IV (sehingga + 360) = 299.5672207

Sudut Jurusan Akhir (ga)

Xa - Xg

Ya - Yg

433914.1438 - 433865.4380

9220458.1361 - 9220485.7680

48.7058

-27.6319

= ArcTan -1.762665615 = -60.43277929

Berada di kuadran II (sehingga + 180) = 119.5672207

= ArcTan = -1.762665615

-1.762665615

Ketelitian Relatif Jarak =

ag = ArcTan

= ArcTan

= ArcTan =

ga = ArcTan

ga = ArcTan


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2 Hitung Syarat Geometrik KPS (Kesalahan Penutup Sudut)

KPS = - ((n-2) x 180) - (ag - ga)

n = 6

= 899.9722222ag = 299.5672207ga = 119.5672207

((n-2) x 180) = 4 x 180 = 720

(ag - ga) = 299.5672207 - 119.5672207 = 180

KPS = - ((n-2) x 180) - (ag - ga)= 899.9722222 - 720 - 180

= -0.027777778

f = -KPS = 0.027777778

f 0.027777778n 6

Toleransi KPS = 7"n = 0.001944444 6= 0.004762897

Sehingga Vi memenuhi syarat Toleransi KPS (V1 < Toleransi KPS)

3. Sudut yang Dikoreksi

ikoreksi = i + Vi

Akoreksi = A + Vi= 111.6997222 + 0.00462963 = 111.7043519

Bkoreksi = B + Vi

= 136.6172222 + 0.00462963 = 136.6218519

Ckoreksi = C + Vi

= 128.6505556 + 0.00462963 = 128.6551852

Dkoreksi = D + Vi

= 99.91805556 + 0.00462963 = 99.92268519

Ekoreksi = E + Vi

= 117.3680556 + 0.00462963 = 117.3726852

Fkoreksi = F + Vi= 263.2847222 + 0.00462963 = 263.2893519

Gkoreksi = G + Vi

= 42.43388889 + 0.00462963 = 42.43851852

= = = 0.00462963Koreksi (Vi)


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4. Hitung Sudut Jurusan Masing-masing Titik

ag = 299.5672207ba = ag - 180 + A koreksi

= 299.5672207 - 180.0000000 + 111.7043519

= 231.2715726cb = ba - 180 + B koreksi

= 231.2715726 - 180.0000000 + 136.6218519

= 187.8934244

dc = cb - 180 + C koreksi

= 187.8934244 - 180.0000000 + 128.6551852

= 136.5486096

ed = dc - 180 + D koreksi

= 136.5486096 - 180.0000000 + 99.92268519

= 56.4712948

fe = ed - 180 + E koreksi

= 56.47129479 - 180.0000000 + 117.3726852

= -6.1560200

= 353.8439800

gf = fe - 180 + F koreksi

= 353.8439800 - 180.0000000 + 263.2893519

= 437.1333318

= 77.1333318

ga = gf - 180 + G koreksi

= 77.1333318 - 180.0000000 + 42.43851852

= -60.4281497

= 119.5718503

5. Hitung x ( Absis)

Xa - Xg

Sin ga

433914.1438 - 433865.4380

Sin 119.5718503

48.7058

0.8697375

Ya - Yg

Cos ga9220458.1361 - 9220485.7680

Cos 119.5718503

-27.6319

-0.49351462

dga 1 (d1) =

=

= = 56.00057487

dga 2 (d1) =

=

= = 55.99003323


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dga 1 + dga 2 56.00057487 + 55.99003323

2 2

= 55.99530405

Jarak Hasil Pembidikan Theodolite :

dba (d2) = 37.88407065 m

dcb (d3) = 26.05124273 m

ddc (d4) = 55.96675971 m

ded (d5) = 29.25121370 m

dfe (d6) = 41.49170883 m

dgf (d7) = 23.98036363 m

d = 214.62535926 m

x ( Absis) :

Xgf = d7 x sin gf= 23.98036363 x sin 77.1333318= 23.98036363 x 0.974890905

= 23.3782384

Xfe = d6 x sin fe= 41.49170883 x sin 353.8439800

= 41.49170883 x -0.107236218

= -4.449413949

Xed = d5 x sin ed= 29.25121370 x sin 56.4712948

= 29.25121370 x 0.833609197

= 24.38408076Xdc = d4 x sin dc= 55.96675971 x sin 136.5486096

= 55.96675971 x 0.687738922

= 38.490519

Xcb = d3 x sin cb= 26.05124273 x sin 187.8934244

= 26.05124273 x -0.137330869

= -3.577639796

Xba = d2 x sin ba= 37.88407065 x sin 231.2715726

= 37.88407065 x -0.780120096= -29.55412482

di . Sin i = 48.67165960

dga (d1) = =


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6. Hitung y ( Ordinat)

Ygf = d7 x cos gf= 23.98036363 x cos 77.13333182

= 23.98036363 x 0.222683011

= 5.340019576Yfe = d6 x cos fe= 41.49170883 x cos 353.84398

= 41.49170883 x 0.994233571

= 41.25244983

Yed = d5 x cos ed= 29.25121370 x cos 56.47129479

= 29.25121370 x 0.552354693

= 16.15704517

Ydc = d4 x cos dc= 55.96675971 x cos 136.5486096

= 55.96675971 x -0.725958108

= -40.629523

Ycb = d3 x cos cb= 26.05124273 x cos 187.8934244

= 26.05124273 x -0.990525231

= -25.80441322

Yba = d2 x cos ba= 37.88407065 x cos 231.2715726

= 37.88407065 x -0.625629792

= -23.70140323

di . Cos i = -27.38582487

7. Hitung Kesalahan Absis (fx)

fx = di . Sin i - (Xa - Xg)

di . Sin i = 48.67165960Xa = 433914.1438

Xg = 433865.4380

(Xa - Xg) = 433914.1438 - 433865.4380 = 48.7058

fx = di . Sin i - (Xa - Xg)

= 48.67165960 - 48.7058= -0.03414040


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8. Hitung Kesalahan Ordinat (fy)

fy = di . Cos i - (Ya - Yg)

di . Cos i = -27.38582487Ya = 9220458.1361

Yg = 9220485.7680(Ya - Yg) = 9220458.1361 - 9220485.7680 = -27.6319

fy = di . Cos i - (Ya - Yg)= -27.38582487 - -27.6319

= 0.24607513

Ketelitian Relatif Jarak :

1 fx2 + fy2

200 di

1

200

fx = -0.03414040

fy = 0.24607513

fx2 + fy2 = 0.248432161di = 214.62535926

fx2 + fy2 0.24843216di 214.62535926

Sehinggamemenuhi syarat Ketelitian Relatif Jarak

= 0.005 0.001157515

9. Hitung Koreksi Absis

VXgf = (d7 / d) x (-fx)23.98036363

214.62535926

VXfe = (d6 / d) x (-fx)41.49170883

214.62535926

VXed = (d5 / d) x (-fx)29.25121370

214.62535926

VXdc = (d4 / d) x (-fx)55.96675971

214.62535926

Ketelitian Relatif Jarak =

= 0.005

= = 0.001157515

= x 0.03414040 =

= x 0.03414040 = 0.006600075

0.00381455

= x 0.03414040 = 0.008902618

= x 0.03414040 = 0.004652983


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VXcb = (d3 / d) x (-fx)26.05124273

214.62535926

VXba = (d2 / d) x (-fx)

37.88407065214.62535926

10. Hitung Koreksi Ordinat

VYgf = (d7 / d) x (-fy)23.98036363

214.62535926

VYfe = (d6 / d) x (-fy)41.49170883

214.62535926

VYed = (d5 / d) x (-fy)29.25121370

214.62535926

VYdc = (d4 / d) x (-fy)55.96675971

214.62535926

VYcb = (d3 / d) x (-fy)26.05124273

214.62535926

VYba = (d2 / d) x (-fy)37.88407065

214.62535926

11. Hitung x ( Absis) yang Terkoreksi

Xgfkor = Xgf + VXgf= 23.3782384 + 0.00381455 = 23.38205295

Xfe kor = Xfe + VXfe= -4.449413949 + 0.006600075 = -4.442813873

Xed kor = Xed + VXed= 24.38408076 + 0.004652983 = 24.38873374

Xdc kor = Xdc + VXdc= 38.490519 + 0.008902618 = 38.49942162

Xcb kor = Xcb + VXcb= -3.577639796 + 0.004143965 = -3.573495831

Xba kor = Xba + VXba= -29.55412482 + 0.006026209 = -29.54809861

= x -0.24607513 =

-0.029868619

= x -0.24607513 = -0.064167757

-0.027494287

= x -0.24607513 = -0.033537492

= x -0.24607513 = -0.047571628

= x -0.24607513 = -0.043435351

= x 0.03414040 = 0.006026209

= x 0.03414040 = 0.004143965

= x -0.24607513 =


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12. Hitung y ( Ordinat) yang Terkoreksi

Ygfkor = Ygf + VYgf= 5.340019576 + -0.027494287 = 5.312525289

Yfe kor = Yfe + VYfe

= 41.25244983 + -0.047571628 = 41.20487821Yed kor = Yed + VYed

= 16.15704517 + -0.033537492 = 16.12350768

Ydc kor = Ydc + VYdc= -40.629523 + -0.064167757 = -40.69369076

Ycb kor = Ycb + VYcb= -25.80441322 + -0.029868619 = -25.83428184

Yba kor = Yba + VYba= -23.70140323 + -0.043435351 = -23.74483858

12. Hitung Koordinat Titik Definitif

XG = 433865.4380

YG = 9220485.7680

XF = XG + Xgf kor= 433865.4380 + 23.38205295 = 433888.8201

YF = YG + Ygf kor= 9220485.7680 + 5.312525289 = 9220491.0805

XE = XF + Xfe kor

= 433888.8201 + -4.442813873 = 433884.3772YE = YF + Yfe kor= 9220491.0805 + 41.20487821 = 9220532.2854

XD = XE + Xed kor= 433884.3772 + 24.38873374 = 433908.7660

YD = YE + Yed kor= 9220532.2854 + 16.12350768 = 9220548.4089

XC = XD + Xdc kor= 433908.7660 + 38.49942162 = 433947.2654

YC = YD + Ydc kor= 9220548.4089 + -40.69369076 = 9220507.7152

XB = XC + Xcb kor= 433947.2654 + -3.573495831 = 433943.6919

YB = YC + Ycb kor= 9220507.7152 + -25.83428184 = 9220481.8809


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XA = XB + Xba kor= 433943.6919 + -29.54809861 = 433914.1438

YA = YB + Yba kor= 9220481.8809 + -23.74483858 = 9220458.1361

Sehingga Koordinat Titik Definitif adalah Sebagai Berikut :

XG = 433865.4380

YG = 9220485.7680

XF = 433888.8201

YF = 9220491.0805

XE = 433884.3772

YE = 9220532.2854

XD = 433908.7660

YD = 9220548.4089

XC = 433947.2654

YC = 9220507.7152

XB = 433943.6919

YB = 9220481.8809

XA = 433914.1438

YA = 9220458.1361

Pengukuran Poligon Tertutup Terikat Koordinat (1)

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