Contoh Pengolahan data Theodolite (Poligon Tertutup)

Pada Artikel ini kita akan membahas contoh pengolahan data dari hasil pembacaan theodolite menjadi data koordinat peta agar selanjutnya dapat diplotkan ke dalam gambar

Berikut disajikan data hasil pembacaan theodolite serta jarak antar titik pembacaan

No	Sudut								Azimuth						Jarak
									α						d (m)
P2	182	°	7	'	0	"			331	°	47	'	48	"	66,9
P3	176	°	46	'	23	"									75,55
P4	280	°	12	'	35	"									41
P5	82	°	37	'	0	"									61,05
P6	90	°	26	'	55	"									99
P7	175	°	31	'	20	"									62
P8	95	°	23	'	10	"									64
P9	177	°	47	'	50	"									66,3
P10	179	°	35	'	35	"									63,75
P11	96	°	25	'	15	"									35
P12	174	°	32	'	35	"									44,15
P13	274	°	35	'	25	"									53
P14	84	°	12	'	55	"									49,1
P1	89	°	45	'	15	"									54,5

Dengan data tersebut maka kita telah dapat mengolah data tersebut untuk menentukan koordinat titik pada setiap titik pengujian, Berikut langkah-langkah perhitungannya,

1. Menghitung Sudut
			Σ Sudut			=			2159	°	59	'	13	"
			(n-2)	.	180	=	(14-2)		180	=	2160			°
Selisih			=		2160	°		-	2159	°	59	'	13	"
			=		47	"
2. Menghitung Azimuth
	331	°	47	'	48	"
	176	°	46	'	23	"		(	-180	°	)	+
	328	°	34	'	11	"		(+	-360	°	)
	280	°	12	'	35	"		(	-180	°	)	+
	68	°	46	'	46	"		(+	360	°	)
	82	°	37	'	0	"		(	-180	°	)	+
	331	°	23	'	46	"
	90	°	26	'	55	"		(	-180	°	)	+
	241	°	50	'	41	"
	175	°	31	'	20	"		(	-180	°	)	+
	237	°	22	'	1	"
	95	°	23	'	10	"		(	-180	°	)	+
	152	°	45	'	11	"
	177	°	47	'	50	"		(	-180	°	)	+
	150	°	33	'	1
	179	°	35	'	35			(	-180	°	)	+
	150	°	8	'	36
	96	°	25	'	15	=		(	-180	°	)	+
	66	°	33	'	51
	174	°	32	'	35	°		(	-180	°	)	+
	61	°	6	'	26	"
	274	°	35	'	25	"		(	-180	°	)	+
	155	°	41	'	51	"
	84	°	12	'	55	"		(	-180	°	)	+
	59	°	54	'	46	"
	89	°	45	'	15	"		(	-180	°	)	+
	-31	°	40	'	1	"		(+	360	°	)
	182	°	7	'	0	"		(	-180	°	)	+
	331	°	47	'	1	"
Koreksi:	331	°	47	'	1	"
	331	°	47	'	48	"		-
	0	°	0	'	13	"			Ok…
3. Menentukan d sin α dan d cos α
∆x =	d sin α
∆XP2	=		66,9			x  Sin (			331	°	47	'	48	"	)    =	-31,61708	m
∆XP3	=		75,55			x  Sin (			328	°	34	'	11	"	)    =	-39,39635	m
∆XP4	=		41			x  Sin (			68	°	46	'	46	"	)    =	38,21995	m
∆XP5	=		61,05			x  Sin (			331	°	23	'	46	"	)    =	-29,22778	m
∆XP6	=		99			x  Sin (			241	°	50	'	41	"	)    =	-87,28553	m
∆XP7	=		62			x  Sin (			237	°	22	'	1	"	)    =	-52,21277	m
∆XP8	=		64			x  Sin (			152	°	45	'	11	"	)    =	29,30090	m
∆XP9	=		66,3			x  Sin (			150	°	33	'	1	"	)    =	32,59703	m
∆XP10	=		63,75			x  Sin (			150	°	8	'	36	"	)    =	31,73679	m
∆XP11	=		35			x  Sin (			66	°	33	'	51	"	)    =	32,11271	m
∆XP12	=		44,15			x  Sin (			61	°	6	'	26	"	)    =	38,65445	m
∆XP13	=		53			x  Sin (			155	°	41	'	51	"	)    =	21,81237	m
∆XP14	=

49,1 x  Sin ( 59 ° 54 ' 46 " )    = 42,48443 m ∆XP₁ =
54,5 x  Sin ( -31 ° 40 ' 1 " )    = -27,52390 m +















-0,34477
Koreksi =
0,34477
: 14 = 0,02463 m


















∆x = ∆X + Koreksi













∆XP₂ =
-31,61708
+ 0,02463
=
-31,59245 m
∆XP₃ =
-39,39635
+ 0,02463
=
-39,37172 m
∆XP₄ =
38,21995
+ 0,02463
=
38,24458 m
∆XP₅ =
-29,22778
+ 0,02463
=
-29,20315 m
∆XP₆ =
-87,28553
+ 0,02463
=
-87,26090 m
∆XP₇ =
-52,21277
+ 0,02463
=
-52,18814 m
∆XP₈ =
29,30090
+ 0,02463
=
29,32552 m
∆XP₉ =
32,59703
+ 0,02463
=
32,62166 m
∆XP₁₀ =
31,73679
+ 0,02463
=
31,76141 m
∆XP₁₁ =
32,11271
+ 0,02463
=
32,13734 m
∆XP₁₂ =
38,65445
+ 0,02463
=
38,67907 m
∆XP₁₃ =
21,81237
+ 0,02463
=
21,83700 m
∆XP₁₄ =
42,48443
+ 0,02463
=
42,50905 m
∆XP₁ =
-27,52390
+ 0,02463
=
-27,49927 m +















0,0000

∆Y = d cos α














∆YP₂ =
66,9 x  cos ( 331 ° 47 ' 48 " )    = 58,95736 m ∆YP₃ =
75,55 x  cos ( 328 ° 34 ' 11 " )    = 64,46495 m ∆YP₄ =
41 x  cos ( 68 ° 46 ' 46 " )    = 14,84032 m ∆YP₅ =
61,05 x  cos ( 331 ° 23 ' 46 " )    = 53,59888 m ∆YP₆ =
99 x  cos ( 241 ° 50 ' 41 " )    = -46,71441 m ∆YP₇ =
62 x  cos ( 237 ° 22 ' 1 " )    = -33,43392 m ∆YP₈ =
64 x  cos ( 152 ° 45 ' 11 " )    = -56,89866 m ∆YP₉ =
66,3 x  cos ( 150 ° 33 ' 1 " )    = -57,73321 m ∆YP₁₀ =
63,75 x  cos ( 150 ° 8 ' 36 " )    = -55,28869 m ∆YP₁₁ =
35 x  cos ( 66 ° 33 ' 51 " )    = 13,92026 m ∆YP₁₂ =
44,15 x  cos ( 61 ° 6 ' 26 " )    = 21,33204 m ∆YP₁₃ =
53 x  cos ( 155 ° 41 ' 51 " )    = -48,30342 m ∆YP₁₄ =
49,1 x  cos ( 59 ° 54 ' 46 " )    = 24,61470 m ∆YP₁ =
54,5 x  cos ( -31 ° 40 ' 1 " )    = 47,03919 m +















0,39540
Koreksi =
-0,39540
: 14 = -0,02824 m


















∆Y = ∆Y + Koreksi













∆YP₂ =
58,95736
+ -0,02824
=
58,92912 m
∆YP₃ =
64,46495
+ -0,02824
=
64,43671 m
∆YP₄ =
14,84032
+ -0,02824
=
14,81208 m
∆YP₅ =
53,59888
+ -0,02824
=
53,57063 m
∆YP₆ =
-46,71441
+ -0,02824
=
-46,74265 m
∆YP₇ =
-33,43392
+ -0,02824
=
-33,46216 m
∆YP₈ =
-56,89866
+ -0,02824
=
-56,92690 m
∆YP₉ =
-57,73321
+ -0,02824
=
-57,76145 m
∆YP₁₀ =
-55,28869
+ -0,02824
=
-55,31693 m
∆YP₁₁ =
13,92026
+ -0,02824
=
13,89202 m
∆YP₁₂ =
21,33204
+ -0,02824
=
21,30380 m
∆YP₁₃ =
-48,30342
+ -0,02824
=
-48,33167 m
∆YP₁₄ =
24,61470
+ -0,02824
=
24,58646 m
∆YP₁ =
47,03919
+ -0,02824
=
47,01094 m +















0,00000



















4. Menentukan Koordinat (X,Y)









XP₄ = XP₃ + ∆XP₃













XP₄  =
1000,00 + ( -39,37172 )
= 960,62828 m
XP₅ =
960,62828 +
38,24458

= 998,87286 m
XP₆ =
998,87286 + ( -29,20315 )
= 969,66971 m
XP₇ =
969,66971 + ( -87,26090 )
= 882,40880 m
XP₈ =
882,40880 + ( -52,18814 )
= 830,22066 m
XP₉ =
830,22066 +
29,32552

= 859,54619 m
XP₁₀ =
859,54619 +
32,62166

= 892,16785 m
XP₁₁ =
892,16785 +
31,76141

= 923,92926 m
XP₁₂ =
923,92926 +
32,13734

= 956,06660 m
XP₁₃ =
956,06660 +
38,67907

= 994,74567 m
XP₁₄ =
994,74567 +
21,83700

= 1016,58267 m
XP₁ =
1016,58267 +
42,50905

= 1059,09172 m
XP₂ =
1059,09172 + ( -27,49927 )
= 1031,59245 m
Koreksi,















XP₃ =
1031,59245 + ( -31,59245 )
= 1000,00 m
















(Koreksi OK!!!)

















YP₄ = XP₃ + ∆XP₃













YP₄  =
1000,00 +
64,43671

= 1064,43671 m
YP₅ =
1064,43671 +
14,81208

= 1079,24879 m
YP₆ =
1079,24879 +
53,57063

= 1132,81942 m
YP₇ =
1132,81942 + ( -46,74265 )
= 1086,07677 m
YP₈ =
1086,07677 + ( -33,46216 )
= 1052,61461 m
YP₉ =
1052,61461 + ( -56,92690 )
= 995,68770 m
YP₁₀ =
995,68770 + ( -57,76145 )
= 937,92625 m
YP₁₁ =
937,92625 + ( -55,31693 )
= 882,60932 m
YP₁₂ =
882,60932 +
13,89202

= 896,50134 m
YP₁₃ =
896,50134 +
21,30380

= 917,80514 m
YP₁₄ =
917,80514 + ( -48,33167 )
= 869,47348 m
YP₁ =
869,47348 +
24,58646

= 894,05994 m
YP₂ =
894,05994 +
47,01094

= 941,07088 m
Koreksi,















YP₃ =
941,07088


58,92912

= 1000,00 m
















(Koreksi OK!!!)

dari Hasil Perhitungan maka diperoleh data sebagai berikut,

No	X	Y
P2	1031,5924	941,0709
P3	1000,0000	1000,0000
P4	960,6283	1064,4367
P5	998,8729	1079,2488
P6	969,6697	1132,8194
P7	882,4088	1086,0768
P8	830,2207	1052,6146
P9	859,5462	995,6877
P10	892,1678	937,9263
P11	923,9293	882,6093
P12	956,0666	896,5013
P13	994,7457	917,8051
P14	1016,5827	869,4735
P1	1059,0917	894,0599

data ini selanjutnya dapat diplotkan pada gambar dan diperoleh Peta Lahan yang kita ukur, Semoga artikel ini bermanfaat