Question

B 106° 120 100 feet feet 60° 599 C A 1350 106 86 feet feet The table below shows the field data for closed traverse ABCD, if the coordinates of A (0, 0). Azimuth for AB is 56°. Compute the coordinates for all other stations. a. Fill up the followings: Stations Observed Azimuth Length EN To Station Angle 56 A 59° 37.22 00 B B 106° 16.71 C 60° 19.55 135 34.12 A Σ b. Calculate the corrected angle Stations АВCD Observed Angles Corrected Angles c. Find dE and dN for latitude and departure d. Find the closing error. e. Find the Relative Accuracy f. Fill up the following table. Station Correct AE AN Correct (E) Correct (N) Correct To Station A C C D A

Answer 1

Hi,

Step 1: Adjusting measured angles:

Observed Angle A = 59^o

Observed Angle B = 106^o

Observed Angle C =60^o

Observed Angle D = 135^o

Total                       = 360^o

Theoretical sum of angles of ploygon= (n-2) x 180^o (where n=number of sides)

Theoretical sum of angles of given quadrilateral = (4-2) x 180^o =360^o

Angular error = 360^o-360^o = 0

Hence the angles measured are correct and no correction is required in angles at this point.

Results are presented below:

Station	A	B	C	D
Observed Angle	59o	106o	60o	135o
Correction in each angle	0o	0o	0o	0o
Adjusted angle	59o	106o	60o	135o

Step 2: Calculation of azimuths of all lines

For a clockwise traverse, azimuth of other lines with one known azimuth is calculated by below formula:

Azimuth of preceding line = Azimuth of previous line - Angle between lines + 180^o

Azimuth of AB                   =                             56^o

Balance azimuths:

Azimuth of BC = 56^o – 106^o + 180^o = 130^o

Azimuth of CD = 130^o – 60^o + 180^o = 250^o

Azimuth of DA = 250^o – 135^o + 180^o= 295^o

Step 3: Calculating Northing and Easting of each line:

Formula:

Northing = Distance x cos (Azimuth)

Easting = Distance x sin (Azimuth)

Accordingly results are furnished in below table:

Line	Length	Azimuth	Northing	Easting
	feet		feet	feet
AB	120	56o	67.1031	99.4845
BC	100	130o	-64.2788	76.6044
CD	106	250o	-36.2541	-99.6074
DA	86	295o	36.3452	-77.9425
Sum	412		2.9154	-1.4609

Step 4: Calculating Coordinates of each line:

Formula:

North Coordinate of an end = North coordinate of another end + Northing of line

East Coordinate of an end = East coordinate of another end + Easting of line

Accordingly results are furnished in below table:

Station	Line	Northing	Easting	Coordinates (N-S)	Coordinates E-W
A				0.0000 N	0.0000 E
	AB	67.1031	99.4845
B				67.1031 N	99.4845 E
	BC	-64.2788	76.6044
C				2.8244 N	176.0890 E
	CD	-36.2541	-99.6074
D				-33.4297 N	76.4815 E
	DA	36.3452	-77.9425

Step 5: Calculating corrected Northing and easting of each line:

As per Bowditch rule for a closed traverse:

Correction in northing of a line = total error in northing x length of line / perimeter of traverse

Correction in easting of a line = total error in easting x length of line / perimeter of traverse

Accordingly results are furnished in below table:

Line	Length	Northing	Easting	Correction in northing	Correction in easting	Adjusted Northing	Adjusted Easting
1	2	3	4	5	6	7 = 3-5	8=4-6
AB	120	67.1031	99.4845	0.8492	-0.4255	66.2540	99.9100
BC	100	-64.2788	76.6044	0.7076	-0.3546	-64.9864	76.9590
CD	106	-36.2541	-99.6074	0.7501	-0.3759	-37.0042	-99.2315
DA	86	36.3452	-77.9425	0.6086	-0.3050	35.7366	-77.6375
Sum	412	2.9154	-1.4609	2.9154	-1.4609	0.0000	0.0000

Step 6: Calculating final coordinates of each line:

Final Coordinates According to adjusted northing and easting are furnished in below table:

Station	Line	Northing	Easting	Coordinates (N-S)	Coordinates (E-W)
A				0.0000 N	0.0000 E
	AB	66.2540	99.9100
B				66.2540 N	99.9100 E
	BC	-64.9864	76.9590
C				1.2676 N	176.8691 E
	CD	-37.0042	-99.2315
D				-35.7366 N	77.6375 E
	DA	35.7366	-77.6375

a) Fill up the table:

Station	Observed Angle	Azimuth	Length	E	N	To Station
A	59o	56o	120	67.1031	99.4845	B
B	106o	130o	100	-64.2788	76.6044	C
C	60o	250o	106	-36.2541	-99.6074	D
D	135o	295o	86	36.3452	-77.9425	A
Sum	360o		412	2.9154	-1.4609

b) Calculate the corrected angles:

Station	A	B	C	D
Observed Angle	59o	106o	60o	135o
Adjusted angle	59o	106o	60o	135o

c) Find DE and DN

d) Find the closing error

Closing error = 3.2610 feet

e) Find the relative accuracy

Relative accuracy = 0.007915 = 1/126

f) Fill up the table

Station	Line	Corrected DN	Corrected DE	(N) Correct	(E) Correct
A				0.0000 N	0.0000 E
	AB	0.8492	-0.4255
B				66.2540 N	99.9100 E
	BC	0.7076	-0.3546
C				1.2676 N	176.8691 E
	CD	0.7501	-0.3759
D				-35.7366 N	77.6375 E
	DA	0.6086	-0.3050