Ex30-1 A closed traverse was run among stations P, Q, R,S and T having following observation :
Stations (1) |
Sides (2) |
IncludedAngle (3) |
Length ( li ) m |
Remarks |
X |
|
|
Sign convension: for Clockwise interior angle + ve Anti-Clockwise interior angle - ve Azimuth of PX = 43° 31' 30" TY = 106° 17' 30" |
|
PX |
|
|||
P |
|
104° 00' 30" |
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|
PQ |
|
305.41 |
|
Q |
|
63° 20' |
||
|
QR |
|
359.61 |
|
R |
|
-101° 49' |
||
|
RS |
|
612.15 |
|
S |
|
120° 45' |
||
|
ST |
|
485.12 |
|
T |
|
-123° 29' 30" |
||
|
TY |
|
|
|
Y |
|
|
|
It is given that the independent coordinates of the stations P and T are (2346.839 , 3157.148 ) and ( 3644.678, 3321.881 ) respectively. Find the adjusted coordinates of the stations using Gale's Traverse table
Solution : Table 30.1 Gale's Traverse Table (Figure 30.1)
Stations (1) |
Sides (2) |
Length (L) m (3) |
Included Angle (4) |
Correction (5) |
Corrected angle (6) |
WCB (7) |
Consecutive coordinates, m (8) |
Bowditch Correction (9) |
Corrected Consecutive Coordinates |
Corrected Independent Coordinates |
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Departure (D) |
Latitude (L) |
Departure |
Latitude |
Departure | Latitude |
Xi |
Yi |
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X
|
||||||||||||||
PX
|
43° 31' 30" |
|||||||||||||
P
|
104° 00' 30"
|
-12" |
104° 00' 18" |
2346.633 |
3157.148 |
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PQ
|
305.41 |
147° 31' 48" |
163.962
|
-257.666
|
0.052
|
0.033
|
164.014 |
-257.633 |
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Q
|
63° 20" |
-12" |
63° 19' 48" |
2510.835 |
2899.515 |
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QR
|
359.61 |
30° 51' 36" |
184.459
|
308.698
|
0.060
|
0.039
|
184.519 |
308.737 |
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R
|
-101° 49' |
-12" |
-101° 49' 12" |
2695.372 |
3208.618 |
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RS
|
612.15 |
109° 02' 24" |
578.660
|
-199.700
|
0.104
|
0.066
|
578.764 |
-199.634 |
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S
|
120° 45' |
-12" |
120° 44' 48" |
3274.136 |
3008.618 |
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ST
|
485.12 |
49° 47' 12" |
370.460
|
313.210
|
0.082
|
0.053
|
370.542 |
313.262 |
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T
|
-123° 29' 30"
|
-12"
|
-123° 29' 42"
|
3644.678 |
3321.881 |
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TY
|
106° 17' 30" |
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Y
|
|
|||||||||||||
S
|
1762.29 |
62° 47' 00" |
1297.541 |
162.542
|
0.298 |
0.191 |
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Error = (S Interior included angle - S Exterior included angle) - (Azimuth of last line - Azimuth of first line)
= (288° 05' 30" - 225° 18' 30") - (106° 17' 30" - 43° 31' 30")
= 62° 47' 00" - 62° 46' 00" = + 1'
Closure corrections =
= 0.354m
Therefore, corection = - 1'
= 32° 39' 26".70
Therefore, Azimuth of closure correction = 57° 20' 33".30