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2 - Correction of Stations

This document summarizes the calculation of angles and coordinates for several triangles used in a bridge site triangulation survey. It lists the measured angles and any corrections made for each triangle. It then uses sine law calculations to determine side lengths and average them when needed. Finally, it calculates the coordinates of each vertex point by using trigonometry based on known angles and one side length. The coordinates are calculated sample-wise to demonstrate the process.

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Santosh Aryal
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100 views5 pages

2 - Correction of Stations

This document summarizes the calculation of angles and coordinates for several triangles used in a bridge site triangulation survey. It lists the measured angles and any corrections made for each triangle. It then uses sine law calculations to determine side lengths and average them when needed. Finally, it calculates the coordinates of each vertex point by using trigonometry based on known angles and one side length. The coordinates are calculated sample-wise to demonstrate the process.

Uploaded by

Santosh Aryal
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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CALCULATION

Fig: Overview of Bridge Site Triangulation

For triangle BAD (Base Triangle)

Angle Value Correction Corrected Angle


< BAD 30°00’13” -2" 30°00’11”
<ADB 61°29’54” -3" 61°29’51”
<DBA 88°29’54” -3" 88°29’51”
Sum 180°00’08” 180°00’00”
Error 00°00’08”
Permissible Error 52” (Hence, error can be distributed along stations.)

For triangle ABC (Base Triangle)

Angle Value Correction Corrected Angle


<BCA 67°17’07” -17" 67°16’50”
<CAB 80°25’19” -17" 80°25’02”
<ABC 32°18’24” 16" 32°18’08”
Sum 180°00’50” 180°00’00”
Error +00°00’50”
Permissible Error 52” (Hence, error can be distributed along stations.)
For triangle GEF

Angle Value Correction Corrected Angle


<GEF 32°53’56” -10" 32°53’46”
<GFE 60°26’41” -10" 60°26’31”
<EFG 86°39’53” -10" 86°39’43”
Sum 180°00’30” 180°00’00”
Error 00°00’30”
Permissible Error 1’44” (Hence, error can be distributed along stations.)

For triangle ECF

Angle Value Correction Corrected Angle


<EFC 91°15’00” -17" 91°14’43”
<FCE 52°03’50” -17" 52°03’33”
<FEC 36°42’0” -16" 36°’41”44
Sum 180°00’52” 180°00’00”
Error 00°00’52”
Permissible Error 1’44” (Hence, error can be distributed along stations.)

For triangle EBC

Angle Value Correction Corrected Angle


<EBC 82°10’46” -17" 82°10’29”
<ECB 42°11’14” -16" 42°10’58”
<BEC 55°38’49” -16" 55°38’33”
Sum 180°00’49” 180°00’00”
Error 00°00’49”
Permissible Error 1’44” (Hence, error can be distributed along stations.)
In ΔABD, Using Sine law:

𝐹𝑖𝑟𝑠𝑡, Sin ∡ABD Sin ∡BDA


=
𝐴𝐷 𝐵𝐴

sin (30°00′11") sin (61°29′51")


𝑜𝑟, =
33.716 𝐴𝐵

⸫ AB = 59.253

In ΔABC, Using Sine law:

sin(67°16′50") sin (32°18′08")


𝐴𝑙𝑠𝑜, =
𝐴𝐵 𝐵(=34.342)

⸫ AB = 59.278 m
Average (AB) =59.275m

Again, Using Sine law in other remaining triangles:


(Note: AB=59.275 and Corrected Angles are used for Computation)
AD= 67.427 m
BC= 63.365 m Observed in Field
BD= 33.730 m
AC= 34.342 m
CE= 76.042 m
CF= 45.450 m
EF= 59.985 m
FG= 32.634 m
BE= 51.542 m
COORDINATE CALCULATION
Sample Calculation:
Bearing of AB = 3590(Measured in Field)
<BAD = 30°00′11"
Bearing of AD = Bearing of AB+ <BAD -3600
= 29°00′11"
Co-ordinate of A = (1000.000mN,1000.000mE) (Assumed)
Northing of D = Northing of A + AD . Cos(Bearing of AD)
= 1000 + 67.427 . Cos(29°00′11")
= 1058.971mN
Easting of D = Easting of A + AD . Sin(Bearing of AD)
= 1000 + 67.427 . Sin(29°00′11")
= 1032.692mN
Similarly, all remaining coordinates of Station Points are calculated.
Vertex Side Bearing Independent coordinate
A AB 359°00′00" (1000.000mN,1000.000mE)
AD 29°00′11"
AC 278°34′58"
B BA 179°00′00" (1059.265mN,998.966mE)
BD 90°30′02"
BC 211°18′08"
BE 293°28′37"
C CB 31°18′08" (1005.123mN,966.045mE)
CE 349°07′10"
CF 297°03′35"
CA 98°34′58"
D DA 209°00′11" (1058.971mN,1032.692mE)
DB 90°30′02"
E EB 113°28′37" (1079.798mN,951.691mE)
EC 169°07′10"
EF 205°48′54"
EG 238°42′40"
F FE 25°48′54" (1025.799mN,925.570mE)
FC 117°03′35"
FG 325°22′23"
G GF 145°22′23" (1052.653mN,907.023mE)
GE 58°42′40"

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