NAME='Robots'/> MY FORWARD WORK: HOW TO CALCULATE LENGTH AND BEARING OF OMITTING MEASUREMENT IN TRAVERSING

HOW TO CALCULATE LENGTH AND BEARING OF OMITTING MEASUREMENT IN TRAVERSING

                           UPENDRA KUMAR





In the traverse, the survey omits the measurement of length and bearing of a line. The omitted
length and bearing of easily calculate with the use of coordinate.



CASE I:-  If the length and bearing of one line is omitted.



HOW TO CALCULATE LENGTH AND BEARING OF OMITTING MEASUREMENT IN TRAVERSING


In the above picture, ABCD is the traverse. During traversing the length and bearing of the EA

is omitted. The length and bearing of the traverse shown below.

                                             


                     
        LINE
  LENGTH
BEARING
        AB
217.5
120º15’
          BC
318.0
62º30’
          CD
375.0
322º24’
          DE
283.5
335º18’
          EA



First calculate the latitude and departure of each line
            
LINE
LATITUDE
L✖COS𝛳
DEPARTURE
L✖SIN𝛳

AB
-109.570
187.884
BC
146.836
282.069
CD
297.108
-228.804
DE
257.562
-118.465
EA


                              


Find the algebraic sum of the latitudes and algebraic sum departures.
⇒-109.570+146.836+197.108+257.562=491.936 OR          
 ∑L=491.936
⇒187.884+282.069-228.804-118.465=122.684
 ∑D=122.684

Subtract the algebraic sum of latitude and departure from zero.
 ∑L=0-491.936 = ∑L-491.936
 ∑D=0-122.684= ∑D-122.684
Then TAN𝛳= departure÷latitude=122.684÷491.936=
𝛳=14º0’12” OR S14º0’12”W 

LENGTH OF EA= LAT÷COS𝛳=491.936÷COS14º0’12” =507.00mt
                            OR
LENGTH OF EA=√(491.936)²+(122.684)²
                          =507.00mt




CASE II:- In the traversing length of one side and bearing of another side missing

LINE
LENGTH
BEARING
LATITUDE
DEPARTURE
AB
217.5

S59º45’E
-109.570
187.872
BC
318.0


CD
N37º36’E


DE
283.5
S55º18’W
-161.390
-233.077
EA
173.15
S2º40’W
-172.962
-8.055

HOW TO CALCULATE LENGTH AND BEARING OF OMITTING MEASUREMENT IN TRAVERSING
In the table and figure the length of CD and bearing of BC is missing.

For this type of problem ignore the affected side BC and CD . Closed the polygon, draw a line 
B TO D, and made a complete polygon ABDEA. 

Compute the length and bearing of the closing line BD.

∑L=443.922
∑D=53.26

Then TAN𝛳= departure÷latitude=53.26÷443.922=6º50’29”
R.B OF BD=N6º50’29”E
Length of BD=LAT÷COS𝛳=443.922÷COS6º50’29” =447.10m.

In the triangle BCD , angle CDB= 37º36+6º50’29=44º26’29”

Here BD=447.10m, and BC=318.0m

∠C= BD/BC✖SinD
∠C= 447.10/318.0✖Sin44º26’29”
∠𝛳2=79º52’39”

Then ∠𝛳1=180º-79º52’39”+44º26’29”
 ∠𝛳1=55º40’52”

R.B OF BC=6º50’29”+55º40’52”

R.B OF BC=N6º231’21”E

Length of CD= BD✖Sin𝛳1÷Sin𝛳2
Length of CD=447.10✖Sin55º40’52”÷Sin79º52’39”

Length of CD=375.10m


CASE III:-  When two sides are omitted. 

HOW -TO- CALCULATE- LENGTH- AND- BEARING -OF- OMITTING -MEASUREMENT -IN -TRAVERSING



In the above figure, ABCDA is a traverse, The length of BC and CD IS not given.



No.
LINE
LENGTH
Bearing
Latitude
Departure
1
AB
217.50
S59º45’E
-109.570
187.884
2
BC
N6230’E
3
CD
N3736’W
4
DE
283.50
S55º18’W
-161.390
-233.077
5
EA
173.50
S2º40’W
-173.312
-8.072


Compute the length and bearing of the closing line BD.


The latitude of closing line BD=444.272
The departure of closing lineBD=53.258


Then reduced bearing of BD= Tan𝛳=53.258÷444.272
                                            = N 6º50’8”E 
                         Length of BD=  444.272÷COS 6º50’8”

                                             = 447.452mt.

Solve the triangle BCD.


In the triangle BCD 

 ∠B=55º39’52”

∠C=79º54’

∠D=44º26’08”


In the triangle BCD 

BC/SinD=BD/SinC
BC=BD/SinC*SinD
BC=447.452/Sin79º54’*Sin44º26’08”
BC= 318.195mt


CD=BD/SinC*SinB

CD=447.452/Sin79º54’*Sin55º39’52”
CD=375.29mt

CASE IV:-  When two angles are omitted. 

Solve the problem as case iii


SEE ALSO:-PLOTTING

HOW TO FIND HEIGHT OF AN OBJECT
WHY USED CORRECTION FOR CURVATURE AND REFRACTION IN LEVELING