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Azhar Shahzad

Closed Traversing with the help of Theodolite including example

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Latitude and Departure

In order to do start with Theodolite Traversing you should familiar with the Latitude and Departure which are discussed briefly below,

 
  • OA is the line with whole circle bearing equal to θ.
  • OC = Latitude = lCosθ
  • OB = Departure = lSinθ
  • By using the above formulae for Latitude and Departure with whole circle bearing, calculator will be giving aljebraic sign automatically for Latitude and Departure.
  • For a closed Traverse ∑ of all Latitude is equal to zero and ∑ of Departure is also equal to zero.

Consecutive co-ordinates

When the Latitude and Departure are calculated at second point of a given line taking first point as a origin then it is called consecutive co-ordinates.

Independent co-ordinates

Independent co-ordinates are the Latitude and Departure of points of a traverse with respect to a common origin, so that all the values are +ve. These are used for plotting purposes.

Bowdich Rule

This rule is used to apply the correction in Latitude and Departure which states that correction in Latitude/Departure is equal to Length of Line multiply by Total correction in Latitude/Departure and then dividing by the perimeter.

Traverse Table

For the following traverse ABCD, I have applied the correction in Latitude and Departure using Bowdich rule.

Line L(m) Beari.(° ′ ″) Latd. Depr. Corrections applied Consecutive co-ord. Independent co-ord.
Latd. Depr. Latd. Depr. Latd. Depd.
AB 148 115 30 -63.27 133.58 -0.26 - -63.98 133.58 500 500
BC 172 42 25 126.98 116.02 -0.30 - 126.68 116.02 628.68 616.02
CD 201 205 30 -181.42 -86.53 -0.36 - -181.7 -86.53 444.90 529.49
DA 202 306 15 119.44 -162.9 -0.36 - 119.08 -162.9 563.98 366.59
723   +1.28 +0.17 -1.28   0 +0.17    

As you can see, correction was not applied in Departure as the error was too small to be neglected. Using Bowdich rule we can apply correction in Latitude and Departure for respective line

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