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Traverse Correction - Bowditch Method


In Traversing the lengths of the line are measured by chain or a tape and the directions are fixed by the compass or theodolite or by forming angles with chain and a tape. The latest instruments like total station captures the co-ordinates of the points along with elevations. These instruments are also capable of recording and string the distances and angles replacing the conventional methods.

There are two types of traverse surveying i.e. Closed Traverse and Open Traverse.


  1. Closed Traverse:
    When a series of connected lines form a closed circuit, ie. When the finishing point coincides with the starting point, then it is called as a closed traverse. These closed traverse surveys has many applications like fixing the boundaries of ponds, forests etc..

 

  1. Open traverse :
    When a sequence of connected lines extends along a general direction and does not return to the starting point, it is known as ‘open traverse’ or ‘unclosed traverse’.

 

Traverse Correction Procedure

Present techniques used in traversing using total station as a open traverse. The steps are as described below…

  1. GPS pair points are fixed at a convenient distance, approximately about 3 to 5km. Care has to be taken that the pair of GPS points is fixed at a reliable distance (at least 60m is advised for better results) and on good monuments. These points are fixed in such a way that they are clearly inter visible and should cater for placing the total station firmly on the GPS stations,
  2. Total station is to be checked for its calibration, prism constants for the prisms to be set in the instrument to avoid errors.
  3. Total station is then used to conduct the traverse between the GPS points. This type of traverse ensures that the survey is started from a known pair of points and is closed on known pair of points. Care has to be taken that the last bearing is also taken for correcting the misclosures.
  4. There are several methods to correct the traverse misclosures. However, in most of the cases Bowditch rule is considered to be most reliable. The other methods like transit method, Crandall method, Least Square Methods are used very rarely. The most accurate method which is known as a misclosures correction by the least square method is used when the accuracy required is very high. This method finds itself applicable in the projects like tunnel works.
  1. Bowditch Rule
  2. Whole Circle Bearing
  3. Quandrantal Bearing
Traverse Correction – Open Traverse Bowditch Method
Traverse Correction – Open Traverse with Known Coordinates
Traverse Correction – Closed Traverse


TOTAL STATION TRAVERSING ADJUSTMENT BY BOWDITCH METHOD


PROCEDURE FOR TRAVERSE CALCULATIONS

  • Adjust angles or directions
  • Determine bearings or azimuths
  • Calculate and adjust latitudes and departures
  • Calculate rectangular coordinates

DETERMINING BEARINGS OR AZIMUTHS

  • Requires the direction of at least one line within the traverse to be known or assumed
  • For many purposes, an assumed direction is sufficient
  • A magnetic bearing of one of the lines may be measured and used as the reference for determining the other directions
  • For boundary surveys, true directions are needed

LATITUDES AND DEPARTURES

Traverse Correction - Bowditch Method

Line

Dir

Deg

Min

Sec

Dir

Degrees

Length

Cumulative
Length

Azimuthal
Angles

Departure

Latitude

AB

N

26

10

0

E

N26.167E

285.1

285.1

26.167

+125.726

+255.881

BC

S

75

25

0

E

S75.417E

610.45

895.55

+104.583

+590.784

-153.700

CD

S

15

30

0

W

S15.5W

720.48

1616.03

+195.500

-192.540

-694.276

DE

N

1

42

0

W

N1.7W

203

1819.03

+358.300

-6.022

+202.911

EA

N

53

0

0

W

N53W

647.02

2466.05

+307.000

-516.733

+389.386

CLOSURE OF LATITUDES AND DEPARTURES

  • The algebraic sum of all latitudes must equal zero or the difference in latitude between the initial and final control points
  • The algebraic sum of all departures must equal zero or the difference in departure between the initial and final control points

ADJUSTMENT OF LATITUDES AND DEPARTURES


Line

Dir

Deg

Min

Sec

Dir

Length

Cumulative
Length

Azimuthal
Angles

Departure

Latitude

AB

N

26

10

0

E

285.1

285.1

26.167

+125.726

+255.881

BC

S

75

25

0

E

610.45

895.55

+104.583

+590.784

-153.700

CD

S

15

30

0

W

720.48

1616.03

+195.500

-192.540

-694.276

DE

N

1

42

0

W

203

1819.03

+358.300

-6.022

+202.911

EA

N

53

0

0

W

647.02

2466.05

+307.000

-516.733

+389.386

Correctioning Latitude

ADJUSTED LATITUDES AND DEPARTURES


Line

Dir

Deg

Min

Sec

Dir

Length

Cumulative
Length

Azimuthal
Angles

Departure
Misclosure

Latitude
Misclosue

Corrected
Departure

Corrected
Latitude

AB

N

26

10

0

E

285.1

285.1

26.167

+0.140

+0.023

+125.586

+255.858

BC

S

75

25

0

E

610.45

895.55

+104.583

+0.301

+0.050

+590.483

-153.750

CD

S

15

30

0

W

720.48

1616.03

+195.500

+0.355

+0.059

-192.895

-694.335

DE

N

1

42

0

W

203

1819.03

+358.300

+0.100

+0.017

-6.122

+202.894

EA

N

53

0

0

W

647.02

2466.05

+307.000

+0.319

+0.053

-517.052

+389.334

                                                                                                                                                αCorr.Dep=0      αCorr.Lat=0

The Sum of total Corrected Departure and Sum of total Corrected latitude is 0.00, proves that the traverse is balanced

RECTANGULAR COORDINATES

  • Rectangular X and Y coordinates of any point give its position with respect to a reference coordinate system
  • Useful for determining length and direction of lines, calculating areas, and locating points
  • You need one starting point on a traverse (which may be arbitrarily defined) to calculate the coordinates of all other points
  • A large initial coordinate is often chosen to avoid negative values, making calculations easier.

CALCULATING X AND Y COORDINATES

Given the X and Y coordinates of any starting point A, the X and Y coordinates of the next point B are determined by:

Calculate XY

 

Line

Dir

Deg

Min

Sec

Dir

Length

Azimuthal
Angles

Calculated
Easting

Calculated
Northing

Adjusted
Easting

Corrected
Northing

AB

N

26

10

0

E

285.1

26.167

+5125.726

+10255.881

+5125.586

+10255.858

BC

S

75

25

0

E

610.45

+104.583

+5716.510

+10102.180

+5716.069

+10102.107

CD

S

15

30

0

W

720.48

+195.500

+5523.970

+9407.904

+5523.174

+9407.772

DE

N

1

42

0

W

203

+358.300

+5517.948

+9610.815

+5517.052

+9610.666

EA

N

53

0

0

W

647.02

+307.000

+5001.214

+10000.201

+5000.000

+10000.000

 

LINEAR MISCLOSURE

The hypotenuse of a right triangle whose sides are the misclosure in latitude and the misclosure in departure.

Linear_Misclosure

TRAVERSE PRECISION

  • The precision of a traverse is expressed as the ratio of linear misclosure divided by the traverse perimeter length.
  • expressed in reciprocal form
  • Example

0.89 / 2466.05 = 0.00036090
1 / 0.00036090 = 2770.8

Precision = 1/2771