TOTAL STATION TRAVERSING ADJUSTMENT BY BOWDITCH METHOD

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

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

 

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:

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.

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