TRAVERSE CALCULATIONS- PROCEDURE

TRAVERSE CALCULATIONS

PROCEDURE FOR TRAVERSE CALCULATIONS

Adjust angles or directions

Determine bearings or azimuths

Calculate and adjust latitudes and departures

Calculate rectangular coordinates

BALANCING ANGLES OF CLOSED TRAVERSES

An example of a calculation involving interior angles is available.

ADJUSTING ANGLES

Adjustments applied to angles are independent of the size of the angle

Methods of adjustment:

Make larger corrections where mistakes were most likely
Apply an average correction to each angle
Or a combination

Never make an adjustment that is smaller than the measured accuracy

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

The latitude of a line is its projection on the north-south meridian and is equal to the length of the line times the cosine of its bearing

The departure of a line is its projection on the east-west meridian and is equal to the length of the line times the sine of its bearing

The latitude is the y component of the line and the departure is the x component of the line

LATITUDES AND DEPARTURES

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

CALCULATION OF LATITUDES AND DEPARTURES

Using bearings

Station
Bearing
Length
Latitude
Departure
A
N 26° 10'E
285.10
+255.88
+125.72
B
S 75° 25'E
610.45
-153.70
+590.78
C
S 15° 30'W
720.48
-694.28
-192.54
D
N 1° 42'W
203.00
+202.91
-6.02
E
N 53° 06'W
647.02
+388.48
-517.41
A
MISCLOSURE
-0.71
+0.53

CALCULATION OF LATITUDES AND DEPARTURES

Using azimuths

Station
Azimuth
Length
Latitude
Departure
A
26° 10'
285.10
+255.88
+125.72
B
104° 35'
610.45
-153.70
+590.78
C
195° 30'
720.48
-694.28
-192.54
D
358° 18'
203.00
+202.91
-6.02
E
306° 54'
647.02
+388.48
-517.41
A
MISCLOSURE
-0.71
+0.53

ADJUSTMENT OF LATITUDES AND DEPARTURES

Compass (Bowditch) Rule 

ADJUSTMENT OF LATITUDES AND DEPARTURES

Station
Azimuth
Length
Latitude
Departure
A
+0.08
-0.06
26° 10'
285.10
+255.88
+125.72
B
+0.18
-0.13
104° 35'
610.45
-153.70
+590.78
C
+0.21
-0.15
195° 30'
720.48
-694.28
-192.54
D
+0.06
-0.05
358° 18'
203.00
+202.91
-6.02
E
+0.18
-0.14
306° 54'
647.02
+388.48
-517.41
A
TOTALS
2466.05
-0.71
+0.53

ADJUSTMENT OF LATITUDES AND DEPARTURES

Balanced
Balanced
Station
Latitude
Departure
Latitude
Departure
A
+0.08
-0.06
+255.88
+125.72
+255.96
+125.66
B
+0.18
-0.13
-153.70
+590.78
-153.52
+590.65
C
+0.21
-0.15
-694.28
-192.54
-694.07
-192.69
D
+0.06
-0.05
+202.91
-6.02
+202.97
-6.07
E
+0.18
-0.14
+388.48
-517.41
+388.66
-517.55
A
TOTALS
-0.71
+0.53
0.00
0.00

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:

COORDINATES

Balanced
Balanced
Station
Latitude
Departure
Y-coord
X-coord
A
10000.00
10000.00
+255.96
+125.66
B
10255.96
10125.66
-153.52
+590.65
C
10102.44
10716.31
-694.07
-192.69
D
9408.37
10523.62
+202.97
-6.07
E
9611.34
10517.55
+388.66
-517.55
A
10000.00
10000.00
TOTALS
0.00
0.00

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

TRAVERSE CALCULATIONS

TRAVERSE CALCULATIONS

PROCEDURE FOR TRAVERSE CALCULATIONS

Adjust angles or directions

Determine bearings or azimuths

Calculate and adjust latitudes and departures

Calculate rectangular coordinates

BALANCING ANGLES OF CLOSED TRAVERSES

An example of a calculation involving interior angles is available.

ADJUSTING ANGLES

Adjustments applied to angles are independent of the size of the angle

Methods of adjustment:

Make larger corrections where mistakes were most likely
Apply an average correction to each angle
Or a combination

Never make an adjustment that is smaller than the measured accuracy

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

The latitude of a line is its projection on the north-south meridian and is equal to the length of the line times the cosine of its bearing

The departure of a line is its projection on the east-west meridian and is equal to the length of the line times the sine of its bearing

The latitude is the y component of the line and the departure is the x component of the line

LATITUDES AND DEPARTURES

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

CALCULATION OF LATITUDES AND DEPARTURES

Using bearings

Station
Bearing
Length
Latitude
Departure
A
N 26° 10'E
285.10
+255.88
+125.72
B
S 75° 25'E
610.45
-153.70
+590.78
C
S 15° 30'W
720.48
-694.28
-192.54
D
N 1° 42'W
203.00
+202.91
-6.02
E
N 53° 06'W
647.02
+388.48
-517.41
A
MISCLOSURE
-0.71
+0.53

CALCULATION OF LATITUDES AND DEPARTURES

Using azimuths

Station
Azimuth
Length
Latitude
Departure
A
26° 10'
285.10
+255.88
+125.72
B
104° 35'
610.45
-153.70
+590.78
C
195° 30'
720.48
-694.28
-192.54
D
358° 18'
203.00
+202.91
-6.02
E
306° 54'
647.02
+388.48
-517.41
A
MISCLOSURE
-0.71
+0.53

ADJUSTMENT OF LATITUDES AND DEPARTURES

Compass (Bowditch) Rule 

ADJUSTMENT OF LATITUDES AND DEPARTURES

Station
Azimuth
Length
Latitude
Departure
A
+0.08
-0.06
26° 10'
285.10
+255.88
+125.72
B
+0.18
-0.13
104° 35'
610.45
-153.70
+590.78
C
+0.21
-0.15
195° 30'
720.48
-694.28
-192.54
D
+0.06
-0.05
358° 18'
203.00
+202.91
-6.02
E
+0.18
-0.14
306° 54'
647.02
+388.48
-517.41
A
TOTALS
2466.05
-0.71
+0.53

ADJUSTMENT OF LATITUDES AND DEPARTURES

Balanced
Balanced
Station
Latitude
Departure
Latitude
Departure
A
+0.08
-0.06
+255.88
+125.72
+255.96
+125.66
B
+0.18
-0.13
-153.70
+590.78
-153.52
+590.65
C
+0.21
-0.15
-694.28
-192.54
-694.07
-192.69
D
+0.06
-0.05
+202.91
-6.02
+202.97
-6.07
E
+0.18
-0.14
+388.48
-517.41
+388.66
-517.55
A
TOTALS
-0.71
+0.53
0.00
0.00

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:

COORDINATES

Balanced
Balanced
Station
Latitude
Departure
Y-coord
X-coord
A
10000.00
10000.00
+255.96
+125.66
B
10255.96
10125.66
-153.52
+590.65
C
10102.44
10716.31
-694.07
-192.69
D
9408.37
10523.62
+202.97
-6.07
E
9611.34
10517.55
+388.66
-517.55
A
10000.00
10000.00
TOTALS
0.00
0.00

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