## TRAVERSE CALCULATIONS

### PROCEDURE FOR TRAVERSE CALCULATIONS

• 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.

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

### 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