Traverse Calculations

1


Geology and Surveying 70380 (Part B - Surveying)

• Traverse Calculations
• and Coordinate Systems

2
Objectives

• Calculate rectangular coordinates from bearings
  and distances
• Calculate bearing and distance between points
  with known rectangular coordinates
• Calculate misclose bearing and distance in a
  traverse figure
• Adjust field traverse data to match existing plan
  information

3
Polar and Rectangular Coordinates
N
Origin
4
Eastings and Northings
N
Departure DE
r
DN
Latitude DN
q
Origin
DE
5
Latitudes and Departures
DE E2 E1 DN N2 N1 l Sinq
l Cosq
N
2
q
DN
Latitude (L) DN
r
1
DE
Origin
Departure (D) DE
6
Bearings and Distances

• From 1 to 2
• DE E2 E1 DN N2 N1
• l Sinq l Cosq

N
1
l
DN
q
2
DE
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Quadrant Calculations
8
Example

• From 1 to 2
• DE 649.222 600.000
• 49.222
• DN 901.899 1000.000
• -98.101

1 E 600.000 N 1000.000
N
Brg
l
DN
q
2 E 649.222 N 901.899
DE
Bearing 1 ? 2 180 - 263842 1532118
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Coordinate Calculations
10
Computation of Closes
2
3
1
Closed Traverse
5
11
Coordinates
N
Bearing 1 ? 2 350000 Distance (l) 164.385
2
DN Latitude (L)
l
q
1
DE Departure (D)
DE D l Sinq 164.385 Sin35 94.287
DN L l Cosq 164.385 Cos35 134.656
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Example Traverse Calcs
L
D
l
q
13
Example with Misclose
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Example with Misclose
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Coordinates from Traverse
Northing
Line
L (DN)
Stn
Easting
D (DE)
l
q
1
0
0
1 ? 2
134.656
2
94.287
164.385
350000
2 ? 3
2.196
3
125.797
125.816
890000
3 ? 4
-175.011
4
175.011
247.503
1350000
4 ? 5
-149.347
5
-144.223
207.617
2240000
5 ? 6
124.920
6
-58.251
137.834
3350000
6 ? 1
62.586
1
-192.621
202.534
2880000
0
0
0.000
0.000
S

• E2 E1 DE N2 N1 DN

E3 E2 DE N3 N2 DN
E4 E3 DE N4 N3 DN
E5 E4 DE N5 N4 DN
E6 E5 DE N6 N5 DN
E1 E6 DE N1 N6 DN
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Practical Application

• See example in study book

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Summary

• We have seen how to
• Calculate rectangular coordinates from bearings
  and distances
• Calculate bearing and distance between points
  with known rectangular coordinates
• Calculate misclose bearing and distance in a
  traverse figure
• Adjust field traverse data to match existing plan
  information

18
Self Study

• Read Module 20
• Do self assessment Questions

19
Questions?