Angular Measurement

1
Angular Measurement

• Requires three points
• From Backsight reference
• At Where the transit is located
• To Foresight
• Established or Determined
• Units of Measure
• Degrees, Min, Sec
• Radians - ? rad 180 degrees
• Gons European, 400 Gon/circle

2
Direction of a Line

• Same units as Angles
• Meridians North/South Lines
• True
• Magnetic
• Grid
• Assumed
• Azimuth
• Bearing

3
Azimuth

• Angles Measured Clockwise from North
• Military and Astronomers use South
• Angle between 0 and 360
• Back Az Az 180
• AzBC Back AzAB ltA

4
Bearings

• Quadrants NE, SE, SW, NW
• Always lt 90
• Written N2315W
• Back Bearing change directions
• Bearing AB N2315W
• Back bearing AB bearing BAS2315E

5
Bearings to Azimuths

• Each quadrant is different
• NE Bearing E from N Az Bearing Angle (BA)

NE
NW

• SE Bearing E from S Az 180 BA

• SW Bearing W from SAz 180 BA

• NW Bearing E from NAz 360 BA

SE
SW
6
Problem 9-3, McCormacs 4th
Az OA 14116 (SE Quad) B.A. 180 - 14116
3884 Bearing S3884E Az OB 21723 (SW
Quad) B.A. 21723 - 180 3723 Bearing
S3723W Az OC 4823 (NE Quad) B.A. Az
Bearing N4823E
7
Problem 9-5, McCormacs 4th
Az OA 172216 Az OB 180 - 701846
1094114 Az OB 180 11852
191852 Az OB 360 - 763052
283298
8
Traverse Directions

• Given
• The direction of a side
• The connecting angle
• Find
• The direction of the adjacent side
• Determine back azimuth
• Add angle
• Clockwise ()
• Counterclockwise (-)

9
Traverse Azimuths Example

• Az AB 3515
• ?ABC 9827
• Find AZ BC

• Back Az Az ? 180
• Az BA 21515

• 21515 9827 31342

10
Problem 9-7, McCormacs 4th
Az AB 7042Az BA 25042 ?ABC 9718 Left
(CCW) so Az BC 25042 - 9718
15324 SE QuadrantB.A. 180 - 15324
2636 Bearing S 2636E
11
Problem 9-7, McCormacs 4th
Az BC 16228Az BA 34228 ?BCD 6738
Left (CCW) so Az CD 34228 - 6738
27450 NW QuadrantB.A. 360 -
27450 8510 Bearing N 8510W
12
Problem 9-17, McCormacs 5th
Az 34 3515000Az 43 1715000- ?4 -
2213756 - 494756
3600000Az 41 3101204 NW Quad, B.A.
360 - Az Bearing 41 N 494756W
13
Problem 9-17, McCormacs 5th
Az 41 3101204 Az 14 1301204- ?1 -
511600Az 12 785604 NE Quad, B.A. Az
Bearing 12 N 785604E Az 21 2585604-
?2 - 362200Az 23 2223404 SW Quad,
B.A. Az - 180 Bearing 23 S423404E
14
Problem 9-17, McCormacs 5th
?3 360 - 2213756 - 511600 -
362200 504404 Az 32
423404- ?3 - 504404
- 81000 3600000Az 34
3515000 NW Quad, B.A. 360 - Az Bearing 34
N 81000W
Closed traverse, Interior angles ??s (n-2)180
(4-2)180 360