UVSC BASIC SURVEYING presents . . .

1. UVSC BASIC SURVEYINGpresents . . . “GETTING YOUR BEARINGS”

2. CALCULATING BEARING LESSON OBJECTIVES After completing this instructional unit, students will be able to . . . Recognize both open and closed traverses. Recognize and understand the difference between interior and deflection angles in a traverse. Understand the terminology used to define angle direction. Understand surveying quadrants. Understand how bearings and azimuths are measured and be able to convert one to the other. Mathematically adjust field angles. Use angles to calculate bearings around a piece of property. Check the accuracy of bearing calculations.

3. BEARINGS 1 – Open & closed traverses 2 – Angular closure of closed traverses 3 – Bearings and Azimuths – definitions 4 – Bearing/Azimuth conversion 5 – Calculating bearings

4. D E F A B B C C D E A F G TRAVERSE TYPES • Open traverses • Closed traverses

5. TRAVERSE USES • Open traverses • Define a path from one point to another • Centerlines of: • Roads • Pipelines • Utilities (sewer, water, power, telephone, cable, etc.) • Closed traverses • Enclose an area • Boundaries of: • Properties • Easements • Rights-of-way (highways, railroads, etc.)

6. TRAVERSE ANGLES • Open traverse angles cannot be balanced because they do not add up to a specific number. • Closed traverse angles must add up to a specific number depending upon type of angles measured and number of angles.

7. ANGLE TYPES • Interior Angles • Zero on backsight, turn to foresight. • May turn right (clockwise) or left (counterclockwise) directions. • Deflection Angles • Zero on backsight, flop telescope, turn to foresight. • May turn right (clockwise) or left (counterclockwise) directions. Direction is determined after ‘scope is flopped.

8. ANGLE TYPES OUTSIDE ∡ INSIDE ∡ INTERIOR ANGLES DEFLECTION ANGLES

9. RIGHT ANGLE (CLOCKWISE) ANGLE DIRECTIONS LEFT ANGLE (COUNTER-CLOCKWISE)

10. INTERIOR ANGLES ∑ ∡ = (N-2)ⅹ180° (N = NUMBER OF ANGLES) DEFLECTION ANGLES ∑OUTSIDE -∑INSIDE = 360° ANGULAR CLOSURE FORMULAS CLOSED TRAVERSES ONLY !

11. D 78° 42’ 78° 40’ C ERROR = - 0° 11’ 220° 16’ 220° 13’ B E 105° 11’ 105° 09’ 41° 42’ 41° 40’ 94° 09’ 94° 07’ A EXAMPLE – INTERIOR ANGLES ACTUAL ∑ = 539° 49’ ∑ ∡ SHOULD BE 540° PROCEDURE ADD 3’ TO LARGEST ANGLE, AND 2’ TO ALL OTHERS, THEN CHECK TOTAL AGAIN.

12. 147° 39’ 147° 37’ 28° 57’ 28° 56’ A ERROR = + 0° 05’ B C 139° 40’ 139° 39’ 101° 41’ 101° 42’ D EXAMPLE – DEFLECTION ANGLES ACTUAL ∑ =360° 05’ ∑ ∡ SHOULD BE 360° PROCEDURE SUBTRACT 2’ FROM LARGEST ANGLE, SUBTRACT 1’ FROM OTHERS (+1’ TO INSIDE), THEN CHECK TOTAL AGAIN.

13. N   NW NE W E   SW SE S SURVEYING DIRECTIONS QUADRANTS

14. BEARING = N 21° W BEARING = S 67° W BEARING = S 38° E BEARING = N 53° E N 53° 21° W E 67° 38° S • BEARING FACTS • Always measured from North or South, never from East or West. • Always < 90°. • Always preceded by N or S and followed by E or W. • Lines lying on an axis are listed as DUE NORTH, DUE SOUTH, DUE EAST, or DUE WEST. SURVEYING DIRECTIONS BEARINGS

15. BEARING = DUE NORTH N BEARING = DUE WEST W E BEARING = DUE EAST BEARING = DUE SOUTH S • BEARING FACTS • Always measured from North or South, never from East or West. • Always < 90°. • Always preceded by N or S and followed by E or W. • Lines lying on an axis are listed as DUE NORTH, DUE SOUTH, DUE EAST, or DUE WEST. SURVEYING DIRECTIONS BEARINGS

16. W E IMPORTANT !!! BEARINGS ARE NEVER MEASURED FROM THE EAST OR WEST LINES !!!

17. AZIMUTH = az 339° AZIMUTH = az 247° AZIMUTH = az 142° AZIMUTH = az 53° N 53° 339° W E 142° 247° S SURVEYING DIRECTIONS • AZIMUTH FACTS • Always measured clockwise from North. • Can be any size, but normally < 360°. • Preceded by “az”. AZIMUTHS

18. N W E S AZIMUTH∡BEARING∡ BEARING/AZIMUTH CONVERSIONS QUADRANT 1 BRG = AZ QUADRANT 4 BRG = 360°- AZ AZ = 360°- BRG QUADRANT 2 BRG = 180° - AZ AZ = 180° - BRG QUADRANT 3 BRG = AZ - 180° AZ = 180° + BRG

19. CALCULATING BEARINGS Bearings are calculated by adding and subtracting angles • Balance angles (closed traverses only). • Determine the basis of bearing for the traverse. • Determine direction to proceed around the traverse. • Determine which station to use for first calculation. • Sketch each station and calculate bearings around the traverse (see following slides). • Calculate beginning bearing to check accuracy. Bearing calculation process

20. D 78° 42’ 78° 40’ C 220° 16’ 220° 13’ B E 105° 11’ 105° 09’ 41° 42’ 41° 40’ 94° 09’ 94° 07’ BASIS OF BEARING N 63°25’ E A BEARING CALCULATIONSINTERIOR ANGLES • Angles previously balanced. • Determine basis of bearing. • Proceed counter-clockwise. • Begin with station “B”

21. ? D C 41°42’ B 78° 42’ 78° 40’ C A 63°25’ 220° 16’ 220° 13’ B E 105° 11’ 105° 09’ 41° 42’ 41° 40’ 94° 09’ 94° 07’ N 63°25’ E A BEARING CALCULATIONS 180°00’ - 63°25’ - 41°42’ =74°53’ BEARING = N 74°53’ W N 74°53’ W • FOR EACH SKETCH • Sketch course in and course out • Sketch three angles • Incoming course bearing angle • Property angle • Outgoing course bearing angle • Calculate outgoing course bearing INTERIOR ANGLES

22. ? D D 220°16’ C 78° 42’ 78° 40’ B C 145°23’ 74°53’ 220° 16’ 220° 13’ B E 105° 11’ 105° 09’ 41° 42’ 41° 40’ 94° 09’ 94° 07’ N 63°25’ E A 220°16’ - 74°53’ =145°23’ BEARING CALCULATIONS 180°00’ - 145°23’ = 34°37’ N 34°37’ W N 74°53’ W BEARING = N 34°37’ W • FOR EACH SKETCH • Sketch course in and course out • Sketch three angles • Incoming course bearing angle • Property angle • Outgoing course bearing angle • Calculate outgoing course bearing INTERIOR ANGLES

23. D D 78°42’ 78° 42’ 78° 40’ C 34°37’ E ? 220° 16’ 220° 13’ B C E 105° 11’ 105° 09’ 41° 42’ 41° 40’ 94° 09’ 94° 07’ N 63°25’ E A BEARING CALCULATIONS 78°42’ - 34°37’ = 44°05’ BEARING = S 44°05’ W N 34°37’ W S 44°05’ W N 74°53’ W • FOR EACH SKETCH • Sketch course in and course out • Sketch three angles • Incoming course bearing angle • Property angle • Outgoing course bearing angle • Calculate outgoing course bearing INTERIOR ANGLES

24. 44°05’ D D E 105°11’ 78° 42’ 78° 40’ C A ? 220° 16’ 220° 13’ B E 105° 11’ 105° 09’ 41° 42’ 41° 40’ 94° 09’ 94° 07’ N 63°25’ E A BEARING CALCULATIONS 180°00’ - 105°11’ - 44°05’ = 30°44’ N 34°37’ W S 44°05’ W BEARING = S 30°44’ E N 74°53’ W • FOR EACH SKETCH • Sketch course in and course out • Sketch three angles • Incoming course bearing angle • Property angle • Outgoing course bearing angle • Calculate outgoing course bearing S 30°44’ E INTERIOR ANGLES

25. E 30°44’ ? B D A 94°09’ 78° 42’ 78° 40’ C 220° 16’ 220° 13’ B E 105° 11’ 105° 09’ 41° 42’ 41° 40’ 94° 09’ 94° 07’ N 63°25’ E A BEARING CALCULATIONS N 34°37’ W S 44°05’ W BEARING = N 63°25’ E 94°09’ - 30°44’ = 63°25’ N 74°53’ W • FOR EACH SKETCH • Sketch course in and course out • Sketch three angles • Incoming course bearing angle • Property angle • Outgoing course bearing angle • Calculate outgoing course bearing  S 30°44’ E INTERIOR ANGLES

26. N 34°37’ W S 44°05’ W N 74°53’ W N S 30°44’ E N 63°25’ E COMPLETED BEARINGS

27. For Next Class . . . In-Class Group Bearing Calculations • Review today’s demonstration presentation • Review bearing calculation procedure • Balance angles on worksheet Prepare by doing the following: Bring the following: • Pencil, eraser, and graph paper • Scientific calculator • Worksheet with balanced angles