Northings & Eastings An Enhancement Lesson Civil Engineering & Architecture

1. Northings & Eastings An Enhancement Lesson Civil Engineering & Architecture Unit 2 Introduction to Projects Unit 4 Site Planning

2. Lesson- Legal Land Descriptions • Metes and Bounds Description: • “; thence N 67° 35’ E along said right of way line of State Road No.1 a distance of 120 ft.” • Rectangular Survey System Description: • “Township 1 South, Range 1 East, 3rd PM • Section 25: S1/2 NW1/4”

3. In this lesson: • Examine Northings and Eastings as a way to describe and define property boundaries. GPS – Global Positioning System

4. UTM • Universal Transverse Mercator Coordinate System • Means of stating any position on the earth by giving two coordinates: An east coordinate (easting) and a north coordinate (northing)

5. Global Zones

6. US Zones - UTM

7. Coordinate System Origin – UTM • The Origin: • Established on the equator exactly 500 meters west of the zone’s central meridian to ensure that all coordinates in the zone are positive

8. SPCS • State Plane Coordinate System • Based on zones described by political boundaries – states or areas within states • More accurate than UTM

9. Zones SPCS

10. Coordinate System Origin - SPCS • Established by each state – Generally 2 million feet west of the zone’s central meridian and some distance south of the zone’s southernmost point. • Northing – North Coordinate • Easting – East Coordinate

11. Important Terms • Departure: • A distance in the east-west direction (x-axis) • Latitude: • A distance in the north-south direction (y-axis)

12. Departure Latitude Graphically Pt. 2 Pt. 1 Professional Development ID Code: 8005

13. β Right Triangle Trigonometry 1 Departure Distance sin β = Departure = (sin β)(Distance)

14. β Right Triangle Trigonometry 2 Latitude Distance cos β = Latitude = (cos β)(Distance)

15. β Ties to Metes and Bounds N 48º E, 200 feet

16. β Ties to Metes and Bounds Latitude = (cos β)(Length of property line) Departure = (sin β)(Length of property line)

17. N 48º E, 200 feet Latitude = (cos β)(Length of property line) = (cos 48°)(200 feet) = 133.826 feet Departure = (sin β)(Length of property line) = (sin 48°)(200 feet) = 148.629 feet

18. Convert to Northing & Easting Latitude added (N direction) or subtracted (South direction) from the previous Northing Departure added (E direction) or subtracted (W direction) from the previous Easting

19. SOUTH WEST An Example

20. Latitude and Departure Latitude = (cos β)(Length of property line) = (cos 73°)(249.08 ft) = 72.82 ft Departure = (sin β)(Length of property line) = (sin 73°)(249.08 ft) = 238.20 ft

21. Northing – End 1st Property Line Latitude = 72.82 ft. Known Benchmark Northing = 1000 ft. Bearing South therefore subtract 72.82 ft. Northing = 927.18 feet at the end of the 1st Property Line

22. Easting – End 1st Property Line Departure = 238.20 feet Known Benchmark Easting = 1000 ft. Bearing West therefore Subtract 238.20 ft. Easting = 761.80 feet at the end of the 1st Property Line

23. End of Second Property Line

24. Latitude and Departure – line 2 Latitude = (cos β)(Length of property line) = (cos 0°)(201.42 ft) = 201.42 feet Departure = (sin β)(Length of property line) = (sin 0°)(201.42 ft) = 0 feet

25. Northings-Eastings End 2nd Line Latitude = 201.42 ft Previous Northing = 927.18 ft Bearing South therefore subtract 201.42 ft Northing = 725.76 ft at the end of the 2nd Property Line Departure = 0 ft Previous Easting = 761.80 ft Bearing West therefore Subtract 0 ft. Easting = 761.80 feet at the end of the 2nd Property Line

26. End of 3rd Property Line

27. Latitude and Departure – line 3 Latitude = (cos β)(Length of property line) = (cos 83°)(368 ft) = 44.85 feet Departure = (sin β)(Length of property line) = (sin 83°)(368 ft) = 365.26 feet

28. Northings-Eastings End 3rd Line Departure = 365.26 ft Previous Easting = 761.80 ft Bearing East therefore add 365.26 ft. Easting = 1127.06 feet at the end of the 3rd Property Line Latitude = 44.85 ft Previous Northing = 725.76 ft Bearing North therefore add 44.85 ft Northing = 770.61 ft at the end of the 3rd Property Line

29. End of 4th Property Line Convert 28º 58´ 53´´ to Decimal: 28º + 58/60º + 53/3600º = 28.9814º

30. Latitude and Departure – line 4 Latitude = (cos β)(Length of property line) = (cos 28.9814°)(262.23 ft) = 229.39 feet Departure = (sin β)(Length of property line) = (sin 28.9814°)(262.23 ft) = 127.06 feet

31. Northings-Eastings End 4th Line Latitude = 229.39 ft Previous Northing = 770.61 ft Bearing North therefore add 229.39 ft Northing = 1000 ft at the end of the 4th Property Line Departure = 127.06 ft Previous Easting = 1127.06 ft Bearing West therefore subtract 127.06 ft. Easting = 1000 feet at the end of the 4th Property Line

32. Finished Property Lines

33. Using Software Click here to download a Template for Calculating Northings and Eastings Using Excel

34. Curriculum Alignment: Unit 2 – Introduction to Projects Unit 4 – Site Planning

35. References: Herubin, C.A. (1982). Principles of Surveying, 3rded, Reston, VA: Prentice Hall Kavanagh, B.F. (1989). Surveying with Construction Applications, 4th ed., Upper Saddle River, NJ: Prentice Hall

36. Credits: Writer: Kevin Roy Content Editor: Steve Carter and Donna E. Scribner Narration: Donna E. Scribner PLTW Editor: Ed Hughes Production: CJ Amarosa Video Production: CJ Amarosa Audio: CJ Amarosa Project Manager: Donna E. Scribner