1. Seventh Edition By David A. Madsen, Terence M. Shumaker, and David P. Madsen Civil Drafting Technology Chapter 7 Location and Direction

2. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 2 Figure 7 – 1: Measuring longitude.

3. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 3 Table 7-1: Length of a degree of longitude

4. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 4 Figure 7 – 2: Measuring latitude.

5. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 5 Figure 7 – 3: Using coordinates of parallels and meridians to find locations.

6. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 6 Figure 7 – 4: Finding the distance between point A at 30° north latitude, 110° east longitude, and point B at 42° north latitude, 110° east longitude.

7. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 7 Figure 7 – 5: Finding the distance between A at 22° south latitude, 65° west longitude, and point B at 22° south latitude, 79° west longitude.

8. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 8 Figure 7 – 6: If the points are fairly close, such as a few hundred miles or less from each other on a different longitude and latitude, you can image the surface of the earth as being flat and use the Pythagorean theorem to find distance.

9. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 9 Figure 7 – 7: The hypotenuse is the longest side of a right triangle, apposite the 90° angle. A right triangle has one 90° angle.

10. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 10 Figure 7 – 8: Using the Pythagorean theorem formula, a 2 + b 2 = c 2, to calculate the distance between paints A and B, where a and b are sides of the right triangle and c is the hypotenuse, which is the distance between points A and B.

11. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 11 Figure 7 – 9: A spherical triangle is shown on the earth ’ s surface between points A, B, and C. Notice how the sides a, b, and c of the spherical triangle are arcs rather than straight lines, as discussed when using the Pythagorean theorem and shown in Figure 7 – 8.

12. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 12 Figure 7 – 10: (a) Mariner ’ s and (b) surveyor ’ s compass.

13. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 13 Figure 7 – 11: Azimuth.

14. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 14 Figure 7 – 12: Bearing.

15. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 15 Figure 7 – 13: Examples of (a) bearings and (b) bearings and equivalent azimuths.

16. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 16 Figure 7 – 14: Sample of magnetic declination.

17. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 17 Figure 7 – 15: UTM grid and 1994 magnetic north declination at center of sheet.

18. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 18 Figure 7 – 16: Magnetic declination changes throughout the United States. (Courtesy of the National Geophysical Data Center, NGDC)

19. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 19 Figure 7 – 17: Formulas used to calculate true azimuth, given magnetic azimuth and magnetic declination.

20. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 20 Figure 7 – 18: A portion of a quadrangle map providing location and direction.

21. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 21 Figure 7 – 19: All angles of a four-sided polygon will equal 360° when added.

22. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 22 Figure 7 – 20: Opposite angles of intersecting lines are equal.

23. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 23 Figure 7 – 21: Example of a typical traverse. Included angles and distances are given.

24. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 24 Figure 7 – 22: Calculating bearings: line BC.

25. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 25 Figure 7 – 23: Calculating bearings: line CD.

26. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 26 Figure 7 – 24: Calculating bearings: line DA.

27. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 27 Figure 7 – 25: Bearings and distances shown on a plat.

28. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 28 Figure 7 – 26: Rough sketch of a plat.

29. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 29 Table 7 – 2: Plotting table

30. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 30 Figure 7-27: Error of closure.

31. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 31 Figure 7 – 28: Correcting the error of closure.

32. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 32 Figure 7 – 29: Closed traverse.

33. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 33 Figure 7 – 30: Positive and negative latitude.

34. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 34 Figure 7 – 31: Positive and negative departures.

35. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 35 Figure 7 – 32: A right triangle created by property lines with latitude and departure.

36. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 36 Figure 7 – 33: Setting up a table for latitude and departure calculations.

37. Civil Drafting Technology, Seventh Edition David A. Madsen, Terence M. Shumaker, David P. Madsen © 2010 Pearson Higher Education, Upper Saddle River, NJ 07458. All Rights Reserved. 37 Figure 7 – 34: Plot information processed by a computer automatically calculates and balances latitudes, departures, and azimuths.