1. POSITION BY INTERSECTION

2. Learning Objectives After this lecture you will be able to: n Determine adjusted geographic coordinates from field distance intersection n Determine adjusted geographic coordinates from field angle intersection

3. Accuracy n Must account for spherical excess n 2.5” over 10km = 0.1m n 2.5” over 45km = 0.5m

4. Distance Intersection l measured and reduced to s C  and unknown  and known A B

5. Step 1 –  and s  and known A B Calculate  A-B,  B-A, and s

6. Step 2 – Plane Trig A B C Calculate  angles

7. Step 3 – Spherical Excess A B C Calculate spherical excess and add 1/3 to each plane angle

8. Step 4 – Calculate  s A B C Use spheroidal angles to calculate forward azimuths  A-C  A-B  B-C  B-A

9. Step 5 – Coordinate Calcs C  and known A B measured s  A-C  B-C measured s  and  Direct Solution

10. Step 6 - Checks C A B  and  Direct Solution Should be equal  C-A Bi-product of Direct Solution  C-B  C-B -  C-A Should equal spheroidal angle from step 4

11. Direction Intersection measured angles C  and unknown  and known A B

12. Step 1 –  and s  and known A B Calculate  A-B,  B-A, and s

13. Step 2 – Plane Trig A B C Use observed  angles and plane trigonometry Approximate s  A-B,  B-A, and s

14. Step 3 – Spherical Excess A B C Use approximate s to calculate spherical excess (approx)

15. Step 4 – Plane Angles A B C Apply 1/3 spherical excess to spheroidal angles to get plane angles

16. Step 5 – Calculate s A B C Use plane trigonometry to calculate s ss

17. Step 6 – Calculate  s A B C Use observed spheroidal angles to calculate forward azimuths  A-C  A-B  B-C  B-A

18. Step 7 – Coordinate Calcs C  and known A B s  A-C  B-C s  and  Direct Solution

19. Step 8 - Checks C A B  and  Direct Solution Should be equal  C-A Bi-product of Direct Solution  C-B  C-B -  C-A Should equal spheroidal angle from step 5 + 1/3 spherical excess

20. Conclusion You can now: n Determine adjusted geographic coordinates from field distance intersection n Determine adjusted geographic coordinates from field angle intersection

21. Self Study n Read relevant module in study book n Do Self Assessment Questions and follow examples

22. Review Questions