1. COMPUTATIONS ON THE SPHEROID

2. Learning Objectives Calculate  and of a point given  and s from a point with known  and. Calculate  and s between points with known  and.

3. Lecture Outline n Direct Problem –Manual –Spreadsheets n Reverse Problem –Manual –Spreadsheets n Conclusion

4. Direct Problem n Know  1, 1,  1  2 and s 1  2 n Need to calculate  2 and 2 n Many formula available –Different accuracy and applications –Manual calculations –Spreadsheets

5. Tangent - Direct  and known  known s known  and unknown

6. Process – Tangent Direct n Step 1 –Draw a diagram –Compute  for known point –Compute approximate  using  –Compute  m  and known   mm

7. Process – Tangent Direct n Step 2 –Compute m using  m –Compute approximate   and known m mm 

8. Process – Tangent Direct n Step 3 –Compute approximate ½  using formula  and known  mm  ½ 

9. Process – Tangent Direct n Step 4 –Compute approximate  + ½  –Check diagram for correct sense –Compute  m mm ½  mm  + ½   1-2 known

10. Process – Tangent Direct n Step 5 –Compute ½  –Compute  m ½ mm

11. Process – Tangent Direct n Step 6 –Compute  m and m using this new  m –Compute ½  mm m mm ½½

12. Process – Tangent Direct n Step 7 –Compute ½  ½½ mm ½  ½  m mm

13. Process – Tangent Direct n Step 8 –Compare earlier results and decide on further iterations (from step 4) –Calculate final  1-2 + ½  –Calculate final  2-1 =  1-2 +  ± 180°  and known ½½ ½  Calculate  and ½   + ½   2-1

14. Spreadsheet - Direct

16. Reverse Problem n Know  1, 1,  2 and 2 n Need to calculate  1  2,  2  1 and s n Again, many formula available n Best explained with an example

17. Tangent - Reverse - Formula

18. Tangent - Reverse - Example

24. Spreadsheet - Reverse

26. Conclusion You can now: Calculate  and of a point given  and s from a point with known  and. Calculate  and s between points with known  and.

27. Self Study n Read relevant module and follow worked examples

28. Review Questions