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COMPUTATIONS ON THE SPHEROID

COMPUTATIONS ON THE SPHEROID. Learning Objectives. Calculate f and l of a point given a and s from a point with known f and l . Calculate a and s between points with known f and l. Lecture Outline. Direct Problem Manual Spreadsheets Reverse Problem Manual Spreadsheets

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COMPUTATIONS ON THE SPHEROID

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  1. COMPUTATIONS ON THE SPHEROID

  2. Learning Objectives • Calculate f and l of a point given a and s from a point with known f and l. • Calculate a and s between points with known f and l.

  3. Lecture Outline • Direct Problem • Manual • Spreadsheets • Reverse Problem • Manual • Spreadsheets • Conclusion

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

  5. a known f and l unknown f and l known s known Tangent - Direct

  6. Df fm Process – Tangent Direct • Step 1 • Draw a diagram • Compute r for known point • Compute approximateDf using r • Compute fm r f and l known

  7. Dl nm Process – Tangent Direct • Step 2 • Compute nm using fm • Compute approximateDl fm f and l known

  8. ½Da Process – Tangent Direct • Step 3 • Compute approximate½Da using formula Dl Df fm f and l known

  9. rm Process – Tangent Direct • Step 4 • Compute approximatea + ½Da • Check diagram for correct sense • Compute rm ½Da a + ½Da a 1-2 known fm

  10. fm Process – Tangent Direct • Step 5 • Compute ½Df • Compute fm ½Df

  11. ½Dl nm rm Process – Tangent Direct • Step 6 • Compute rm and nm using this new fm • Compute ½Dl fm

  12. ½Da Process – Tangent Direct • Step 7 • Compute ½Da ½Dl ½Df fm nm rm

  13. ½Da a + ½Da a 2-1 Calculate f and l ½Dl ½Df Process – Tangent Direct • Step 8 • Compare earlier results and decide on further iterations (from step 4) • Calculate final a1-2 + ½Da • Calculate final a2-1 = a1-2 + Da± 180° f and l known

  14. Spreadsheet - Direct

  15. Spreadsheet - Direct

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

  17. Tangent - Reverse - Formula

  18. Tangent - Reverse - Example

  19. Tangent - Reverse - Example

  20. Tangent - Reverse - Example

  21. Tangent - Reverse - Example

  22. Tangent - Reverse - Example

  23. Tangent - Reverse - Example

  24. Spreadsheet - Reverse

  25. Spreadsheet - Reverse

  26. Conclusion You can now: • Calculate f and l of a point given a and s from a point with known f and l. • Calculate a and s between points with known f and l.

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

  28. Review Questions

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