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COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate  and of a point given  and s from a point with known  and. Calculate  and s between points.

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Presentation on theme: "COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate  and of a point given  and s from a point with known  and. Calculate  and s between points."— Presentation transcript:

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  ½  –Calculate final  2-1 =   ± 180°  and known ½½ ½  Calculate  and ½   + ½   2-1

14 Spreadsheet - Direct

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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

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24 Spreadsheet - Reverse

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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


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