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Published byDwight Dowen Modified over 3 years ago

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COMPUTATIONS ON THE SPHEROID

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

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

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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

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Tangent - Direct and known known s known and unknown

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Process – Tangent Direct n Step 1 –Draw a diagram –Compute for known point –Compute approximate using –Compute m and known mm

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Process – Tangent Direct n Step 2 –Compute m using m –Compute approximate and known m mm

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Process – Tangent Direct n Step 3 –Compute approximate ½ using formula and known mm ½

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Process – Tangent Direct n Step 4 –Compute approximate + ½ –Check diagram for correct sense –Compute m mm ½ mm + ½ 1-2 known

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Process – Tangent Direct n Step 5 –Compute ½ –Compute m ½ mm

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Process – Tangent Direct n Step 6 –Compute m and m using this new m –Compute ½ mm m mm ½½

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Process – Tangent Direct n Step 7 –Compute ½ ½½ mm ½ ½ m mm

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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 ½½ ½ Calculate and ½ + ½ 2-1

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Spreadsheet - Direct

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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

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Tangent - Reverse - Formula

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Tangent - Reverse - Example

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Spreadsheet - Reverse

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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.

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Self Study n Read relevant module and follow worked examples

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Review Questions

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Draw a line through the points A(1,-2) and D(4,4). Find the coordinates of 2 more points on the line.

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