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 with known and .

Lecture Outline

Direct Problem– Manual– Spreadsheets

Reverse Problem– Manual– Spreadsheets

Conclusion

Direct Problem

Know 1, 1, 12 and s 12

Need to calculate 2 and 2

Many formula available– Different accuracy and applications– Manual calculations– Spreadsheets

Tangent - Direct

and known

known

s known

and unknown

Process – Tangent Direct Step 1

– Draw a diagram– Compute for known point– Compute approximate using

– Compute m

and known

m

Process – Tangent Direct

Step 2– Compute m using m

– Compute approximate

and known

m

m

Process – Tangent Direct

Step 3– Compute approximate ½ using formula

and known

m

½

Process – Tangent Direct

Step 4– Compute approximate + ½ – Check diagram for correct sense

– Compute m

m

½

m

+ ½

1-2 known

Process – Tangent Direct

Step 5– Compute ½– Compute m

½ m

Process – Tangent Direct

Step 6– Compute m and m using this new m

– Compute ½

m

m m

½

Process – Tangent Direct

Step 7– Compute ½

½

m½

½

m m

Process – Tangent Direct 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

Calculateand

½ + ½ 2-1

Spreadsheet - Direct

Spreadsheet - Direct

Reverse Problem

Know 1, 1, 2 and 2

Need to calculate 12 , 21 and s Again, many formula available Best explained with an example

Tangent - Reverse - Formula

Tangent - Reverse - Example

Tangent - Reverse - Example

Tangent - Reverse - Example

Tangent - Reverse - Example

Tangent - Reverse - Example

Tangent - Reverse - Example

Spreadsheet - Reverse

Spreadsheet - Reverse

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 .

Self Study

Read relevant module and follow worked examples

Review Questions