POSITION BY INTERSECTION
Learning Objectives After this lecture you will be able to: n Determine adjusted geographic coordinates from field distance intersection n Determine adjusted geographic coordinates from field angle intersection
Accuracy n Must account for spherical excess n 2.5” over 10km = 0.1m n 2.5” over 45km = 0.5m
Distance Intersection l measured and reduced to s C and unknown and known A B
Step 1 – and s and known A B Calculate A-B, B-A, and s
Step 2 – Plane Trig A B C Calculate angles
Step 3 – Spherical Excess A B C Calculate spherical excess and add 1/3 to each plane angle
Step 4 – Calculate s A B C Use spheroidal angles to calculate forward azimuths A-C A-B B-C B-A
Step 5 – Coordinate Calcs C and known A B measured s A-C B-C measured s and Direct Solution
Step 6 - Checks C A B and Direct Solution Should be equal C-A Bi-product of Direct Solution C-B C-B - C-A Should equal spheroidal angle from step 4
Direction Intersection measured angles C and unknown and known A B
Step 1 – and s and known A B Calculate A-B, B-A, and s
Step 2 – Plane Trig A B C Use observed angles and plane trigonometry Approximate s A-B, B-A, and s
Step 3 – Spherical Excess A B C Use approximate s to calculate spherical excess (approx)
Step 4 – Plane Angles A B C Apply 1/3 spherical excess to spheroidal angles to get plane angles
Step 5 – Calculate s A B C Use plane trigonometry to calculate s ss
Step 6 – Calculate s A B C Use observed spheroidal angles to calculate forward azimuths A-C A-B B-C B-A
Step 7 – Coordinate Calcs C and known A B s A-C B-C s and Direct Solution
Step 8 - Checks C A B and Direct Solution Should be equal C-A Bi-product of Direct Solution C-B C-B - C-A Should equal spheroidal angle from step 5 + 1/3 spherical excess
Conclusion You can now: n Determine adjusted geographic coordinates from field distance intersection n Determine adjusted geographic coordinates from field angle intersection
Self Study n Read relevant module in study book n Do Self Assessment Questions and follow examples
Review Questions