Geodesy and Surveying

Disciplines/professions aimed at measuring positions. Reading: Geodesy for the Layman

Purpose of Lecture:

• Terminology of Geodesy as an element of Lineage
• Practices of Surveying: evolution of availability
• Debriefing from Event 2

Earth Measurement (Geodesy)

Ellipsoid (Spheroid) is the assumed surface of rotation ­ defines lat/long (horizontal spatial reference system)
The Geoid is the complex surface of gravity at "Mean Sea Level" (vertical reference)

Eratosthenes 250 BC estimated circumference at 46250km (only 15% high),
using two points of observation (angles of sun in wells at Aswan & Alexandria)
Ptolemy "corrected" it to a value which was 25% small.

Selected Ellipsoids	major axis [a] (meters)	1/f (flattening) [f= (a­b) /a]
Bessel 1841	6377397.2	299.15
Everest 1830	6377276.3	300.80
Clarke 1866 (NAD27)	6378206.4	294.98
Clarke 1880	6378249.2	293.47
World Geodetic System 1972	6378135.0	298.26
GRS-80 (NAD 83, etc.)	6378137.0	298.26

Terms you need to know:

• Ellipsoid
• Datum
• NAD 27
• NAD 83
• HARN

More resources on Geodesy in 465 course notes...

What is measured: depends on collection system

• Astronomic positioning: observing angles of stars (and sun and moon); tied in to TIME
• Traditional triangulation: one baseline, then angles
  unoccupied points have no cross-check on error in angles
  vertical component must be carefully processed out.
  • plane table: a graphic construction technique that uses triangulation
• Trilateration: measures all three SIDES of a triangle (as distances), infers angles; (much stronger solution than triangulation) [a curiousity until the advent of laser ranging]
  • GPS: timing differences (or interferometry) in signals from satellites gives distance
    from four or six known orbital paths.
• Total Station: instrument that measures both angles and distances [laser ranging] (note redundancy)
• Inertial navigators: (three gyroscopes) measure acceleration over time
  position is the integral of acceleration (velocity) integrated over time.

Debriefing on Event 2: What errors can occur in triangulation?

Adjustment computations: data quality work

Basically, there was no "source of higher accuracy", all assessments from internal evidence

Early schemes had no cross-check (buried the topic)

Closure of traverse: apportioning error in getting back to the same point.

Resolve redundancy: (triangulation produces little triangles (big?), not points) What to pick?

Mathematical models (least squares now) used to apportion errors out along a traverse.

(Compass rule to Weighted Least Squares)

Modern systems are self-error-checking; massive systems of simultaneous equations.

Version of 23 January 2004