geodesy university course

Geodetic Reference Systems

Week 6

Lecture 1

Coordinate Systems

• Means of expressing point positions with

respect to the ellipsoid

• Origin, orientation of axes, and triplet

values are required

• Curvilinear or Cartesian (rectangular)

3D Coordinate Systems

1. Geodetic Coordinates φ,λ,h – Curvilinear

2. Geocentric Coordinates X,Y,Z – Cartesian

3. Local Geodetic Coordinates e,n,u -

Cartesian

C

X

Y

Z

3. Local Geodetic Coordinate System

• Origin and Axes:

– Origin at a local point φ, λ, h

– u-axis points up along the normal

– e and n axes point to east and north in the

local tangential plane

• Cartesian (Rectangular) Coordinates:

– e, n, u

Azimuth, Zenith Angle, Slant Range

• Local Geodetic coordinate system can be

defined at each instrument (e.g. total station)

setup

• Geodetic Azimuth, α

• Vertical (altitude) angle, v

• Zenith angle, z

• Slant range, r

Datums and

Spheroids

The Earth’s Shape and Size

©2008 Austin Troy

• Only recently have we known both

• Estimates of shape by the ancients

have ranged from a flat disk, to a

cube to a cylinder to an oyster.

• Pythagoras was the first to postulate

it was a sphere

• By the 5th century BCE, this was

firmly established.

• But how big was it?

The Earth’s Size

©2008 Austin Troy

Posidonius used the stars to

determine the earth's

circumference. He observed

that the star Canopus could

be seen just on the horizon at

Rhodes (Greece) but

appeared above the horizon

when viewed from Alexandria,

Egypt (1st century BCE).

-source: ESRI

Spheroids

©2008 Austin Troy

•Note how two different spheroids have slightly

different major and minor axis lengths

Source: ESRI

Surface Based Datums

©2008 Austin Troy

•NAD27 resulted in lat/long coordinates for about

26,000 survey points in the US and Canada.

•Limitation: requires line of

sight, so many survey points

were required

•Problem: errors compound

with distance from the initial

reference. This is why central

location needed for first point

Datum Shift

©2008 Austin Troy

• NAD83 is superior to NAD27 because:

• NAD83 is more accurate and NAD27 can result in a

significant horizontal shift

• When we go from a surface-oriented datum to a spheroid-

based datum, the estimated position of survey benchmarks

improves; this is called datum shift

• That shift varies with location: 10 to 100 m in the cont. US,

400 m in Hawaii, 35 m in Vermont

• Click here for an example from Peter Dana

Datum Shift Example

©2008 Austin Troy