Maps: Projections and Datums -
Maps: Projections and Datums
Where did you say you were calling from?
  • The round earth on a flat map = "a projection"
  • imagine putting a strong light bulb in the globe and then holding flat piece of paper around it.
  • answer? Flat, wrapped cylinder, wrapped cone, cut up into wedges.
  • Some common ones (ask what the poles/greenland will look like)
In ArcGIS, open ....Demo\projections\project the world.
  •  cylindrical (Mercator)
  • Azimuthal (for poles)
  • Conic (one latitude is tangent, called the standard parallel)
  • Poly-conic (multiple latitudes tangent)

Here's a comparison of some, with some projection views.

(excellent source for more information here)


Projections create distortion

ArcGIS Help on projections says

All map projections distort shape, area, distance or direction to some extent. The impact of this distortion on your work depends on what you will be using your map for, and its scale:
......and extent of area

The map has different names, depending on what you hold constant:

  1. equal area--homolographic

  2. if you put a dime on a map, it'll always cover the same area, but shapes and angles are distorted
  3. shape - conformal

  4. at a point, relative local anles are preserved
    meridians intersect parallels at right angles
    areas enlarged or reduced
  5. Scale - equidistant

  6. equidistant between two points and rest of map only, or along meridians
  7. directional - azimuthal

  8. all rhumblines (lines of constant direction) are straight

Create a new blank arcmap document, then open VA_counties.shp from your GIS\demo\intro folder and change the coordinate system of the frame to

  • state plane=polyconic
  • utm, grid zone 17
  • equal area
  • decimal degrees (geographic)


Geoid and reference elipsoids

The earth is an oblate spheroid with the minor axis 1/300th shorter than major axis but the earth also has an irregular undulating surface that varies by +/- 100m from the oblate spheroid.  So the geoid is the approximation for shape of earth at "sea level" that takes into account gravitational and rotational inconsistencies.

this irregular shape is approximated by "elispoids" with a major and minor axis that fit particular parts of the globe better than others.  In the US, the North American Datum of 1927 (NAD 27) uses the Clarke66 (that's 1866) elipsoid, named for British geodisist Alexander Ross Clarke.  He measured the meridian arcs in Europe, Russia, India, S. Africa and Peru (with chains and surveying instruments).  His radii are 6,378,206.4 m and 6,356,583.8 m for the equatorial and polar axes, respectively. In ArcGIS, open the Data Frame Properties/coordinate system box, and choose the "predefined-geographic-spheroid based-clarke66" coordinate system and click "modify..." to see its parameters.


Datums fix the zeros

A reference elipsoid must have a zero point somewhere and the mean sea level must be established from the geoid.  These are fixed for a particular UTM zone, for example, or standard parallel.

Satellite data are currently being gathered and fitted to world-centered elipsoids (e.g., WRS80) that do a better job for the entire surface of the earth as a whole, but less well than the hundred year old regional elipsoids at any given location.

And so there's a problem.  Some USGS data come from NAD27 maps (Clarke66 elipsoid) while others, like the microsoft terraserver use NAD83 (WRS80 elipsoid).....
look at datum shift (for lat long) for NAD27 to NAD83 on BV quad
Want to see it?
open demo\projections\projections_and_datums.mxd

So where are you????

The datum shift includes
initial point change (to center of earth from reference elipsoid matched to earth's surface)
change in length of elipsoid axes
ground survey network changes (local deviations, distortions, errors, tectonics)
Plate tectonics?? (opening is 15 cm/year * 60 years....)


UTM (Universal Transverse Mercator)
computers eat it for breakfast.
it reads like cartesian coordinates

here's a picture of how it works (by Peter H. Dana, The Geographer's Craft Project, Department of Geography, The University of
Colorado at Boulder)

Grid zones are 6 degrees wide with a central meridian
They start at 180 degrees west of Greenwhich and go east.  In Lexington, we're in grid zone 17, which has 81 degrees W as the central meridian.
US Grid Zones and World Grid zones

ArcMap: For UTM / Geographic comparison,

  • Open projections_and_datums.mxd from the Demo\projections folder
  • Move the dataframe projection from one grid zone to another (eg. zone 17 to zone 18, then to zone 10 !)


Source: (