GPS Waypoints MAP Projections

A Brief Examination of MAP Projections and Datums

(with acknowledgement to The SeisSoft Company at http://www.connect.net/jbanta/datumbs.html)

So, what's a Projection, and what's it got to do with ME?

Summary: If You use a map, you use Projections.Well... basically, the Earth's a Sphere (more or less) and maps are flat.A projection is the operation used to convert between a location on the surface of a sphere (latitude/longitude) to a location on a plane (x/y). Any such projection requires distortion. Selecting a projection to minimize the distortion over a mapping area is a problem that has been bothering people for a long time. Projections were known, used and argued about in Ancient Greece before 200 B.C. The famous Greek astronomer Claudius Ptolemy ( circa 150 A.D.) wrote extensively on the subject. Europeans, having always been a little behind those from the Mediterranian, only started worrying about the subject in the early 16th Century (when they finally figured out that the world was a sphere (sort of)).Now, you may ask, what's so difficult about converting from spherical coordinates to cartesian coordinates? Well, try this experiment: using an exacto knife, try to cut a ping-pong ball into pieces that lie flat. Can't be done. Now, also using a knife, cut the peel of an orange into pieces that lie flat. This can be done, sort of, if you are willing to stomp on the pieces until they stretch some. So... you can't convert between the surface of a sphere and a plane without distortion. But, in planning your projection, you can choose what type of distortion you introduce into your map.For a technical view on Map projections - look here for info from the Chief Directorate Surveys and Mapping, Department of Land affairs, South Africa

So, What's this Spheroid Stuff?

The Earth is not a sphere. It is approximately a spheroid. The relative difference in length between the Earth's Polar / Semiminor / Short radius and its Equatorial / Semimajor / Long radius is around 1 part in 300. This is insignificant in maps of global scale, but significant for maps of continental or smaller scales. For most purposes, the shape of the Earth can be described with a pair of constants:

Semimajor and semiminor radii
Semimajor radius and flattening
Semimajor radius and eccentricity

These three pairs of constants are interchangeable. This is not surprising, as flattening and eccentricity are just permutations of the semimajor and semiminor radii.

Ok Now, What's a Datum?

Basically, a datum is an admission of failure. With satellites, Mankind can now measure the shape of the Earth with fair accuracy. But before this, men measured the Earth with very-long surveys. Everyone knew that the estimates derived from these data were wrong. The proof of the pudding was that no two geodesists ever came up with the same figure. In fact, single geodesists couldn't come up with the same figure twice in a row (e.g. Clarke 1866, Clarke 1880). A datum is when surveyors all get together and agree to be wrong. They take a spheroid model of the Earth and fix it to a base point. For NAD27, the U.S.G.S. decided that Clarke 1866 was a good approximation, and they fixed it at Meade's Ranch, Kansas. Unfortunately, because the datum is wrong, and because it is fixed, as one moves away from this point, errors pile up. To eliminate these errors, the surveyor is eventually forced to switch to a different datum. When this happens, maps no longer tie. Very scary things happen when you switch datums. Even (or maybe especially) when you switch datums without moving. If I stand in the middle of the intersection of Baseline Road and County Line Road near Boulder, Colorado. I am standing at exactly 40 N. Latitude, 105 W. Longitude (really, that's why they named it Baseline Road). This is true, as long as I am using NAD27. But when I change to NAD83, without moving an inch, I'm no longer at 40 N, 105 W. In fact, I'm now at 39deg 59min 59.97sec N, 105deg 00min 01.93sec W. This is four feet south and fifty feet west from 40 N, 105 W. That's right, Latitude / Longitude alone does not uniquely describe a location on the surface of the Earth. Changing the datum changes the Lat/Lon of a point on the surface of the Earth. This is important, let me say it again: Describing a place by Lat/Lon is not good enough.The ideal solution to all of the above problems would be an spheroidal model that has both the correct equatorial and polar radii, and is then centered on the actual center of the Earth. One would then have a spheroid, that when used as a datum, would accurately map the entire Earth. All lat/lons on all maps would agree. That spheroid, derived from satelite measurements of the Earth, is GRS80, and the datums that match it are NAD83 and WGS84.

So what's the REAL shape of the Earth? or... Who's got the Geoid?

So what's the Earth really shaped like? It's not a sphere, it's only sort of a spheroid. The actual shape of the Earth depends upon who you talk to. There are two surfaces that people refer to as the 'shape' of the Earth. The first is the topographic surface of the Earth. This one's easy to understand. It's where the Lithosphere meets either the Atmosphere or the Hydrosphere. The second is the Mean Sea Level (MSL) Geoid. It is necessary to preface 'The Geoid' (in capital letters) with MSL, as there are an infinite number of geoids. A geoid is an equipotential surface with respect to the gravitational acceleration of the Earth. That is to say, an object anywhere on the surface of the geoid will have the same potential energy. Another aspect of an equipotential surface is that the acceleration due to gravity is always perpendicular to the geoid. Or, gravity always points straight down towards the geoid. Or, an equipotential surface is 'flat' with respect to gravity. A picture of the MSL Geoid appears rugose, (rippled) from above, and in fact is rugose due to local variations in the Earth's gravitational field (See the NOAA picture of the MSL Geoid under North America). To a person walking however, a geoid appears 'flat'. More importantly, to a person surveying, the geoid is 'flat'. So, if the MSL Geoid is the 'true shape of the Earth', how well does the WGS84 datum match this surface? It turns out to be an amazingly good fit. For most of the Earth the deviation between the MSL Geoid and the WGS84 Datum is within +/- 40 meters. The two exceptions are a Northern Mid-Atlantic high in the MSL Geoid, centered on the Mid-Atlantic Ridge, where the geoid reaches slightly more than 60 meters above the datum, and a Southern India low, just off the Southern tip of India, where the geoid reaches slightly more than 100 meters below the datum.

For a really neat picture of the North American Geoid and other cool Geoid stuff, click here. (Brought to you by NOAA).For related info try these links to the University of Calorado's archives:

Map Projections

Co-ordinate systems

GPS system