Cartography Word of the Day: Spheroid, Datum

It’s a globe…but it’s a little thick around the middle

It’s a well known fact that the earth is a sphere.

Image courtesy Great Images In NASA (grin.nasa.gov)

Really? Well, no, not really.

Our planet is actually a little thick around the middle. When we say that Earth is about 8,000 mi/12,700 km through, we’re actually speaking of a mean diameter. If the Earth didn’t rotate, then it would be more nearly spherical, but the one-a-day whirling of our home planet makes the distance through the Equator 7,926 mi/12,756.27 km and through the poles 7,900 mi/12,713.5 km. About 1/300 wider than it is tall, the Earth isn’t a sphere, but an oblate spheroid–a fat ball. Since cartography proceeds from such conceptually simple bases as the size and shape of the earth, this is an important thing to be aware of.

The Spheroid

If the polar diameter is less than that the equator, then it follows that the cross section of this ball isn’t a circle, but rather a squashed circle–an ellipse. If one takes this ellipse and extrapolates mathematically into a solid, rotating it along the polar axis, we have what mathematicians call an ellipsoid or revolution, or a spheroid.

We know this is getting a bit dry, but bear with us.

Before any good map gets made, surveys are performed. Surveyors gather the raw data that go into maps from highly-detailed maps for government, science and industry and trickle down to the street-map and road-atlas user. In order to quantify everything surveyors record, to assign numbers to assign distances, altitudes, depths, and accurately locate features, surveyors require a reference to measure against. The spheroid of the Earth, as commonly known, forms the basis for that reference.

The Datum

According to the glossary produced by the Perry-Castañeda Map Collection at the University of Texas, the essential definition of datum is:

There are actually two datums, one vertical (for altitudes) and one horizonal (for distances).

The vertical datum reference surface in the United States is the National Geodetic Vertical Datum of 1929, which is essentially the mean sea level established by the U.S. Coast and Geodetic Survey in 1929.

The horizontal datum has been determined by two methods, both based on our spheroid; the North American Datum of 1927 is comprised of an initial point (Meade’s Ranch in Kansas), the direction of a line between this and a specified second point, and the dimensions of the terrestrial spheroid. However, since 1983, surveyors have used the North American Datum of 1983, based on the terrestrial spheriod defined by a standard called GRS80, being based on the known shape of the earth, having no initial point or direction.

Indirect influence

Datum information is most often found in maps used for technical purposes, and mapping done by the U.S. Geological Survey such as topological quadrangles. Popular maps, such as the average street map or road atlas, may not specifiy datum information, but since the surveying done for more technical maps can form the informational basis for the more popular maps, they do determine the information we see on them.