Maps can be prepared on many forms Earliest portable form would have

been drawn on parchment Linen Paper Plastic/Mylar

What data do maps provide us?

Date / Publisher / Printer Scale / direction / Distance / ratios Geographical Position Coordinates/ projection Features / places / legends Other information?

You can classify maps into the followingtypes

Topographical: Represents objectssuch as roads, rivers, coastline

Thematic: Represents themes suchas soil types

Chloropleths: Represents interpretedboundaries e.g. census

Isopleth: Represents imaginary lineswith “equal value” e.g. contours

All maps will provide you with a Arrow indicating both truth North (the precise top axis of the earth’s spheroid) and a magnetic north which indicates where our compasses will point to as north

North Pole

South Pole

MagneticNorth Pole

MagneticSouth Pole

For global represented of position we use degrees of Latitudes (parallels) and Longitude (meridians). The largest in length degree of latitude is the equator and forms the base line for measurements of degrees of latitude which increase until you reach the north or south pole at which point a right angle has been formed (hence the poles are 900 latitude). At 23.5 north and south latitude the tropics of Cancer and Capricorn occur respectively.

23.50

N

S

Tropicof Cancer

Equator900

In contrast to these degrees of latitude which become smaller the degrees of longitude inscribe the same-sized circumferences but do not lie parallel to each other

N900

A

aB

b

DistanceA-a > B-b

Projections In all maps an attempt is made to represent something that is curved and therefore part of the earth's surface as a flat representation. In order for a map which is a two dimensional representation of a three-dimensional earth's surface various mathematical functions are applied to transform a sphere into a plane. Since a spherical object cannot be flattened without distortion, no map projection can do more than approximate the region it attempts to represent. Lengths, areas, shapes and angles are distorted to varying degrees for different map projections.

Cylindrical projections are derived from projecting a spherical surface onto a cylinder. For example if you took you’re orange and wrapped an A4 sheet of paper around it. The paper can be arranged around the orange in a variety of arrangements

A Tangent Projection would result if you wrapped your paper vertically so that the cylinder was parallel to the meridians (lines of longitude).

Area: Many map projections are developed to be an equal area representation of the real world but distort spatial information in some way or another . Shape, direction or scale are distorted in order to achieve the equal area criteria. Albers and Azimuthal Lambert and are equal area conic projections.

Shape: Projections which represent theshape of features are referred to asconformal. Conformal projectionsusually maintain the accuracy of relativedirections. Most large-scale maps areprepared using conformal projections.Lambert conformal conic is a goodexample of this projection.

Distance: Projections which correctlyrepresent the lengths between twopoints are referred to as equidistant.Equidistant projections are useful forcalculating and summarizing lengthsand perimeter measurements offeatures

Direction: Projections which correctly depict directions (azimuths) between points on the map and its centre are referred to as azimuthal. These projections will distort one of the other maps parameters, but will represent all routes from the centre to other points as straight lines. Mercators projection work on these assumptions and are derived from estimates based on cylindrical estimates.

In the secant case, the cylinder touches the sphere along two lines, both small circles (a circle formed on the surface of the Earth by a plane not passing through the center of the Earth).

Cylindrical projections

When the cylinder upon which the sphere is projected is at right angles to the poles, the cylinder and resulting projection are transverse.

Cylindrical projections

When the cylinder upon which the sphere is projected is at right angles to the poles, the cylinder and resulting projection are transverse.

Cylindrical projections

When the cylinder is at some other, non-orthogonal, angle with respect to the poles, the cylinder and resulting projection is oblique.

Cylindrical projections

The Mercator projection is one of the best known and has straight meridians and parallels that intersect at right angles. Scale is true at the equator or at two standard parallels equidistant from the equator. This projection seriously distorts distances and areas.

The Universal Transverse Mercator (UTM) is probably the best known projection system for displaying large surfaces of the earth since it provides high levels of precision. To minimize the distortion the cylinder is wrapped around the earth transversely and is place at 60 of rotation East and West of 1800 meridian for each hemisphere. Consequently 60 zones north and 60 zones south are generated and are numbered eastward from the 1800 meridian. Cape Town lies in the 34th Zone and is referred to as UTM 34S. The UTM system is only applied from 840 North to 800 South Latitude.

Conic projections which result from projecting a spherical surface onto a cone. When the cone is tangent to the sphere contact is along a small circle such as a latitude. You can view this by twisting your A4 sheet into a cone and placing over the orange.

Albers Equal Area Conic projection allows areas to be proportional and directions true in limited areas but distorts scale and distance except along standard parallels. This is one of the most common projection used to map large countries where the east-west distances are greater than the north-south extent (e.g. USA and Russia). It is often used to represent South Africa.

Azimuthal or Planar projections are where a flat sheet is placed in contact with a sphere, and points are projected from the sphere to the sheet. You can do this by taking your A4 sheet and pressing it against the orange.

NON-PROJECTIONS

Plane: (Cartesian) - not a projection but truth to earth surface - data may be stored in this form, but it is not good for accurate measurements of distance e.g. metres.

Datums

While we often refer to the earth as a sphere, it is more correctly referred to as a geoid (defined as a hypothetical surface of the earth that corresponds to mean sea level). The earth is not a sphere since it is flattened at both poles and bulges at the equator. In addition there are significant bulges and depressions on the surface. The are hundreds of different datums which have been used to estimate the size (areas and distances) of features on the earth. Datums have evolved from those describing a spherical earth to ellipsoidal models derived from years of satellite measurements.

To best describe this geoid mathematically, we use reference ellipsoids to approximate the size and shape of the earth.

Lets look at a Map - Saldanha Bay

The name is 3217DD, what does this mean? The32 refers to the degrees South and the 17 todegree East, these two numbers define the top leftcorner of a one minute by one minute grid on thesurface of the earth. This grid square can then dedivided into four quarters each representing 30minute by 30 minutes grids and from the top leftare label A, B, C and D respectively. Each ofthese half-degree grids are in turn divided intoquarters and they to are labeled A, B, C and Drespectively.

Consequently we have divided our grid into sixteenquarter degree grids and can be represented asfollows:-

A B

DC

B

D C

A A

C

B

D

A

C

B

D C

A

D

B

References

Peter H. Dana: Coordinate Systems Overview -http://www.colorado.edu/geography/gcraft/notes/coordsys/coordsys_f.html

Peter H. Dana: Map Projection Overview -

http://www.colorado.edu/geography/gcraft/notes/coordsys/coordsys_f.html

Peter H. Dana: Geodetic Datum Overview -http://www.colorado.edu/geography/gcraft/notes/coordsys/coordsys_f.html

Copyright for pictures used

Peter H. Dana, The Geographer's Craft Project, Department of Geography,The University of Colorado at Boulder.

Please contact the author or Kenneth E. Foote at k.foote@colorado.edu.