Map ProjectionsDo you know where you are?

Mike Horsfall, Bentley

What do we know so far?

• Is the world spherical?

• What is the circumference of the earth?

• How fast are we spinning?

• What is the difference between a latitude and a longitude?

• Why do we have seasons?

• What is GPS?

Is the world spherical?

It’s not flat, it’s not round, it is an Oblate Spheroid!

What is the circumference of the earth?

• The circumference of the earth at the equator is 24,901.55 miles / 40,075.16 kilometers

• Circumference of a circle = 2*pi*radius

• Clarke 1866 radius is 6,378,206.4 meters

How fast are we spinning?

• At the equator 24, 901 miles around / 24 hrs = ~1000 mph

• One revolution every 24 hrs = 1 earth day

• 365.25 days to revolve around the sun

• Are we spinning at the poles?

What is the difference between a latitude and longitude?

Latitudes are parallel to equator, Longitude run pole to pole

Prime meridian = Greenwich Meridian ~ GMT

Why do we have seasons?

The earth is tilted at 23.5 degrees, to celestial horizon

Summer Northern Hemisphere

Winter Northern Hemisphere

Is the North Pole really north on a compass?

Compass points to magnetic north

Magnetic North wanders

Grid north points to North Pole on the Central Meridian

What is GPS?

Conceived by DOD in 1973

Now 24 satellites, 20,000 km above earth, 12hr orbit

Broadcasts two signals, one open for public, one coded for military purposes

What is a Datum?

• A map datum is a mathematical model that describes the shape of an ellipsoid (the earth). Some examples:– Clark 1880, 1886– NAD27, NAD83, WGS84

• World Geodetic System of 1984 (WGS84) based on the GRS ellipsoid – virtually identical with the NAD83. WGS84’s previous version is WGS72.

• Prior to NAD83, the most popular datum in U.S. was NAD27, based on parameters determined by Clarke in 1866

• NAD27 from observation on earth, NAD83 from Satellites

The basics of a projection

The mathematical model to transfer a spherical object onto a flat surface.

Map Projections

(a) Azimuthal (b) Cylindrical (c) Conic. Light source positions, also called perspective positions, play an especially important role in planar projections. Different aspects, such as polar, equatorial, or oblique, will also affect the map projection.

Projection Classifications

• Spherical (Latitude, Longitude)

• Cylindrical (Mercator or Transverse Mercator)

• Conic (Lambert, Albers)

• Azimuthal (Stereographic)

Mercator

Transverse Mercator

Conic

Conic

Azimuthal

The conversion of geographic locations from a spherical coordinate system to a flat surface causes distortion.

The projection process will distort one or more of the four spatial properties listed below.

Distortion of these spatial properties is inherent in any map.

• Shape

• Area

• Distance

• Direction

Why we have different projections

Projection benefits

UTM projection has been used by several coordinate systems:

• Part of the civilian UTM system – USGS, 1977

• Part of the state plane system (SPC)

• And the military grid

It has been used for mapping:

• Most of United States

• Many other countries

• The planet Mars

The Universal Transverse Mercator Projection

UTM Zones

23 | WWW.BENTLEY.COM

UTM – Scale Ground to Grid

UTM – coordinate range

Northings Eastings

UTM in Alberta

26 | WWW.BENTLEY.COM

UTM Zones in Alberta

27 | WWW.BENTLEY.COM

3TM Zones in Alberta 10TM Projection

UTM example – Maine Zone 19

69 degrees W

State Plane Coordinate System

State Plane Projections – NAD 27

UTM, Oblique Mercator, or Lambert Projections

State Plane Example LADWP

Los Angeles Department of Water and Power

• Existing mapping is NAD27 State Plane, Zone VII feet

• Want to upgrade to NAD83 State Plane, Zone V feet,

• Compatible with City

State Plane Example LADWP

• V7 design files have 4 million false Northings and Eastings

• Could have set Global Origin to “shift” design plane to fit coordinates.

Coordinates should be: X=4136897.7790, Y=4219006.600

State Plane Example LADWP

Created user coordinate system (copy existing NAD27, Zone VII foot, subtracted 4 million off false easting and northing)

New Projection LADWP-27

Cut 4 million off False Easting and False Northing

State Plane Example LADWP

Create KMZ file overlays with Google Earth

Thank You