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Map Projections Do you know where you are? Mike Horsfall, Bentley

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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?

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Is the world spherical? It’s not flat, it’s not round, it is an Oblate Spheroid!

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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

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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?

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What is the difference between a latitude and longitude? Latitudes are parallel to equator, Longitude run pole to pole Prime meridian = Greenwich Meridian ~ GMT

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Why do we have seasons? The earth is tilted at 23.5 degrees, to celestial horizon Summer Northern Hemisphere Winter Northern Hemisphere

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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

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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

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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

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

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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.

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Projection Classifications Spherical (Latitude, Longitude) Cylindrical (Mercator or Transverse Mercator) Conic (Lambert, Albers) Azimuthal (Stereographic)

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Mercator

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Transverse Mercator

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Conic

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Azimuthal

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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

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Projection benefits

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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

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UTM Zones

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23 | WWW.BENTLEY.COM

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UTM – Scale Ground to Grid

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UTM – coordinate range Northings Eastings

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UTM in Alberta 26 | WWW.BENTLEY.COM UTM Zones in Alberta

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27 | WWW.BENTLEY.COM 3TM Zones in Alberta 10TM Projection

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UTM example – Maine Zone 19 69 degrees W

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State Plane Coordinate System

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State Plane Projections – NAD 27 UTM, Oblique Mercator, or Lambert Projections

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State Plane Example LADWP

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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

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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

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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

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State Plane Example LADWP Create KMZ file overlays with Google Earth

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Thank You

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