Transcript Map Projections Do you know where you are?

Map Projections
Do 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
Why we have different projections
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
Projection benefits
The Universal Transverse
Mercator Projection
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
UTM Zones
23 | WWW.BENTLEY.COM
UTM – Scale Ground to Grid
UTM – coordinate range
Northings
Eastings
UTM in Alberta
UTM Zones in Alberta
26 | WWW.BENTLEY.COM
3TM Zones in Alberta
27 | WWW.BENTLEY.COM
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