### Projections and Coordinates

```Grid Systems
Transverse Mercator Projection
Universal Transverse Mercator
South Dakota
Zone 16
• Based on Transverse Mercator (cylindrical) projection
• World divided into 60 zones 6 degrees wide
• Distortion is minimal within each zone
• Maps of different areas use best zone
Copyright
© 2009for
by Maribeth
• Best
maps covering small3-3area in one zone
H. Price
UTM Zones
UTM Pole to Pole
Halfway to the Pole
Using UTM
Using UTM
Using UTM
Three Kinds of North
• True North – Along Meridians
• Magnetic North – What a compass detects
– Important in field
– Not important in most GIS
• Grid North – Along N-S grid lines
– Minor importance for compass work
– Be aware there’s a difference!
– Military uses exclusively
Cautions About UTM
• Military maps use two letter codes for each
100-km square, but maps will have
information to enable conventional UTM
• With military grid references, number of digits
indicates level of precision
• Older maps will sometimes have obsolete
grids
• Datum, datum, datum!
Military Grid System
•
•
•
•
•
•
45N 89 W = E 342,369, N 4,984,896 Zone 16T
Digraph = CQ
1 km accuracy = 16T CQ 42 84
100 m accuracy = 16T CQ 423 848
10 m accuracy = 16T CQ 4236 8489
1 m accuracy = 16T CQ 42369 84896
• Ticks on USGS topo map = 342,000, 4,984,000
Where Zones Meet
Why a Grid?
Latitude /Longitude
Grid System
North varies from place to
place on the map
Grid north is always the same
direction
Angular units differ in scale
between N-S and E-W
Grid scale the same in all
directions
E-W angular units vary in scale
with latitude
Grid squares are always the
same size and shape
Hexadecimal Scale
Decimal Scale
State Plane System
• States divided into
one or more
zones identified
by a unique FIPS
number
• Uses several types
of projections
• E-W zones
generally Conic,
N-S zones
generally UTM
Copyright © 2009 by Maribeth
H. Price
3-15
Projections for large scale maps
• Local, city, county maps, smaller states
– Projection systems virtually eliminate distortion
– Choose appropriate UTM or State Plane zone
Copyright © 2009 by Maribeth
H. Price
3-16
Wisconsin
State
Plane
Zones
Wisconsin
Grid
Systems
Projections for smaller scales
• Distortion is inevitable, so
purpose drives the choice
– Equidistant maps when
distances are important
– Equal area maps when areas
are important
– Conformal or compromise
projections for general
purpose maps
Copyright © 2009 by Maribeth
H. Price
Coordinate system names generally
indicate the locale and purpose it is
optimized for. Use for clues to choice.
3-19
Metes and Bounds System
Public Land Survey System
• AKA Congressional System
• Established 1785
• Does not apply to:
– 13 Original Colonies
– Derivative States (VT, KY, TN, ME, WV)
– Texas (Former independent country)
– Hawaii (Uses Kingdom of Hawaii system)
• Land Division
– 6 x 6 mile townships, 36 sections, quarter sections
USA Public Land Surveys
NonCongressional
Grids
Before
Greenwich
Arbitrary Geography
More Arbitrary
Geography
Grid vs. No Grid
Gridded Landscape
Where Wisconsin’s Grid Starts
Where California’s Grid Starts
Section Numbering
Wisconsin
Townships
Township Labels
Section
Descriptions
Limitations of
the
Congressional
Land Survey
System
Congressional Land Survey System
• Not an accurate grid!
• Locations within subdivisions may be
imprecise
• Data points used in GIS may be tied to system
• Authoritative surveys are forever
– French strips in LA, MO, WI
– Spanish and Mexican land grants
French Long Lot System
French Long Lot System
California: PLSS and Land Grants
California: PLSS and Land Grants
Oh, Canada
• Eastern Canada: Metes and Bounds, Long Lot
• Northern Ontario: 6 and 10-mile townships
• Western Canada: Dominion Land Survey
–
–
–
–
–
–
–
Modeled on PLSS
6-mile townships
Townships numbered N-S with Arabic numerals
Ranges numbered E-W with Arabic or Roman numerals
Road allowances between sections
Sections zigzag from 1 in SE to 36 in NE (Opposite US)
¼-1/4 sections numbered from 1 in SE to 16 in NE
Dangers of Cheap Work
Missed It By That Much
```