Projections
Projections used in State Plane Coordinate Systems
 "To convert geodetic positions of a portion of the Earth's surface
to plane rectangular coordinates, points are projected mathematically
from the ellipsoid to some imaginary developable surface
a surface that can conceptually be developed or 'unrolled and laid
out flat' without distortion of shape or size. A rectangular grid
can be superimposed on the developed plane surface and the
positions of points in the plane specified with respect to X and Y
grid axes. A plane grid developed using this mathematical process is
called a map projection.... Today, two of the most commonly
used mapping projections are the Lambert conformal conic and the
Transverse Mercator projections." (Elementary Surveying,
12th Edition by Ghilani and Wolf, p. 580)
Types of Projections
State Plane Coordinate System (SPCS)
 "...points couldn't be projected from the ellipsoid to developable
surfaces without introducing distortions in the lengths of lines
or the shapes of areas. However, these distortions are held to a
minimum by selected placement of the cone or cylinder secant to the
ellipsoid, by choosing a conformal projection (one that
preserves true angular relationships around points in a small region),
and also by limiting the zone size or extent of coverage on the Earth's
surface for any particular map projection. If the width of zones is
held to a maximum of 158 mi (254 km), and if twothirds of this zone
width is between the secant lines, distortions (differences in line
lengths on the two surfaces) are kept to 1 part in 10,000 or less.
The NGS intended this accuracy in its development of the state plane
coordinate systems." (Elementary Surveying, 12th Edition by Ghilani
and Wolf, p. 5812)
 Clark County uses StatePlane Coordinate Nevada East Zone (NVE)
along with other local agencies (e.g. City of Las
Vegas, Henderson, North Las Vegas, and so on)
 Map of all Stateplane coordinate zones is included with ArcMap,
depending upon where you installed the program, e.g.
C:\Program Files\ArcGIS\Reference Systems\usstpln83.shp
(download zip of shapefiles from UNLV,
usstpln83.zip 
Geographic Coordinate System  GCS_WGS_1984)

 State Plane Coordinate System of 1983 NOAA
Manual NOS NGS 5 by James E. Stem
 "A new figure of the Earth, the Geodetic Reference System
of 1980 (GRS 80), which approximates the Earth's true size
and shape, supplied a better fit than the Clarke 1866 spheroid,
the reference surface used with NAD 27." (ibid p. 2)
 "The ellipsoid that forms the basis of NAD 83, and consequently
the SPCS 83, is identified as the Geodetic Reference System of
1980 (GRS 80). GRS 80 provides an excellent global approximation
of the Earth's surface. The Clarke spheroid of 1866, as used for
NAD 27 approximated only the conterminous United States. Because
the geoid separation at point MEADES RANCH was assumed equal to
zero, a translation exists between ellipsoids. The ellipsoid change
is the major contributor of the coordinate shift from NAD 27 to NAD 83."
(ibid p. 12)
 NAD 27  U.S. coast and Geodetic Survey (USC&GS) Special
Publication 235  The State Coordinate Systems
 Fundamentals of the State Plane Coordinate Systems
 U.S. Coast and Geodetic Survey. Manual of Traverse Computation on
the Transverse Mercator Grid by Oscar S. Adams, Senior Mathematician
and Charles N. Claire, Associate Mathematician. GPO, Washington, DC, 1935.
199 pages. Special Publication No. 195.
 Publication of North American Datum of 1983 State Plane Coordinates in Feet in Nevada
State Plane Coordinates Presentation by Dr. Ghilani
National GeospatialIntelligence Agency Geodesy and Geophysics
Fundamentals of the State Plane Coordinate Systems by
Joseph F. Dracup, Sept 1974. National Geodetic Survey
Map Projections: A Working Manual by John P. Snyder. USGS
Professional Paper 1395. Washington, D.C.: USGS, 1993.
 GRS 80
 Equatorial Radius/Semiaxis, a = 6,378,137 meters
 Polar Radius/Semiaxis, b = 6,356,752.3 meters
 Flattening, f = 1/298.257
 "in computations if the ellipsoid is assumed a sphere, its radius is
usually taken such that its volume is the same as the reference
ellipsoid. It is computed from (a^{2}b)^{1/3}. For
the GRS80 ellipsoid, its rounded value is 6,371,000 meters."
(Elementary Surveying, 12th Ed, Ghilani and Wolf, p. 523)
 WGS 84
 Equatorial Radius, a = 6,378,135 meters
 Polar Radius, b = 6,356,750.5 meters
 Flattening, f = 1/298.26
 Nevada East Zone Map Projectsion: A Working Manual, p. 53 and 374
 Transverse Mercator Projection
 Central meridian = 115°35' West
 ESRI uses 115.583333333333300000 decimal degrees = 115°35'
 Scale reduction = 1:10,000
 ESRI uses a scale factor of 0.999900000000000010
 "Lines of contact. Any single meridian for the tangent project.
For the secant projection, two almost parallel lines equidistant from the
central meridian...Accurate scale along the central meridian if the scale
factor is 1.0. If it is less than 1.0, there are two straight lines
with accurate scale equidistant from and on each side of the central meridian."
(ESRI ArcGIS Transerve Mercator)
 Origin (latitude) = 34°45' North
 ESRI uses 34.7500 decimal degrees = 34°45'
 Coordinates of Origin (meters): False Easting x=200,000 and False Northing y=8,000,000
 "State plane coordinate systems are generally designed to have a
scale error maximum of about 1 unit in 10,000. Suppose you calculated
the Cartesian distance (using the Pythagorean theorem) between two
points represented in a state plane coordinate system to be exactly
10,000 meters. Then, with a perfect tape measure, pulled tightly
across an idealized planet, you would be assured that the measured
result would differ by no more than 1 meter from the calculated one.
The possible error with the UTM coordinate system may be larger:
1 in 2500." (Introducing Geographic Information Systems with ArcGIS,
2nd Edition by Michael Kennedy, p. 18)
 Datum: NAD 1983 (Conus) (Mol) is used on the Trimble TSC2


 GPS Course Lesson 6: TwoCoordinate Systems and Heights by Jan Van
Sickle, Senior Lecturer
 "...the projection of points from the Earth's surface onto a reference
ellipsoid and finally onto flat maps..." (ibid)

 Stateplane Coordinates in USA use Secant Projections to minimize distortion
by providing 2 lines of intersection instead of one line with the Tangent case.
Secant Projection intersect the ellipsoid at two areas and these two lines
are of exact scale (also known as standard lines) to the ellipsoid.

 Ellipsoidal lengths = geodetic distances
 Lengths on the map projection surface = grid distances
 Grid North is parallel to the Central Meridian. Convergence is the angle
between Grid North and Geodetic North
 False Easting and Northing
 False easting is a linear value applied to the origin of the x coordinates.
 False northing is a linear value applied to the origin of the y coordinates.
 False easting and northing values are usually applied to ensure that all x
and y values are positive.
 False easting and false northing adjustments by Margaret M. Maher
 "False easting and false northing values are sometimes inserted into
a projection file in order to make all the x and ycoordinate values
across the area of the data positive numbers. False easting and false
northing values can also be used to adjust the position of the data in
either the eastwest or northsouth direction in order to align the
data.
Making the false easting value in the projection file larger will adjust
the position of the data to the west, moving the data to the left in the
ArcMap display. Making the false easting value in the project file smaller
will adjust the position of the data east, to the right in the ArcMap
display.
Adjustments to the false northing value in the projection file will move
the data display north or south, though they are not as intuitive as the
false easting adjustments. Making the false northing value in the projection
file larger will move the data display south in the ArcMap window. Making
the false northing value smaller will move the data display north in
the ArcMap window.
Keep these adjustments in mind while creating the custom projection file
to align your data in ArcMap." (Lining Up Data in ArcGIS by Margaret
M. Maher, p. 55, ISBN 9781589482494)
 "A constant E_{0} is adopted to offset the N grid axis from
the central meridian and make E coordinates of all points positive. Similarly,
a constant N_{b} can be adopted to offset the E grid axis from the
southern edge of the projection." (Elementary Surveying, 12th Edition
by Ghilani and Wolf, p. 587)
 You can also use the false easting and northing parameters to reduce the range
of the x or y coordinate values. For example, if you know all y values are greater
than 5,000,000 meters, you could apply a false northing of 5,000,000.
 ESRI ArcGIS Desktop 10  Projection parameters

 False Northing  NAD27 vs NAD83
 According to David Doyle with NGS, metadata is hard to obtain on current surveying
work but was extremely difficult in the 1980s. So, the State of Nevada wanted to ensure
when surveyors where working with the two different Datums (NAD27 and NAD83) that
a surveyor could easily tell from the coordinate values, which Datum is being used.
So the NAD83 coordinates have a 8,000,000 meters added to the Northing (Y)
coordinate values.
 NAD27  Nevada East Zone uses a False Northing of 0 ft
 NAD83  Nevada East Zone uses a False Northing of 8,000,000 meters (26,246,666.66666666 feet)
 Notice how the same data (city boundaries in Clark County NV) do not overlay,
that is the NAD83 is shifted 8,000,000 meters north of the NAD27 layer
 Conversion from NAD83/27 to Geodetic/Geographic
 Central Meridian (Longitude)
 Notes from Earl F. Burkholder, PS, PE with
Global COGO, Inc., Las Cruces NM 88003
 Central Meridian (Longitude) is a north/south line and secant lines in a transverse
Mercator projection are parallel to the central meridian. Problem is Longitude lines
are not parallel because the all converge at the poles.
 The easting of a secant line will vary slightly from the south end of the state to
the north end.
 secant line in state plane coordinates is always a constant distance from the
central meridian.
UTM
How to draw the SPCS origin
 Step 0: download the World GeoReference Lines
 Step 1: Identify the SPCS Defining Parameters
 If you have ArcGIS installed on your computer, view the projection file (.prg)
C:\Program Files\ArcGIS\Coordinate Systems\Projected Coordinate Systems\State Plane\NAD 1983\NAD 1983 StatePlane Nevada East FIPS 2701.prj
 Elementary Surveying, 12th Edition by Ghilani and Wolf,
Appendix F (and definitions on p. 586) U.S. State Plane Coordinate System Defining Parameters
 Step 2: Create a shapefile using WGS84 geographic coordinates (e.g. GCS_WGS_1984)
 Use ArcCatalog to create a new shapefile. Assign it the GCS_WGS_1984 projection
 Step 3: create gratitcules
 Using an ArcMap edit session, add the line features using Absolute X,Y to enter the
latitude and longitude values
Scale Factors
 scale factors move distances from the stateplane grid to the ellipsoid
 "After a distance has been reduced to its ellipsoidal equivalent, it
must then be scaled to its grid equivalent. This is accomplished by multiplying
the ellipsoidal length of the line by an appropriate scale factor."
(Elementary Surveying, 12th Ed, Ghilani and Wolf, p. 599)

 Scale, Elevation, Grid, and Combined Factors Used in Instrumentation.
Professional Surveyor Magazine  Feb 2006
Coordinate Systems (Geographic and Projected) in ArcMap
When adding data to ArcMap, will sometimes get a warning message "One or
more layers is missing spatial reference information, Data from those layers
cannot be projected"
 "If you add a layer that is in a projected coordinate system to ArcMap,
and the coordinate system information is missing" will get that message.
Much of the time this is not a problem. You can still display and work with
this data as long as ArcMap does not need to project it on the fly. ArcMap
will not be able, however, to align this data with data in a different
coordinate system."
[Ormsby
01, p. 340]
Map Projections
 Mathematical transformation of a model of the earth's shape (i.e. Oblate
Spheroid) to a flat surface (grid). [Ormsby
01, p. 324]
 Can distort shape, area, distance, and direction
 Geographic Coordinates System (GCS)
 based on a curved surface
 Sphere  less accurate approximation of the shape of the earth
 Spheroid  more accurate approximation of the shape of the earth (most widely used)
 Geoid  most accurate model of the shape of the earth
 a measurement of a location on the earth's surface expressed in
degrees of latitude and longitude. Tend to have a "taffypull appearance" when displaying
[Ormsby
01, p. 331]
 GCS includes: angular unit of measure (e.g. degrees), prime meridian
(i.e. line of zero longitude which passes through Greenwich England), and
a datum (e.g. position of spheroid relative to the center of earth,
typically use North American Datum of 1983 a.k.a. NAD83)
 Latitude: horizontal lines (e.g. equator) and also known as parallels.
Measurement values range from 90 to 90 degrees
 Longitude: vertical lines, also known as merdians. Measurement values
range from 180 to 180 degrees.
 Degrees  1/360th of a cirle
 Minutes  1/60th of a degree, or 60 minutes = 1 degree
 Seconds  1/60th of a minute, or 60 seconds = 1 minute

 See ESRI Virutal Campus  Learning ArcGIS 9, Module 3 for more details
 Projected Coordinates
 based on a flat surface
 does NOT use spheriods, spheres, or geoids since these are approximations of the shape of the earth
 also known as planar coordinates
 a measurement of a location on the earth's surface expressed in a
twodimensional system that locates features based on their distance from
an origin (0,0) along two axes.
 Map projections transform latitude and longitude to x,y coordinates in a
projected coordinate system.
 Latitude and Longitude can located exact locations on the earth, but no
uniform units of measurement (see figure on [Ormsby 01, p. 326])
 If all your GIS data is using the same coordinate system, don't have to
worry about projections
 Empty data frames inherit the projection of the first layer added to it.
[Ormsby 01, p. 333]
 Onthefly Projections, [Ormsby 01, p. 328, 336]
 ArcMap determines if the coordinate system is geographic or projected by
comparing the coordinates. Lat/Long values will be in the tens (Lat=36
degrees) and hundreds (Long=115 degrees), where as Stateplane coordinates
hundred thousand (e.g. x=800,000) and tens of million (y=26,750,000)[Ormsby
01, p. 340]
 Onthefly projections are less mathematically rigorous than permanent
projections done using the ArcToolbox Projection Wizard.
[Ormsby 01, p. 330]
 Onthefly projections are defined by the Layer Properties. Note this
doesn't change the actual file. Projection only applied to data frame.
[Ormsby 01, p. 330]
 "... a coordinate system is a framework for locating features on the
earth's surface using either latitudelongitude or x,y values."
 Works well when the data has the same geographic coordinate system
(GCS). [Ormsby 01, p. 329]
 To transform the coordinate location of a CAD file using coordinate
values in ArcMap, see
ESRI Article Number 20860
 Projection info is assigned to the feature dataset, not the geodatabase.
Note all feature classes in a feature dataset must have the same projection.
Doesn't appear that all feature datasets need to have the same projection in
a geodatabase. Remember a feature class can be contained in a feature
dataset, which will ensure it has the same projection info, or can be a
standalone feature class.
 ESRI software does not support vertical datums. Only reads the zvalue
as is, you must perform any preprocessing/corrections to the vertical data
before entering into ArcGIS. Appears the projection metadata doesn't allow
you to enter any additional zvalue related data (for example NAVD88 datum,
elevation units of feet, and so on).fs
How to Project Geodatabases and Shapefiles
 Projections in ArcMap
 Can project the data frame, not the actual feature class, shapefile,
or coverage.
 Can export the layer with the same projection as the data frame, so in
a sense your actually reprojecting the layer.
 ArcMap will not project data on the fly if the coordinate system for
the data set has not been defined.
 Additional info, see ESRI
Article ID 24893,
How to identify an unknown coordinate system using ArcMap.
 ESRI Article ID 20837, how to align vector data in ArcMap
 Projections in ArcCatalog
 Can only define a projection for a layer, not reproject it.
 Data frame will inherit the projection of the first layer added to it.
 ArcCatalog: select a geodatabase feature, right mouse click to bring
up the context menu, Properties > Fields tab, select Shape, then at
the bottom of that window, click the ellispe (...) and either Select or
Import.
 Projections in ArcToolbox
 Will reproject the layer permentently
 ArcToolbox: Data Management > Projections > Project Wizard
(shapefiles, geodatabase)
 Reference: see ESRI Article ID 21447 how to project shapefiles or geodatabase feature
classes with the ArcToolbox Project wizard
Define a Shapefile's Projection
 Using ArcCatalog
 Problem: metadata, spatial reference property says "unknown" or
"assumed geographic" projection.
 File > Properties > Fields tab: click Shape column. In
Properties list below, select ellipses button to open the Spatial
Reference Properties window. Click Select... button. Browse through
Projected Coordinate Systems folder > State Plane folder > NAD
1983 (Feet) folder > NAD 1983 StatePlane Nevada East FIPS 2701
(Feet).prj
 Metadata should now say the projected coordinate system name.
 Shapefile's coordinate system parameters are stored in the same
location and name as the shapefile but with a .prj extension
 see ArcGIS Desktop Help > ArcCatalog > Working with shapefiles
> Defining a shapefile's coordinate system

 Using ArcToolbox
 ArcToolbox > Data Management Tools > Projections > Define
Projection Wizard (shapefiles, geodatabase). Then give same inputs as the
"Using ArcCatalog" solution above.
 see [Ormsby 01, p. 341346]
Define a ArcInfo Coverage's Projection
Define a GeoDatabase feature class Projection
Common Coordinate Systems used in Clark County NV
 StatePlane Coordinate System (SPCS)
 Projection used by local agencies (e.g. Clark County, City of Las
Vegas, Henderson, North Las Vegas, and so on)
 Map of all Stateplane coordinate zones is included with ArcMap,
depending upon where you installed the program,
c:\arcgis\arcexe83\Reference Systems\usstpln83.shp or
C:\Program Files\ArcGIS\Reference Systems\usstpln83.shp
(download shapefiles from UNLV,
usstpln83.zip 
Geographic Coordinate System  GCS_WGS_1984)
 Clark County uses StatePlane Coordinate Nevada East Zone (NVE)

 ArcGIS Resource Center  view of
USSTPLN83.shp
 Universal Transverse Mercator, UTM
 Earth is divided into 60 zones (each zone 6 degrees of longitude)
 Origin for each zone is the Equator and its central meridian (3
degrees west and 3 degrees east). To eliminate negative coordinates, a
false easting of 500,000 is applied
 Typically used for statewide datasets
 Map of all UTM zones is included with ArcMap, depending upon where you
installed the program, c:\arcgis\arcexe83\Reference Systems\utm.shp or
c:\Program Files\ArcGIS\Reference Systems\utm.shp (download shapefiles from UNLV,
utm.zip 
Geographic Coordinate System  GCS_WGS_1984) and overlay with the USA Counties Layer
countyp020.zip
from the National Atlas
 Best way to show two datasets that are in different UTM zones, is to
project one into the other zone.
 State of Nevada uses UTM Zone 11

 Margaret Maher (mmaher@esri.com) with ESRI Tech Support  specialize in Map Projections and Symbology
 Local/Surface Coordinates
 Used extensively for small development projects by surveyors
 referred to as ground distances by surveyors
 different origin for each design project
 To project into another coordinate system, need 2 points and have
coordinate values in both systems.
Define Local/Surface Coordinate Projection in ArcMap
 Objective is to create a projection file so ArcMap can project on the
fly from local/surface coordinates to stateplance coordinates. The
projection file (.prj) will be similar to a shapefile file .prj file but for
the AutoCAD .dwg, example anyfilename.dwg and anyfilename.prj (note cannot
have any spaces in the filename for the .dwg and .prj files). Then ArcMap
will automatically project the dwg.
 Most difficult step is determining the local/surface coordinate
parameters
 ArcMap Data Frame Properties > New > Projected Coordinate System
 Projection name cannot contain spaces
 Custom Projection File options for 7 local/surface projections
 Local
 Parameters
 False_Easting
 False_Northing
 Scale_Factor
 Azimuth
 Longitude_Of_Center
 Latitude_Of_Center
 Linear Unit = Foot_US
 Datum is defined by Select... button under Geographic Coordinate
System, select North America folder
 North American Datum 1983.prj
 North American 1983 HARN.prj (use if survey done to HARN accuracy)
 North American 1983 (CSRS98).prj is for Canada
 Hotine_Oblique_Mercator_Azimuth_Center
 Hotine_Oblique_Mercator_Azimuth_Natural
 Hotine_Oblique_Mercator_Two_Point_Center
 Hotine_Oblique_Mercator_Two_Point_Natural
 Rectified_Skew_Orthomorphic_Center
 Rectified_Skew_Orthomorphic_Natural_O (has a rotation parameter)
Alternative method is to Define a Projection using ArcToolbox
Indepth Discussion on Projections