what you need to use the state plane coordinate...
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WHAT YOU NEED TO USE THE STATE PLANE COORDINATE SYSTEMS
N & E State Plane Coordinates for Control Points
AZIMUTHS- True, Geodetic, or Grid- Conversion from Astronomic to Geodetic
(LaPlace Correction)- Conversion from Geodetic to Grid
(Mapping Angle)
DISTANCES- Reduction from Horizontal to Ellipsoid
“Sea-Level Reduction Factor”- Correction for Grid Scale Factor- Combined Factor
THREE DISTANCES:
• “GROUND” DISTANCE = NORMAL TO GRAVITY BETWEEN TWO POINTS
• “GEODETIC” DISTANCE = ALONG THE ELLIPSOID
• “GRID” DISTANCE = ALONG THE MAP PROJECTION SURFACE
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• PROJECTED COORDINATES ARE ALWAYS DISTORTED
DEFINITIONS
• GRID SCALE Factor
– Multiplier to change geodetic distances based on the Earth model (ellipsoid) to the grid plane.
• ELEVATION Factor (a.k.a. Sea Level Reduction or Ellipsoid Reduction Factor)
– Multiplier to change horizontal ground distances to geodetic (ellipsoid) distances
• GRID-ELEVATION or COMBINED Factor
– Gird Scale Factor times the Elevation Factor
• This factor changes horizontal ground distances to grid distances
Normal to ellipsoid
AZIMUTH RELATIONSHIP
“True” Azimuth – Derived from astronomic observations (e.g. Solar/Polaris) –this can usually be considered the same as a geodetic azimuth.
Geodetic Azimuth – Derived from the inverse between two points of known latitude and longitude, or from a LaPlace corrected astronomic azimuth or a
grid azimuth with the mapping angle () applied
Grid Azimuth – Derived from the inverse between two points defined in northing & easting, or from a
geodetic azimuth - the mapping angle ()
(e.g. State Plane, UTM, local grid coordinates)
ELLIPSOID - GEOID RELATIONSHIP
EllipsoidGRS80
Geoid
LaPlace Correction+/- 0 ~ 25” Lower 48 states
NGS Tool – DEFLEC09
LAMBERT CONFORMAL CONICWITH 2 STANDARD PARALLELS
Approximately 154 miles
CENTRAL MERIDIAN
STANDARD PARALLELS
N
S
λO
CONVERGENCE ANGLE(Mapping Angle)
CENTRAL MERIDIANλO
Convergence angles () always positive (+) East
Convergence angles () always negative (-) West
The Convention of the Sign of the Convergence Angle is Always From Grid To Geodetic
TRANSVERSE MERCATOR
CENTRAL MERIDIAN
SC
AL
E E
XA
CT
SCALE < 1 SCALE > 1SCALE > 1
λO
Pennsylvania State Plane Coordinate System – NAD 83
False Northing and Easting Changedand defined in meters
Conversion to Feet left up to individual states
U.S. Survey or International Feet
Geometric Parameters remain the sameAs NAD 27
Zone BoundariesCentral Meridian
North/South Standard ParallelsLatitude/Longitude of Origin
ORIGIN39o 20’ 00”77o 45’ 00”
N = 0 mE = 600,000 m
COORDINATE CHANGES(STATE PLANE)
STATION: STRAUSS (pid KW0527)
PENNSYLVANIA SOUTH ZONE (NAD 27/NAD 83)
Northing Easting Converg Angle Scale Factor428,352.11 ft. 2,433,279.72 ft. +1o 00’ 39.0” 0.99995985130,575.318 m. 732,088.384 m. +1o 00’ 39.8” 0.99995985
(428,395.86 ft)* (2,401,859.97 ft)*(428,396.71 ft)# (2,401,864.78 ft)#
(0.15) (4.81)
* Converted using U.S. Survey Foot, 1 M = 3.2808333333 Ft.# Converted using International Foot, 1 M = 3.2808398950 Ft.
Michigan Compiled Laws, Public Act 9 of 1964, Sections 54.231- .239,
STATE PLANE COORDINATE COMPUTATION
STRAUSS (pid KW0527)
N = 428,395.86 U.S. Survey Feet
E = 2,401,859.97 U.S. Survey Feet
Orthometric Height (H) = 642.24 Feet
Geoid Height (N) = - 113.32 Feet
Laplace Correction = - 2.6”
Grid Scale Factor (k) = 0.99995985
Meridian Convergence () = + 1o 00’ 39.8”
Observed Astro Azimuth (A) = 253o 26’ 14.9”
Horizontal Distance (D) = 3,314.91 Feet
STATE PLANE COORDINATE COMPUTATION
N1 = N + (Sg x cos g)
E1 = E + (Sg x sin g)
Where:
N = Starting Northing Coordinate
E = Starting Easting Coordinates
Sg = Grid Distance
g = Grid Azimuth
REDUCTION TO THE ELLIPSOID
h
N
H
REarth Radius
6,372,200 m
20,906,000 ft.
S
D
S = D * ___R__
R + h
Where: h = H + [N]
S = D *
R + H + (N)
___R___
REDUCTION TO THE ELLIPSOID(The correct method)
WHERE
_____________N
1 – e’2 cos2 f cos2 R =
_____________a
(1 – e’2 cos2 f)1/2
N =
e’2 = (a2 – b2) / b2
N = Radius of Curvature in Azimutha = Ellipsoid semi-major axisb = Ellipsoid semi-minor axis= Azimuth of the linef = Latitude of the Station
REDUCTION TO ELLIPSOIDEllipsoid Ht /Orthometric Ht
Sgeodetic = D x [R / (R + h)]D = 3,314.91 ft (Measured Horizontal Distance)R = 20,906,000 ft (Mean Radius of the Earth)h = H + N (H = 642 ft, N = - 113 ft)
= 529 ft (Ellipsoid Height)
S = 3,314.91 [20,906,000 / 20,906,000 + 529]S = 3,314.91 x 0.99997470S = 3,314.83 ft
Sgeodetic = 3,314.91 [20,906,000 / 20,906,000 + 642]Sgeodetic = 3,314.91 x 0.99996929Sgeodetic = 3,314.81 ft
Diff = 0.02 ft or ~ 1:166,000
REDUCTION TO ELLIPSOIDMean Radius vs. Computed Earth Radius
Sgeodetic = D x [R / (R + h)]D = 3,314.91 ft (Measured Horizontal Distance)R = 20,906,000 ft (Mean Radius of the Earth)R = 20,936,382 ft (Computed Radius of the Earth)h = 529
Sgeodetic = 3,314.91 [20,906,000 / 20,906,000 + 529]Sgeodetic = 3,314.91 x 0.99997470Sgeodetic = 3,314.83 ft
Sgeodetic = 3,314.91 [20,936,382 / 20,936,282 + 529]Sgeodetic = 3,314.91 x 0.99997473Sgeodetic = 3,314.83 ft
Diff = 0.00 ft
GRID SCALE FACTOR (k) OF A POINTGRID CONVERGENCE ANGLE () OF A POINT
Easiest to obtain by using
NGS SPCs tool kit utilityor
CORPSCON
GRID SCALE FACTOR (k) OF A LINE
k 12 = (k1 + 4km + k2) / 6
(m = mean of k1 & k2)
Typically the Average Value Works Fine
k 12 = (k1 + k2) / 2
REDUCTION TO GRID
Sgrid = Sgeodetic * k (Grid Scale Factor)
Sgrid = 3,314.83 x 0.99995985
Sgrid = 3,314.70 meters
COMBINED FACTOR (CF)
CF = Ellipsoidal Reduction x Grid Scale Factor (k)
= 0. 0.99997470 x 0.99995985
= 0.99993455
CF x D = Sgrid
0.99993455 x 3,314.91 = 3,314.69 ft
GRID AZIMUTH COMPUTATION
grid = Astro + Laplace Correction – Convergence Angle ()
= 253o 26’ 14.9” (Observed Astro Azimuth)
- 2.6” (Laplace Correction)
= 253o 26’ 12.3” (Geodetic Azimuth)
- 1 00 39.8 (Convergence Angle)
= 252o 25’ 32.5” (Grid Azimuth)
The convention of the sign of the convergence angle is always from Grid to Geodetic
STATE PLANE COORDINATE COMPUTATION
N1 = N + (Sgrid x cos grid)
E1 = E + (Sgrid x sin grid)
N1 = 428,395.86 + (3,314.70 x Cos 252o 25’ 32.5”)
= 428,395.86 + (3,314.70 x -0.301942400)
= 428,395.86 + (-1,000.85)
= 427,395.01 U.S. Survey Feet
E1 = 2,401,859.97 + (3,314.70 x Sin 252o 25’ 32.5”)
= 2,401,859.97 + (3,314.70 x -0.953326170)
= 2,401,859.97 + (-3,159.99)
= 2,398,699.98 U.S. Survey Feet
GROUND LEVEL COORDINATESSURFACE LEVEL COORDINATESPROJECT DATUM COORDINATESLOW DISTORTION PROJECTIONS
“I WANT STATE PLANE COORDINATES RAISED TO GROUND LEVEL”
GROUND LEVEL COORDINATES ARE
NOT STATE PLANE COORDINATES!!!!!
GROUND LEVEL COORDINATESPROBLEMS
RAPID DISTORTIONS*
PROJECTS DIFFICULT TO TIE TOGETHER*
CONFUSION OF COORDINATE SYSTEMS
LACK OF DOCUMENTATION
* Can be minimized with LDP
GROUND LEVEL COORDINATES“IF YOU DO”
TRUNCATE COORDINATE VALUES
SUCH AS:
N = 404,648.89 ft becomes 4,648.89
E = 26,341,246.75 ft becomes 1,246.75
AND
The NSRS has evolved
1 Million Monuments
(Separate Horizontal and
Vertical Systems)
Passive Marks(Limited
Knowledge of Stability)
GPS CORS GNSS CORS
70,000 Passive Marks
(3-Dimensional)
1,500+ GPS CORS
(Time Dependent System Possible; 4-Dimensional)
Problems with NAD 83 and NAVD 88NAD 83 is not as geocentric as it could be (approx 1-2 m).
Data users don’t see this – Yet
NAD 83 is not well defined with positional velocities.
Most users still think of NAD 83 as 2-dimensional (lat/long, N/E)
NAVD 88 is realized by passive control (bench marks) most of which have not been releveled in 40 years.
NAVD 88 does not account for local vertical velocities (subsidence and uplift)
Post glacial isostatic readjustment
Subsurface fluid withdrawal
Sediment loading
Sea level rise
.
The National Geodetic Survey 10 year planMission, Vision and Strategy
2008 – 2018http://www.ngs.noaa.gov/INFO/NGS10yearplan.pdf
Official NGS policy as of Jan 9, 2008
Modernized agency
Attention to accuracy
Attention to time-changes
Improved products and services
Integration with other fed missions
2018 Targets:
NAD 83 and NAVD 88 re-defined
Cm-accuracy access to all coordinates
Customer-focused agency
Global scientific leadership
Simplified Concept of NAD 83 vs. ITRF00
NAD 83Origin
ITRF 00
Origin
Earth’s
Surface
h83
h00
Identically shaped ellipsoids (GRS-80)a = 6,378,137.000 meters (semi-major axis)1/f = 298.25722210088 (flattening)
Predicted Positional Changes in 2018Vicinity of Silver Spring, MD.
(Computed for HASSLER pid HV9698)
HORIZONTAL = 1.31 m (4.3 ft)ELLIPSOID HEIGHT = - 1.25 m (- 4.1 ft)
Predicted with HTDP
ORTHOMETRIC HEIGHT = - 0.47 m (- 1.5 ft)Predicted with HTDP and USGG2009
2020 GEOMETRIC DATUM OPTIONS
Option 1: Adopt ITRF20xx and compute new coordinates based on the best available
Velocity model(Coordinates du Jour)
Option 2: Adopt a reference frame that agrees with ITRF20xx at some instant of time,
(e.g. Epoch 2020.00)but does not move relative to “stable” North
American tectonic plate similar to NAD 83
GOOD COORDINATION BEGINS WITH GOOD COORDINATES
GEOGRAPHY WITHOUT GEODESY IS A FELONY