# WHAT YOU NEED TO USE THE STATE PLANE COORDINATE SYSTEMS

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1 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

2 THREE DISTANCES: GROUND DISTANCE = NORMAL TO GRAVITY BETWEEN TWO POINTS GEODETIC DISTANCE = ALONG THE ELLIPSOID GRID DISTANCE = ALONG THE MAP PROJECTION SURFACE PROJECTED COORDINATES ARE ALWAYS DISTORTED

3 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

4 Normal to ellipsoid

5

6 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)

7 ELLIPSOID - GEOID RELATIONSHIP LaPlace Correction +/- 0 ~ 25 Lower 48 states NGS Tool DEFLEC09 Geoid Ellipsoid GRS80

8 LAMBERT CONFORMAL CONIC WITH 2 STANDARD PARALLELS STANDARD PARALLELS N Approximately 154 miles S λ O CENTRAL MERIDIAN

9 CONVERGENCE ANGLE (Mapping Angle) The Convention of the Sign of the Convergence Angle is Always From Grid To Geodetic Convergence angles ( ) always positive (+) East Convergence angles ( ) always negative (-) West λ O CENTRAL MERIDIAN

10 TRANSVERSE MERCATOR SCALE > 1 SCALE EXACT SCALE < 1 SCALE > 1 λ O CENTRAL MERIDIAN

11 Pennsylvania State Plane Coordinate System NAD 83 Geometric Parameters remain the same As NAD 27 Zone Boundaries Central Meridian North/South Standard Parallels Latitude/Longitude of Origin False Northing and Easting Changed and defined in meters Conversion to Feet left up to individual states U.S. Survey or International Feet

12 N = 0 m E = 600,000 m ORIGIN 39 o o 45 00

13 COORDINATE CHANGES (STATE PLANE) STATION: STRAUSS (pid KW0527) PENNSYLVANIA SOUTH ZONE (NAD 27/NAD 83) Northing Easting Converg Angle Scale Factor 428, ft. 2,433, ft. +1 o , m. 732, m. +1 o (428, ft)* (2,401, ft)* (428, ft)# (2,401, ft)# (0.15) (4.81) * Converted using U.S. Survey Foot, 1 M = Ft. # Converted using International Foot, 1 M = Ft.

14 Michigan Compiled Laws, Public Act 9 of 1964, Sections ,

15 STATE PLANE COORDINATE COMPUTATION STRAUSS (pid KW0527) N = 428, U.S. Survey Feet E = 2,401, U.S. Survey Feet Orthometric Height (H) = Feet Geoid Height (N) = Feet Laplace Correction = Grid Scale Factor (k) = Meridian Convergence ( ) = + 1 o Observed Astro Azimuth ( A ) = 253 o Horizontal Distance (D) = 3, Feet

16 STATE PLANE COORDINATE COMPUTATION N 1 = N + (S g x cos g ) E 1 = E + (S g x sin g ) Where: N = Starting Northing Coordinate E = Starting Easting Coordinates S g = Grid Distance g = Grid Azimuth

17 REDUCTION TO THE ELLIPSOID D H h N S R Earth Radius 6,372,200 m 20,906,000 ft. S = D * R R + h Where: h = H + [N] S = D * R R + H + (N)

18 REDUCTION TO THE ELLIPSOID (The correct method) R = N 1 e 2 cos 2 f cos 2 N = WHERE a (1 e 2 cos 2 f) 1/2 N = Radius of Curvature in Azimuth a = Ellipsoid semi-major axis b = Ellipsoid semi-minor axis = Azimuth of the line f = Latitude of the Station e 2 = (a 2 b 2 ) / b 2

19 REDUCTION TO ELLIPSOID Ellipsoid Ht /Orthometric Ht S geodetic = D x [R / (R + h)] D = 3, ft (Measured Horizontal Distance) R = 20,906,000 ft (Mean Radius of the Earth) h = H + N (H = 642 ft, N = ft) = 529 ft (Ellipsoid Height) S = 3, [20,906,000 / 20,906, ] S = 3, x S = 3, ft S geodetic = 3, [20,906,000 / 20,906, ] S geodetic = 3, x S geodetic = 3, ft Diff = 0.02 ft or ~ 1:166,000

20 REDUCTION TO ELLIPSOID Mean Radius vs. Computed Earth Radius S geodetic = D x [R / (R + h)] D = 3, 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 S geodetic = 3, [20,906,000 / 20,906, ] S geodetic = 3, x S geodetic = 3, ft S geodetic = 3, [20,936,382 / 20,936, ] S geodetic = 3, x S geodetic = 3, ft Diff = 0.00 ft

21 GRID SCALE FACTOR (k) OF A POINT GRID CONVERGENCE ANGLE ( ) OF A POINT Easiest to obtain by using NGS SPCs tool kit utility or CORPSCON

22 GRID SCALE FACTOR (k) OF A LINE k 12 = (k 1 + 4k m + k 2 ) / 6 (m = mean of k 1 & k 2 ) Typically the Average Value Works Fine k 12 = (k 1 + k 2 ) / 2

23 REDUCTION TO GRID S grid = S geodetic * k (Grid Scale Factor) S grid = 3, x S grid = 3, meters

24 COMBINED FACTOR (CF) CF = Ellipsoidal Reduction x Grid Scale Factor (k) = x = CF x D = S grid x 3, = 3, ft

25 GRID AZIMUTH COMPUTATION grid = Astro + Laplace Correction Convergence Angle ( ) = 253 o (Observed Astro Azimuth) (Laplace Correction) = 253 o (Geodetic Azimuth) (Convergence Angle) = 252 o (Grid Azimuth) The convention of the sign of the convergence angle is always from Grid to Geodetic

26 STATE PLANE COORDINATE COMPUTATION N 1 = N + (S grid x cos grid ) E 1 = E + (S grid x sin grid ) N 1 = 428, (3, x Cos 252 o ) = 428, (3, x ) = 428, (-1,000.85) = 427, U.S. Survey Feet E 1 = 2,401, (3, x Sin 252 o ) = 2,401, (3, x ) = 2,401, (-3,159.99) = 2,398, U.S. Survey Feet

27 GROUND LEVEL COORDINATES SURFACE LEVEL COORDINATES PROJECT DATUM COORDINATES LOW DISTORTION PROJECTIONS I WANT STATE PLANE COORDINATES RAISED TO GROUND LEVEL GROUND LEVEL COORDINATES ARE NOT STATE PLANE COORDINATES!!!!!

28 GROUND LEVEL COORDINATES PROBLEMS RAPID DISTORTIONS* PROJECTS DIFFICULT TO TIE TOGETHER* CONFUSION OF COORDINATE SYSTEMS LACK OF DOCUMENTATION * Can be minimized with LDP

29 GROUND LEVEL COORDINATES IF YOU DO TRUNCATE COORDINATE VALUES SUCH AS: N = 404, ft becomes 4, E = 26,341, ft becomes 1, AND

30 The NSRS has evolved 1 Million Monuments (Separate Horizontal and Vertical Systems) 70,000 Passive Marks (3-Dimensional) Passive Marks (Limited Knowledge of Stability) 1,500+ GPS CORS (Time Dependent System Possible; 4-Dimensional) GPS CORS GNSS CORS

31 Problems with NAD 83 and NAVD 88 NAD 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.

32 The National Geodetic Survey 10 year plan Mission, Vision and Strategy 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

33 Simplified Concept of NAD 83 vs. ITRF00 h 83 h 00 Earth s Surface ITRF 00 Origin NAD 83 Origin Identically shaped ellipsoids (GRS-80) a = 6,378, meters (semi-major axis) 1/f = (flattening)

34 Predicted Positional Changes in 2018 Vicinity of Silver Spring, MD. (Computed for HASSLER pid HV9698) HORIZONTAL = 1.31 m (4.3 ft) ELLIPSOID HEIGHT = m (- 4.1 ft) Predicted with HTDP ORTHOMETRIC HEIGHT = m (- 1.5 ft) Predicted with HTDP and USGG2009

35 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 ) but does not move relative to stable North American tectonic plate similar to NAD 83

36 GOOD COORDINATION BEGINS WITH GOOD COORDINATES GEOGRAPHY WITHOUT GEODESY IS A FELONY

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