WHAT YOU NEED TO USE THE STATE PLANE COORDINATE...

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