Technical Details: How to Use a Handheld GPS to Display State Grid Coordinates - Part One
Professional Surveyor Magazine -
May 2012
by Henry L. Berg
DISCLAIMER:
No warranty is given for the included procedures, and the user assumes full responsibility of verification of procedures and computations. The use of information contained here is at the user’s sole risk and without liability, risk, or legal exposure to the author, referenced sources, technical advisors, and/or Professional Surveyor Magazine.
This series demonstrates the procedure for using a
Garmin eTrex Venture handheld GPS to display the Oregon Coordinate Reference System of 2011 (OCRS–2011, Transverse Mercator Projection) coordinates in either meters [m] or international feet [ift]. Part two of this series covers a simplified version of this procedure.
The process outlined here can be applied to any Transverse Mercator coordinate system, substituting the correct parameters where appropriate. While the Garmin eTrex will work with over 100 world-wide coordinate systems, it will not function with the Lambert Grid that many states use. However, you may create a local user-defined grid based on the Transverse Mercator projection to overlay the Lambert Grid area (caution: accuracy degrades as you move away from the created grid origin).
Overview
The State of Oregon, with the support of the Oregon Department of Transportation (ODOT), created the OCRS–2011 (effective June 1, 2011). It’s a new series of elevation-based, low-distortion projections throughout the state, which will practically eliminate the tedious and sometimes confusing conversions between grid distances and ground elevation distances. Previous state plane coordinate systems used information on a flattened plane projection that required the application of a combined factor (grid factor * sea level factor) to measurements. I owned and used a Garmin eTrex Legend GPS for several years, and I upgraded to a Garmin eTrex Venture HC unit in 2011. In my survey and mapping reference files I discovered an article from 2008 that described setting up the Garmin to display user-defined units for Transverse Mercator projections. With assistance from the author, Steven Weible, LS, I successfully configured my Garmin eTrex Legend and Venture to display Eugene zone grid coordinates in metric units. Later I found an article on the internet by Dale DePriest for “tricking” the Garmin to display X and Y grid coordinates in international feet.
Warning: The results from the Garmin units do not yield the accuracy needed for control surveying, land boundary surveying, or accurate GIS mapping. However, while walking along a highway ROW, stumbling through dense brush and ankle-grabbing ground cover, or trudging through the snow or a swamp, you can use them to get close enough to where you can search for bearing trees or use your machete, metal detector, or shovel to find those sneaky, hidden survey monuments. And there is a function for entering a waypoint (X and Y coordinates) of the required monument and a search distance radius to sound a proximity alarm when nearing the monument location. You can use these units for getting close enough to search for sneaky survey monuments, obtaining rough positions of GIS features, computing acreages for timber/agriculture tracts, finding your way back to the survey rig, and other useful field activities.
If you have your handheld GPS, a scientific calculator, and your old college “hierarchy of operations” 101 math notes handy, along with a desire for a challenge, then let’s start.
The Technique
The particular area of my investigation and field testing is in the Eugene Zone of the OCRS–2011, at a dam stability observation pier identified as USACE “FD-1,” located at Foster Dam in Sweet Home (Figure 1; also see photo, page 30).
Oregon Coordinate Reference System of 2011
– Eugene Zone Parameters
Latitude: 43°45’00” N
Central Meridian: 123°10’00” W
False Northing: 0.000 m
False Easting: 50 000.000 m
Central Meridian Scale: 1.000 015 (Exact)
Unfortunately, the computations needed to obtain the necessary precise data require a complex set of equations (rather than a single equation). The equations are from the NGS State Plane Coordinate System of 1983 Manual, March 1990. The parameters and equations begin on page 32 of the manual, with the final equation for computing the northing given near the top of page 35 (as N = S – So + No + . . . etc.).
The computation process is somewhat challenging in that this solution requires over a dozen related equations to be solved first. However, it is possible to combine all of the needed equations into to one compact equation, especially if simplified by restricting certain parameters. (Thanks to Michael Dennis, PE/PLS for his geodetic expertise and the solution of this equation.)
For the Eugene Zone (Transverse Mercator projection), the longitude is set equal to central meridian, and both the false northing and latitude of origin are set to 0. The following equation yields a northing of:
N = ko • r • (p + {sin p • cos p}*[U0 + U2*(cos p)^2 + U4•(cos p)^4 + U6*(cos p)^6])
where ko = central meridian scale =
1.000 015 (exact)
p = latitude = 43.750° (exact) =
0.76358 15477 47519 radians
And, for the GRS-80 ellipsoid:
r = 6,367,449.14577 m
U0 = – 0.00504 82507 76
U2 = 0.00002 12592 04
U4 = – 0.00000 01114 23
U6 = 0.00000 00006 26
Entering these values into the equation results in N = 4 846 117.609 82 m (False Northing value) which later in this article is converted to -15,899,335.99022 ift (rounded to –15899336.0 for Garmin entry, and use in “tricking” the Garmin).
Setting Up the Garmin User Grid for the Eugene Zone Metric Coordinates
- With the Garmin eTrex powered up, push the page key until you get to the Main Menu screen.
- Using the click-stick (mouse-like key) [aka rocker key, toggle key, four-way arrow, thumb stick, and/or enter key] for movement and
selections, scroll down and select Setup. (Figures 2, 3)
- Scroll down and to the right and
select Units.
- Scroll down to Map Datum and
select NAD83.
- Scroll up and select Position Format on the Units Setup screen.
- From the drop down list, scroll up or down until User UTM Grid is displayed and select it.
- At the top of the display, User Grid should be displayed.
- Scroll down and select Longitude Origin.
- Using the drop down numeric keypad and the click-stick, enter the Longitude of the Central Meridian, which is W123°10.000’.
- Select OK on the keypad and press the click-stick.
- Returning to the User Grid page, scroll down, and select Scale.
- In the Scale box, using the drop down numeric keypad and the click-stick, enter the Scale factor at the Central Meridian, which is +1.0000150.
- Select OK on the keypad and press the click-stick.
- Returning to Main Menu, select Waypoint and enter data as shown in Figures 4 and 5.
- In the False Easting box, using the drop down numeric keypad and the click-stick, enter the Easting Coordinate value of the origin, which is 50 000.000m (rounded to +0050000.0 for Garmin entry).
- Select OK on the keypad and press the click-stick.
- Returning to the User Grid page, scroll down and select False Northing.
- In the False Northing box, using the drop down numeric keypad and the click-stick, enter the False Northing value (computed using the procedure in this article), which is 4 846 117.609 82 m (rounded to –04846118.0 for Garmin entry).
- Select OK on the keypad and press the click-stick.
- Scroll down and select the Save box.
- Press the page key twice to return to the Main Menu.
- Scroll up to the Satellite icon (Figure 6), and press the click-stick to display the Location page. This page will list satellites available at bottom of the display (with numbers); satellite signal strength bars (“D” inside the bar indicates WAAS-enablement); position as OCRS–2011 Eugene Zone coordinates in meters (or Lat/Lon, if selected), in the upper-right corner; and approximate position accuracy in upper left corner.
- Using the Page button on the upper right, return to the Waypoints list and select Waypoint 101 Grid Orig. (Grid Origin of the Eugene Zone) by pressing the click-stick.
- The value of X should display 0164042.
- The value of Y should display USR 0000000.
- Elevation should display 617 ft.
Note: The display on the Garmin is shown as X above Y or Easting first and Northing second (the reverse of the normal order for survey and COGO computations in the United States).
“Trick” the Garmin to Display International
Feet Grid Coordinate Values
OCRS-2011 – EUGENE ZONE, Modified Data Input and Display for Grid Coordinates in International Feet (using steps 3-20 for metric values)
Use the following settings:
- CM Scale: 1.000 015 (Central Meridian Factor) • 3.280 839 895 013 (Constant for converting meters to international feet) = Modified Scale Factor to be entered into the Garmin as CM Scale…3.280 889 107 611 (rounded to +3.2808891 for Garmin entry).
- False Easting: 50 000 m = 164,041.994 ift (rounded to +164042.0 for Garmin entry)
- False Northing: –4 846 118 m or –15,899,335.990 ift (rounded to –15,899,336.0 for Garmin entry)
User Grid Parameters Based on International Feet Settings
Longitude Origin
[W 123°10.000’]
Scale
[+3.2808891]
False Easting
[+164042.0m ]
(though the Garmin Venture displays as m – the value is really ift)
False Northing
[–15899336.0m]
(though the Garmin Venture displays as m – the value is really ift)
Practical Verification of Results
After initializing the Garmin, I obtained readings with the Garmin resting on an USACE observation pier identified as “FD-1” located at the Foster Dam and Reservoir in Sweet Home. The readings were recorded when the satellite signal strength bars displayed a “D” (indicates WAAS enabled). Note: When WAAS is enabled, the maximum positioning satellites will be 11; and at times, better positioning accuracy may be obtained by disabling the WAAS and having 12 satellites available.
The results were compared with USACE GPS values (Lat/Lon Epoch 2009) translated to Eugene Zone grid coordinates. Setting the Garmin unit’s setup to User UTM Grid units for my observations (Figures 7, 8, 9), the X (East Coordinate) and Y (North Coordinate) averages were within the Garmin estimated position error accuracy of three meters (10 ift) 95% of the time (Figure 10).
Are you having difficulty solving the equation? If you discovered your college math notes had been eaten by your dog or you’re a little fuzzy on the proper processing, there is an alternate method that yields the same results. Part two of this series covers a simplified version of this procedure in which the Garmin eTrex Venture HC is used to solve the needed calculations to yield OCRS-2011 metric and international feet coordinates.
Technical Advisors
Thanks to Steven Weible, LS for the walk-through in setting up the Garmin eTrex for use with the OCRS–2011, and a thank you is extended to Michael Dennis, RLS/PE geodesist who reviewed my procedures, compiled the simplified equation for determining the required precise false northing, and furnished transformed grid coordinates for several Linn County GPS control points.
Reference Sources
Dennis, Michael L., RLS/PE geodesist, NGS, Consultant to ODOT
DePriest, Dale. "Datums, Grids, and Other Measures, 2002," www.gpsinformation.org
An Introductory Venture HC Handbook for Natural Resources Managers, VirginiaTech, 2009
NOAA State Plane Coordinate System of 1983 Manual, March 1990
Oregon Coordinate Reference System – Handbook and User Guide, Version 2.00, March 2011
Weible, Steven E., LS, "Getting More from Your Handheld GPS Unit," The American Surveyor, Volume 5, No. 9, October 2008
Read Part Two Here
Hank Berg, PLS (retired), began his career with the 880th Engineer Battalion (Heavy Construction) MOANG in 1957 as an engineering drafter and finished his enlistment as a topographic and construction surveyor. Prior to retiring, he held registration as a land surveyor in seven states. You can reach him at Hank_Berg@hotmail.com
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