Objective:
The project was undertaken by Brent Jorgensen, NE LS-621, and Steve Cobb, NE LS-412, to
create projection zones, preferably at the county level, that minimized the
distortion between grid and ground measurement. The low distortion projection parameters would eliminate the need
for constant calibration\localization of GPS units prior to field work.
Distortion Issues:
Distances
measured on the ground and then projected on to any designed grid are subject
to distortion due to elevation and curvature along the ellipsoid from the point
to the standard parallel or central meridian in a Lambert or Transverse
Mercator projection respectively.
Design Method:
Elevation:
The
30 meter, 7.5 minute topographic quadrangle DEM files, available from the
Nebraska Department of Natural Resources, were used to create a state coverage.
The point information was extracted at a 25% level leaving approximately 170 points
per section for evaluation. The DEM files are in UTM, ortho height format.
The
DEM files were combined by UTM range, converted to Nebraska State Plane 2600,
HAE format. The three converted ranges were combined to create a statewide
coverage in State Plane 2600 format.
A
GIS program was used to overlay county boundaries over the elevation coverage
and extract elevation files on a county by county basis.
Projection and Parameter Determination:
Each
county elevation file was converted to a geographic projection (Lat\Long\HAE)
and read by custom software which reported the average distortion, created by
both elevation and curvature, of each latitude and longitude in the county on a
minute by minute basis. Latitudes and longitudes with the lowest averages were
candidates for either standard parallels or central meridians. The selected
latitude, longitude or county configuration determined the projection. The
origins were established within the county and the false northings and eastings
were determined to avoid any negative coordinates within the county.
Note:
The designers were aware of suggestions that a standard parallel or central
meridian should be centered in the projection area. The designers felt this was
counterproductive and opted to select locations which minimized distortion.
Scale Factor:
An
initial scale factor was suggested by the custom software used in the previous
section. A spreadsheet was used to fine tune the scale factor by observing the
PPM (parts per million) spread over the county. The spreads were listed in 5
PPM increments from -25 PPM to +25 PPM. The scale factor was adjusted to center
the maximum percentages near the middle of the spread. The design goal to keep
50% of the county within the ±5 PPM range and 85% of the county within the ±10
PPM range was met in many of the smaller counties.
In
the larger counties and\or those with greater elevation change such a goal was
difficult to achieve yet ±15 PPM was still attainable in many circumstances.
PPM Reference:
PPM per mile:
5ppm\0.03’
10ppm\0.05
15ppm\0.8’
20ppm\0.11’
25ppm\0.13’
10ppm\0.05
15ppm\0.8’
20ppm\0.11’
25ppm\0.13’