18
January 2016
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
mathematical machinations nowadays, there was a valid and
practical reason for such aphylactic projections back then.
Another aphylactic projection common in Europe is the
Cassini- Soldner (rectangular spheroidal) while in the United
States, the American Polyconic was used for decades by the
U.S. Army Corps of Engineers for the World Polyconic Grid
(predecessor of the Universal Transverse Mercator or UTM).
Furthermore, the American Polyconic was also used by its
originators, the U.S. Coast &Geodetic Survey as well as by the
U.S. Geological Survey for the National Mapping Program.
The polyhedric projection can be characterized in a
variety of ways; the easiest for the photogrammetrist to
relate to is the Local Space Rectangular (LSR), a variant
on the Geocentric Coordinate System. When we consider an
analytical model for our photogrammetric computations, we
usually need to take the ellipsoidal curvature of the earth
into account. Our defining parameters are established by our
datum, be it a classical horizontal geodetic datum such as
the Hermannskogel 1871 and NAD 1927, or an inertial mass-
centered datum, such as NAD 1983 and WGS 1984.
The LSR equations can be found in both the 3 rd
through 6 th editions of the
Manual of Photogrammetry
. In
aerotriangulation, we use the ellipsoid height (h) and the
optionally- transformed LSR (ZL) of our points as they are to
compensate for ellipsoidal earth curvature. For the polyhedric
projection, we force the LSR (ZL) to be equal to zero. For a
secant case, we merely assign the ellipsoid height of the point
of origin (ho) a value less than zero.
The most common classical datum (prior to the European
1950) found in the former Yugoslavia is the Hermannskogel
1871 Datum with
j
o
= 48° 16´ 15.29˝ N, Λ
o
= 33° 57´ 41.06˝
East of Ferro, where Ferro = 17° 39´ 46.02˝ East of Greenwich
and azimuth to Hundsheimer is α
o
= 107° 31´ 41.7˝. The most
common grid found on that datum is the Yugoslavia Reduced
Gauss-Krüger Transverse Mercator. The scale factor at
origin (m
o
= 0.9999) , the central meridians of the belts (C.M.
= λ
o
= 15°, 18°, 21° East of Greenwich) and the False Easting
at C.M. = 500 kilometers. The Ministry of Finance used the
non- reduced version only between 1938-40 where mo = 1.0.
About fifty years ago, the Army Map Service transformed
Hermannskogel 1871 Datum to the European Datum 1950.
However, large data sets still survive on that old datum.
The author examined the relation between the two datums
recently and computed new transformations. Twenty two
points were used that are common to both datums in the
former Yugoslavia and a simple three-parameter shift
analysis yielded the following: ∆X = +770.417 meters, ∆Y
= -108.432 meters, ∆Z = +600.450 meters. The accuracy
of this transformation when expressed in terms of actual
geodetic coordinates is: Latitude change (∆φ) = ± 3.74 meters,
Longitude change (∆λ) = ± 4.54 meters, and Ellipsoid Height
change (∆ h) = ± 12.70 meters. On the other hand, a seven-
parameter shift analysis yielded the following: ∆X = +758.53
meters, ∆Y = +259.52 meters, ∆Z = +542.18 meters, Scale
= -6.0X10
-6
, Z-rotation (ω) = +11.29 seconds, Y-rotation (ψ)
= +2.06 seconds, and X-rotation (ξ) = -5.66 seconds. The
accuracy of this transformation when expressed in terms
of actual geodetic coordinates is: Latitude change (∆φ) =
± 1.07 meters, Longitude change (∆λ) = ± 1.44 meters, and
Ellipsoid Height change (∆ h) = ± 0.64 meters. For example,
station Vel Gradiste has the following EU50 coordinates:
45° 09´ 17.3501˝ N, 18° 42´ 44.9479˝ E, 0.0 m. and the
following Hermannskogel 1871 coordinates: 45° 09´ 14.4675˝
N, 18° 43´ 00.7696˝ E, 0.0 m. The Yugoslavian Reduced Grid
coordinates are: Northing (X) = 5,001,303.81 m., Easting (Y)
= 556,359.65 m.
The contents of this column reflect the views of the author, who is
responsible for the facts and accuracy of the data presented herein.
The contents do not necessarily reflect the official views or policies of
the American Society for Photogrammetry and Remote Sensing and/
or the Louisiana State University Center for GeoInformatics (C
4
G).
This column was previously published in
PE&RS
.
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