[OSRS-PROJ] Horrors of --- Krovak projection

Clifford J Mugnier cjmce at lsu.edu
Fri Feb 14 11:37:27 EST 2003

Extracted from my January 2000 column on the Grids and Datums of the Czech
Republic and still available for downloading from:


Professor Ing.  Josef Krøvák (commonly spelled Krovák or Krovak) prepared
the Conformal Oblique Conic Projection of Czechoslovakia in 1922 for the
preparation of cadastral (tax) maps and topographic maps of medium scales
for the civil geodetic service of Czechoslovakia.  The ?starting meridian?
was termed Ferro where the MGI usage differed from the civilian definition
listed above.  The MGI used the relation: Ferro = 17° 39' 45.90" East of
Greenwich.  The Krovak Projection is a double projection in that the
oblique conic is projected from the Gaussian Sphere where the radius =
6,380,703.6105 meters.  The Gaussian Sphere was ?invented? by Carl
Friederich Gauss, and is also commonly known as the ?conformal sphere.? It
is simply the geometric mean of the ellipsoidal normal (at a point)
terminated by the semi-minor axis and the radius of the ellipsoid (at the
same point) in the plane of the meridian.  .  The oblique cone has a pole
centered at φ = 59° 42' 42.6969" N, λ = 42° 30' East of Ferro (southwest of
Helsinki, Finland).  The spherical cartographic coordinates are transformed
into the rectangular plane coordinates of the uniform cadastral system.
For this purpose the reduced (0.9999) Gaussian Sphere is projected on the
surface of an oblique cone touching the sphere around the central
cartographic parallel, having a cartographic latitude of 78° 30' N, with
the vertex in the extended axis connecting the center of the sphere at the
rotation angle of 30° 17' 17.3031".  This is still in use as of 2000, and
is known as Systém - Jednotné Trigonometrické Sítì Katastrální or S-JTSK
(System of the Unified Czech/Slovak Trigonometrical Cadastral Net).  The
Czechs state (Prof.  Ing.  Bohuslav Veverka, DrSc., Prague, November 1997)
that the ?scale, location and orientation of the S-JTSK on the surface of
the Bessel?s ellipsoid was derived from the results of the historical
Austro/ Hungarian military surveys in the years 1862-98. .  There are 42
identical points on the Czech territory used for transformation
computations.  Astronomical orientation was measured only on the
Hermannskogel trigonometrical point in Austria, scale factor was derived
from the basis of the geodetic length in Josefov.? Professor Veverka
published a program written in the Pascal language that performs the direct
and inverse transformations with the Krovak Projection.  Note that the
X-axis normally coincides with the meridian 42° 30' East of Ferro
increasing South, and the orthogonal Y-axis is increasing West.  A test
point provided lists: φ = 48° 07' 46.2973, λ= 35° 42' 35.2147", Y =
504,691.675 m, X = 1,289,068.724 m.  The Krovak Projection was officially
adopted by the Czech military in 1932.

Cliff Mugnier
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