Computation of Scale-factor & Standard Parallel For The Polar Stereographic Projection

In the pattern of most map projections, the polar stereographic projection comes with some parameters that must be supplied to fully specify the map projection and obtain grid coordinates. Two of these parameters are the central scale and the latitude of unity scale. Central scale (k0) tells how a short (infinitesimal) curved segment at the Pole is reduced in size when represented on the map. It is a number between 0 and 1. The latitude of unity scale1) tells where on the ellipsoid a short (infinitesimal) curved segment is preserved in size when represented on the map. It is a number between –90 and 90 for latitude in degrees. This parameter is also called the “standard parallel”.

The two parameters are dependent. Either one may be chosen freely. After that, the other one is calculated from the first.

Many software packages which perform polar stereographic projection calculations allow either parameter to be the chosen user-entered one. Not all these packages report the calculation of the other. The attached technical memo and sample programs do exactly that for both calculations − φ1 to k0 and k0 to φ1.

The equations are presented in this technical memo:
  • Polar_Stereo_phi1_from_k0_memo.pdf

  • Then, two programs are offered to do the calculations. An Excel spreadsheet is:
  • Calculator_for_polar_stereo_scale_v_std_parallel.xls

  • An executable file which runs in a DOS prompt window is:
  • Calculator_for_polar_stereo_scale_v_std_parallel.exe

  • The C-language source code for the above is contained in:
  • Calculator_for_polar_stereo_scale_v_std_parallel.c

  • To download the items mentioned above please click on the link below:
  • Polar_Stereographic_Computations.zip

  • C. Rollins
    B. Akers
    M. Factor
    National Geospatial-Intelligence Agency
    December, 2011

    Point of Contact: Coordinate Systems Analysis Team
    phone (314) 676-9124, DSN 846-9124

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