Stereographic Projections in Air Traffic Control Systems

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Abstract
The mathematical technique chosen to present targets from many radars on a single two–dimensional plane is discussed herein. The choice was based upon accuracy needed as well as computational simplicity. This presentation uses the simplest possible mathematics in order to make the technique understood by a diverse audience. Definitions and orientations with respect to longitudes, latitudes, and mathematical coordinate systems are contained in Section 2. Supporting diagrams are also included. The derivation of projection equations from earth points to coordinates in the stereographic plane is discussed in Section 3; while contained in Section 4 is the derivation of the tan ψ, which represents a rotation of radar azimuth into the systems plane to compensate for the varying orientation of North in different radar planes. The negative of ψ, the angle β, is then introduced. β appears in the equations of Section 5. Lastly, presented in Section 5, is the derivation of the equations for mapping a radar target from a radar plane to a systems plane.

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