Geometric analysis of an observer on a spherical earth and an aircraft or satellite

Details

• Alternative Title:
  Project Memorandum - September 2013
• Creators:
  Geyer, Michael
• Corporate Creators:
  John A. Volpe National Transportation Systems Center (U.S.)
• Corporate Contributors:
  United States. Department of Transportation. Federal Aviation Administration
• Subject/TRT Terms:
  • Geometry
  • Trigonometry
  • Functions (Mathematics)
  • Geodesy
  • Air traffic control
  • Altitude
  • Taxonomy
  • Vector analysis
  • Vertical plane formulation
  • Spherical surface formulation
• Publication/ Report Number:
  DOT-VNTSC-FAA-13-08
• Resource Type:
  Tech Report
• Geographical Coverage:
  United States
• Corporate Publisher:
  John A. Volpe National Transportation Systems Center (U.S.)
• Abstract:
  This memorandum contains a large amount of technical detail. However, in significant contrast, ; it addresses an easily-understood and fundamental need in surveillance and navigation systems ; analysis — quantifying the geometry of two locations relative to each other and to a spherical ; earth. Here, geometry simply means distances and angles. Sometimes, distances are the lengths ; of straight lines; in other cases they are the lengths of arcs on the earth’s surface. Similarly, angles may be measured between lines on a plane or between lines on a spherical surface. ; Because the earth has an established latitude/longitude coordinate system, the approach that first ; comes to mind is to address this situation as a three-dimensional problem and use vector analysis. ; However, the approach preferred here is that, to simplify and clarify the analysis process, the ; three-dimensional problem should be re-cast as two separate two-dimensional problems: ;  Vertical Plane Formulation (Section 1.2 and Chapter 3)*— This analysis considers ; the vertical plane containing the two locations of interest and the center of the earth. ; The two locations are unconstrained vertically, although one altitude must be known. ; Plane trigonometry is the natural analysis tool for this problem. Latitudes and ; longitudes are not involved, which is its biggest limitation. ;  Spherical Surface Formulation (Section 1.3 and Chapter 4)— This analysis— ; which is sometimes called great-circle navigation —only considers two locations on ; the surface of a spherical earth. Spherical trigonometry is a natural analysis tool in ; this setting, and latitudes and longitudes are inherent in this method. A significant ; limitation of this analysis is that altitudes cannot be accounted for.
  More +
• Format:
  PDF
• Funding:
  FA27C6/LLG59
• Download URL:
  https://rosap.ntl.bts.gov/view/dot/10098/dot_10098_DS1.pdf
• File Type:
  [PDF - 2.08 MB]
• Collection(s):
  Volpe Center
• Main Document Checksum:
  urn:sha256:8ff78b8e6b62e83e6712897a788df9661eb045de27ca04d247d59cad0a3eeabd