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:
[+]
Air Traffic Control Altitude Functions (Mathematics) Geodesy Geometry Spherical Surface Formulation Taxonomy Trigonometry Vector Analysis Vertical Plane 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.


Format:
PDF
Funding:
FA27C6/LLG59
Collection(s):
Volpe
Main Document Checksum:
[+]
urn:sha256:8ff78b8e6b62e83e6712897a788df9661eb045de27ca04d247d59cad0a3eeabd
Download URL:
https://rosap.ntl.bts.gov/view/dot/10098/dot_10098_DS1.pdf
File Type:

Supporting Files

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