ABSTRACT: This document is the first industry document completely dedicated to explaining the underlying mathematical principles involved in converting the Latitude and Longitude of a given point to Vertical and Horizontal (V&H) Coordinates.

The V & H Coordinate system was developed by Mr. Jay K. Donald of AT&T Long Lines in the late 1950s to simplify rating and billing associated with Private Line Service and Message Telecommunications Service. Rating of these services was based on the mileage between rate centers and the V & H Coordinate system simplified the computation of such mileage. Subsequent introduction of access tariffs in the early 1980s introduced the need for wire center V & H Coordinates and associated distance computations.

Since their introduction, V & H Coordinates have become widely used throughout the telecommunications industry, not only for determining distances between points, but also for designating the locations of switches, transmission facilities, and other items of telephone plant. Since the V & H Coordinate system was developed, the underlying mathematical principles seem to have been shrouded in mystery. Little information has been made available to the general public and many of the lines of code in programs that are used to perform the conversions represent the result of numerous complex calculations that have never been publicly identified.

This document is intended to serve as an authoritative reference source for information relating to the calculation and application of V & H Coordinates. With this document, you will learn:

1. The step-by-step process (and underlying mathematical principles) of converting the latitude and longitude of a given point to V & H Coordinates

2. The differences between the North American Datum of 1927 (NAD 27) and the North American Datum of 1983 (NAD 83) and the corresponding impact on V & H Coordinates

3. Steps required to convert "Basic" V & H Coordinates to "Final" V & H Coordinates, and

4. Distance calculations.

This comprehensive document addresses, through sample calculations, all steps and underlying mathematical principles relating the conversion of Latitude and Longitude to V & H Coordinates. 14 Appendixes are provided that include supplemental information regarding Radian Measure, Plane Trigonometry, Mapping Surfaces, Origin and Rotation Of Coordinate Systems, Scale Adjustments, Calculation Flow Diagrams, Series Calculation Of Trigonometric Functions and, most importantly, derivation of the Power Series Formula used to adjust the geodetic latitude, as measured on the ellipsoidal earth, to its equivalent "adjusted" latitude as measured on a (perfectly round) sphere.

This SR is part of the Telcordia Notes on Technology series of documents. With this series, Telcordia Technologies has devised a starting point for your search through the rapidly developing world of telecommunications. Written by the authors of the successful Telcordia Notes on the Networks document (SR-2275), this series similarly contains technical material of interest to engineering and planning groups, as well as descriptions of the characteristics and background of these subjects in layman's terms. The difference is that Telcordia Notes on Technology zeroes in on one technology in each document and breaks it down into manageable terms. From the history, background, and basic elements through a discussion of what the future may bring, our subject matter experts cover the important aspects in as few words as possible. Each document in the series deals with complex, highly technical subjects, and presents the information in a way that makes it accessible and understandable to a variety of readers.

Related document is SR-2275.