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Vertical and Horizontal Coordinates

Telcordia has prepared an extensive and detailed technical overview of the history and background of V&H Coordinates (Telcordia® Notes on V&H Coordinates: The Mystery Unveiled), for further information click here.

Vertical and Horizontal (V&H) coordinates result from a complex algorithm that projects the curvature of the earth onto a flat plane. These coordinates have been used in telephony since the late 1950's as a means to determine "airline" distance between two points via a simple "distance" formula.   The projection algorithm uses latitude and longitude as well as various other factors in deriving V&H values.  The result is a basic 10,000 x 10,000 "V&H grid" covering North America as depicted below. V&H's are used to identify locations and hence relative distances between network elements (e.g. switch locations), and between "rate centers" (e.g. the "center" of a rate exchange area).  Such computations are necessary in cases where rates and costs for services are based on distance factors.

The following map shows the V&H grid overlaid on the U.S. and Canada. Coordinates greater than 10000 and less than zero are possible if the grid is extended, although technically, the grid lines do not remain parallel.    Minor V&H values in Alaska are based on a different "center" than that of the grid depicted below. 

Click here to download a self-extracting (.exe) file that contains sharper (.gif) versions of this map, one in color, one in black and white.

Vhpgmap1.gif (25197 bytes)

Telcordia® Routing Administration (TRA) has a software product called VHCALC which can be used to convert latitude/longitude to V&H Coordinates, as well as the reverse. Results of VHCALC have been compared with other like software and results of test cases are essentially identical.

Variations of +/- 1 "V&H coordinate" for a given location can sometimes be found among varying data sources. This is usually due to the rounding of final results and/or the degree of mathematical precision used in the intermediate steps of different programs. A V&H "coordinate" does not have a uniquely defined unit name, however, one "coordinate" is approximately equal to one-third of a mile.

V&H Coordinates: The Mystery Unveiled

Telcordia® Notes on V&H Coordinates: The Mystery Unveiled, which is also a module of the Telcordia Notes on Technology series, 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, and often still is, based on the mileage between Rate Centers. 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. However, ever since the V&H Coordinate system was developed, the underlying mathematical principles 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. the steps required to convert "Basic" V&H Coordinates to "Final" V&H Coordinates
  4. the techniques used in distance calculations

Telcordia® Notes on V&H Coordinates: The Mystery Unveiled consists of 190 pages that address, through sample calculations, all the steps and underlying mathematical principles relating the conversion of latitude and longitude to V&H Coordinates. Fourteen appendices are provided that include supplemental information regarding Calculation Flow Diagrams, Radian Measure, Cartesian (XYZ) Coordinates, Plane Trigonometry, Mapping Surfaces, Shift of Origin and Rotation of Coordinate Systems, Scale Adjustments, Series Calculation of Trigonometric Functions and, most importantly, derivation of the Power Series Formula used to convert the geodetic latitude, as measured on the ellipsoidal earth, to its equivalent "adjusted" latitude as measured on a (perfectly round) sphere.

As mentioned above, this document is part of the Telcordia® Notes on Technology series of documents. With this series, Telcordia Technologies has devised a starting point for your research through the rapidly evolving world of telecommunications. Written by the authors of the well revered 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 benefit of the Telcordia Notes on Technology series is that it zeroes in on one technology in each document, as may be specific to the reader's needs, and breaks it down into manageable terms. Reviewing the history, background, and basic elements of a subject, our subject matter experts cover each topic 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. Packaged together with a bonus CD-ROM version, this release in the Notes on Technology series is a must for your technical library.

Four convenient ways to order V&H Coordinates: The Mystery Unveiled:

Phone: 800-521-2677 (U.S. & Canada), +1-732-699-5800 (Worldwide)

Fax: 732-336-2559

Telcordia Routing Administration (TRA)
One Telcordia Drive
Room 4A738
Piscataway, NJ 08854-41567

Visit and bookmark the Telcordia Information SuperStore. Once at the site:

  • Enter V&H Coordinates or SR-NOTES-SERIES-20 in the search box, then click GO
  • On the next screen click Special Report, then click SR-NOTES-SERIES-20 Telcordia Notes on V&H Coordinates: The Mystery Unveiled, scroll to the bottom of the screen and click on Add Item to the Shopping Basket.
  • Once done at the site, click on Go to Check Out and follow the screen prompts to complete the order

Alternatively, click here to go directly to the SERIES-20 document page at the SuperStore.

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