V & H Coordinates: The Mystery Unveiled
Document Number SR-NOTES-SERIES-20
Issue Number 01
Issue Date July, 2002
?Telcordia Notes on V & H Coordinates: The Mystery Unveiled, which is also a module of the FD-NOTES-?SERIES-1, 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 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. However, since the V & H Coordinate system was developed, the underlying mathematical principles seem to have been shrouded in mystery. Very 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:
A, The step-by-step process (and underlying mathematical principles) of converting the latitude and
longitude of a given point to V & H Coordinates,
B, 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,
C, steps required to convert "Basic" V & H Coordinates to "Final" V & H Coordinates, and
D distance calculations.
V & H Coordinates: The Mystery Unveiled consists of 190 pages that address, through sample calculations,
all steps and underlying mathematical principles relating the conversion of latitude and longitude to V & H Coordinates. Fourteen appendixes 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.
Page 1 of 2
?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 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. Packaged
together with a bonus CD-ROM version, this release in the Notes on Technology Series is a must for your
Four convenient ways to order V & H Coordinates: The Mystery Unveiled:
Phone: 1.800.521.2673 (U.S. & Canada)
+ 1.732.699.5800 (Worldwide)
Mail: Customer Service Center
Telcordia Technologies, Inc.
One Telcordia Drive, RRC 1B-180
Piscataway, NJ 08854 - 4156
On Line: Visit and bookmark our SuperStore at:
? Go to the "product search" input field and enter V&H Coordinates or SR-NOTES-SERIES-20.
? Follow the screen prompts to review the document summary and to place an order on our
?Questions may also be directed to the Telcordia Routing Administration (TRA) Customer Care Center at
Telcordia is a registered trademark of Telcordia Technologies, Inc.
Page 2 of 2