The V and H coordinate system is used in many telephone databases such as the Telcordia® LERG™ to map geographic location. Jay K. Donald of AT&T created the V&H coordinate system in 1957 to simplify the calculation of distance between telephone rate centers. The system is based on the Donald Elliptic Projection. It is a two-point equidistant projection for the continental United States and Canada. The system was designed allow calculations in the field using a slide-rule. It uses units of the square root of one-tenth of a mile (approximately .316 miles).

Once the coordinates of switching sites are known, distances between sites can be simply found by calculating the square root of the sum of the squares of the differences in the vertical and horizontal coordinates divided by ten.

Calculating Distances

To calculate the distances between a point 1 and 2 each with V and H coordinates use this formula:

Distance in miles = SQRT(((ABS(V1-V2))**2+(ABS(H1-H2))**2)/10)

e.g. - Abilene, TX (V=08698, H=04513) to Abilene, KS (V=07235, H=04599)

SQRT(((ABS(08698-07235))**2 + (ABS(04513-04599))**2)/10) =
SQRT(((1463)**2 + (86)**2)/10) = 
SQRT((2140369 + 7396)/10) =
SQRT((2147765)/10) =
SQRT(214776) = 

463 miles between Abilene, TX and Abilene, KS

Converting Between V & H and Latitude & Longitude

Converting from V and H to or from Latitude and Longitude is not simple. V&H is a system of coordinates (V and H) for describing locations of rate centers in the United States. The projection, devised by J. K. Donald, is an "elliptical," or "doubly equidistant" projection, scaled down by a factor of 0.003 to balance errors.

The foci of the projection, from which distances are measured accurately (except for the scale correction), are at 37d 42m 14.69s N, 82d 39m 15.27s W (in Floyd Co., Ky.) and 41d 02m 55.53s N, 112d 03m 39.35 W (in Webster Co., Utah). They are just 0.4 radians apart.

Telcordia® sells a document with detailed explanation of how the conversion between V & H coordinates and Latitude & Longitude is accomplished. This document is Telcordia Notes on V & H Coordinates: The Mystery Unveiled.