Method of Calculation of Intercity Mileage for Metered Use Service
The airline mileage between two cities can be calculated using the Vertical (V) and Horizontal (H) Coordinates as obtained by reference to AT&T's Tariff F.C.C. No. 10 according to the following methods:
To determine the mileage between any two cities proceed as follows:
1. Obtain the "V" and "H" coordinates of the two cities. Obtain the difference between the "V" coordinate and the "H" coordinates.
Note: The difference is always obtained by subtracting the smaller coordinate from the larger coordinate for both V and H.
2. Divide each of the differences obtained in 1 by three, rounding each quotient to the nearer integer.
3. Square these two integers and add the two squares. If the sum of the squares is greater than 1777, divide the integers obtained in 2 by three, and repeat step 3. Repeat this process until the sum of the squares obtained in 3 is less than 1778.
4. The number of successive divisions by three in steps 2 and 3 determine the value of "N". Multiply the final sum of the two squares obtained in step 3 by the multiplier specified in the following table for this value of "N" proceeding:
N Multiplier Minimum Rate Mileage
1 0.9 ‑
2 8.1 41
3 72.9 121
4 656.1 361
5 5,904.9 1,081
6 53,144.1 3,241
5. Obtain square root of product in 4 and, with any resulting fraction, round up to next higher integer. This is the rate mileage except that when the mileage so obtained is less than the minimum rate mileage shown in 4, preceding, the minimum rate mileage corresponding to the "N" value is applicable.
Example:
The rate mileage between New York, New York and Chicago, Illinois is calculated as follows:
V H
(a) New York 4997 1406
Chicago 5986 3426
(b) difference 989 2020
(c1) divide each difference by three and round to nearer integer, 330 and 673 in this example
(d1) square integers and add, 330 x 330 = 108,900
673 x 673 = 452,929
sum of squared integers 561,829
sum of squared integers is greater than 1777, so divide integers in (c1) by three and repeat (d1)
(c2) divide integers in C1) by three and rounding = 110 and 224
(d2) square integers and add, 110 x 110 = 12,100
224 x 224 = 50,176
sum of squared integers 62,276
sum of squared integers is greater than 1777, so divide integers in (c2) by three and repeat (d2)
(c3) divide integers in (c2) by three and rounding = 37 and 75
(d3) square integers and add, 37 x 37 = 1,369
75 x 75 = 5,625
sum of squared integers 6,994
This sum of squared integers is greater than 1777, so divide integers in (c3) by three and repeat (d3)
(c4) divide integers in (c3) by three and rounding = 12 and 25
(d4) square integers and add, 12 x 12 = 144
25 x 25 = 625
sum of squared integers 769
This sum of squared integers is less than 1778 and was obtained after four successive divisions by three, therefore, "N" = 4.
(e) Multiply final sum of squared 769
integers by factor 656.1 x 656.1
(corresponding to "N" = 4) = 504,540.9
(f) Square root of 504,540.9 = 710 and a fraction, which is rounded up to 711 miles (fractional miles are considered full miles). The 711 miles is larger than the minimum of 361 miles applicable when "N" = 4, so the rate mileage is 711 miles.
V & H COORDINATES
LOCATION V H
(All other V and H Coordinates shall be obtained by reference to AT&T's Tariff FCC No. 10.)