§  1.958   Distance computation.

   The method given in this section must be used to compute the distance
   between any two locations, except that, for computation of distance
   involving stations in Canada and Mexico, methods for distance
   computation specified in the applicable international agreement, if
   any, must be used instead. The result of a distance calculation under
   parts 21 and 101 of this chapter must be rounded to the nearest tenth
   of a kilometer. The method set forth in this paragraph is considered to
   be sufficiently accurate for distances not exceeding 475 km (295
   miles).

   (a) Convert the latitudes and longitudes of each reference point from
   degree-minute-second format to degree-decimal format by dividing
   minutes by 60 and seconds by 3600, then adding the results to degrees.
   [er13ap05.008.gif]

   (b) Calculate the mean geodetic latitude between the two reference
   points by averaging the two latitudes:
   [er13ap05.009.gif]

   (c) Calculate the number of kilometers per degree latitude difference
   for the mean geodetic latitude calculated in paragraph (b) of this
   section as follows:

   KPD[lat]= 111.13209 − 0.56605 cos 2ML + 0.00120 cos 4ML

   (d) Calculate the number of kilometers per degree of longitude
   difference for the mean geodetic latitude calculated in paragraph (b)
   of this section as follows:

   KPD[lon]= 111.41513 cos 5ML − 0.09455 cos 3ML + 0.00012 cos 5ML

   (e) Calculate the North-South distance in kilometers as follows:

   NS = KPD[lat]× (LAT1[dd]− LAT2[dd])

   (f) Calculate the East-West distance in kilometers as follows:

   EW = KPD[lon]× (LON1[dd]− LON2[dd])

   (g) Calculate the distance between the locations by taking the square
   root of the sum of the squares of the East-West and North-South
   distances:
   [er13ap05.010.gif]

   (h) Terms used in this section are defined as follows:

   (1) LAT1[dd]and LON1[dd]are the coordinates of the first location in
   degree-decimal format.

   (2) LAT2[dd]and LON2[dd]are the coordinates of the second location in
   degree-decimal format.

   (3) ML is the mean geodetic latitude in degree-decimal format.

   (4) KPD[lat]is the number of kilometers per degree of latitude at a
   given mean geodetic latitude.

   (5) KPD[lon]is the number of kilometers per degree of longitude at a
   given mean geodetic latitude.

   (6) NS is the North-South distance in kilometers.

   (7) EW is the East-West distance in kilometers.

   (8) DIST is the distance between the two locations, in kilometers.

   [ 70 FR 19306 , Apr. 13, 2005]