Sec.  73.184   Groundwave field strength graphs.

   (a) Graphs 1 to 20 show, for each of 20 frequencies, the computed values of
   groundwave field strength as a function of groundwave conductivity and
   distance from the source of radiation. The groundwave field strength is
   considered to be that part of the vertical component of the electric field
   which has not been reflected from the ionosphere nor from the troposphere.
   These 20 families of curves are plotted on log-log graph paper and each is
   to be used for the range of frequencies shown thereon. Computations are
   based on a dielectric constant of the ground (referred to air as unity)
   equal to 15 for land and 80 for sea water and for the ground conductivities
   (expressed in mS/m) given on the curves. The curves show the variation of
   the groundwave field strength with distance to be expected for transmission
   from a vertical antenna at the surface of a uniformly conducting spherical
   earth with the groundwave constants shown on the curves. The curves are for
   an antenna power of such efficiency and current distribution that the
   inverse distance (unattenuated) field is 100 mV/m at 1 kilometer. The curves
   are valid for distances that are large compared to the dimensions of the
   antenna for other than short vertical antennas.

   (b) The inverse distance field (100 mV/m divided by the distance in
   kilometers) corresponds to the groundwave field intensity to be expected
   from an antenna with the same radiation efficiency when it is located over a
   perfectly conducting earth. To determine the value of the groundwave field
   intensity corresponding to a value of inverse distance field other than 100
   mV/m at 1 kilometer, multiply the field strength as given on these graphs by
   the desired value of inverse distance field at 1 kilometer divided by 100;
   for example, to determine the groundwave field strength for a station with
   an inverse distance field of 2700 mV/m at 1 kilometer, simply multiply the
   values given on the charts by 27. The value of the inverse distance field to
   be used for a particular antenna depends upon the power input to the
   antenna, the nature of the ground in the neighborhood of the antenna, and
   the geometry of the antenna. For methods of calculating the interrelations
   between these variables and the inverse distance field, see “The Propagation
   of Radio Waves Over the Surface of the Earth and in the Upper Atmosphere,”
   Part II, by Mr. K.A. Norton, Proc. I.R.E., Vol. 25, September 1937, pp.
   1203–1237.

   Note: The computed values of field strength versus distance used to plot
   Graphs 1 to 20 are available in tabular form. For information on obtaining
   copies of these tabulations call or write the Consumer Affairs Office,
   Federal Communications Commission, Washington, DC 20554, (202) 632–7000.

   (c) Provided the value of the dielectric constant is near 15, the ground
   conductivity curves of Graphs 1 to 20 may be compared with actual field
   strength measurement data to determine the appropriate values of the ground
   conductivity and the inverse distance field strength at 1 kilometer. This is
   accomplished by plotting the measured field strengths on transparent log-log
   graph paper similar to that used for Graphs 1 to 20 and superimposing the
   plotted graph over the Graph corresponding to the frequency of the station
   measured. The plotted graph is then shifted vertically until the plotted
   measurement data is best aligned with one of the conductivity curves on the
   Graph; the intersection of the inverse distance line on the Graph with the 1
   kilometer abscissa on the plotted graph determines the inverse distance
   field strength at 1 kilometer. For other values of dielectric constant, the
   following procedure may be used to determine the dielectric constant of the
   ground, the ground conductivity and the inverse distance field strength at 1
   kilometer. Graph 21 gives the relative values of groundwave field strength
   over a plane earth as a function of the numerical distance p and phase angle
   b. On graph paper with coordinates similar to those of Graph 21, plot the
   measured values of field strength as ordinates versus the corresponding
   distances from the antenna in kilometers as abscissae. The data should be
   plotted only for distances greater than one wavelength (or, when this is
   greater, five times the vertical height of the antenna in the case of a
   nondirectional antenna or 10 times the spacing between the elements of a
   directional antenna) and for distances less than 80f ^1/3 MHz kilometers
   (i.e., 80 kilometers at 1 MHz). Then, using a light box, place the plotted
   graph over Graph 21 and shift the plotted graph vertically and horizontally
   (making sure that the vertical lines on both sheets are parallel) until the
   best fit with the data is obtained with one of the curves on Graph 21. When
   the two sheets are properly lined up, the value of the field strength
   corresponding to the intersection of the inverse distance line of Graph 21
   with the 1 kilometer abscissa on the data sheet is the inverse distance
   field strength at 1 kilometer, and the values of the numerical distance at 1
   kilometer, p[1], and of b are also determined. Knowing the values of b and
   p[1] (the numerical distance at one kilometer), we may substitute in the
   following approximate values of the ground conductivity and dielectric
   constant.
   [MATH:  :MATH]

   (R/λ)[1]=Number of wavelengths in 1 kilometer,

                      *                 *                 *                 *
                  *

   f[MHz]=frequency expressed in megahertz,
   [MATH:  :MATH]

   ε=dielectric constant on the ground referred to air as unity.

   First solve for χ by substituting the known values of p[1], (R/λ)[1], and
   cos b in equation (1). Equation (2) may then be solved for δ and equation
   (3) for ε. At distances greater than 80/f^1/3 MHz kilometers the curves of
   Graph 21 do not give the correct relative values of field strength since the
   curvature of the earth weakens the field more rapidly than these plane earth
   curves would indicate. Thus, no attempt should be made to fit experimental
   data to these curves at the larger distances.

   Note: For other values of dielectric constant, use can be made of the
   computer program which was employed by the FCC in generating the curves in
   Graphs 1 to 20. For information on obtaining a printout of this program,
   call or write the Consumer Affairs Office, Federal Communications
   Commission, Washington, DC 200554, (202) 632–7000.

   (d) At sufficiently short distances (less than 55 kilometers at AM broadcast
   frequencies), such that the curvature of the earth does not introduce an
   additional attenuation of the waves, the curves of Graph 21 may be used to
   determine the groundwave field strength of transmitting and receiving
   antennas at the surface of the earth for any radiated power, frequency, or
   set of ground constants. First, trace the straight inverse distance line
   corresponding to the power radiated on transparent log-log graph paper
   similar to that of Graph 21, labelling the ordinates of the chart in terms
   of field strength, and the abscissae in terms of distance. Next, using the
   formulas given on Graph 21, calculate the value of the numerical distance,
   p, at 1 kilometer, and the value of b. Then superimpose the log-log graph
   paper over Graph 21, shifting it vertically until both inverse distance
   lines coincide and shifting it horizontally until the numerical distance at
   1 kilometer on Graph 21 coincides with 1 kilometer on the log-log graph
   paper. The curve of Graph 21 corresponding to the calculated value of b is
   then traced on the log-log graph paper giving the field strength versus
   distance in kilometers.

   (e) This paragraph consists of the following Graphs 1 to 20 and 21.

   Note: The referenced graphs are not published in the CFR, nor will they be
   included in the Commission's automated rules system. For information on
   obtaining copies of the graphs call or write the Consumer Affairs Office,
   Federal Communications Commission, Washington, DC 20554, Telephone: (202)
   632–7000.

   [ 28 FR 13574 , Dec. 14, 1963, as amended at  50 FR 18823 , May 2, 1985;  51 FR 45891 , Dec. 23, 1986;  52 FR 36878 , Oct. 1, 1987;  56 FR 64866 , Dec. 12, 1991;
    57 FR 43290 , Sept. 18, 1992]