§  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^1/3MHz 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]