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

[[Page 54]]

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

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abscissa on the data sheet is the inverse distance field strength at 1 
kilometer, and the values of the numerical distance at 1 kilometer, 
p1, and of b are also determined. Knowing the values of b and 
p1 (the numerical distance at one kilometer), we may 
substitute in the following approximate values of the ground 
conductivity and dielectric constant.
[GRAPHIC] [TIFF OMITTED] TC13NO91.018


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

                                * * * * *

fMHz=frequency expressed in megahertz,

[GRAPHIC] [TIFF OMITTED] TC13NO91.019


=dielectric constant on the ground referred to air as unity.
    First solve for  by substituting the known values of 
p1, (R/)1, and cos b in equation (1). 
Equation (2) may then be solved for  and equation (3) for 
. 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) -7000.


[28 632 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]