Modeling Radiation Patterns of Whip Antennas
January 1967 QST Article
modeling of antenna radiation patterns has evolved from a relatively
simple electric field equation that diminishes as the inverse of the
distance from the source, to exotic, highly sophisticated numerical
methods that account for conducting and dielectric surfaces and volumes.
A spreadsheet can be built rather quickly to calculate and graph the
free-space azimuth and elevation e-field patterns for a 1/4-wave whip
or a dipole antenna using textbook formulas, but building a model for
displaying the 3D radiation patterns of a cellphone placed next to a
human head, or a UHF radio antenna on top of an aircraft takes some
pretty serious computing power. In large part we owe a debt of gratitude
to the Ph.D. types who have labored hard to make such tools available
to us commoners. As with PCB layout software and circuit simulators,
chances of success with a first pass prototype has increased significantly
as software has improved. Even with the advent of near-miraculous software,
there is still a need to verify empirically that the design matches
the predicted results. That's where taking physical measurements comes
in. Fortunately, there is a lot of great software for automating testing
as well, but occasionally, especially for the less well funded amongst
us, measuring points manually is required. Even with automated
systems at your disposal a few quick "sanity check" points are measured
prior to submitting the design to a full barrage of tests. This article
describes how the author first calculated the expected pattern for a
1/4-wave vertical whip antenna mounted on a car, and then went about
validating his predictions.
January 1967 QST
of Contents]These articles are scanned and OCRed from old editions of the
ARRL's QST magazine. Here is a list of the
QST articles I have already posted. All copyrights (if any) are hereby acknowledged.
See all available
vintage QST articles.
Modeling Radiation Patterns of Whip Antennas
By Dale W. Covington, K4GSX
The rapid development of efficient transceivers and power supplies has
solved many of the problems of going mobile. Furthermore, old Sol is
playing a strong supporting role by improving propagation conditions
on the very bands for which the mobile antenna is most efficient. While
the bandwidth and efficiency of the whip antenna have been extensively
studied and improved, any description of the resulting radiation patterns
has received only light treatment. Such patterns would be useful guides,
for example, in calling DX or in beginning to conclude a contact before
making a major change of route direction. Therefore the intent of the
following note is to call on stage yet another actor portraying a simplified
picture of mobile whip radiation.
Scale-model car used for obtaining data plotted in Fig. 3B.
Fig. 1 - Coordinate system for the model. Ground-plane radials
and vertical element are 1/4 wavelength long.
Actually it is a complicated
matter to describe this radiation precisely as a function of the total
elliptical polarization of the radiated E-field, the distorted currents
flowing on sculptured car bodies and loaded whips, the frequency dependence
of the ground conductivity, and so on. On the other hand, the principal
features can be exhibited by using a model of a vertical element over
an incomplete ground plane.
Employing a model
for a complicated analysis usually implies a certain degree of approximation.
The case in point is no exception. Cars are about 1/4 wavelength long
at 20 meters and almost 1/4 wavelength wide at 10 meters. As the whip
itself is a 1/4 wavelength at 10 meters, it seemed appropriate to restrict
the analysis primarily to this 10- to 20-meter range. Fig. 1 shows the
general shape and the coordinate position of the model, which had ten
1/4-wave ground radials from 0 to 90 degrees beneath a vertical 1/4-wave
element fixed in the normal-180-degree plane. The ground plane was spaced
1/10 wave above ground. Crudely speaking, the model thus represented
a car with a whip mounted on the left rear deck. The driver's side is
along the 0-degree direction, and the rear bumper is along the 90-degree
The actual calculation of the patterns
consisted of computing the far E-field from cosinusoidal currents flowing
on 1/4 wave elements1 as arranged in Fig. 1. All of the resulting
vector fields were then added to yield a polar plot of the radiation
patterns as a function of the angle of elevation. Since an actual whip
does not remain truly vertical once the car starts moving, the equations
for the model were solved for the vertical element normal to and tilted
away from the ground radials.
The close spacing between the model and ground requires that ground
effects be included in the analysis. A review of the interrelations
between frequency, antenna height above ground, angle of elevation,
and ground constants has been given by G3HRH(note 2). Using
standard techniques3 the E-field expressions were corrected
by the ground factors for 28 Mc. and angles of elevation, Δ, of
15 and 30 degrees. Higher wave angles are less useful for contacts from
14 to 28 Mc.4. These ground factors revealed that, at their
maximum point, the horizontally polarized E-fields from the model over
dry soil were 11.7 and 5.9 db. below the corresponding vertically polarized
fields for Δ of 15 and 30 degrees respectively. As the conductivity
approached sea-water values, the horizontal terms were even smaller:
namely, 14.2 and 8.3 db. For simplicity only vertical terms were retained
in the patterns.
Fig. 2 - A: Calculated patterns of relative E-field strength
for a radiation angle of 15 degrees above the horizon; dry soil.
Solid curve, whip vertical; dashed line, whip tilted 45 degrees.
B: Some for a radiation angle of 30 degrees.
Fig.3 - A: Solid points, experimental data taken on model antenna
system shown in Fig. 1, at a frequency of 430 Mc. Open points,
14-Mc. data taken on actual automobile installation.
B: Solid points, experimental data on scale-model car shown
in photograph, at 430 Mc., whip vertical. Open points, same
with whip tilted 45 degrees.
The patterns of the calculated E-fields are
presented in Fig. 2 for the 15- and 30-degree wave angles. Solid lines
show the fields from the vertical element normal to ground while the
dotted lines denote a rather extreme element tilt of 45 degrees. The
relative field strengths can be directly compared from one wave angle
to the other; however, directly comparing field values of the normal
and tilted configurations automatically implies a constant input current.
It is immediately noted in Fig. 2 that the quadrant containing the ground
plane also contains the strongest fields. Moreover, these fields generally
change only slightly from 0 to 90 degrees.
When the vertical
element is perpendicular to the radials, the field pattern is symmetric
about the 45-225 degree directions. Here orientation is more important
at the high elevation angle where the pattern undergoes a maximum/ minimum
variation of 6.4 db. compared to a 3.3-db. variation at the lower angle.
As mentioned before, the attractive increase in field strength at the
higher angle usually cannot be advantageously employed on the higher-frequency
Pattern symmetry becomes lost as the vertical element
tilts back from the normal. Not only does the direction of maximum field
shift from 45 degrees toward 20 degrees, but also the field strength
from the rear of the model is particularly reduced. Numerically the
fields in front of the model are 8.3 and 13 db. stronger at the 15 and
30 degree elevations.
operation on 40 and 80 meters is more difficult to analyze. Even in
Texas cars and whips don't come equipped with 1/4-wavelength dimensions.
Instead, the sizes of both the car body and the whip approach small
fractions of a wavelength. Also, in this range the loading coil becomes
increasingly important in relation to the current distribution on the
whip. Finally, contacts can be made on these bands by radiation at fairly
high angles of elevation, which complicates the previous polarization
argument by filling in certain parts of the pattern with a significant
combination of vertically- and horizontally-polarized fields.
The relative directivity pattern for a very small dipole has only
a slightly greater beam width than the similar figure-8 pattern for
a half-wave dipole having 1/4-wave elements4. Thus it would
be reasonable to expect that the character of the patterns of Fig. 2
would be more nearly omni-directional because of the short length of
the radiating elements. Consequently this factor along with the increased
usefulness of the higher angles of elevation would reduce any directivity
effects for 80- and 40-meter mobile contacts.
It is interesting
to speculate about the patterns predicted by the model for an incomplete
ground plane installation at a fixed station. On the lower bands, particularly,
it is not always practical to extend the long ground radials in a symmetric
shape about the base of a vertical antenna. The model should be useful
in understanding such cases if the obstruction limiting the ground plane
to less than a circle does not likewise prevent the vertical element
from being installed in the clear. For example, the patterns for a vertical
installed at one corner of a garden would probably differ from those
for a vertical next to the corner of a house, even though both conditions
might have a 90-degree area that was unavailable for ground radials.
Basically, the model suggests that a hole or depression exists in the
radiation pattern centered in the area having no radials. Directly opposite
the hole is centered a broad field maximum over the ground radials.
The hole is a function of the angle of elevation, and its maximum depth
is of the order of 6 db. or so below the field in the opposite direction
at elevations near 40 degrees. Naturally the hole width could be greatly
reduced as the area about the base is more evenly covered with radials.
The computed patterns were subjected
to several checks. One check utilized an experimental model of Fig.
1 at 430 Mc. The wire model was located about three wavelengths from
a two-element beam fed by a 6J6 rig from an old Handbook design. The
detector was a 1N23 crystal operating in the square-law region. The
measured E-field pattern is given in Fig. 3A for the vertical element
perpendicular to ground and an angle of elevation of 15 degrees. There
is good general agreement with the calculated pattern of Fig. 2A. Tilting
by 45 degrees produced a maximum/minimum gain of 5 db. An increase of
radiation in the forward directions was noted at higher elevations.
Of course the primary reason for examining the incomplete ground
plane model lay in the degree that it approximated 10-20 meter mobile
radiation. Included in Fig. 3A is a mirror image (whip mounted on right
rear fender) of some 20-meter E-field data taken on the mobile installation
of WA4KQO. While the receiving antenna was higher than the whip-Hillman
combination, the angle of elevation unfortunately was not measured.
It was less than 5 degrees. The experimental points are characteristic
of the low-angle radiation from the model.
To further confirm
the effects of tilting the whip away from the normal, a 1/15.4 scale
model of a Toronado was constructed. At this scale, the 430-Mc. whip
was equivalent to a 1/4 wave whip on 10 meters. An aluminum foil skin
0.00125 inches thick covered the balsa stringer shell. Fig. 3B presents
the measured field strengths at a 15-degree wave angle. Input power
remained constant as the whip was tilted. Again comparing the experimental
data with the curves of Fig. 2A, it is apparent that the ground-plane
model does agree fairly well with the scale model. Indeed, the standard
deviation of the measured points was 1.2 db. for both the normal and
The radiation patterns
of a 1/4-wave ground plane model have been employed to approximate the
patterns from a mobile whip in the 10-20 meter range. For these bands
the operating experiences of several mobile hams indicate that the field
strength over the car body is on the average 3 to 6 db. stronger than
the field in the opposite direction. This magnitude and direction are
confirmed by the model. The model also predicts that the patterns are
more directive when the soil conductivity increases, when the contact
is by means of a short skip, or when the whip curves back from the normal
at high speeds. Low angle DX work is less sensitive to ground-plane
orientation. Large variations from the patterns could arise from field
distortions produced by nearby objects, poor electrical contact over
various parts of the car body, and a bumper mount instead of a deck
mount. A tilted ground plane instead of a horizontal ground plane would
be a more accurate model in this latter case. The net effect would reduce
the fields over the ground plane and increase the fields in the opposing
In addition to the references listed, helpful ideas
are gratefully acknowledged from two other sources: first, from conversations
with K8MBV and a number of other mobile hams, and second, from the pleasant
and informative hours spent in assembling, testing, and operating mobile
equipment with W A4KQO.
Theory of Linear Antennas, University Press, Cambridge, Massachusetts,
1956, p. 395, 421, 687.
2 Hills, "The Ground Beneath Us,"
R.S.G.B. Bulletin, June 1966, p. 375.
3 Schelkunoff and Friis,
Chapter Seven, Antennas/Theory and Practice, John Wiley and Sons, Inc.,
New York. 1952.
4 Chapter Two, The A.R.R.L. Antenna Book.