The Slippery Sloper Argument

L. B. Cebik, W4RNL (SK)



A perennial e-mail question that I receive is why there are no notes at the site on the sloper. This antenna has become very popular for amateurs with limited space under certain conditions. Hence, it seems to deserve some kind of treatment. For reasons that will become clear as we proceed, these notes are about the best I can do in terms of the antenna's basic operating characteristics.

One of the most common sloper installations uses an existing tower that supports a beam at the top as the upper-end support for a sloper. Other amateurs string them from trees or other existing structures. While we can begin by looking at the sloper as if it stood free and clear of everything, reality intrudes its multi-faceted set of interactions that will prevent us from drawing too neat a set of conclusions about sloper performance.

In these notes, we shall work with a sloper made from AWG #12 copper wire. The test frequency will be 7.1 MHz, since the 40-meter band is the lowest band for the common use of a sloping dipole, otherwise known as a full sloper. (A sloper fed at the upper end, nearest the support, has been dubbed a half-sloper.) We shall pose a number of fundamental questions first, such as when a sloper becomes a sloper and not just a vertical with a slight tilt, and what may be the best (rough) angle for a sloper.

Our second set of questions will involve the sloper and its support. We shall begin by contrasting true vertical dipoles and nearby vertical objects with a roughly preferred slope and the vertical object that supports the upper end. Those questions will very quickly become too complex in terms of installation variables for us to give anything like a systematic set of answers. Ultimately, it will become the responsibility of the installer and the user to evaluate whether the sloper is the right antenna for a particular job.

Vertical and Sloper Basics

Let's begin in the abstract world in which we can construct an antenna that is free and clear of all supports. The world is antenna-modeling software, of course, where we may support an antenna wire simply by specifying its coordinates. This world is limited, but it does offer us the opportunity to contrast true vertical dipoles with slopers having various tilt angles. I all cases, we shall specify a sloper's tilt by its departure from a true vertical orientation. Fig. 1 shows the range of sloper models that we shall consider.

As the sketch suggests, one of the variables that we can work with within modeling software is the base height of the sloper above ground. Base height simply means the height of the antenna element's lower end above the surface of the ground. A second variable that we can use in the evaluation of basic performance is the ground quality. We shall use 3 types of ground. At one extreme is very poor ground with a conductivity of 0.001 s/m and a permittivity or dielectric constant of 5. More the norm is the so-called average ground with a conductivity of 0.005 s/m and a permittivity of 13. A few fortunate amateurs live above very good soil with a conductivity of 0.0303 s/m and a permittivity of 20. As we shall see, for any degree of slope from 0 through 45 degrees, both the base height above ground and the ground quality will make a difference in the anticipated performance.

1. The True Vertical: A 40-meter vertical dipole is a very useful antenna for amateurs who desire a very low elevation angle and very little radiation at (or reception from) very high angles. Table 1 catalogs the modeled performance of 7.1-MHz vertical dipoles with base heights from 1' to 20' over each of the three soil types. We can draw a few immediate inferences from the data. First, the greater the base height (up to only the limit of the table), the lower will be the TO angle (take off angle or elevation angle of maximum gain). Second, the better the soil, the higher will be the antenna's gain for any given base height. However, note that over very good soil, the gain peaks with a base height of 10', but over worse soils, the gain continues to increase to the sampled limits. We might also note in passing that the gain variation from the lowest to the highest base level decreases as we improve the soil quality.

The feedpoint impedance entries simply give us an idea of how the impedance changes of over each soil type as we change the base height. The model was resonated (approximately) over average soil with a base height of 10'. The data change as a body as we change the soil type. Within each soil type, we find a range of impedance variation that is interesting. The values are always within the range of our ability to prune the dipole length.

The table also lists a vertical beamwidth, the angular distance between the half-power points. To gain a sense of what those values mean to operation, we should examine the gallery of sample patterns in Fig. 2. At very low base heights, the pattern shape does not vary much as we change soil types. However, as we increase the base height, we find the emergence of secondary lobes at high elevation angles. At a height of 10', the secondary lobes are not significant, although we should note that as the soil quality improves, the lobes are much more distinct. At a height of 20' at the lower end of the vertical dipole, the secondary high-angle lobes are becoming stronger. This factor may play a role in planning a vertical dipole installation in terms of a compromise between obtaining the lowest TO angle possible and the strength of high-angle noise that we are willing to handle during operation.

We have reviewed the basic properties of vertical dipoles because these are the antennas against which we measure the potential advantages and disadvantages of a sloper.

2. The 15-Degree Sloper: Fortunately, vertical dipole properties do not change rapidly as we tilt the antenna from its initial position. In fact, a 15-degree sloping vertical dipole (using the same base height and ground quality variations) shows very little change in its performance values relative to the vertical dipole. As shown in the data in Table 2, the maximum gain and TO-angle values are only marginally higher than those we encountered with the true vertical antenna. The feedpoint impedance values are almost identical.

The most noticeable increases occur in the vertical beamwidth entries. To understand how these values grow, we may examine Fig. 3. In all cases, the antenna is set so the its lower end is right of its upper end relative to the elevation patterns. The 15-degree tilt is sufficient to increase the vertical beamwidth of the lobe away from the angle and to shrink the beamwidth of the lobe included by the antenna. In the direction of maximum gain, the lobe is strong enough to admit considerably more higher angle radiation and noise than we obtain with the true vertical dipole, and we lose a little bit with respect to our desire for a very low TO angle.

The elevation patterns alone might be misleading, since they appear similar to the elevation patterns of 2-element beams with a poor front-to-back ratio. Therefore, I have included a set of representative azimuth patterns--all at the listed TO angles in the table--for 15-degree slopers with a 10' base height. Although the rearward (or left) portion of the pattern has a smaller beamwidth, the overall azimuth pattern is simply a distorted circle. Whether the small changes in pattern shape justify a 15-degree sloper is a question that we shall hold open until we complete our survey.

3. The 30-Degree Sloper: 30 degrees is a handy angle for a sloping dipole, since it parallels the angle of typical guy wires or ropes stabilizing typical amateur tower-and-beam installations. As we examine the data on 30-degree slopers in Table 3, we can see that the trends started with the 15-degree version continue. The maximum gain and TO angle values continue to rise, at least over very poor and average soil. Over very good soil, the gain values decline. Moreover, the gain values over very poor soil are now systematically higher than the values over average soil. For a home installation, soil quality does make a difference in the final decision on whether to install a true or nearly true vertical or whether to move to a 30-degree tilt angle.

The vertical beamwidth angles in the table alert us to the fact that we should expect some very different patterns in the gallery in Fig. 4. The additional tilt of the antenna produces strong radiation (and reception sensitivity) at quite high angles. As we improve the soil quality, we begin to see that the very large vertical beamwidth is a function of 2 elevation lobes that essentially merge at an angle where we might expect to find a null.

With the increased tilt angle, we begin to see a more distinct potential for a usable front-to-back ratio. The sample azimuth patterns for a base height of 10' show that the potential is highest over very poor soil, with an 8-9-dB difference between the forward and rearward directions. The ratio decreases to about 2-dB by the time we use very good soil. Indeed, over very good soil, we find in the elevation patterns very little difference between the forward and the rearward direction, with a consequent decrease in the maximum gain that we can obtain from the antenna.

The 45-Degree Sloper: I have included the 45-degree sloping dipole to show that there is a limit to how much we can tilt a dipole from the vertical and still gain some advantage. As shown by the data in Table 4, there is very little difference among the maximum gain values for equal base heights over the different soil types. Moreover, the TO angles have increased to values that we normally do not associate with long-distance communications. Indeed, these values resemble more the TO angles we might expect from a horizontal dipole at a relatively low highest (as a fraction of a wavelength).

A further alert that we may be exceeding the boundaries of good sloper tilt angles appears in the vertical beamwidth column. All of the versions of the 45-degree sloper show strong radiation straight upward, a trait that we normally associate with antenna expressly designed for NVIS operation. The pattern gallery in Fig. 5 confirms this suspicion. Over very poor soil, we still obtain a good front-to-back ratio, despite the vary high TO angle, but as we improve the soil, the TO angle continues to climb, while the difference in radiation forward and aft disappears.

The 45-degree sloper is, in general, a good NVIS antenna. In fact, many amateurs who do not have ready-made support points for a level dipole make use of this form of sloper, even though they set out to install a horizontal dipole. However, most amateurs who consciously wish to install a sloper are seeking long-distance communications. The 45-degree version of the slope offers perhaps the worst of all options, with the combination of a high TO angle and very strong sensitivity to high-angle radiation and noise.

In the abstract, then, the 30-degree sloper is the best in show. The 15-degree version acts much like a true vertical, while the 45-degree version acts like a horizontal dipole (over most soils). The 30-degree sloper provides some directivity, a little front-to-back ratio, and finally the primary ingredient in sloper installations: convenience. It needs only one high support point and a ground anchor of some sort. Remember that our survey has used 15-degree increments, so all angles are approximations. Plus or minus 5 degrees from a target angle will make little or no difference to performance. In fact, other installation considerations will create much greater performance variations and mess up our seemingly systematic progressions.

The Support Question

The realities of 40-meter true verticals and full slopers is that they often depend upon a nearby structure to support the upper end. We usually acknowledge that a nearby vertically oriented object may have "some" effect on performance without fully appreciating the extent of the effect. Therefore, I ran a series of modeling tests to gauge the general parameters of the effect. Precision is not possible in this realm. Support objects may range from masts to towers to trees. Masts and towers vary in diameter from a little over an inch to towers with faces up to 24", but more normally, 12" or 18", with some crank-up towers using a graduated face width. Moreover, these supports may be ungrounded, poorly grounded, or well grounded.

Tree supports are even more variable, since they may differ in both diameter and in the resistivity of the material. A single tree may vary its resistivity according to the current weather, the season, and numerous other environmental variables. Trees are not insulators, but at best semi-conductors. Experiments have shown that we can even use trees as antennas, although very lossy ones.

As a consequence, we cannot be as systematic in looking at verticals and slopers plus their supports as we managed to be with slopers in the abstract. However, we can perform a few tests to obtain a general idea of the interaction between verticals and slopers on the one hand and their supports on the other. Let's begin by using a 40-meter antennas with its base 10' above ground. The support will be a vertical object that is 90' tall and 12" in diameter. The 12" diameter is a compromise between the circular equivalent of towers with a face width of 12" and a face width of 18". The AM BC industry uses (and has confirmed by both models and measurements) a simple set of equivalence equations. The diameter of a circular element is 0.74 times the face width of a triangular tower (relevant here) and 1.12 times the face width of a square tower. A 12" 3-sided tower face calls for an 8.88" diameter, while a 12" tower face requires a 13.44" element diameter.

To preserve a reasonable segment length to diameter ratio, the 90' support object uses 31 segments. In raw NEC, I might have used the LD2 or LD3 command to continuously load the tower at various levels to simulate the range (but in no case the specific value) of a lossy support object. Since only spot loads are available within the software used (EZNEC), I simply placed a load on each segment of the support tower or object. The values in the next two tables will show the load value per segment, and the total resistance across the length of the object is that value times 31. There is no magic in the selection of resistance values except for one. I stopped the progression when the performance of the antenna came close to suggesting that the support object was RF transparent.

We shall create two sets of tests using a true vertical antenna, one with the support tower ungrounded (that is, separated from the ground by 0.1'), and the other with the tower grounded by a tower extension of 9' below the ground surface. We shall repeat these tests for the 30-degree sloper.

1. The True Vertical: Since we have set up a true vertical dipole as a baseline against which to compare and contrast various sloper angles, we might as well use it in our first test series. Indeed, I often receive the question of how far from an existing structure, such as a tower or a tree, to place a vertical antenna. Assuming that "the next county" is not a usable answer, let's see what the spacing should be between a vertical dipole and a support object that has various levels of resistance. Remember that we are working with only one object height and one configuration (truly vertical with no taper and no branches), so the data can only be suggestive at a first-order level. We shall begin with the ungrounded tower.

Table 5 shows the results of the initial tests for spacing values of 1, 2, 5, 10, and 17 feet. (The last entry is roughly 1/8 wavelength at 40 meters.) Just above the notes are the modeled performance values of the same vertical dipole when free and clear of all surrounding objects. As the feedpoint impedance entries indicate, the closer the vertical dipole is to a support object, the more profound is the effect on performance. Likewise, as we increase the resistance of the support object, the interaction weakens. With 1000-Ohms per segment, the interaction is minimal with a spacing of at least 5' between the antenna and the object. However, lesser values of resistance show significant interaction across the entire range of spacing values used in the sampling.

With very low resistance values, the interaction can be significant at least up to 1/8-wavelength and possibly farther. A resistance value of zero in these tests does not indicate a perfect conductor. The load value is in addition to the material loss assigned to the antenna element and its support object. Increasing the resistance in the object, especially at relatively close spacing values (for example, 2' or 5' at 40 meters) results in power absorption and dissipation by the support object. The table shows a consistent reduction in the elevation lobe strengths as we move from zero Ohms to about 10 Ohms or more. These are values that we might expect from trees or uncoated wooden structures used to support a vertical dipole. The numbers in the table do not hide the emergence of strong lobes at 90 degrees to the elevation pattern, which is in a line from the tower to the dipole. Fig. 6 overlays elevation and azimuth patterns for a spacing of 1' using zero and 10 Ohms added resistance per segment. As the patterns show, when we use the 10-Ohm value, some energy is simply missing from the far-field radiation patterns, relative to zero Ohms. Also note that as we exceed 100 Ohms per segment and move toward 1000 Ohms per segment, the support object becomes virtually RF transparent.

For spacing values less than 10' and depending upon the lossiness of the support, the vertical dipole gain can be significantly lower than when the antenna is free and clear. Moreover, some combinations of tower height and spacing between the tower and the dipole can result in parasitic element effects from the tower. Fig. 7 overlays elevation patterns for a tower and a dipole at various spacing values, ranging from 2' to 17'. Note that the 17' spacing--about 1/8-wavelength at 40 meters--results in a directional pattern with about 2-dB forward gain and 5-dB front-to-back ratio relative to a freestanding vertical dipole. Not all combinations of support tower and dipole spacing will yield this result.

To use this effect, the individual installer must establish that the right relationship exists between the support tower and the dipole element, a task that might be difficult if the tower also supports a beam for the upper HF region. To preserve omni-directional coverage, one suggested vertical dipole support system seems to have merit, assuming that the antenna builder wishes to preserve the omni-directional pattern. That system uses two supports at a considerable distance from each other, with a non-conductive support rope between them. The wire dipole extends downward from a point midway between the distant support objects. The alternative to this method of support is to create a wire dipole that is freestanding.

The numbers, of course, apply only to a 90' support object with a 1' diameter. Other support lengths will yield different results using the same tests. As well, the tests used only a single base height and did not account for any other possible objects near to either modeled object. Therefore, the results are in no way exhaustive or definitive. However, they do show the potential for interaction between a vertical dipole and one kind of support object.

Before we leave the true vertical and its nearby support tower, let's consider an additional factor: how well the tower is grounded. I repeated the same series of tests that we found in Table 5, but extended the tower 9' below ground. We may compare the modeled performance values by examining Table 6. For the particular tower that we are using for the tests, improved grounding results in lower gain values, less directionality, and higher TO angles, as a general rule. However, with high values of resistance per segment, the support object becomes just about as RF transparent as the ungrounded tower. Generally, the region of about 10-Ohms per segment shows the greatest absorption and dissipation of energy.

How well a supporting tower (or simply a nearby tower) is grounded suffices to significantly alter the vertical's pattern. Thus it adds one more variable to our growing collection. We shall see this variable at work again as we turn to the 30-degree sloper.

The 30-Degree Sloper: The most usual form of full-sloper installation supports the upper end of the antenna near a tower or other tall vertical object. The wire then extends away from the support object toward its base. With a 10' base height (to be roughly comparable to the vertical dipole tests), the remaining distance to the ground is normally a non-conductive line to a ground anchor of some sort. Because the sloper has a 30-degree tilt angle, the lower end is about 35' from the support object, and the dipole feedpoint is about 17' from the support. Since the dipole is slightly less than 70' long, the upper end will be about 0.75' (or about 9") away from the surface of the 12" diameter support object.

One consequence of the necessary conditons of installing a 30-degree 40-meter sloper is that we need only one test sequence to test the effects of varying the support object resistance. However, we shall run two tests, one with a support object that is 70' tall, and the other with a 90' tall object. These heights correspond to two heights of towers in wide amateur use. Our goal is to see whether support-object height makes a difference to the sloper's performance. We shall again use ungrounded and grounded support objects for each tower height. Table 7 provides some interesting tabular data for the 70' support object.

The 70' support object shows significant directionality in the sloper pattern with both ungrounded and grounded supports up to loss levels of 10 Ohms per segment. The ungrounded tower acts more like a parasitic reflector than the grounded version, but the data show that both versions increase the front-to-back ratio over the natural values of an independent full sloper with the same 10' base height. The relatively high front-to-back ratios for the ungrounded tower also accompany more radical changes in the sloper feedpoint impedance and lower values of vertical beamwidth until the tower loss approaches RF transparency.

If we replace the 70' tower with a 90' tower, the numbers change, as shown in Table 8. There is little difference in the gain values between the two grounding states for the 90' support, although the ungrounded tower yields higher front-to-back ratios. We do find a differential effect on the feedpoint impedance values, with the ungrounded support (at low-loss assignments) yielding impedances that are lower than a free-standing sloper and the grounded version providing impedance values that are higher.

Fig. 8 reveals part of the reason for the numerical differences by showing the current magnitude distribution along each of the tower situations (with zero additional loss). Grounded and ungrounded towers show different points along the height at which the current is maximum. As well the peak current on all four tower models shows different values. (The curves for the sloper itself have been equalized to the degree possible within the graphical system used by EZNEC. These same limits also do not allow the 4 model outlines to be in exact scale with each other.)

Some of the far-field radiation pattern differences among the 4 variations of a support tower do not become evident from the tabular data alone. Fig. 9 shows the elevation patterns that accompany the current magnitude distribution curves in Fig. 8. The shape of the main forward lobe is one significant area of interest, since it largely determines the vertical beamwidth. Both ungrounded towers yield smaller vertical beamwidth values with less sensitivity to very high-angle radiation and noise. Unfortunately, failing to ground a tower tends to raise serious safety issues.

Although our survey so far has introduced us to a number of variables that have consequences for full sloper performance, we need to add a final variable that generally affects only highly conductive towers.

The Tower Support with a Beam on Top: Many slopers use an existing tower as the support for the top of a 30-degree full sloper. Normally, the tower has an appurtenance at the top, namely, an upper-HF beam. The beam may be simple or complex. At the small end, we might find a 10-meter 2-element Yagi. At the large end of the scale might be a 16-element tri-band array on a 30' boom--or something even larger.

The beam at the tower top usually has an electrical connection to the tower, although that connection may or may not include the driven element. It we treat the tower as a vertical element, the beam becomes a form of "top" or end loading, that is, an irregularly shaped extension of the element with its structure at right angles to the tower. Normally, such structures on active elements lower the resonant frequency of the element without altering the current distribution along the element. Essentially, the beam-hat plays little or no role in the radiation from the tower itself. However, the sloper antenna to which we supply energy has both a vertical and a horizontal component to its radiation, and the horizontal component is more than incidental. Therefore, the top section of the beam-hatted tower may interact directly with the sloper antenna.

In this space, we cannot sample every possible combination of beam and tower. We can look at two simple cases: a 3-element 20-meter Yagi with a 24' boom and a 6-element 20-meter Yagi on a 48' boom. We can place each antenna on either a 70' or a 90' tower to which we have attached our 7.1-MHz AWG #12 copper-wire 30-degree sloper. Of course, given our recent modeling, we can have each tower in an ungrounded condition or a well-grounded condition. As well, we can align the Yagi boom with the tower-sloper line or set the beam cross-wise to that line (or at any intermediate angle). Since our variations are already numerous, we shall set the sloper with a base height of 10' above average soil as fixed values, even though we might easily vary both the base height and the soil quality. Even within these restrictions, we end up with the 2-column data set on Table 9. For reference, the table includes values for each tower with no beam on top.

The tabulated data show no clear trends in the numbers. Changing the beam orientation does affect the values, as does changing the beam size. It is likely the even changing the beam design with the same general boom length and the same number of elements might occasion changes in the modeled values. For the 3-element beam, at least, we do find a greater difference in pattern shapes between ungrounded and grounded 70' towers than for the same grounding states for 90' towers. Fig. 10 shows the overlaid azimuth patterns for the two tower heights.

Nevertheless, the 4 variations on the 3-element aligned Yagi do have significant consequences that appear in the elevation patterns shown in Fig. 11. Grounding either tower reduces the vertical beamwidth dramatically, but perhaps more radically with a 70' tower than with a 90' version. Both models of the 70' tower show the appearance of a secondary lobe (which most NEC software implementations would identify by a definite reversal in the progression of gain values in the trace progression, regardless of the size of that variation). At least three of the sloper installations modeled would be useful for NVIS communications.

Our graphic sampling so far has used the 3-element Yagi aligned with the tower-sloper line. Fig. 12 provides a sample using the 6-element beam crosswise to the tower-sloper line. If we contrast grounded and ungrounded 90' support towers, we find very different current distribution curves. Not only do the current magnitude values on the tower differ in placement and value, but as well we find differences in the current magnitudes on the beam elements. The result is a set of quite different elevation patterns for the two situations, with the ungrounded tower and beam yielding the greatest change from the pattern we would expect of a free-standing full 30-degree sloper.

We cannot extrapolate from these cases any general conclusions. Even monoband beams for 20 meters come in different element configurations, and--of course--the beam on top of the tower might be of any design that has appeared commercially or been developed as strictly a personal project. All that our simple demonstration can show is that a top beam can and often does make a difference to the performance of the sloper attached at its upper end to the tower supporting the beam.

Conclusion

As soon as we pass from the abstractions of independent element performance to the realm of actual installations, both the true vertical antenna and the 30-degree sloper fall into a realm of almost innumerable variables for which no set of calculations or models can provide much usable guidance. The utility of the exercise has been to show that any one or more of these variables can alter the actual performance of the sloper. Moreover, we saw that even true vertical antennas are subject to interaction with both highly conductive and lossy nearby objects, whether or not they play an active role in support the antenna. In the case of the sloper, such objects are unavoidable in a real installation.

The performance of a sloper results from the totality of the property variables, including the sloper position, the diameters of the materials, the lengths of the elements (sloper and tower), the base height of the sloper above ground, the ground quality, the quality of support tower grounding, and the loading effects of an indefinitely large variety of beams that might be on top of the tower. This list does not include other nearby objects that may also affect especially the vertical component of the sloper's radiation and potential interactions.

For most antennas, we can work with the basic antenna design in isolation and then make adjustments for the installation environment. The sloper differs in having a necessary upper support point in proximity to an existing structure. Under these conditions, the data about the antenna in isolation holds far less guidance than it does for most other types of antennas. In the end, no sloper is a textbook case. Rather, each one is an experiment that combines differing values for each of the many variables. The sloper builder can only make his best estimate and then proceed by operating tests and measurements to find, within the real limitations of the installation site and available materials, the adjustments that yield as close as possible to optimal operation.

These notes perhaps do only one thing well: they explain why I tend not to provide notes at this site on the sloper antenna.

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