I am not asking about the fairly well-known effect of the earth "appearing less curved to radio waves" that are otherwise still essentially line-of-sight, but a deeper arcanum:

In the ARRL Antenna Book, 17th edition (1994) there is a discussion of "Reliable VHF coverage" in starting on page 23-7 in the Radio Wave Propagation chapter. The claim is made,

Because of age-old ideas, misconceptions about the coverage obtainable in our VHF bands persist. This reflects the thoughts that VHF waves travel only in straight lines, […] However, let us survey the picture in the light of modern wave-propagation knowledge and see what the bands above 50 MHz are good fro on a day-to-day basis, ignoring the anomalies [presumably referring to the tropospheric ducting of previous section] that may result in extensions of normal coverage.

It goes on, after mentioning an article by D.W. Bray, K2LMG in the November 1961 QST magazine, to present two graphs that plot "tropospheric path loss" against distance. The curves therein rise steeply from 120 dB of loss at a distance of 0 miles [?!] to around 180 dB near 50 miles, then level off slightly so that at 500 miles there is a path loss around 240 dB. (That's reading the 50% reliability chart roughly, there's actually 4 lines plotted for 144/50, 220, 432, and 1296 MHz, as well as a second separate chart showing 99% reliability; the 99% reliability chart is very approximately 10–20 dB worse than the 50% one at any given point.)

UPDATE: thanks to W0BTU Mike, here's the actual charts scanned from an earlier edition:

Path loss vs. distance for amateur frequencies above 50 MHz

What "modern wave-propagation knowledge" is this referring to? What mechanism(s) would allow VHF signals to be 99% reliably received 500 miles away, albeit with more than 250 dB of path loss, or 50%-of-the-time reliability with a little less loss? (These path-loss charts do NOT assume any antenna-height gain.)

  • $\begingroup$ Troposcatter? EME? $\endgroup$ Commented Feb 24, 2017 at 14:09
  • $\begingroup$ Here are some nomographs and accompanying text from an earlier version of the ARRL VHF Manual. Go to w0btu.com/files/vhf and download VHF_distance_coverage_nomographs.zip. I've found them to be a good predictor of VHF coverage back when I was operating SSB and CW on the low end of 2m back in the 1980s. And somewhat related is this webpage: w0btu.com/VHF-UHF_vertical_antenna_stacking.html $\endgroup$ Commented Mar 7, 2017 at 15:14
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    $\begingroup$ @MikeWaters Thanks, those are very similar to my edition! I've grabbed the chart I tried to describe and added it to my question, hope you don't mind. (Was on your site just the other day while researching beverage antennas and glad to meet you on this site now too!) $\endgroup$ Commented Mar 7, 2017 at 20:03
  • $\begingroup$ @natevw-AF7TB I don't mind at all! In August 2018 I converted the TIFF files to four PNG files there. Feel free to add those. $\endgroup$ Commented Oct 5, 2018 at 18:38

4 Answers 4


Turns out that, after turning to discussion of HF propagation for a number of intervening pages, this Antenna Book ends up getting back around to its own answer for this question!

From the "Scatter Modes" section on page 23-30 of the same 17th edition:

The wave energy of VHF stations is not gone after it reaches the radio horizon, described early in this chapter. It is scattered, but it can be heard to some degree for hundreds of miles. Everything on Earth, and in the regions of space up to at least 100 miles, is a potential scattering agent.

Tropospheric scatter is always with us […] this is what produces that nearly flat portion of the curves given in an earlier section on reliable VHF coverage. … As long ago as the early 1950s, VHF enthusiasts found that VHF contests could be won with high power, big antennas and a good ear for signals deep in the noise. … Ionospheric scatter works much the same as the tropo version, [… and] can fill in the skip zone with marginally readable signals scattered from ionized trails of meteors, small areas of random ionization, cosmic dust, satellites and whatever may come into the antenna patterns at 50 to 150 miles or so above the Earth. […]

[bold added for emphasis]

It goes on similarly to discuss "backscatter" and "transequatorial scatter" before going on to a different section on "auroral propagation" (which can also affect VHF but is probably not related to the reliable propagation graphs).

So in short, "scatter" (in many forms) is claimed as the mechanism that allows VHF signals to be heard hundreds of miles beyond the primary "radio horizon".

I also believe the ARRL editors consider the experimental discoveries of the various scatter modes to be the "modern wave-propagation knowledge" referred to earlier — in this "Scatter Modes" section there are a couple historical references around the same dates as the QST article, including the "early 1950s" one quoted above as well as Transequitorial scatter as "an amateur 50-MHz discovery in the years 1946–1947".


Terrestrial, point-point propagation paths can exist due to diffraction of the radiated e-m fields over terrain peaks and man-made structures, with each diffraction adding loss at the receive antenna to the normal inverse-distance field loss for an LOS path of that total length.

The graphic below illustrates this for an FM broadcast station, where the line-of-sight path is severely obstructed, but the signal can be received well beyond those obstructions.

The real propagation path would consist of several straight-line segments over terrain peaks, joined together to connect the transmit and receive antennas.

In this example, the additional loss due to diffractions compared to an LOS path of that total length is shown to be 76.59 dB.

The received field will vary over time depending on atmospheric K-factor and other conditions. enter image description here

  • $\begingroup$ Older ARRL publications I have refer to what you describe in the first paragraph as knife edge diffraction, IIRC. But they don't mention man-made structures (clusters of tall buildings in cities?), only jagged mountain peaks. That's intriguing! Do you happen to know of any examples? $\endgroup$ Commented Oct 5, 2018 at 18:48
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    $\begingroup$ Here is a quote with a short reference about this from Engineering Considerations for Microwave Communications Systems (GTE Lenkurt, Inc, 1970): "The effect of man-made obstacles depends entirely upon their shape and position, Microwave- transparent objects, which are few, are ignored. A large round container such as a gas storage reservoir, if partially in the path, causes both diffraction and dispersion as well as some blocking.". $\endgroup$ Commented Oct 5, 2018 at 19:51

I really don't know – in a review, I'd have marked that sentence as far too vague – what the author means with "modern wave-propagation knowledge". If I need to benchmark that knowledge against a 31 year old Ham article, well… I don't really think it's a great advocate. "Modern knowledge", to me, is probably something that is what research on an academic level has yielded and is now dissipating into technological areas such as amateur radio, and thus, an article in a ham mag might by definition, not be used as describing the state of the sciences in 1961¹.

So, I dispute your "expected radio horizon"; just because a ham expert in 1961 modeled something is really no great reason to expect the same to be accurate in 1994.

Anyway, having minimal knowledge of earth observation and radio propagation modelling, I'd go for:

  • having the ability to actually simulate non-trivial situations, including:
    • clearer idea of atmospheric properties such as permittivity ($\epsilon_r$) and magnetic permeability ($\mu_r$) as well as charge density ($\rho$),
    • non-linear gradients of above properties,
    • non-perfectly-spherical atmosphere,
    • actually looking into things that are far, far more granular than just saying "ok, here's the troposphere that we model as thing with the following diffractive index and a constant attenuation $\alpha$", including effects like weather-based inversion of conductivities etc.
    • being able to model effects of ground conductivity etc.
  • actually having data on how charged, conductive, vapor-saturated and shaped strata of the atmosphere are, based on a lot of satellite and radioastronomy experiments
  • having a far better understanding of the interaction between large antennas and their surroundings

¹I know that article is cited in many ham places. I've never read it.
However, it seems to me that modeling VHF transmission's reach in 1961 should basically be equivalent to asking a couple of WWII and cold war radio engineers; it's really not like radio reach is not a very important strategic factor, and I'm very certain that all involved parties had very accurate recordings of how far they could reach, and will have worked to improve their models to match that, long before 1961.

These models might not have been public back in the day, but really, they also shouldn't be that much of rocket science to recreate. In 1994, there should be no "surprise" in how VHF propagates terrestrially – I really think it's very worth writing articles that bring research-level theory, models and experimentation to the amateur masses (which, by the beard of Hertz, are pretty good at such things), but you must then compare these to state-of-back then in academics, not in ham mags. That's just unfair – many countries simply had restrictions on radio usage during WWII, so the amateur radio community just needed a decade or two to catch up. That catching-up phase was an especially fruitful one, what with all the semiconductor technology emerging at the same time.

Downside of that being a phase is that if you look online, you still find a lot of people trying to build the 1960's kits nowadays, even trying to get the same diodes and transistors of the day – there's really no good reason you'd want a Germanium noise gen– err transistor amplifier if you can have a silicon one for cheap, if you just don't stick to material from the "golden era of rediscovering possibilities". I attribute that to a lot of Kit manufacturers and mag publishers just copying articles from back then, until the original source and its restrictions got lost. Enough ranting for today.

  • $\begingroup$ Hi Marcus, I don't begrudge your rant; I hear what you're saying but would appreciate a bit more balance towards explaining "ϵ, μ gradients" (you mean EM fields?) and your other ideas for the mechanisms there. $\endgroup$ Commented Feb 23, 2017 at 18:11
  • $\begingroup$ You're right – though I must admit that I'm looking at this a bit from an "aftermath" position. It's kind of hard for me to know to what state to compare – for example, 1961's models definitely had tropospheric diffraction models, but I don't know how well they actually modelled things like large-scale "waveguiding" due to relatively strong changes of atmospheric properties within a couple m of height difference (i.e. weather), or whether the models assumed effects of ionized upper atmosphere and so on. $\endgroup$ Commented Feb 23, 2017 at 18:24
  • $\begingroup$ Thanks! And re. "expected radio horizon" I am not sure what you are disputing? My intent was to draw a distinction between the notion of a basically "hard" radio horizon 15% further away than the visual horizon (e.g. en.wikipedia.org/w/… expectations) versus the notion that signals propagate weakly beyond that — how? $\endgroup$ Commented Feb 23, 2017 at 18:25
  • $\begingroup$ I must admit I wasn't even aware of this 115% Line-Of-Sight model! $\endgroup$ Commented Feb 23, 2017 at 18:26
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    $\begingroup$ I'd have to get a large stack of paper out and get going,but the idea is: As light entering water,beams always bend towards the normal at a medium interface if they enter a medium with higher refractive index $n$ (optical density),and away from it when going into one of lower refractive index.Electromagnetically,this is an effect of how the poynting vector shifts if you increase $\epsilon$ or $\mu$ ($n=\sqrt{\epsilon\mu}$, by the way).You can now model the atmosphere as a ball with decreasing $n$ the further you go from the center;thus,you can,analytically,find an equation for EM "beam-bend". $\endgroup$ Commented Feb 23, 2017 at 18:33

Historically, this is the best time of year (Late September through early December) in the northern hemisphere to enjoy VHF and UHF propagation enhancements ("band openings") caused by sharp air temperature differences between two (or more) distinct layers of air. These occur far below the ionosphere.

However, band openings can occur in any season. The two types --somewhat related-- are described below.

Temperature Inversions

By far, the most common type. Just two layers in the troposphere are are involved.

Often incorrectly referred to as "ducting", these occur where there is a sudden change in air temperature vs. height, and can even cover an area encompassing many hundreds of square miles. They usually occur along a cold occlusion or occluded front.

While most common in the fall and spring, I know a ham in Ohio who observed a spectacular band opening years ago in January, where the temperature dropped from above freezing to -20° F in a matter of hours. (It would have been even more spectacular had other hams known about it, but there was no Internet or VHF DX clusters in those days.)

Tropospheric Ducting

A genuine duct consists of three layers of air.

They can be spectacular and extend over a greater distance, but are rare.

A true tropo duct almost never covers an area anywhere near as large as a temperature inversion. By *waveguiding" I assume that Marcus means "tropospheric ducting".

Below is what a duct looks like. More details can be found here.

Tropospheric duct

Features common to both inversions and ducts

Both inversions and ducts usually occur when the air is relatively calm. Once it gets windy, the air masses start to mix and the band opening gradually disappears.

Experienced VHF/UHF enthusiasts understand that whenever a hot day followed by a rapid and large temperature drop in the evening occurs, there might be a good opening. The larger the drop, the better the DX.

You can tell if you have a band opening in your area by transmitting on 146.94 (or another very common FM repeater frequency) followed by receiving countless beeps, heterodynes, and distant repeater IDs when you unkey and listen. During the better band openings, all it takes is an HT to experience that.

Depending on who you ask, that can either be a blessing or a nuisance. ;-) They can and do cause interference to both local and distant repeater groups. Hams operating SSB or CW below ~144.250 or on simplex FM frequencies within that area are treated to a special delight.

  • $\begingroup$ I just discovered a site that claims to forecast when a "duct" might occur. Select your region in the drop-down list. It looks to me like that when he says "duct", he actually means two-layer temperature inversions. Regardless, it may well very be useful assuming it is at least somewhat accurate. $\endgroup$ Commented Oct 6, 2018 at 2:42
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    $\begingroup$ I’d just like to point out that the refraction of electromagnetic waves by a temperature inversion, is exactly why you see the ‘mirage’ effect on a hot road (which has very hot air in contact with the road, with cooler air above it) $\endgroup$
    – Scott Earle
    Commented Oct 7, 2018 at 12:54

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