Chordal Hop Propagation: When HF Signals Skip the Ground

Every HF operator learns the simple picture first: the signal climbs to the ionosphere, comes back to the ground, is reflected and goes up again. Sometimes the numbers do not fit that picture. A path of 15,000 kilometers arrives louder than a two-hop path of 6,000, or a signal is strong although every calculation says the ground reflections on the way should have eaten most of it. One explanation that DXers and propagation writers use is chordal hop propagation: the wave is refracted inside the F layer, then travels across the “chord” of the Earth’s curve to a distant point in the layer and is bent again, without returning to the ground between the hops. This guide explains the idea, why it is attractive, how it differs from ordinary multi-hop paths and how an operator can look for it without being fooled.

The Ordinary Picture: Hops with Ground Reflections

In ordinary skywave propagation the signal leaves the antenna at a low angle and is refracted by an ionized layer. The Wikipedia article on skywave propagation explains that the ionosphere bends the wave back towards the Earth when the frequency is below the maximum usable frequency for that angle. At the ground the wave is reflected, either by land or by the sea, and the cycle repeats. Each full cycle is one hop, and a long path is a chain of hops.

Every ground reflection is a cost. A reflection from the sea loses little, but a reflection from dry ground, ice or mountains can lose a lot, and the loss depends on the polarization and the angle. Every time the wave goes up and down through the D layer in the daytime there is also absorption. For that reason the number of hops is as important as the distance. Our guide to antenna height and takeoff angle shows why a low angle gives fewer hops, and the idea of chordal hop is the same wish taken one step further: no ground reflections at all in the middle of the path.

What a Chordal Hop Is

The idea is a geometry one. A wave that enters the F layer at a very shallow angle is refracted gradually. If the layer bends it only a little, the wave does not come down; it continues inside or just below the layer, following a curve with a larger radius than the Earth, which is where the word “chord” comes from. A chord connects two points on a circle and runs inside it, while an ordinary hop follows the arc between the ground and the layer. When the wave is refracted again at the far end of the chord, it can continue in the same way, hop after hop, always staying at the height of the layer.

The result is a path that behaves like a duct. A signal inside such a duct avoids two of the largest losses of the ordinary path: the ground reflections and the repeated passes through the lower ionosphere, where the D layer absorbs. That is why chordal propagation is described as low in loss and why it is blamed, or credited, for signals that seem too strong for the number of hops that would be needed.

It is fair to say that this is a theory of a special mode, not an everyday event. Propagation models used by amateurs, including the programs described in our article on VOACAP and prediction tools, normally assume ordinary hops with ground reflections. A chordal path is therefore something you recognise from observations, not from the forecast.

Where and When It Is Reported

Reports of chordal-type paths come mainly from high bands on high-solar-activity years, and from paths that cross the equatorial region, where the ionosphere has strong gradients and the layer is higher and denser. At those latitudes the F layer shows large changes with local time. Around sunset the ionization on the sunlit side differs sharply from that on the night side, and that gradient is what can tilt the layer enough to trap a wave. The trans-equatorial paths familiar on the higher bands, which our article on transequatorial propagation covers for VHF, are connected with the same structure of the equatorial ionosphere.

The conditions that make chordal hops more likely are the ones that raise the density of the F layer: a high solar flux, local afternoon and evening on the paths that cross the equator, and the equinox seasons, when the ionosphere is more active than in midsummer. In practice that places the phenomenon on 15, 12, 10 and sometimes 6 meters, with an occasional report on 20 meters. When the solar flux is low, the layer is too thin to hold the wave and the effect disappears. Our guide to solar flux, A index and K index helps you to see which kind of day you are in.

Chordal Hop Compared with Ordinary Multi-Hop

The two modes can look similar on the receiver, so the table shows how they differ in the points that matter to an operator.

The very low angle is the key practical point. A wave that must graze the layer needs an antenna with a good response near the horizon, which is the case for a high yagi, a long wire at a good height or a vertical with a good radial system. A low dipole sends most of its energy upward and is poor for this kind of path. If your station is limited, our guide to long path and short path shows another way of reaching the same distant place.

Why Signals on Such Paths Can Sound Different

Operators who believe they have worked a chordal path often describe a signal with a clean, smooth sound, a smaller amount of flutter than expected and a slow, deep fading instead of the fast flutter of multi-hop paths. The reason is plausible: a signal that has not been reflected from the rough ground several times has not been scattered as much, so its different components stay closer in phase. That does not prove the mechanism, because a short-path signal on a good day can sound the same, but it is a clue.

The reverse is also common. When the duct is not stable, the signal can disappear for a short time as the layer moves, then return. This can give the impression of a sudden opening in a place where nothing was heard a minute before. A chordal path is not a guarantee of a long contact, but it can give a few minutes in which a distant station is as readable as one on the other side of the country.

Why the Layer Can Guide a Wave

The ionosphere is not a uniform mirror. Its electron density rises with height up to a peak and then falls, and it also changes along the surface of the Earth: higher near the equator, lower towards the poles, higher in the afternoon, lower at night. A radio wave is bent away from the regions of higher electron density, because the refractive index of the ionized medium falls as the electron density rises, and it is turned back completely when the wave frequency is not far above the local plasma frequency for that angle. For a wave that travels almost horizontally, a small horizontal gradient is enough to change the direction of the bending. Where the gradient has the right sign, the wave is turned back before it can leave the layer, and a duct-like path is formed.

That explains why a chordal path needs three things at the same time: a very shallow entry angle, a frequency that is high enough to avoid being reflected too soon and low enough not to escape, and a suitable gradient along the path. Any of these can change in minutes. A small change in the frequency, in the takeoff angle or in the state of the layer can end the duct. That is also the reason why two stations in the same town can hear the same distant signal at different levels, and why the effect is hard to reproduce on demand.

The same gradients are the cause of other well-known effects, among them the evening enhancement of the trans-equatorial paths and the sunset and sunrise changes that DXers know from the gray line. Seen in this light, a chordal hop is not a strange exception; it is one of several results of the shape of the F layer, and the same discipline of watching the time, the band and the solar data applies to all of them.

How to Look for Chordal Hop in Your Own Log

The best evidence is your own data, and it is easy to collect. First note the paths that seem too good: distance, band, time in UTC, takeoff direction and the report. Then compare them with what a prediction program expected. A path that was predicted as closed, or as a three-hop path with high loss, but was heard at 59, is a candidate.

Reporting networks are the second tool. Our article on PSK Reporter shows how to see where a signal was received, and beacon projects such as the NCDXF and IARU beacon network transmit on the same schedule on several bands, which makes comparisons between days easy. If a beacon on the far side of the equator is received strongly at your location on 21 and 28 MHz for a long time after the predicted close, and not on the lower bands, you are watching something worth recording. Keep a short note for each such observation, because a pattern over many days is much stronger evidence than a single surprise.

Finally, be critical. A strong signal can also come from sporadic E, from an ordinary two-hop path over the sea, from scatter in the ionosphere or from a path along the gray line, which our article on sporadic E and the gray line describes. The label “chordal hop” should come last, after the simpler explanations have been excluded.

What You Can Do With It

• Listen on the higher bands in the evening. When the solar flux is high, check 15, 12 and 10 meters after sunset on the paths that cross the equator, because the band can stay open after the ordinary prediction says it is closed.
• Use a low-angle antenna. A high yagi or a good vertical gives you the response near the horizon that such a path needs.
• Call early. If the signal is strong, call at once: a duct can fade in a few minutes.
• Compare the reports. Use the reporting networks and the beacons to see whether the same path is open for others.
• Log the conditions. Record the solar flux, the K index and the time for every unusual path, and review the notes after a few weeks.

The Bottom Line

Chordal hop propagation is the idea that an HF signal can travel inside the F layer, from one refraction to the next, without reflections from the ground in between. It is attractive because it avoids ground losses and D-layer absorption, and it is associated with high solar activity, the high bands, equatorial paths and a very low takeoff angle. It is not a mode that standard prediction models describe, so it must be recognised from observations. Collect your own data, use beacons and reporting networks, rule out simpler explanations and keep a low-angle antenna ready for the evening openings on 15, 12 and 10 meters.

Frequently Asked Questions

What is chordal hop propagation?

It is a proposed mode in which an HF signal is refracted inside the F layer and travels along a chord to the next refraction point, without a reflection from the ground between the hops.

Why would a signal avoid the ground in this mode?

The wave enters the layer at a very shallow angle and is bent only slightly, so it continues inside the layer instead of returning to the Earth. The structure of the equatorial ionosphere can help to hold it there.

Which bands are affected?

Reports come mostly from 15, 12, 10 and sometimes 6 meters, in years of high solar activity. The lower bands are rarely mentioned.

Can I predict chordal hops with software?

Not with the usual models, which assume ordinary hops with ground reflections. You recognise the mode from observations, for example from strong signals on paths that were predicted as poor.

What antenna helps most?

One with a strong response close to the horizon: a high yagi, a long wire at a good height or a vertical with a good radial system. A low horizontal dipole sends most of its energy upward.

How can I tell it from sporadic E or ordinary two-hop propagation?

Compare the path with beacons, reporting networks and the solar data, and exclude the simpler explanations first. A repeated pattern over many days is better evidence than a single strong signal.