Multi-Hop Propagation: How Many Hops Does Your DX Signal Take?

When you hear Japan from Europe on 20 meters, your signal did not travel in one long leap. It climbed to the ionosphere, came back down, was reflected by the ground or the sea and went up again, perhaps three times before it reached the antenna on the other side. That chain of reflections is called multi-hop propagation, and understanding it explains many puzzles that DXers meet: why a path is open at one takeoff angle and dead at another, why a nearby station may be inaudible while a distant one is loud, and why the best antenna for working far away is not the one with the highest gain at the horizon in every case. This guide explains what a hop is, how far it can reach, how the number of hops depends on the angle of the signal and what each hop costs.

What a Hop Is

The Wikipedia article on skywave propagation describes how high-frequency signals that enter the ionosphere at a low angle are bent back towards the Earth by the ionized layer. When the operating frequency is just below the maximum usable frequency, the losses can be quite small, so the signal may effectively bounce or skip between the Earth and the ionosphere two or more times. That is multi-hop propagation, and it is what allows signals of only a few watts to be received many thousands of miles away. One hop is the path from the transmitter up to the ionosphere and down to the ground; the second hop begins at the point where the signal returns to the Earth and is reflected back up.

In practice the reflection point is not a mirror. The wave is refracted gradually, which makes it seem to arrive from a higher virtual height than the place where it turns. For the geometry that follows, the virtual height is a convenient figure: roughly 100 to 110 kilometers for the E layer and about 250 to 400 kilometers for the F2 layer, depending on the time of day, the season and the solar cycle. Our guide to MUF maps and ionosonde data shows how to see the current state of those layers.

How Far Can One Hop Go?

The longest possible single hop is set by geometry. A signal that leaves the antenna exactly along the horizon, at a takeoff angle of zero, and is reflected at a virtual height h, covers a ground distance of about 2 times the Earth radius times the arc cosine of R divided by R plus h. With R of 6371 kilometers and a virtual height of 300 kilometers this gives roughly 3800 kilometers. For 250 kilometers the answer is about 3500 kilometers, and for 400 kilometers about 4400 kilometers. For the E layer, at 110 kilometers, the figure is about 2350 kilometers. These are upper limits for a flat reflection and a zero angle, and real antennas and real paths usually fall short of them.

Raise the takeoff angle and the hop becomes shorter, because the signal goes up more steeply and returns closer to the transmitter. The table shows the calculated ground distance of one hop for a reflection at a virtual height of 300 kilometers, which is a typical value for the F2 layer.

The figures are calculated with a simple flat-layer model on a spherical Earth, so treat them as a guide. They agree with the statement in the skywave article that for every distance there is an optimum takeoff angle, and that the longest distances need a lobe at a low angle. Our article on antenna height and takeoff angle shows how the height of the antenna controls that lobe.

Counting Hops on a Real Path

The number of hops follows from the distance and the angle. A path of about 7000 kilometers, such as the one between the Baltic states and the east coast of North America, needs at least two F2 hops, because a single hop cannot exceed roughly 4000 kilometers even in the best case, and a realistic angle gives about 3000. A path to Japan, about 9000 kilometers, normally needs three hops. A path to the antipode of the transmitter or to Australia and New Zealand from Europe is more than 15000 kilometers and needs four or five hops by the short path, which is why those contacts are usually possible only when conditions are very favorable or when the long path is better. Our article on long path and short path explains when to turn the antenna the other way.

The simplest way to estimate the count is to divide the distance by an effective hop length of about 3000 kilometers for an F2 path with a low angle, and to round up. You then get the number of reflections in the ionosphere, and the number of reflections on the ground is one fewer. Use a great-circle map to measure the distance and the bearing; our guide to great circle maps shows how.

What Each Hop Costs

Every hop adds loss. Part of the signal is absorbed in the lower ionosphere, especially in the D layer in the daytime, as the signal passes through it on the way up and on the way down. Part is lost in the ground reflection, which is excellent over salt water and much worse over dry land, ice or mountains. And some of the energy is scattered, because the reflecting layer is not smooth. The result is that a four-hop path is considerably weaker than a two-hop path even for the same distance covered. The total is roughly the sum of the losses of each hop, in decibels, plus the spreading of the wave with distance.

This is why operators speak of a path being open on one side of the day and closed on the other. During the daytime the D layer absorbs signals on the lower HF bands, which is why 80 and 160 meters are poor for DX at noon and why the higher bands, with their smaller absorption, carry signals on multiple hops. At night the D layer disappears and the lower bands open, with signals returning with low loss. The same mechanism makes a path across the dark side of the Earth better than one across the sunlit side. Our article on HF propagation covers the daily pattern in more detail.

The Role of the Takeoff Angle

A DX path wants the fewest hops possible, and the fewest hops mean the lowest angle that the ionosphere will accept. A low angle produces a long first hop, which reduces the number of ground reflections and ionospheric passes. On the other hand, a very low angle is hard to produce, because the ground in front of the antenna interacts with the wave and may cancel the radiation at the horizon. Height is the main factor: a horizontal dipole at a quarter wavelength has most of its energy at a high angle, while at one half wavelength or more the main lobe moves down to a more useful range.

The result is a trade-off for the operator. A low antenna is excellent for medium distances that need a high angle, and for NVIS, but a high antenna or a vertical with a good radial system is better for a distant path. Several layers of signals can also arrive from different hop counts at different angles; a stacked array of beams, often used in contest stations, lets the operator choose the angle that matches the path. If you cannot raise the antenna, a vertical or an inverted L may be the better tool for a low angle.

Reading Multi-Hop Behaviour on the Air

Experience with multi-hop paths changes how you listen. A signal that arrives by two hops often has more flutter and fading than one that arrives by one, because the paths wander and interfere. Signals that arrive by different numbers of hops can be heard at the same time, producing an echo or a rough sound; this is common on long-path openings, where the short-path and the long-path signals both arrive. If a station has a strong signal that suddenly drops while a more distant one rises, the cause is often that the number of hops has changed because the layer height moved.

Check the data before you decide that nothing is possible. Beacons are useful, and reporting networks can show where your signal is being heard. Use a propagation prediction program to see which paths are likely to be open and by how many hops, and compare the prediction with reports from the air. The agency in charge of space weather forecasts, the NOAA Space Weather Prediction Center, publishes the solar and geomagnetic data that drive the ionosphere and indicates when conditions are disturbed. A geomagnetic storm can destroy the higher hops by reducing the density of the F2 layer at high latitudes, and a path that normally crosses the polar region may be silent while a path across the equator remains good.

One more point deserves attention: the E layer and the F2 layer can work together. A path may use a sporadic-E reflection for the first hop and an F2 reflection for the next, or the reverse, and the mixed paths are among the hardest to predict. Software that assumes a single layer will not show them, which is why a quick check against real reports from the air is always worth the effort. If your own signal is reported in an area where the model says nothing should be heard, take the report seriously and note the time, the band and the conditions for the next occasion.

Practical Tips for DXers

• Match the angle to the distance. For paths of more than 5000 kilometers, aim for the lowest takeoff angle your station can provide, around 3 to 10 degrees.
• Prefer sea paths. Ground reflections over water lose less, so paths whose reflection points lie in the ocean tend to be stronger than the same distance over land.
• Use the right band for the time. Move up in frequency during the day, where absorption is lower, and down at night.
• Do not ignore the gray line. The terminator can allow signals to travel with little absorption, as discussed in our article on sporadic E and the gray line.
• Listen for the opening. A path may be open for ten minutes. Be ready to call, and use a cluster or reporting network to find where signals are heard.

The Bottom Line

Multi-hop propagation is the repeated reflection of an HF signal between the ionosphere and the ground. One F2 hop can reach at most about 4000 kilometers in the ideal case and usually about 3000 kilometers or less at a realistic angle, so intercontinental paths take two to five hops. Every hop costs signal in absorption, ground reflection and scattering, so low takeoff angles, sea paths and the right band for the time of day matter. Plan paths with a great-circle map and a prediction tool, build an antenna that can launch a low angle if DX is your aim, and watch the solar data before you decide that a path is dead.

Frequently Asked Questions

What is multi-hop propagation?

It is the repeated reflection of a radio signal between the ionosphere and the Earth. The signal bounces more than once, which lets it reach distances far beyond a single hop.

How far can a single hop reach?

For the F2 layer the geometric limit is about 4000 kilometers, and in practice about 3000 kilometers or less. A single E-layer hop is limited to about 2000 kilometers or less.

How many hops does a path to Japan need from Europe?

The distance is about 9000 kilometers, so a low-angle path normally needs about three F2 hops.

Does each hop reduce the signal?

Yes. Each pass through the lower ionosphere and each reflection from the ground adds loss, so a path with more hops is generally weaker.

Which takeoff angle is best for DX?

A low angle, typically between about 3 and 10 degrees for paths of more than a few thousand kilometers, because it gives the longest hops and the fewest reflections.

Why do I hear echoes on long paths?

Signals that arrive by different paths, for example the short path and the long path, or by a different number of hops, reach the receiver at slightly different times, which produces an echo.