Category Archives: Propagation

Measuring The Speed of Light Using a Shortwave Radio

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I thought it would be interesting to see whether or not it was possible to crudely measure the speed of light using a shortwave radio and a time station.

Various time stations transmit precise time on several shortwave frequencies. Here in the USA, we have WWV in Ft. Collins, Colorado, which transmits on 2.5, 5, 10, 15, and 20 MHz. We also have WWVH in Kekaha, Hawaii, which transmits on 2.5, 5, 10, and 15 MHz. These stations transmit an audio “tick” at exactly each UTC second.

One way to measure the speed of radio waves (and light) would be to measure how long it takes for the tick to travel a fixed distance. Divide the distance by the time, and we have the speed of light. However, that requires knowing the exact UTC time locally. While this can be done with a GPS unit that outputs a 1 PPS (pulse per second) signal, I thought it would be more interesting to do it using just a shortwave radio without any extra hardware, other than a computer to record the audio.

Both WWV and WWVH transmit on several of the international time frequencies. And it turns out that at certain times of the day, it is possible to receive both of them on the same frequency. The following recording was made on 15 MHz at 1821 UTC on January 1, 2011: Recording of WWV and WWVH

You can hear the time announcement for WWVH first, by a woman, followed by a man giving the WWV time announcement.

I am roughly at a location of 77W and 40N. WWV is located at roughly 105W and 41N, and is about 2,372 km away. WWVH is located at roughly 160W and 22N, about 7,883 km away. The actual path the radio waves takes to reach me is longer, due to the fact that they reflect off the ionosphere, a few hundred km high. We’ll neglect that for now.

The difference in distance between WWV and WWVH is 7883 – 2372 = 5510 km.

The following is a display of the waveform from the above recording, centered around one of the second ticks. You can see the stronger WWV second tick centered at about 19.086 seconds into the recording. You can also see the weaker WWVH second tick centered at about 19.105 seconds: wwv and wwvh

The other waveforms you see before and after the second ticks are the audio that each station always transmits.

If we subtract the time markers for the two ticks, we get 19.105 – 19.086 = 0.019 seconds (19 milliseconds). That’s the time delay between the two ticks. Next, performing our division, 5510 km / 0.019 seconds = 290,000 km/second. The generally accepted value for the speed of light is 299,792 km/second. That’s pretty close!

In all fairness, the time resolution is not that good, and I had to eyeball the readings. Plus, a one millisecond difference in the time delay would have resulted in about a 15,000 km/sec difference in the speed of light. So a slight difference in eyeballing these broad time ticks would result in a large error in our estimate of the speed of light.

If you listened carefully to the recording, you no doubt heard a fluttery or watery quality to the sound. This is often indicative of multipath, where the radio waves take two (or more) paths between the transmitter and receiver.

Here’s another waveform from the recording, centered at 27 seconds into the recording: wwv and wwvh long path

In this case, we can clearly see the second tick from WWVH. But there’s no second tick from WWVH, just silence. Where is it?

Looking further into the recording, we see another second tick delayed much further. Eyeballing it, the delayed tick is at about 27.187 seconds into the recording. And the first tick, which we believe is from WWV is at about 27.087 seconds. The difference between the two is 0.100 seconds. Using the accepted speed of light, this difference in time could be due to a distance of 299,792 km/sec * 0.100 sec = 29,972 km. What could account for this delay?

One possibility is that during this time period, the signal from WWVH was not taking the normal or short path to my location, but was instead travelling around the other side of the Earth, taking the long path.

The circumference of the Earth is about 40,075 km (the exact value depends on which path around the Earth you take, as the Earth is not a perfect sphere). We know the short path is 7,883 km, so the long path is about 40075 – 7883 = 32192 km. There is still the delay due to the time it takes the radio waves to get from WWV to my location, that path is 2,372 km. The net difference between the two is 32192 – 2372= 29820 km.

We can divide that distance by the speed of light to see what the time delay should be: 29820 km / 299792 km/sec = 0.099 seconds. This is extremely close to our measured period of 0.100 seconds, and suggests that the long delayed second tick really is from the WWVH signal taking the long path around the Earth to reach us.

The following map, generated with the DX ToolBox Radio Propagation Forecasting Program, shows both the short path (white line) and long path (gray line) between my location and WWVH: WWVH Path

Comments appreciated!

An Interesting Example of a Station Going Long

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A fairly active pirate station the past week or so has been the “Fruitcake” station, which plays songs and sound clips related to, well, fruitcake. Hence the name. On December 20, 2011 at 2300 UTC I recorded a transmission of this station with my netSDR. What I ended up capturing was a very interesting and educational example of a station going long.

Here is a graph of the received signal strength:
Signal Strength in dBm

An S9 signal is -73 dBm, right about the received signal level at the beginning of the broadcast. There is some fading up and down, typical with shortwave radio. What’s interesting is that the change in signal strength seems to have a definite period, rising and falling every few seconds. After a few minutes, the period starts to become longer, and the amplitude of the variation also increases. About half way through the transmission, the amplitude becomes quite large. There is then one deep fade, one large increase in signal strength, and then the signal almost fades out, going down to about -95 dBm (about S4). Notice that 10 minutes ago it was S9.

Next, here is a waterfall of the recorded transmission:
Waterfall

A waterfall is a color coded representation of the signal strength of a band of frequencies over time. In this case, it shows us the signal strength from about 2300 to 2310 UTC, over a frequency range of 6900 to 6950 kHz. The blue background represents the weak background noise that is always present, in this case about -97 dBm. The brighter colors towards green represent stronger signals. We can see the station’s carrier at 6924 kHz, and the sidebands containing the audio modulation (this is an AM signal).

The change in bandwidth of the received signal about a minute and a half into the transmission is due to the audio that was transmitted, one song ended, and another sound clip, with wider audio, began.

This is an extremely educational image. We can see several things happening here:

1. The short choppy fades at the beginning of the transmission are evident.

2. As time goes on, the fades become more prominent, and we can see the increase in their period.

3. We can see the background noise levels increasing in amplitude. Look just outside the passband of the station itself, and you can see waves of increasing and decreasing background noise.

4. The fades all start at a higher frequency, and drift down to lower frequencies over time. This is a type of phenomena called selective fading, which you may have read about.

So, what is the cause of the selective fading? There are several possibilities.

One is when both ground wave and sky wave signals are being received. If there are phase differences between the two signals, they cancel out, reducing the received signal strength. Likewise, if they are in phase, they support each other, and add together, increasing the signal strength. One common example of this is with medium wave (AM broadcast) stations. When you are close to the station, the ground wave signal is extremely strong, and the sky wave is relatively weak, resulting in excellent reception with no fading. At a long distance away from the station, the ground wave is extremely weak or nonexistent, resulting in only a sky wave. Reception is weaker than the first example, but often reliable for stronger stations. This is why you can pick up AM stations over long distances at night. However, if you are at an intermediate distance, you can receive both the sky wave and ground wave. As the relative phase between them changes, you get fades. I’ve noticed this with a semi-local AM station. It has excellent reception in the daytime, but once evening approaches, reception gets very choppy. This is even before other stations begin to roll in.

I don’t think this is the cause in this case, as there should be little or no ground wave. And if there was, I would still be able to pick up the station after the band went long, since the ground wave was present. (Being HF instead of MW, the ground wave does not travel very far anyway)

Another possibility is due to propagation via both the E and F layers. In this case, it is again relative phase differences that cause the fading. I’m not sold on this scenario either, because I don’t believe the E layer would support propagation of 7 MHz signals. (E layer propagation should not be confused with sporadic E layer propagation that often causes VHF skip)

Next up, and the idea I am presently sold on, is propagation via both the F1 and F2 layers. During the daytime, when ionization is strongest, the F layer splits into two layers, the F1 at about 150-220 km and the F2 at 220-800 km. At night, the F1 layer merges with the F2 layer.

Perhaps, during the daytime, only one layer is responsible for NVIS propagation. My thought is that the F1 layer is providing the propagation, as it is the lower layer, and the first one the radio waves would interact with. Then, in the evening, when the band is going long and the F1 layer starts to dissipate allowing some radio waves to reach the F2 layer, propagation is occurring via both layers. Relative phase differences between the signals propagated by each layer cause the selective fading effects. Once the F1 layer completely dissipates, only the F2 layer is left, but it is unable to support NVIS propagation at 7 MHz.

Comments welcome and appreciated!

NVIS Near Vertical Incident Sky Wave

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While shortwave radio is commonly thought of as being used for long distance communications, it also functions for local and medium distance links. This is accomplished by a method known as NVIS, or Near Vertical Incident Sky Wave, and is in fact what most US pirate operators are using, even if they have never heard of it before.

I touched on NVIS in my previous post Going Long, which readers may wish to read before continuing.

To summarize, the ability of HF radio waves to get from the transmitter to target location depends on the ionosphere being able to refract (or reflect) them back to the Earth. The stronger the ionization level, the higher the frequency that can be refracted back, as most radio enthusiasts know. This is why during periods of high solar activity, the higher bands (up to 30 MHz and even beyond) are useful for long distance communications during much or even all of the day. Whereas when solar activity is low (as it has been until recently) the higher frequencies are often dead, and lower frequencies must be used.

But there’s a second factor as well – the angle that the radio waves strike the ionosphere. For a given ionization level, the lowest maximum frequency that can be reflected occurs when the radio waves are directed straight up. In this case, they would be reflected right down, for local reception. As the radio waves strike the ionosphere at more shallow angles (as would be the case for waves that are going to reach the Earth further away), higher frequencies will be reflected.

critical angle

In the above picture, paths A and B are at shallow enough angles that the radio waves get reflected back to the Earth. For path C, the angle is too steep, and the radio waves are not reflected, but pass into space.

The maximum frequency that will be reflected straight back is called the foF2 frequency. It is continuously varying, based on solar activity, and what part of the Earth the Sun is over. You can find a real time map at this URL: http://www.spacew.com/www/fof2.gif

http://www.spacew.com/www/fof2.gif

During the daytime, it lately has been reaching 10 or 12 MHz over the USA. At night, it drops down to 3 or 4 MHz.

The angle that the radio waves strike the ionosphere depends on the distance between the transmitter and receiver, and the height of the ionosphere, which unfortunately also varies. This is called the hmF2, and there’s a real time map of it also: http://www.spacew.com/www/hmf2.gif

The Maximum Usable Frequency (MUF) can be found by:
MUF = foF2 * sqrt( 1+ [D/(2*hmF2)]^2) where D is the distance in km.

Obviously, if the foF2 frequency is above your transmitter frequency, you don’t need to worry, you’ll be able to operate NVIS and be heard (assuming you have enough power to overcome noise, of course)

Once foF2 drops below your operating frequency, radio waves directed straight up keep going into space. Waves at more shallow angles (reaching the earth some distance away) could still be reflected, depending on the geometry. This creates what is referred to as the skip zone, the distance around the transmitter where the signal cannot be received.

For example, assuming a hmF2 height of 300 km (fairly average) here’s the skip zone distance for several different foF2 values, for a transmitter frequency of 7 MHz:
3 MHz 1270 km
4 MHz 860 km
5 MHz 580 km
6 MHz 360 km

As I type this at 0030Z on December 15, 2011, foF2 has dropped to 5 MHz over the northeast US. This leaves an approximately 350 mile diameter skip zone around the transmitter, where the broadcast cannot be received.

For good NVIS operation, an operator wants most of the transmitted RF to go straight up. This suggests the use of simple antennas like dipoles at low heights, which as it turns out is what most operators are doing anyway. A 43 meter band dipole at 30 feet up has radiation patterns like this:
http://www.hfunderpants.com/mypics/6.9_dipole_above_ground.png

The graph on the left is the pattern around the points of the compass, and the one on the right is the elevation. As you can see from the graph on the right, most of the RF energy is going up. This is bad for long distance DX, but good for NVIS operation.

The key point to remember is that when the band closes for NVIS, you will lose your local audience, where local could mean a radius of several hundred miles around your station. Dropping to a lower frequency (like 5, or even 3 MHz which operators have used in the past) regains your local audience. There’s a reason WBCQ uses 5110 kHz. Absorption losses increase as you go down in frequency, however, roughly inversely to the square of the frequency. So the absorption losses at 3 MHz are four times that at 6 MHz, and about 5.4 times that at 7 MHz. Operating earlier in the evening, before the band closes for NVIS, is another solution.

Going Long

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Have you ever wondered why other listeners are hearing a pirate with a very strong signal, while you can’t hear it at all? Or have you been listening to a station with a solid SIO of 555, only to have it fade to nothing, while others on IRC are still reporting solid copy? Chances are, the station was operating in NVIS (Near Vertical Incident Sky Wave) mode, where the radio signals go straight up from the transmitter, and down to the receiving site. NVIS is the mode used for all short distance communications on HF. Think of it as the opposite of “skip”.

In radio-speak, “going long” means a band is no longer able to support short distance communications. The maximum frequency that is reflected (actually refracted, but I’ll use the term reflected as most people are accustomed to that) by the ionosphere is a function of the characteristics of the ionosphere (due to solar activity), and the angle of the radio waves. The maximum frequency gets lower as the angle becomes more steep, reaching a minimum for radio waves directed straight up. This final frequency is called the foF2 or critical F2 layer frequency. Any radio waves directed straight up that are higher than this frequency will pass through the ionosphere into space. There is a real time foF2 map here: http://www.spacew.com/www/foF2.gifhttp://www.spacew.com/www/fof2.gif

For other angles, the maximum frequency that can be propagated is equal to foF2 divided by the sine of the angle. This tells is that as the angle gets smaller (not straight up) the maximum frequency increases. 

Critical Angle

In the above picture, paths A and B are at shallow enough angles that the radio waves get reflected back to the Earth. For path C, the angle is too steep, and the radio waves are not reflected, but pass into space.

During the daytime, the ionosphere is able to support propagation of higher frequencies. As the sun sets and the ionization levels start to decrease, the maximum frequency begins to drop. For a given frequency, shorter transmission path distances will be affected first. The path will “close” very suddenly, sometimes over the span of just a few minutes or even seconds.

Here is a graph plotting the received signal level for WFMT on Dec 10, 2011:

WFMT Signal Strength

The signal strength is shown in dBm. Refer to the previous entry How many watts do you need? for a refresher course in dBm. In general, an S9 signal is -73 dBm, every S unit is theoretically 6 dB, so S8 is -81 dBm, etc.

You can see that the signal was varying between -60 and -70 dBm, so about S9+10 dB. Then quite suddenly, it dropped to about -85 dBm, and then continued to decline to about -90 dBm.

Here is a closeup graph showing one minute of signal strength during the time WFMT went long. You can see that it went long between 20 and 30 seconds. That is, it only took 10 seconds.

one minute of signal strength

Looking carefully, you’ll also observe an increase in signal level just before WFMT went long. I have noticed this many times. My theory is that propagation is best when the incident angle of the radio waves to the ionosphere is very close to the critical angle. In this case, the incident angle is of course fixed, but the critical angle is changing as the ionosphere weakens to nighttime levels.

Note that even though the critical angle was exceeded, some radio waves are still being reflected, as the signal level has not dropped to zero yet (although it does continue to trend down, at some point the station will completely fade out).

The critical angle determines the maximum frequency that can be propagated between two points.

Remember from above that the maximum frequency that can be propagated is equal to foF2 divided by the sine of the angle. We can use some simple math to calculate what frequencies will work, knowing foF2.

The Maximum Usable Frequency (MUF) can be found by:
MUF = foF2 * sqrt( 1+ [D/(2*hmF2)]^2)

Where hmF2 is the height of the F2 layer. There is a map of the F2 height here:
http://www.spacew.com/www/hmf2.gifhttp://www.spacew.com/www/hmf2.gif

For example, if the distance between the two stations is 690 km, and the F2 height is 250 km, and foF2 is 3.5 MHz, then plugging into the above formula gives us a MUF of 5.97 MHz. So we can use frequencies up to that. But, if the stations were closer together, say 300 km, then the MUF is only 4.1 MHz. (Note: It’s for long distances, it is important to remember that the signal probably takes several hops, and you need to use a value of D that is the distance between stations divided by the number of hops)

Note that like foF2, hmF2 is continuously varying. At 1600 UTC on December 14, 2011, the foF2 is about 9 MHz over the eastern USA, and the mmF2 is about 240 km. So 43 meters is potentially open to anywhere on the east coast, even using NVIS. Of course this only takes the MUF into account, there is also the LUF, or Lowest Usable Frequency, which is mostly a function of transmitter power and D layer absorption.

At night, foF2 dramatically drops. Lately it has been going below 7 MHz in around 2300 UTC, turning off NVIS for 43 meter band transmissions. With an foF2 of 6 MHz (observed today at 2330z) the MUF is around 7 MHz for a distance of 200 miles.

For this reason, operators who want to reach their target area (east coast ops reaching east coast listeners) should consider using lower frequencies at nighttime. Years ago, the 3 MHz band was somewhat popular for pirate operations. Even somewhere in 5 MHz would be useful.

NVIS itself is worthy of an entry by itself, which is coming up next.

If you’re interested in getting real time propagation information, take a look at DX ToolBox which is available for both Windows and Mac OS X.