Can I talk to you? Antenna Take-off angles and the Ionosphere
Radio waves leave an antenna and radiate outwards. Real antennas do not radiate equally in every direction. A tool like MMANA-Gal can plot what directions radiate more strongly than others. The range is determined by the vertical angle plots and the height of the layers of the ionosphere unless we are talking about a line of sight path, or the ground wave, neither of these are very important at HF. This article considers radio propagation but not prediction. It uses actual current values of the ionosphere (within 5 minutes).
The longest range DX antenna might radiate mainly at 5° from the horizon. A more general purpose antenna might mainly radiate from 5° up to 50°. An antenna for talking locally might radiate most of its energy nearly straight up.
There are a number of factors to consider to see if communication is possible (or likely) with a particular country. TX power, RX sensitivity and received noise matter. As do the take-off angle of your antenna (and how good it is) as well as the height and strength of the ionosphere.
Figure 1 One HF station transmitting to another, on planet Earth
How do you work out the take-off angle to get a certain distance if you know the height of the ionosphere? Google had trouble answering this and I haven’t tried “ai” yet, so I tried to derive my own formula. The mathematical calculations are A-Level Maths but I present a simple table later. Figure 1 has the relevant parts of the system. The thin green line is the earth, the thick green line the layer in the ionosphere we want the (thick blue) radio wave coming from TX to bounce off to the receiver RX. We know the radius of the earth “R” and the height above earth of the ionosphere “h”. We want to find the distance along the green line between the TX and RX, the arc “d”, the range.
You need to know a few trig identities to be able to work things out from the diagram. The first is that the angles inside a triangle add up to 180. The second is the cosine rule that is used when you have two sides of any triangle and the angle between them. The rule states that the third length is given by
C*C = A*A + B*B − 2∗π΄∗π΅∗cos(π)
And the third is the sine rule which is used when you work with two angles and the sides that they are opposite.
π΄ / sinπ = π΅ / sinπ = πΆ / sinπ
If you look at the triangle made up of the two thin blue lines and the left hand thick blue line then the two thin lines have lengths of R and (R+h). We can work out the length of the thick blue line. It’s
√ [π ^2+(π +β)^2−2∗π ∗(π +β)∗cosπ/2) ]
Now we can use the sine rule, rearrange things noting that the sin(Ξ± + 90) = cos(Ξ±)
Ξ±=cos−1{(π +β)sin(π/2)π πππ‘[π ^2+(π +β)^2−2π (π +β)cosπ/2]} .. Equation 1
The last remaining part of the puzzle is that, if you express ΞΈ in radians instead of degrees than you can say that the distance along the curve of the earth (the arc) is R ΞΈ. Anywhere we see ΞΈ/2 we can replace it with d/2R.
The spreadsheet on my blog has all this in it and also converts from degrees to radians. If you enter a value for “h” you get a table listing take-off angles and distance travelled, for example if h=200 miles you get table 1 below.
The range d in miles for a take-off angle Ξ± in degrees is marked in bold. Google finally found a different formula with a much more complicated derivation, Alan, G4KNA has it in his blog. I am pleased to report his formula and mine give the same results, at least for signals above the horizon.
This table only works if the frequency of transmission is suitable for “bouncing” off the ionosphere at height “h” and the radio wave does not get attenuated on the way to or from the “bounce”. In other words we do not want the D -layer to attenuate our signal too much. The D layer only matters during the day. It appears slowly at sunrise (takes up to two hours sometimes) but fades rapidly
away at sunset, this matters above your head if you are transmitting and also above your recipient’s head when they attempt to receive your signal. Its effect is more noticeable below 8MHz.
We see in table 1 that a take-off angle of five degrees will get 3000km or 1,900 miles on a single bounce.
What ionospheric height “h” we use is also an issue, because radio waves slow down slightly, both in passing the D and E layers and on their way into and out of the F layers so we don’t use the actual height of the maximum electron density (hmF2) but a calculated “virtual height” (h’F2). There are devices called ionosondes that produce ionograms with these calculated values, they put the answers on the web. See the figures below.
The next issue is what frequency to use? The ionosphere can only bounce signals back to earth within a certain range and it varies minute by minute, day by day and season by season, as well as being affected by various random events such as solar storms, coronal mass ejections and other perturbations to the magnetic fields. I won’t talk about the way the height and intensity change with time here. I find it all too complicated and can’t retain it all in my failing memory.
Getting to talk to a particular country depends on your signal reaching it, as well as the take-off angle and the height of the ionosphere it depends on getting the frequency right.
It’s a bit like Goldilock’s porridge you want it not too low, not too high. Having got your antenna beaming in the right direction, how do you work out the best frequency? The answer depends on the density of free electrons above our heads, or more correctly the density at the midpoint of the range (assuming only one bounce for the minute), where the signal hits the ionosphere. I am mainly concerned with the highest layer as it is the most important for long distance HF communications.
As you probably know there are a number of layers in the ionosphere. The D, E and F with F splitting into F1 and F2 during the day and D disappearing at night. Physically these layers have two important parameters, their height taken as the peak of their electron density and their strength, how strong the electron density is.
During the day the D-layer is not our friend as it absorbs our radio signals from 2 to 6dB, which gets doubled as we pass through it twice. Your signal is down up to 2-S points at the receiving station since each 6dB represents one S number on your S-meter. The effect gets worse rapidly as the frequencies gets lower, the LUF (Lowest Usable Frequency) is reported in various websites, it’s hard (nearly impossible for amateurs) to get much below this and bounce your signal
Night time is simpler as not only do the F1 and F2 layers combine into one F layer, the D layer disappears, removing the signal loss in the path. Unfortunately, this combined F layer has a lower electron density than daytime levels, which lowers the maximum frequency of signals reflected by the F-layer at night, meaning the “DX bands” like 20 metres may not work as well at night for DX contacts, 40 metres and below are more likely to keep bouncing signals off the Ionosphere. A very weak F layer will not bounce the higher frequencies at all, they continue into outer space and are never heard (probably).
The F layer is most important in deciding how well your HF signal will travel; it might usefully bounce signals back to earth. It’s the highest level and will get you the furthest with a single bounce.
The D layer is important in deciding if your HF signal will not travel. It might absorb your signal and it never gets heard, it just disappears. At least the D layer is decent enough to disappear at night.
The E layer can be a bit like a lower F layer and a lower D layer. I will only consider simple single bounces here, in practice you get multiple bounces, you get the radio wave splitting into two components and each travels slightly differently, you get bounces off more than one layer at the same time and you can get a half bounce where the radio wave(s) bend enough to not go into space but not enough to get back to ground, they travel around the layers and may exit at some stage to get back to earth somewhere.
Phew, I am not a propagation expert and only analysed what you read here to help me gain some understanding, we are all on this journey of discovery together.
In a previous sunspot maximum, I remember being amazed at hearing an echo when working Australia, I was hearing a signal that had come direct to me and also a signal that had gone around the earth in the opposite direction to arrive here as well. Not bad for 100W and a piece of wire.
The layers in the ionosphere can be measured by finding out the highest frequency that will bounce back to earth to the sending station (i.e. a radio wave that can go straight up and straight back down) and measuring the time delay. The time delay gives us the height the same way radar measures distance and the highest frequency that bounces straight up and straight back down again allows calculation of the actual electron density. We call that frequency the Critical Frequency (Fc often labelled F0).
There are a number of sites that measure the ionosphere and they publish real time maps on their websites. There was one in the Ulster University in Jordanstown for a while, when a friend of mine was working on his Phd (DPhil) but I think our nearest is now at Chilton in England. It has been down lately and https://digisonde.oma.be/ionogif/latest.html in Dourbes, Belgium is useful as an alternative. These maps are called ionograms and whilst they look complicated, they are useful for hams – if all we take from them is the critical frequency foF2 and the height of the F layer (or the F2 during the day) h’F or h’F2 in figure 2 and possibly the MUF vs skip distance in the bottom red circle.
The site at Chilton ( https://www.ukssdc.ac.uk/) requires you to register with an email and then you can access the data. Its data is available in a variety of formats. You can also get a good graph at https://propquest.co.uk/graphs.php?type=NVIS as well as through links found on the RSGB website. (pick ionosounde links at https://rsgb.org/main/technical/propagation/propagation-beacons/ .
Figure 2 shows the dourbes ionogram. See https://rsgb.org/main/technical/propagation/current-ionograms-critical-frequencies/ ) These can be hard to read and often have various strange things going on that obscure a simple reading, the E layer can get in the way and there can be layer to layer echoes and other blanketing effects. But the headline data is reproduced on the left-hand side. I have ringed in red the main data we want; FoF2 and h’F2 (9.2MHz and 208 km) Note also the MUF table of D and MUF.
We are trying to refract a beam of energy and how well this works depends on the angle that the beam hits the layer. The worst case is if you hit the layer head on, 90 degrees to the layer which is what happens when you send a radio wave directly upwards. We know (by definition) that we can’t use a frequency higher than the critical frequency, Fo for this straight up and down wave.
However, if we hit the layer at an angle less than 90 degrees it can bounce down, if we use frequencies higher than Fc and less than a “maximum” frequency. The MUF varies according to the angle of incidence.
Theoretically the Maximum Useable Frequency (MUF) can be calculated approximately from Fo using equation 2 below, if we know the angle of incidence (i) and we can get the angle of incidence from the take-off angle of our antenna.
π΄πΌπ=ππ/ππ¨π¬π . (Approximate) Equation 2
Equation 2 tells us that the MUF varies according to what angle you hit the ionosphere at. What this means is that each range has a maximum frequency that will work, the further away from overhead the radio wave bounces, the higher in frequency it can be. If it is too high it doesn’t bounce and just keeps going into outer space. The MUF will always be bigger than Fo and at low take off angles the MUF might be 3 or 4 times Fc. Mind you, you get more reliable HF communications if you operate at the Optimum Working Frequency (OWF) and this is usually taken to be 85% of the MUF.
Rather than use spherical geometry to get an expression for MUF (which I did but it was inaccurate) you use a more complex calculation because the radio wave slows down as it passes the lower layers, if it passes through the D and E layers at an angle it spends more time there and slows down more. I gave up trying to derive a formula when I noticed the table at the bottom of the Ionogram.
The ionogram also lists the MUF(3000) as 28.88MHz (halfway down the lefthand side)
Another very useful site is https://www.propquest.co.uk/graphs.php although the site is mainly concerned with the E layer, it has a great graph for listing all the layers including the F layers. If you hover your mouse over the graphs it gives you the MUF for the F layers at distance of 100, 500, 1000 and 3000km. Not as detailed as the full ionosonde but useful as it shows the graphs varying over time, one day at a time. There are also archives of previous days.
The graph in Figure 4 is derived from the Belgium data I show in Figure 3, (not the same time)
Pulling all this knowledge together we can contrive a number of scenarios; See figure 5 below
Your signal can be below the critical frequency in which case it bounces at any angle, unless it is so low it can’t get through the D layer.
If it is above the critical frequency then there is a starting, minimum distance that it can bounce, it can’t bounce a shorter distance as that would imply a steeper angle of incidence at the ionosphere and the signal just passes through, into outer space. This means there is a minimum distance before the signal can bounce, this is the skip zone.
If you want to talk to someone in the skip zone, not only do you have to have the correct take-off angle (Table 1) you must also drop your frequency to get a smaller skip zone. As you drop in frequency, the D-layer attenuates you more so you want to use the highest frequency that will work, close (85%) to the MUF for that distance
The "skip zone" is simply the areas which are too far away for line-of-sight or groundwave, but close enough that the effective MUF at that distance is lower than your chosen frequency. As such, it's completely dependent on the frequency you're using. You can get into the skip zone if you lower your frequency towards the critical frequency. When they are equal there is no skip zone at all.
For frequencies less than the "critical frequency" (foF2), there is no skip zone (these are the NVIS frequencies). If you transmit a signal lower than the critical frequency your signal will bounce if powerful enough at any take-off angle. We can use this to generate a NVIS or Near Vertical Incidence Skywave and work stations near us.
Note, I mentioned the words “powerful enough” If all we had was the F layer then we need not care about power, the only things that matter for it are the height and the critical frequency.
Unfortunately, there is the matter of the D Layer, more a hindrance than a blessing. It disappears at night but during the day it absorbs radio signals and it absorbs lower frequencies more. In fact the absorption depends inversely on the square of frequency so the halving your frequency will give you four times more attenuation. (k is just a constant in equation 3)
π«_π³ππππ_π¨ππππππππππ=π/ππ ……… Equation 3
You can overcome the absorption by dramatically increasing the power, or moving higher in frequency, the higher the better, as long as you are below the MUF for the range that you want. As radio hams we can’t use enough power to succeed in getting through the D layer at low frequencies and this gives us another important frequency. The LUF is the lowest frequency that can get through. You will fail to get through if your frequency is below this, at least with our limited power. You need ten times more power to get through when operating just 2MHz below the LUF (https://www.electronics-notes.com/articles/antennas-propagation/ionospheric/maximum-lowest-critical-optimum-usable-working-frequency.php ). Obviously on the rare occasions that the MUF is below the LUF there can be no radio communications using the ionosphere at all!
Hopefully you found the text and diagrams above useful, it took me a couple of goes before I understood it. It might help if you sketch a few diagrams yourself. There is no doubt that the two websites are worth looking at.
https://digisonde.oma.be/ionogif/latest.html
And the Propquest site has a good daily summary for either Dourdes (Belgium) or Chilton (UK)
https://propquest.co.uk/graphs.php?type=live
You should pick sites other than Belgium or Chilton. Ideally pick ones that are at the midpoint of where you want to communicate and your own location – see the list at
https://digisonde.com/ and https://www.ngdc.noaa.gov/stp/IONO/rt-iono/
In summary, knowing the critical frequency, the height of the F or F2 layer and the resultant MUFs at various distances allows you to decide what take-off angle and frequency is needed to get to a particular place. That is the starting point in knowing about “propagation”. The next big issue is to look at how the heights and strengths vary over the planet and as time goes by but it is good to first understand what is happening right now. For simplicity we have only looked a single F layer bounce.
No comments:
Post a Comment