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The August 1994 issue of Six News
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the doughnut effect
Emil Pocock, W3EP


Your appeal to explain why it is more difficult to work 2400-2800 km on sporadic E than shorter or longer distances has a relatively straight-forward answer (see page 47, January issue). The effect, by the way, was perfectly described by DL7AV. We have seen that same effect time and time again over here. I call it the doughnut effect.

The Doughnut Effect

Sporadic-E paths between 2400 and 2800 km are more difficult to complete than longer and shorter paths. The maximum single-hop distance for sporadic-E contacts is about 2300 km, a geometric restraint based on an average height of E-layer ionization of 105 km or so. Curiously enough, sporadic-E paths in the 1800-2200-km range are probably the most common. This is because the single-hop distances near the maximum useable frequency (MUF) are also the longest. As the MUF rises above 50 MHz, the paths shorten up.

It may be possible that some sporadic-E paths at 2400 km or even longer are also completed by unusually long single hops, perhaps from patches of E-layer ionization that are somewhat higher than the average 105 km. Even so, it is more likely that sporadic-E paths longer than 2400 km are via multiple hops.
If that is indeed the case, then a 2400-km path must involve two hops with an average of 1200 km each (the hops do not have to be of equal length, so long as they total 2400 km). The problem is that 1200-km paths are unusual at 50 MHz, because the required MUF to create such short hops is high, perhaps in the 100 MHz range. Thus in order to complete a 2400-km path at 50 MHz, two separate sporadic-E centers with MUFs of 100 MHz and spaced 1200 km apart are needed. That is a pretty stiff requirement!

As the path lengthens from 2400 km, the required MUF for the two sporadic-E centers drop, thus making it more likely that the required geometry will be achieved. In theory, this suggests that as the distance approaches 4600 km, there should be a greater incidence of double-hop sporadic-E.

When the probability of sporadic contacts are graphed in two-dimensional space, a sort of doughnut shape emerges. Sporadic-E contacts are rare shorter than 400 km. That is the hole. As the distance lengthens from 400 km, the occurrence of sporadic-E contacts increases until 2300 km is reached. That is the main part of the doughnut. There is a sharp drop-off at 2300 km amounting to a sharp boundary until around 2800 km or so, then contacts become more and more likely until 4600 km, when the second, but less sharply defined boundary is reached.

At 4600 km and longer, there are many possible configurations of hops that make the 4600 to 5200-km void less clearly defined. A 4800-km path could be completed by three 1600-km hops, for example. The MUF requirements for 1600-km hops are not as high as for 1200-km, although finding three sporadic-E centers lined up optimally is not common either. You can make your own calculations and discover the various possibilities for difficult distances.

This line of logic suggest that there may be some prime distances for multi-hop sporadic E. If the most common single-hop contacts near the MUF fall into the 1800 to 2200 km range, then the most common multi-hop paths might be expected at 3600-4400, 5400-6600 km, and so forth.

UKSMG Six News issue 45, April 1995


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