The German WWII "Knickebein" Navigation System and the Curvature of the Earth

Hepper

New Member
During WWII, the Germans were using radio beacons (the "Knickebein" system) to guide their bombers into English territory. They set up two beacons, one in Kleve, a city in western Germany, and one at Stollberg Hill (North Frisia). The two radio beams intersected over Derby.

Source: https://de.wikipedia.org/wiki/Knickebein_(Funkfeuer)

A Flat Earther has claimed that this would be impossible on a globe earth (see here, timestamp: 6:46). This is his main argument: the knickebein beacons relied upon line-of-sight propagation of radio beams. The distance between Kleve and Derby or Stollberg and Derby however is simply too great to allow for line-of-sight propagation on a globe earth. So this is his central claim:
There is simply no way that there should've been any line-of-sight between the towers and the German bombers, which only flew at 19,200 ft.
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(timestamp: 7:54). I can't find any solution to this. According to William CY Lee, the radio horizon (i.e. the service range of the beacons) can be calculated as R= √2ha + √2hb where R is the distance in miles, ha is the aircraft altitude and hb is the ground-station antenna height in feet. If we plug in the numbers (say, the height of the beacon in Kleve (239ft) and the flight height of the German bombers), we get a maximum beam range of 217,8 miles. This means that the German bombers would have lost the transmission signal of the Kleve Knickebein tower after traveling ~218 miles. However, most British cities were more than 300 miles away. So how could these beams have reached the German bombers over Derby? Is the Earth flat afterall? What are your thoughts?

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Mick West

Staff member
This means that the German bombers would have lost the transmission signal of the Kleve Knickebein tower after traveling ~218 miles. However, most British cities were more than 300 miles away. So how could these beams have reached the German bombers over Derby? Is the Earth flat afterall? What are your thoughts?

I suspect there's a number of factors at play here. Firstly the radio range is not a hard limit, you can go further with ground wave propagation, especially over salt water.

Knickebein was actually just one over several naviagation systems used. There's a good overview here:
Discussing range:
However, for long-distance navigation, a system with a much larger range (500 to several 1000 km) would be needed. The concept of the Telefunken system is independent of the operating frequency. During the second half of 1940, a rotary beacon was built to investigate the performance on shortwave frequencies. I.e., on HF instead of UHF. As already mentioned, UHF radio waves basically propagate along the (straight) line-of -sight. On HF, however, radio waves to some extent follow the curvature of the earth ("groundwave"), and are also refracted by the ionosphere.
...
After the invasion of their neighbor countries, the Germans installed another nine Knickebein stations along the coasts of Norway (1x), The Netherlands (2x), and France (6x, from the Channel coast down to Brittany). Construction of an additional station in Italy was never completed. However, these nine stations had a smaller antenna system: about 1/4 the size of the Large Knickebein. The Small Knickebein had a width 45 m, a track diameter of 31 m, and had 2x4 dipoles plus reflectors per beam, instead of 2x8. Hence, the width of the equi-beam was larger (≈0.6º). On the other hand, they were installed closer to the targets in Britain than the large stations in Germany. In September of 1941, the aircraft receivers were upgraded from FuBl 1 to FuBl 2, which supported a large increase in the number of available frequency channels in the same band, and a range of 600 km [373 miles] at 6000m altitude (20 thousand feet).
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I think also the illustration used seems rather optimistic and not based on a real historical case. Why are they using the stations that are furthest away?

There's an interesting 1946 discussion here, based on limited information.
https://archive.org/details/electronicnaviga02unit/page/n335

Mick West

Staff member
And regarding "flat Earth" claims. The fact that the range of all these systems depends on the altitude is a great demonstration that the Earth is not flat.

DavidB66

Senior Member
I don't know the answer to Hepper's questions, but there is an interesting article here on the 'Battle of the Beams', i.e. between the German targeting systems and the British countermeasures: https://en.wikipedia.org/wiki/Battle_of_the_Beams It appears from this that there was argument between British scientific experts, including Churchill's chief scientific adviser, Frederick Lindemann, about whether or not the radio beams would bend around the curve of the earth. Since these elite scientists must inevitably have been part of the Great Globe Conspiracy, one wonders what they would have been arguing about, and who they were trying to fool. The top brass at the RAF? Churchill himself? But wouldn't they also be in on the secret?

Hepper

New Member
And regarding "flat Earth" claims. The fact that the range of all these systems depends on the altitude is a great demonstration that the Earth is not flat.

I agree.

I think also the illustration used seems rather optimistic and not based on a real historical case. Why are they using the stations that are furthest away?

The illustration is definitely based on a real historical case. From Wood D. and Dempster D. (2010) The Narrow Margin: The Battle of Britain and the Rise of Air Power 1939-1940. Pen & Sword Books Ltd:
Early in June 1940 the Luftwaffe made widespread probing attacks over Britain which led Professor Jones at the Air Ministry to suspect that the aircraft were testing a new bombing aid. [...] Radio monitors also picked up a mysterious message beginning 'Willi Knickebein...' and giving frequency and position references which indicated Cleve in West Germany and Derby in the midlands, where the Rolls-Royce works were situated. [pp. 54-55]
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So the Knickebein beam, emitted by the tower in Kleve, was evidently able to travel 330 miles, reaching Derby. This is confusing because most sources claim that the maximum range of Knickebein was at best 270 miles (Haysom D. and Jackson P (2014) Covert Radar and Signals Interception: The Secret Career of Eric Ackermann. Pen & Sword Ltd., p. 19).

the radio range is not a hard limit, you can go further with ground wave propagation, especially over salt water.

In his book 'Introduction to RF Propagation', John S. Seybold explains the following:
The very high frequency (VHF) and ultra-high frequency (UHF) cover frequencies from 30MHz to 3GHz. [...] For the most part, VHF and UHF travel by LOS [line-of-sight] and ground-bounce propagation. [p.9]
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I don't know what he means by "ground-bounce propagation." But it seems to me that LOS and groundwave propagation are two different modes of propagation and hence, they are mutually exclusive, as also indicated by this Wikipedia article:
In contrast to line-of-sight propagation, at low frequency (below approximately 3 MHz) due to diffraction, radio waves can travel as ground waves, which follow the contour of the Earth.
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And according to the article that you posted, Knickebein operated at very high frequencies. That's why I doubt that groundwave propagation could account for Knickebein's anomalously high transmission range.

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DavidB66

Senior Member
... according to the article that you posted, Knickebein operated at very high frequencies. That's why I doubt that groundwave propagation could account for Knickebein's anomalously high transmission range.

I don't have any expertise on this, but according to the various sources Knickebein transmitted in a frequency between 30 and 33Mhz. This is at the lower end of what is classified as 'VHF' (Very High Frequency), from 30 to 300 Mhz. The frequency range below this, 'HF' (High Frequency'), from 3Mhz to 30Mhz, is usually suitable for long distance transmission via the ionosphere. The VHF range is not in general suitable for this, but the effective limit is variable due to weather conditions, sunspots, and other factors. I have seen several sources which quote 40 rather than 30 Mhz as the usual upper limit, for example this Britannica article: https://www.britannica.com/science/electromagnetic-radiation/Radio-waves So without a firm source for 30 Mhz as the usual limit, the claim that Knickebein could not reach beyond 270 miles seems dubious.

Hepper

New Member
I did a bit of research and I think I've found a (somewhat) plausible explanation. In his book "The wizard war: British scientific intelligence, 1939-1945" R.V. Jones describes how he came to be convinced that radio transmissions coming from Germany could be detected up to the British coast:
Scott-Farnie showed me a report by Mr. T.L. Eckersley of the Marconi Company, who was the country's leading expert in radio propagation. On a purely theoretical basis, Eckersley had computed the range at which a transmitter sited at the top of the Brocken [...] and working on a wavelength of 20 centrimetres, could be heard. If Eckersley's calculations were correct, the waves would bound around the earth to a surprising extent, and might well be received by a bomber flying at twenty thousand feet over our east cost. [p. 87]
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Herein lies the solution: Eckersley's calculations were based on a wrong estimate of the wavelength. A wave 20 centimetres in length (i.e. Ultra high frequency waves) will, according to Wikipedia, enter and pass trough the ionosphere; there will be little to no ionospheric refraction/reflection in this case. Hence, there was no reason for Eckersley to consider this particular mode of radio propagation. Instead, he tried to show that such waves could bend to some extent. But the German Knickebein system operated at wavelengths of 9-10 metres (i.e. 30-33 MHz), which is at the lower end of the Very high frequency spectrum. Such waves essentially behave like High Frequency waves and those are reflected/refracted by the ionosphere, as already mentioned by DavidB66. This webpage discusses this effect in detail. There's also a very good illustration:

I am still hesitant to call this a "Debunk" because some sources seem to imply that Knickebein worked exclusively via line-of-sight propagation. Any opinions on this?

DavidB66

Senior Member
This is just to note that the book described by Hepper as Wizard War, by R. V. Jones, is known in the UK as Most Secret War. I remember reading this some years ago, but I don't recall any details on Knickebein. I will try to read the relevant chapters again when I next go to my usual Library, if the book is available.

Hepper

New Member
Update: I finally found a source that supports my contention. Wolfgang Holpp provided an overview about the history of the science of radar systems in a relatively short article titled "Das Jahrhundert des Radars: Von Christian Hülsmeyer zur Shuttle Radar Topography Mission." It's written in German but that's my first language, so I can translate what Holpp has to say about the Knickebein system:
Another milestone of German radar technology was the radar station Knickebein, one of the first over-the-horizon devices. The operating frequency was 30 MHz, i.e. at the upper end of the shortwave range. By using the reflection of the emitted and received signals on conductive ionospheric layers and on the earth's surface, ranges of several thousand kilometers have been achieved. [p.9, my emphasis]
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I think this settles this issue conclusively.

Clouds Givemethewillies

Senior Member
"

The way in which signals travel at frequencies of VHF and above is of great importance for those looking at radio coverage of systems such as cellular telecommunications, mobile radio communications and other wireless systems as well as other users including radio hams.

It might be thought that most radio communications links at VHF and above follow a line of sight path. This is not strictly true and it is found that even under normal conditions radio signals are able to travel or propagate over distances that are greater than the line of sight.

The reason for the increase in distance travelled by the radio signals is that they are refracted by small changes that exist in the Earth's atmosphere close to the ground. It is found that the refractive index of the air close to the ground is very slightly higher than that higher up. As a result the radio signals are bent towards the area of higher refractive index, which is closer to the ground. It thereby extends the range of the radio signals.

The refractive index of the atmosphere varies according to a variety of factors. Temperature, atmospheric pressure and water vapour pressure all influence the value. Even small changes in these variables can make a significant difference because radio signals can be refracted over whole of the signal path and this may extend for many kilometres.

N units
It is found that the average value for the refractive index of air at ground level is around 1.0003, but it can easily vary from 1.00027 to 1.00035. In view of the very small changes that are seen, a system has been introduced that enables the small changes to be noted more easily. Units called "N" units are often used. These N-units are obtained by subtracting 1 from the refractive index and multiply the remainder by a million. In this way more manageable numbers are obtained.
N = (mu-1) x 10^6

Where mu is the refractive index

It is found that as a very rough guide under normal conditions in a temperature zone, the refractive index of the air falls by about 0.0004 for every kilometre increase in height, i.e. 400 N units / km. This causes the radio signals to tend to follow the earth's curvature and travel beyond the geometric horizon. The actual values extend the radio horizon by about a third. This factor is often used in most radio communications coverage calculations for applications such as broadcast radio transmitters, and other two way radio communications users such as mobile radio communications, cellular telecommunications and the like."

https://www.electronics-notes.com/a...ion/tropospheric/tropospheric-propagation.php

Sporadic E propagation and the like would not be reliable.

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DavidB66

Senior Member
As promised earlier, I have borrowed a copy of R. V. Jones's Most Secret War (1978), known in the US as Wizard War. While at the Library I also noticed and borrowed Alfred Price, Instruments of Darkness (1967), which is a general study of the night-time air war in WWII. Price acknowledges discussions with R. V. Jones as one of his main sources, so the two books are not entirely independent.

On checking Jones's account of the Knickebein problem, I do not find much of substance to add to what has already been said above. Jones confirms (p.104) that British searches identified two radio beams, with a carrier frequency of 31.5 Mc/sec [Megaherz] whose bearings were consistent with transmitters at Cleves [Kleve] and Bredstedt [near the coast of Jutland]. I cannot explain the reference in the Wikipedia article on the 'Battle of the Beams' to a transmitter at Stollberg, also shown in the Wikipedia map as being on the Jutland coast. Neither Jones nor Price refer to Stollberg, and the only German town called Stollberg listed in Wikipedia and Google Earth is far inland, near Dresden. This would not be a suitable location, and I can only assume that someone has blundered.

The book by Price gives a little more detail on the argument between British experts on the problem of range:

Lindemann was unimpressed [in his first discussion with Jones] on a technical ground: he did not believe that a long-range beam on 30 megacycles would bend itself round the curvature of the earth...All the information available in England showed that radio waves on a frequency around 30 megacycles - i.e. those that could be picked up by the Lorenz receivers - did not curve round the earth's surface, but travelled in straight lines. [*] This limited their range to about 180 miles... [*Footnote: In fact partial bending to conform with the earth's curvature does occur with beamed transmissions on 30 megacycles, but this was not known in Britain at the time.] - Price, p.26-7.

R. V. Jones however obtained an unpublished paper by Thomas Eckersley:

...a leading authority on the propagation of radio waves. The paper contained an important series of graphs drawn by Eckersley to illustrate the maximum ranges at which radio signals on various frequencies could be received. By taking the extreme end of one of the curves, there seemed to be evidence that signals on 30 megacycles could be picked up by aircraft flying at 20,000 feet over much of England, if transmitted from high ground in Germany. - Price, p.27.
Eckersley later backtracked on this opinion, but was proved wrong in this by the RAF's search results. (Incidentally, neither Kleve nor Bredstedt could be described as 'high ground'.) Taking the various sources together, there seems to be agreement that beams at the lower end of the VHF range, i.e. at 30-40 Mhz, could travel considerably beyond the 'line-of-sight' distance. However, there does not seem to be a clear consensus whether this was due to reflection from the ionosphere or to some form of atmospheric refraction.

On a somewhat different note, while reading Jones I noticed a comment he made on another German system, the X-Gerat. This operated at a higher frequency (around 70 Mhz) than Knickebein, and it seems to be agreed that it could only be effective at shorter range, from transmitters on the coast of occupied France, but within this range could in principle be much more accurate than Knickebein. Jones was in charge of British research and countermeasures, and he notes that:

Incidentally, the potential accuracy of the system was so great that in calculating the path of the beams, it was necessary to take into account the fact that the earth is not a simple sphere, but is somewhat flattened towards the Poles. This made a difference of three hundred yards or so in where a beam starting from Cherbourg would actually cross London, compared with where one would calculate it on the assumption that the earth was a true sphere. - Jones, p.142.
So much for flat earth!

DavidB66

Senior Member
Correction to my previous comment: the Wikipedia reference to Stollberg is not to the town of Stollberg, but to a Stollberg Hill, which really does exist in the stated place. My apologies.

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