The flat earth

There have been a lot of videos posted on You Tube recently about the subject of the flat earth. No, this isn't a joke and the posters aren't kidding, nor are these parody videos. In most cases, the video will include a map of the flat earth similar to the illustration shown below, on the left:

Map of the flat earth
Map of the flat earth
Map of the flat earth
Great circle map centered on the North Pole
Now, let's suppose I'm an amateur radio operator. You don't have to suppose, because I actually am, thus the "ham" part of my domain. Now let's suppose I wanted to talk to a YL named Barbara in Sydney Australia. Where should I point my beam? To figure out the beam heading I might use something called a great circle map such as the one shown above to the right.

You'll probably notice that the great circle map, centered on the North Pole, bears a remarkable resemblance to the map of the flat earh. Just replace Antartica with an ice wall, color Greenland white and show the Artic ice cap as if it was an actual land mass. This is not coincidental. So, using this map, or the map of the flat earth, I would point my beam "NW"(320°).

However, when I rotated my beam until I got the strongest signal from Barbara in Sydney, I found it was pointed "SW" (241.1°)! How could that be? There should be nothing there but empty ocean!

Great circle map centered on Sacramento
Great circle map centered on the Sacramento CA U.S.A.
Great circle map centered on Sydney
Great circle map centered on the Sydney Australia
If I use a great circle map centered on Sacramento , such as the one shown above to the left, I find that a beam heading of "SW" (241.1°) should get me to Australia, which is right where I found it! Barbara, on the other hand, might use a map like the one on the right to find beam headings and would find true beam heaings for her location.

Now let's suppose that we tire of talking to each other and we both decide to contact an OM named Klaus who is operating a special event station in Berlin, Germany. According to my map, I should aim my beam "NE"(29°) , which would be right for that part of Europe from Sacramento, and that Barbara should aim her beam roughly "NE"(39°).

According to Barbara's map, however, I should aim my beam due "West"(270°) and she should aim hers "NW"(315°). How is it that the same map gives correct beam headings for one part of the world but is so completely wrong for another part of the world? If the map represents the true shape of the earth, shouldn't it give the right direction for all parts of the world?

Great circle map centered on Sydney
Great circle map centered on Berlin , Germany
Map of the flat earth
Map of the flat earth
Now let's consider OM Klaus in Berlin. According to the flat earth map, he should aim his beam roughly "NW"(310°) to get to Sydney, but the great circle map centered on Berlin (above, left) shows that he needs to aim it roughly "NE"(75°), which would be a true beam heading for someone in Berlin aiming at Sydney.

People used to pay a lot of money for Great Circle maps customized for their locations. Now you can generate a great circle map for any spot on earh using a free program. But, if you're using a computer you could use a program where you just enter your own lattitude/longitude and the lattitude/longitude of the place you want to aim at and it will give you your beam heading, just like that!

So what does the beam heading program know that all these maps don't?

THE EARTH IS ROUND!
Disagree with that statement? Vote!

On a round earth these beam headings make perfect sense, but on a flat earth you cannot make sense of the beam headings from different parts of the world. A great circle map will show the correct direction (and distance, if calibrated) from and to the spot it is centered on, but will be wrong for any other two points. The further the two points are from the center, the more inaccurate it becomes.

So if you actually live at the North Pole the map of the flat earth, essentially just a great circle map centered on the North Pole, will give you accurate beam headings to any other spot in the world, but for any other spot it is worthless. Just for grins, look at the great circle maps centered on the South Pole and Johannesburg, South Africa:

Great circle map centered on the South Pole
Great circle map centered on the South Pole
Great circle map centered on Johannesburg, South Africa
Great circle map centered on Johannesburg, South Africa


I wonder just how many beam using amateur radio operators think the earth is flat ...

A note about beam headings:
You'll notice that the "directions" given above for beam headings are in quotations marks. That's because, though they are often given as N, NW NNW, etc., beam heading are more precisely given in terms of degrees. In most parts of the world saying your beam is aimed "SW" when it is at 225° would be a reasonably accurate statement, but what if you are at the north pole? Obviously everything is due south from the north pole, but your beam heading could be anywhere from 0° to 359°, depending on where you're aiming at. So although the directions might still seem to make sense when you go out and look at where you're beam is pointed, they would be completely wrong in a navigational sense.

Another example would be if you point your beam due east (90°) from sacramento, you'll find that this is an ideal beam heading for southern tip of Africa, but your geography teacher would never be convinced that South Africa is due east of Sacramento! This is a direct result of using radio signals, which travel in straight lines, to navigate a round earth. Note that the map of the flat earth, and the great circle map centered on the north pole would both say that due east from Sacramento is about 1000 miles south of the tip of Africa!

In navigational sense, going due east would mean staying on the same lattitude, but staying on the same lattitude would mean a skewed path, shaped like an arc. That's why lattitude lines are curves on a great circle map. The one exception would be at the equator on a great circle map centered on the equator, and if you look at the great circle located to the right, or you might say to the "east" of this paragraph, you'll see that the line of lattitude which corresponds to the equator actually is a straight line. This is the only case where a line of lattitude appears as a straight line on a great circle map and one the few times a beam heading corresponds exactly to a navigational direction.

A radio signal travels in a straight line, not an arc, although if you mapped out the actual path of a raido signal on an oridnary flat map, such as a Mercator projection, it would look like an arc. It really boggles the mind to try to imagine how a flat earther would explain the fact that I aim my beam "SW" (241.1°) from Sacramento and get a 59+ signal into Australia! Just how would you draw the path on the map of the flat earth that starts out going "SW" (241.1°) from Sacramento yet somehow winds up in Australia?

Great circle map centered on The equator, west of Africa
Great circle map centered on the equator
Straight lines?
Now, in case any of you are not familiar with HF communications and and you are wondering how it is possible for radio signals, which travel in straight lines, to follow the curve of the earth, well, they don't, at least not at frequencies most people use today. Ground waves* can follow the curve of the earth, but this requires using LF (below 300 Khz) huge antennas and huge amounts of power, far beyond the capabilities of most amateurs.

HF (3 Mhz - 30 Mhz) long distance communications are carried out using "sky waves" which go up into the ionosphere at an angle and "bounce"** off the ionosphere at the opposite angle, making it possible to communicate thousands of miles under the right conditions without using sattellites. This is also known as "skip" and was first discovered early in the 20th century when amateurs were banished to frequencies of 1.5 Mhz (wavelength 200 meters) and higher, aka "200 meters and down", the prevailing notion being "they won't get out of their backyards with that!".

Little did they know ...

*The term "ground wave" is often misused by people who are actually talking about "direct" or "line of sight" waves. Driect waves are used for local communications, especially on HF(3 to 30Mhz), VHF(30-300Mhz), UHF(300Mhz - 3 Ghz) and "microwave" (1Ghz and higher). Most of the radio signals you use in everyday life, including Television and cellphones are direct wave. Direct waves can also be aimed upward at sattellites for global comminications.
Ground waves, on the other hand, occur mainly at LF(30-300Khz) and VLF(3-30Khz). They literally travel along the ground, and can thus follow the curve of the earth, but they lose power quickly. It is possible to reliably communicate anywhere on the globe using groundwaves, but it requires massive amounts of power and huge antennas for transmission. This can be used to transmit to submarines while they are under the ocean.


**Technically "bounce" is not really the right word, it's actually refraction which is a kind of bending, but "bounce" is a good enough description of the end result.



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