Flat earthers will quote the height and range of a lighthouse and then claim the light should be hundreds of feet below the horizon at that range if the world were spherical. So therefore the world is flat. But they are assuming the listed range of a lighthouse is the maximum range it can be seen from a ship at sea; it is not.
The range listed is the "nominal range" of the light, i.e. the range the light can be seen when the meteorological visibility is 10 nautical miles. It is solely a function of the light's brightness. Why make a light brighter than it could ever possibly be seen at those distances on a spherical Earth? Fog. A very bright light will still be visible from several miles away in light fog. That was very important in the days before electronic navigation methods became available.
None of the claims about lighthouses are the original work of today's flat earthers; they all copied their claims from very old and outdated sources, in most cases from books written in the 19th century. For example, one of the most often mentioned lighthouses is the "Isle of Wight" lighthouse (actually it is the St. Catherine's Point lighthouse) with a quoted height of 180 feet and a range of 42 "miles". But it was lowered to 135 feet in 1875. In 140 years, not a single flat earther has ever bothered to verify this claim. This doesn't mean flat earthers are wrong about the shape of the world; it just means none of them actually did any real research on the subject despite their claims that they did. They're just repeating what they read.
The claim it can be seen from 42 miles comes from a 19th century flat earther who wrote in his book Zetetic Cosmogony: "A lighthouse on the Isle of Wight, 180 feet high (St. Catherine's), has recently been fitted with an electric light of such penetrating power (7,000,000 candles) that it can be seen 42 miles. At that distance, according to modern science, the vessel would be 996 feet below the horizon."
Aside from screwing up his calculation (you can't simply subtract the height of the light from the drop and get the right answer), he is incorrectly assuming the light was built with that intensity for the purpose that it can be seen from 42 miles away. As already pointed out in the OP, modern flat earthers are still making the same mistake.
Yes, you are right, not only the argumentation, but also the calculations are wrong. If you had a light source at 135 ft above the sea surface, strong enough to be seen at 42 nautical miles (48.33 miles), the receiver at that distance would have to be 775 ft above the water surface, not 996 ft. If the light source were at 180 ft and the range 42 miles (not nautical miles), the the receiver at that distance would need to be only at 436 ft above the sea surface.
Yes, you are right, not only the argumentation, but also the calculations are wrong. If you had a light source at 135 ft above the sea surface, strong enough to be seen at 42 nautical miles (48.33 miles), the receiver at that distance would have to be 775 ft above the water surface, not 996 ft. If the light source were at 180 ft and the range 42 miles (not nautical miles), the the receiver at that distance would need to be only at 436 ft above the sea surface.
The refraction of the earth's atmosphere is not taken into account in this calculator. According to the following source, http://www-rohan.sdsu.edu/~aty/explain/atmos_refr/horizon.html , the horizon distance is further away. To calculate the more realistic (although not exact) distance one may multiply the earth's radius in the calculator with (at least) 7/6.
Running the calculations with this value you may multiply the value of the horizon distance with 1.08. (8% more)
Recalculating your two examples:
source at 135 ft; distance 48.33 mi; reciever at most 534 ft above sealevel
source at 180 ft; distance 42 mi; reciever at most 281 ft above sealevel
Interesting. 281 ft is already in the reach of the tallest ships (I saw a reference of 300 ft mast on a cruise ship). Besides it, lighthouses are used for secondary visual navigation also by plane and airship pilots, so the longer reach may be useful even in such cases.
There seems to be some strange fascination that Flat Earthers have with Lighthouses. I have seen many memes which make claims yet offer no visual evidence to support it.
Nearly every meme or post I have seen about lighthouses, and the distance in which they are visible, claim that the curvature of the Earth should not allow the lighthouse to be seen. Yet not one, literally, not one post has backed up the claim with any evidence at all.
Flat Earther Eric Dubay's page is filled with the inconsistency issues.
If you visit the page, you will see outlandish claims. The problem is that he is not quoting actual maritime lighthouse references. Instead he is quoting from the Zetetic Cosmogony book from 1899. Not one Flat Earther has gone out to verify these claims in over 100 years as Chew pointed out. But here is the bigger issue. Flat Earthers are taking this Zetetic reference information at face value without even checking the facts. And when they post about these measurements they fall FLAT on their faces.
Case in point “The Isle of Wight” or “St. Catherine’s” lighthouse Chew mentions above.
Both on Eric Dubay's page and in his book he states: "The Isle of Wight lighthouse in England is 180 feet high and can be seen up to 42 miles away, a distance at which modern astronomers say the light should fall 996 feet below line of sight."
Is he saying that the lighthouse can be seen?
Or is he saying the light from the lighthouse can be seen?
HUGE DIFFERENCE!
If he is saying the lighthouse can be seen from that distance, then he is flat our WRONG!
Or there was an awesome superior mirage! But at night?
The claims appear to come from the book "Zetetic Cosmogony" and you can see what it says and download it for FREE from Google Books. It clearly says the LIGHT is visible from 42 miles and that is it 7,000,000 candle power. So sure I believe the light can be seen and here is why.
The luminous intensity of a light, or its candlepower, is expressed in international units called candelas. Intensities of lighthouse beams can vary from thousands to millions of candelas. The range at which a light can be seen depends upon atmospheric conditions and elevation. Since the geographic horizon is limited by the curvature of the Earth, it can be readily calculated for any elevation by standard geometric methods. In lighthouse work the observer is always assumed to be at a height of 15 feet, although on large ships he may be 40 feet above the sea. Assuming a light at a height of 100 feet, the range to an observer at 15 feet above the horizon will be about 16 nautical miles. This is known as the geographic range of the light. (One nautical mile, the distance on the Earth’s surface traversed by one minute of arc longitude or latitude, is equivalent to 1.15 statute miles or 1.85 kilometres.)
The luminous range of a light is the limiting range at which the light is visible under prevailing atmospheric conditions and disregarding limitations caused by its height and the Earth’s curvature. A very powerful light, low in position, can thus have a clear-weather luminous range greater than that when first seen by the mariner on the horizon. Powerful lights can usually be seen over the horizon because the light is scattered upward by particles of water vapour in the atmosphere; this phenomenon is known as the loom of the light.
The new lighthouse, built by Trinity House in 1838, was constructed as a 40-metre (130 ft) stone tower; however, its light was often obscured by fog, which led to its height being reduced by 13-metre (43 ft) in 1875. It has a range of 25 nautical miles (46 km; 29 mi) and is the third-most powerful of all the lights maintained by Trinity House.[2] Another tower, built immediately alongside in 1932, houses the now redundant fog signal (discontinued in 1987).
Assuming a light at a height of 100 feet, the range to an observer at 15 feet above the horizon will be about 16 nautical miles. This is known as the geographic range of the light. (One nautical mile, the distance on the Earth’s surface traversed by one minute of arc longitude or latitude, is equivalent to 1.15 statute miles or 1.85 kilometres.)
The luminous range of a light is the limiting range at which the light is visible under prevailing atmospheric conditions and disregarding limitations caused by its height and the Earth’s curvature. A very powerful light, low in position, can thus have a clear-weather luminous range greater than that when first seen by the mariner on the horizon. Powerful lights can usually be seen over the horizon because the light is scattered upward by particles of water vapour in the atmosphere; this phenomenon is known as the loom of the light.
This is the key distinction they fail to make: between geographic range and luminous range.
And if they actually stopped to think, they would see that lighthouses are in fact a very good piece of evidence against a flat Earth. Why? Because if the Earth were flat, a 10ft-high lighthouse would have exactly the same range as a 100ft one, light intensity being equal. OK, maybe 10ft is a little low, as it could be obscured by decent size waves, but there would certainly be no reason whatsoever to build one 180ft high, or even 436ft high. How do FEers explain why lighthouses are tall?
As I pointed out in the OP, the flat earthers don't know the published range of a light is the nominal range. Nominal range is often confused with luminous range and often incorrectly used interchangeably with luminous range. The luminous range is the range it can be seen in the prevailing meteorological visibility. The Coast Guard Light List has a Luminous Range Diagram. The inputs are meteorological visibility, nominal range, and luminous range.
