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Originally Posted by William Cloud Hicklin
Assuming that Numenoreans have RW human vision or close to it (and they seem not to have Elvish eyes, since Aragorn is always using Legolas as his binoculars), then their angular resolution is approx one arc-minute or 1/60 of a degree. That's why you can't look up at the moon and see flags and old lunar rovers there, and why the military relies on radar to pick up approaching aircraft that the Mk 1 eyeball hasn't a chance of seeing before it's too late..
So, even if we assume absolutely clear air without haze or turbulence, the maximum distance at which an unaided human eye could pick out a tower of ~ 30m diameter would be around 100 kilometers.
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I will accept your maths.
The source text is:
Quote:
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Originally Posted by Silm: Akallabeth
...at times, when all the air was clear and the sun was in the east, they would look out and descry far off in the west a city white-shining on a distant shore, and a great harbour and a tower. For in those days the Númenóreans were far-sighted; yet even so it was only the keenest eyes among them that could see this vision, from the Meneltarma, maybe, or from some tall ship that lay off their western coast as far as it was lawful for them to go.
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So could everyone see the city? Assume it's a km across & 100km away, and you get a width of ~30 arc-minutes (half a degree). From the top of Meneltarma, that should be visible to almost everyone. A nice addition to the religious ceremonies. Then the keen-eyed could catch a glimpse of the tower.
This does mean that Eressea itself would be a major presence on the 'horizon' - it would be impossible to miss from anywhere on the slopes of Meneltarma! But I guess Numenor doesn't really have other mountains, so that's not necessarily a problem. (I am now imagining young Numenorean kids in the west climbing trees and insisting "I can totally see it! Wow, that tower's so tall!" and suchlike.)
So why
couldn't they see Taniquetil? Surely the tallest mountain in the world would be... kind of hard to miss?
hS