Sight range

[Rich H]

Here's a further link: http://en.wikipedia.org/wiki/Horizon

For an observer standing on the ground with h = 1.70 metres (5 ft 7 in) (average eye-level height), the horizon is at a distance of 4.7 kilometres (2.9 mi).

For an observer standing on the ground with h = 2 metres (6 ft 7 in), the horizon is at a distance of 5 kilometres (3.1 mi).

For an observer standing on a hill or tower of 100 metres (330 ft) in height, the horizon is at a distance of 36 kilometres (22 mi).

For an observer standing on a hill or tower 100 feet (30 m) in height, the horizon is at a distance of 12.2 miles (19.6 km).

For an observer standing at the top of the Burj Khalifa (828 metres (2,717 ft) in height), the horizon is at a distance of 103 kilometres (64 mi).

For an observer on the summit of Aconcagua (22,841 feet (6,962 m) in height), the sea-level horizon to the west is at a distance of 184 miles (296 km).

For an observer atop Mount Everest (8,848 metres (29,029 ft) altitude), the horizon is at a distance of 336 kilometres (209 mi).

[Glorelendil]

So here are some possible conclusions:

1) The scale of the map is off and Erebor is not 250 miles from the High Pass

2) The High Pass is higher than Everest

3) Middle-Earth has a larger radius than Earth

4) Bilbo only thought he saw Erebor

5) Possession of the Ring gave him some powers of sight that can't be explained by normal physics

[Rich H]

The most likely is...

6) Tolkien didn't understand or care about line of sight ranges and was just writing a story about pretend elves.

[Glorelendil]

The most likely is...

6) Tolkien didn't understand or care about line of sight ranges and was just writing a story about pretend elves.

Wait...I thought Tolkien was an expert on everything and was meticulously accurate...historically, scientifically, linguistically, sartorially, militarily...in every sentence he wrote?

[Otaku-sempai]

I'm not sure from where anyone is getting the figure of 250 miles. Cross-referencing Tolkien's map in FotR with the maps in Unfinished Tales, Karen Wynn Fonstad's The Atlas of Middle-earth, and the Loremaster's Map from TOR, I consistantly get a figure of about 300 miles! That is line-of-sight from the High Pass to Erebor.

Since Tolkien intended Arda to be our own Earth in a mythic past, we can rule out Middle-earth having a larger circumference. The most logical (in-story) explanation is that Bilbo was mistaken. Perhaps he saw a glimmer from some forgotten tower in the Mountains of Mirkwood, only around 150 miles away. Or Tolkien should have consulted a geographer.

[Rich H]

I really can't be arsed calculating it but the following introduces the concept of objects above the horizon:

To compute the greatest distance at which an observer can see the top of an object above the horizon, compute the distance to the horizon for a hypothetical observer on top of that object, and add it to the real observer's distance to the horizon. For example, for an observer with a height of 1.70 m standing on the ground, the horizon is 4.65 km away. For a tower with a height of 100 m, the horizon distance is 35.7 km. Thus an observer on a beach can see the top of the tower as long as it is not more than 40.35 km away. Conversely, if an observer on a boat (h = 1.7 m) can just see the tops of trees on a nearby shore (h = 10 m), the trees are probably about 16 km away.

Just substitute the observer on a boat and the tops of trees for the Lonely Mountain and the High Pass and the concept can be applied to discussions here.

For those people among us with nothing better to do the link for the formula is here: http://en.wikipedia.org/wiki/Horizon and just do a search on "Objects above the horizon" to get to the pertinent section.

... I don't know if all this means that Bilbo could see Erebor from the High Pass, it all depends on how high both of these points in the landscape are.

We don't half discuss some stuff on this forum! Part of me loves it, but another part despairs.

[Glorelendil]

Oh, right....those first computations assume that the observer is at altitude but the observee is at ground level. If both are at altitude it all changes.

I'll have to add this to my Interactive Atlas...

[Robin Smallburrow]

You are all forgetting the 'Subtle Magic of Middle-earth' in operation to allow Bilbo to see the Lonely Mountain, and I am sure that is what Tolkien would say if brought to his attention - just as the clouds above Mordor impossibly part briefly to allow Sam to see the star when all seems hopeless - Subtle Magic at work!!

Robin S.

[aramis]

300 miles (~480 km) is just barely visible for a pair of mountains.... assuming Lonely Mountan hits 20,000', and the pass is close to that. And it would be just a glimpse... of the tip.

But I agree with Rich - Tolkien didn't bother looking up the horizon....

Remember, if the horizon itself is 2.5 km, you can spot a person to almost double that... at 2.5 km, you see all of them. At 3.5 km, you'll see only the upper 3/5 (thighs up). At 4.5km, you'll see just the upper 1/5th... head and shoulders.

But also remember: if you're on an elevated surface, you still can't see past horizon distance on that surface... only an elevated edge is useful.

[alaskan15]

300 miles (~480 km) is just barely visible for a pair of mountains.... assuming Lonely Mountain hits 20,000', and the pass is close to that. And it would be just a glimpse... of the tip.

But 20,000 feet is only a 'pass' if the mountains around it are higher than 20,000 feet. That seems unlikely. In the Letters of JRR Tolkein it says that the Misty Mountains were inspired by the professors visit to the Swiss Alps in 1911. The Swiss Alps are far shorter than 20,000 feet with only one peak over 15,000 feet. Few mountains in the world are over 20,000 feet from base to peak (not counting underwater parts), so it seems unlikely that an entire large mountain chain would be.

If the High Pass was really that high travelers would have serious problems with altitude sickness. This is the same pass that Gil-Galad marched a whole army over in the Second Age. Even if Elves are immune to altitude sickness the Men in the army would not have been. Unless very dry, the pass would see even more snow and worse weather than we see in the books. It seems to me that the High Pass is no more than 10,000 feet high. Additionally if the Misty Mountains were that tall then the Anduin river valley should be much dryer, as it would be in a rain-shadow.

Another answer would be that Arda does not have the same diameter as modern earth. We know it used to be flat and was made into a ball. Can we be sure what size of a ball? The main problem with this theory is that Arda was probably smaller, not larger, so this would make the mountain even harder to see. Fonstad gives its diameter as about 6,800 miles.