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A question on The Stone of Erech.....

Bracegirdle
Tol Eressea


Mar 24 2014, 7:35pm

Post #1 of 22 (422 views)
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A question on The Stone of Erech..... Can't Post

I fibbed - 2 questions: (2 possible winners.) Winner(s) will be those closest to MY approximations and will receive one plate of cookies. Smile

1. Approximately what was the size of the Stone of Erech? Diameter please!

2. Approximately how much did it weigh? Long tons please!

Bonus Question: (worth 3 extra cookies).
Why did Isildur bring it to Middle-earth from Numenor?

Two possible answers to the Bonus Question. Anyone getting either of MY answers recieves two, I say, two plates of cookies. Smile

From World's End then he turned away,
and yearned again to find afar .
his home through shadows journeying,
and burning as an island star . . .

-Bilbo Baggins

(This post was edited by Bracegirdle on Mar 24 2014, 7:36pm)


Bracegirdle
Tol Eressea


Mar 25 2014, 7:10pm

Post #2 of 22 (269 views)
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Ok! No takers? [In reply to] Can't Post

Yes it does take a tad of research and a modicum of mathmatics.

Should anyone be interested I will give myanswers tomorrow, 3-26-14.

Unsure

From World's End then he turned away,
and yearned again to find afar .
his home through shadows journeying,
and burning as an island star . . .

-Bilbo Baggins


MistyMountain
Lorien

Mar 25 2014, 7:27pm

Post #3 of 22 (268 views)
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research? [In reply to] Can't Post

Are you saying we can actually look in our books? I thought we were supposed to not "cheat". There is NO WAY I would know the answers without peeking into the book!

And what is a "long ton"?

And what kind of cookies? Evil


(This post was edited by MistyMountain on Mar 25 2014, 7:28pm)


Bracegirdle
Tol Eressea


Mar 25 2014, 9:17pm

Post #4 of 22 (257 views)
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Far over the MistyMountain cold, [In reply to] Can't Post

we seek our pale enchanted gold..

'Cheating' is allowed. Oh yes.
Since this is all relative please feel free to peek in any books.

Did I say 'long tons'.... Sorry Wink regular 'short tons' will do nicely (2,000 lbs). A long ton is a couple hundred lbs more than our usual short ton. Thanks for catching that! Smile

Most likely 'computer' cookies - Aaw, and you wanted chocolate chip w/ raisins.........

(This post was edited by Bracegirdle on Mar 25 2014, 9:18pm)


Ruxendil_Thoorg
Grey Havens


Mar 26 2014, 2:16am

Post #5 of 22 (249 views)
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Stone of Errrr.... [In reply to] Can't Post

....wreck.

Guesswork here, and math is not my strong suit.

1. Approx. diameter 12 feet.

2. Approx weight 79 tons (2,000 lbs per ton, per your clarification post, rather than "long tons")

Bonus question:
Why did Isildur bring it to Middle-earth from Numenor?

Isildur brought it from Numenor because he wanted to save part of his homeland for remembrance's sake, and because it was quite a remarkable stone in itself, being a huge boulder of pretty much perfect sphere shape.

(I'm glad you didn't ask *how* he brought it....)

Things overheard during games of chess in Middle-earth:

Galadriel (any and every time she advances her pawn to the last row): "In its place you would have a QUEEN!!!!" (thunder booms)

http://newboards.theonering.net/...forum_view_expanded;


MistyMountain
Lorien

Mar 26 2014, 3:08am

Post #6 of 22 (242 views)
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I'll give it a go [In reply to] Can't Post

1. The book describes the stone as bring the height of a man; I took this to mean roughly 6 feet. Book also says it is round but half sunk in the ground. I wasn't sure if that meant that 6 feet were sticking ABOVE ground and it was actually 12 feet in diameter but that would make for a VERY large stone and one I can't imagine Isildur carrying onto a ship so 6' in diameter it is. That's my answer to #1.

2. Now the weight. There is no description of the stone composition. If it wasn't so late at night as I type this, I'd call my brother (the geologist) for some advice but, alas, I will have to just make an educated guess. As the book says it was considered "other-worldly", I thought it might be a smooth granite so I figured its volume and then found the weight of granite per cubic foot and came up with 19,000 pounds or 6.5 tons.

Bonus question? I have no idea. Looked in the Sil and in ROTK but could find no reason for Isildur dragging a huge rock onto a ship and plopping it into the ground in the middle of nowhere. Why DID he do it?


(This post was edited by MistyMountain on Mar 26 2014, 3:09am)


Darkstone
Immortal


Mar 26 2014, 1:25pm

Post #7 of 22 (239 views)
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Since you didn't ask... [In reply to] Can't Post

I may mention two cases where I was not, at the time of making use of them, aware of 'borrowing', but where it is probable, but by no means certain, that the names were nonetheless 'echoes'. Erech , the place where Isildur set the covenant-stone. This of course fits the style of the predominantly Sindarin nomenclature of Gondor (or it would not have been used), as it would do historically, even if it was, as it is now convenient to suppose, actually a pre-Númenórean name of long-forgotten meaning. Since naturally, as one interested in antiquity and notably in the history of languages and 'writing', I knew and had read a good deal about Mesopotamia, I must have known Erech the name of that most ancient city. Nonetheless at the time of writing L.R. Book V chs. II and IX (originally a continuous narrative, but divided for obvious constructional reasons) and devising a legend to provide for the separation of Aragorn from Gandalf, and his disappearance and unexpected return, I was probably more influenced by the important element ER (in Elvish) = 'one, single, alone'. In any case the fact that Erech is a famous name is of no importance to The L.R. and no connexions in my mind or intention between Mesopotamia and the Númenóreans or their predecessors can be deduced.
-Letter #297

******************************************
The audacious proposal stirred his heart. And the stirring became a song, and it mingled with the songs of Gil-galad and Celebrian, and with those of Feanor and Fingon. The song-weaving created a larger song, and then another, until suddenly it was as if a long forgotten memory woke and for one breathtaking moment the Music of the Ainur revealed itself in all glory. He opened his lips to sing and share this song. Then he realized that the others would not understand. Not even Mithrandir given his current state of mind. So he smiled and simply said "A diversion.”


Bracegirdle
Tol Eressea


Mar 26 2014, 8:41pm

Post #8 of 22 (222 views)
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ANSWERS- In our own way We Each Reach Erech [In reply to] Can't Post

ain't it a Peach?

My answers:

1. Size of the Stone? “ . . .round as a great globe, the height of a man, though its half was buried in the ground.” RotK The Passing of the Grey Company The “height of a man” indicates to me ABOVE GROUND. So the ‘visible’ stone would be 5 – 6 feet in height.
Using the upper six foot height this would mean the Stone en toto was about 12 feet in diameter.
Also assuming the Stone to be of the heavier hardier type rock such as granite. (The Stone of Erech was half buried for 3,139 years before Aragorn saw it and apparently showed little sign of weather, wind, rain wear. “..round as a great globe,..”) Were it of a softer material such as sandstone it would surely show large anomalies (and not be “round as a great globe” after over 3,000 years).

2. Weight of the Stone? Wow! The consensus seems that granite weighs in at about 165 lbs/cu ft. The formula to find the volume of a sphere is 4/3 Pi R3 (R3- that's cubed) where R is the radius (6’). (4/3 x 3.14 = 417 x 216 = 90,000 cubic feet x 165 lbs = 148,000 lbs = 74 tons). I’ve rounded some figures. Remember this is an exercise in approximation. I reserve the right to be dead wrong!
So my estimate is 74 tons (regular 2,000 lb tons – sorry folks – not that it would make much diff… A HEAVY DUDE!)
Even though the formula seems quite straightforward I really found it very difficult to compute. My mathematics brain cells were the first to take a holiday. But, we’re dealing with approximations, so . . . (Maybe a mathematician will step in and show where I have gone wrong?)

3. Why did Isildur bring it to Middle-Earth from Numenor?
Whether it be 6.5 tons as Misty says or 79 tons as Rux says, why oh why was this SUPER HEAVY object loaded aboard ship?
The correct answer is I don’t know!
Secondary answer: His daddy Elendil told him to. “Hey Isildur, grab that 74 ton rock and load it aboard! And leg it!”

Aside to Darkstone: The element ER - ‘one, single, alone’, consider also: “ERebor” Lonely Mtn., “ERelas” (single leaf); Tol ERessea (Loney Isle); even “ERchamion” (one-handed).

From World's End then he turned away,
and yearned again to find afar .
his home through shadows journeying,
and burning as an island star . . .

-Bilbo Baggins

(This post was edited by Bracegirdle on Mar 26 2014, 8:44pm)


DanielLB
Immortal


Mar 26 2014, 10:43pm

Post #9 of 22 (211 views)
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At a glance ... [In reply to] Can't Post


In Reply To
2. Weight of the Stone? Wow! The consensus seems that granite weighs in at about 165 lbs/cu ft. The formula to find the volume of a sphere is 4/3 Pi R3 (R3- that's cubed) where R is the radius (6’). (4/3 x 3.14 = 417 x 216 = 90,000 cubic feet x 165 lbs = 148,000 lbs = 74 tons). I’ve rounded some figures. Remember this is an exercise in approximation. I reserve the right to be dead wrong!
So my estimate is 74 tons (regular 2,000 lb tons – sorry folks – not that it would make much diff… A HEAVY DUDE!)
Even though the formula seems quite straightforward I really found it very difficult to compute. My mathematics brain cells were the first to take a holiday. But, we’re dealing with approximations, so . . . (Maybe a mathematician will step in and show where I have gone wrong?)


The missing decimal means the answer should be wrong, but I think ~ 74 tons is about right. It all makes sense to me (using roughly similar numbers):

Diameter = 144 in / 12 feet
Density = 0.09935005 lbs/in3

Weight = Density x Volume
Volume = 4/3 Pi R3

Volume = ~1563457 in3
Weight = ~155329lb or ~78 tons

Top job! I wouldn't have liked to be the one to haul that around. According to Google, the heaviest stone in the Pyramid of Giza is thought to weigh 70 tons. If the Egyptians could move them around, then the Númenóreans must have had no problems.

Smile


(This post was edited by DanielLB on Mar 26 2014, 10:47pm)


MistyMountain
Lorien

Mar 27 2014, 12:55am

Post #10 of 22 (192 views)
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devil's advocate [In reply to] Can't Post

For the sake of argument, how would anyone, even the sainted Numenoreans, move a 74 TON rock to Erech?
It is over 300 MILES from Pelargir and then it is over hilly terrain, not like the flat land around the pyramids.
Maybe they convinced Smaug to move it for them? Or maybe a few of Manwe's eagles? Now we need to calculate the weight of the eagles and the maximum weight they could carry (todays birds of prey can carry no more than half their body weight).


Silverlode
Forum Admin / Moderator


Mar 27 2014, 12:58am

Post #11 of 22 (194 views)
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They played a giant game of killer croquet with it? [In reply to] Can't Post

It's a great game, if......Tongue

Silverlode

"Dark is the water of Kheled-zâram, and cold are the springs of Kibil-nâla, and fair were the many-pillared halls of Khazad-dûm in Elder Days before the fall of mighty kings beneath the stone."



Bracegirdle
Tol Eressea


Mar 27 2014, 1:03am

Post #12 of 22 (197 views)
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The Great Stone quest............. [In reply to] Can't Post

The missing decimal means the answer should be wrong, but I think ~ 74 tons is about right. It all makes sense to me (using roughly similar numbers):
----------------------------------------------------------------------------
Thank you. You seem to have a much better grasp of volumes, densities, weights etc. than the average bear.
I recall over 30 years ago figuring this out (the weight), and I calculated in vicinity of 70 tons, although I don’t recall how I came up with this figure, or what formula I used.
In this case I believe I just ignored the “missing decimal” as an error on my part.

I also recall also calculating the weight of the Orthanc Stone which I believe was one foot in diameter.
I came up with a weight for a one foot crystal ball at 58 lbs. (Not to conducive for Gandalf to carry “in the folds of his cloak” for any distance.) And a two lb. sphere at 464 lbs.; a 3 lb. sphere at 1568 lbs. (Goes up exponentially quite rapidly.)

Cheers

(This post was edited by Bracegirdle on Mar 27 2014, 1:04am)


Bracegirdle
Tol Eressea


Mar 27 2014, 1:13am

Post #13 of 22 (196 views)
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Thorondor had a wingspan of 180 feet. Care to figure his weight? [In reply to] Can't Post


Quote
For the sake of argument, how would anyone, even the sainted Numenoreans, move a 74 TON rock to Erech?
It is over 300 MILES from Pelargir and then it is over hilly terrain, not like the flat land around the pyramids.
Maybe they convinced Smaug to move it for them? Or maybe a few of Manwe's eagles? Now we need to calculate the weight of the eagles and the maximum weight they could carry (todays birds of prey can carry no more than half their body weight).

How was it moved. Sea or Land; therein lies the rub.
Correct answer: I dunno!
Some birds of prey can carry twice their weight for short distances. Flap, flap, flap...
Cheers and cookies for you Misty


DanielLB
Immortal


Mar 27 2014, 8:05am

Post #14 of 22 (178 views)
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Let's see ... [In reply to] Can't Post

This forum has caulculated an approximate weight for Thorondor at 1400lb or 0.7 ton. It would have to be 100 times bigger for it to weigh the same as the Stone of Erech.

Which leads me to think there might be three possibilities:

(1). The Valar helped in moving the Stone. It's the only way I see possible of moving such a large mass.
(2). Isildur was lying. He did not bring the stone from Numenor. It really was a meteorite.
(3). The Stone of Erech isn't what it seems.

If we assume (1), then I imagine it was effortless for them to do so.

If we assume (2), then the Stone wasn't actually made of granite. Let's assume it was solid iron. Crikey, my rough estimates make it in the region of 218 tons. But it is also perfectly round - I doubt a 218 ton meteor would land there without breaking up. So what if it was volcanic in origin? It might be a concretion as a result of volcanic activity. So let's assume it could either be pure calcite (2a) or gypsum (2b) or even pumice (2c).

(2a) Weight of Stone if calcite = 65 tons
(2b) Weight of Stone if gypsum = 62 tons
(2c) Weight of Stone if pumice = 29 tons

So it would weigh less, but still rather substantial for Isildur to carry around.

If we assume (3), then we might also assume that we can't actually know or calculate it's weight. Tolkien originally intended the Stone of Erech to be a palantir, so perhaps it has some sort of magical property. Let's assume that the Stone was actually hollow, and the shell of the Stone was infinitesimally small (think of a hollow M&M), so that it's weight is simply due to it's shell/skin. You can work that out by calculating it's surface area:

4 x Pi x R2 = 65144 in2

Multiply that with the density of granite, gives a weight of just over 3 tons. Now that seems reasonable. So depending on whether the stone was hollow or not, the Stone of Erech *could* have weighed anywhere between 3 to 70 tons.

(4) Or one last possibility is that the Stone was not 12 feet in diameter, but actually 6 feet. In that case, all the values above can be halved.

(Disclaimer - I can't actually guarantee any of that maths is right. It's too early for these kind of sums.)


noWizardme
Tol Eressea


Mar 27 2014, 8:48am

Post #15 of 22 (166 views)
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Killer croquet set? - The hoops got washed overboard & ended up at Stonehenge, England // [In reply to] Can't Post

 

~~~~~~

"… ever let your aim be to come at truth, not to conquer your opponent. So you never shall be at a loss in losing the argument, and gaining a new discovery.”
Arthur Martine

"nowimë I am in the West, Furincurunir to the Dwarves (or at least, to their best friend) and by other names in other lands. Mostly they just say 'Oh no it's him - look busy!' "
Or "Hold off! unhand me, grey-beard loon!"


noWizardme
Tol Eressea


Mar 27 2014, 8:52am

Post #16 of 22 (170 views)
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I think sometimes it's time to remember its a fantasy story :) [In reply to] Can't Post

Tolkien is remarkably good at avoiding things which "couldn't happen" when they have a major bearing on the plot. The stone seems to me more like a fine literary gesture - personally I'm amused but not too bothered if it is preposterous when you think about it.

~~~~~~

"… ever let your aim be to come at truth, not to conquer your opponent. So you never shall be at a loss in losing the argument, and gaining a new discovery.”
Arthur Martine

"nowimë I am in the West, Furincurunir to the Dwarves (or at least, to their best friend) and by other names in other lands. Mostly they just say 'Oh no it's him - look busy!' "
Or "Hold off! unhand me, grey-beard loon!"


Bracegirdle
Tol Eressea


Mar 27 2014, 1:26pm

Post #17 of 22 (164 views)
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Oh, NO!! [In reply to] Can't Post


Quote
I think sometimes it's time to remember its a fantasy story



You just broke 20,000,000 hearts !!


MadHeartFrown

From World's End then he turned away,
and yearned again to find afar .
his home through shadows journeying,
and burning as an island star . . .

-Bilbo Baggins

(This post was edited by Bracegirdle on Mar 27 2014, 1:26pm)


noWizardme
Tol Eressea


Mar 27 2014, 1:58pm

Post #18 of 22 (155 views)
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Oops - should I have used [spoiler] tags? // [In reply to] Can't Post


In Reply To
Quote
I think sometimes it's time to remember its a fantasy story


You just broke 20,000,000 hearts !!


~~~~~~

"… ever let your aim be to come at truth, not to conquer your opponent. So you never shall be at a loss in losing the argument, and gaining a new discovery.”
Arthur Martine

"nowimë I am in the West, Furincurunir to the Dwarves (or at least, to their best friend) and by other names in other lands. Mostly they just say 'Oh no it's him - look busy!' "
Or "Hold off! unhand me, grey-beard loon!"


Riven Delve
Grey Havens


Mar 27 2014, 2:13pm

Post #19 of 22 (211 views)
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I think you all deserve cookies [In reply to] Can't Post


for Awesome and Supreme Geekiness (in a very good way, of course!) Cool


“Tollers,” Lewis said to Tolkien, “there is too little of what we really like in stories. I am afraid we shall have to try and write some ourselves.”



noWizardme
Tol Eressea


Jan 11, 11:46am

Post #20 of 22 (131 views)
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I've realised, oh so belatedly, that my earlier posts could seem rude - my apologies [In reply to] Can't Post

I enjoyed these calculations. What I meant to say was that it doesn't phase me if our conclusion is that the Stoen is preposterously big and heavy. - as I see it (others might disagree), the point of the Strone of Erech is to set the Numenoreans up to be a fading culture that was once mighty to an almost incomprehensible degree. We're invited to be like Dark Ages Britons , admiring and sometimes adapting the works of the departed Romans, whose engineering solutions and resources are long gone and forgotten.


I revisited this old thread as part of a discussion now going on about different ways of enjoying Tolkien - mythic, novelistic and "gamic" themes - http://newboards.theonering.net/...i?post=824808#824808

(Sorry about "gamic" - it's meant to suggest 'treating the works as if they are a game'. Perhaps someone can suggest a better term...)

~~~~~~

"nowimë I am in the West, Furincurunir to the Dwarves (or at least, to their best friend) and by other names in other lands. Mostly they just say 'Oh no it's him - look busy!' "
Or "Hold off! unhand me, grey-beard loon!"

This year LOTR turns 60. The following image is my LOTR 60th anniversary party footer! You can get yours here: http://newboards.theonering.net/...i?post=762154#762154


Bracegirdle
Tol Eressea


Jan 11, 2:36pm

Post #21 of 22 (126 views)
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Naw, apology not necessary [In reply to] Can't Post

There are many Tolkienisms that we must accept without complete understanding. It has never distracted me from the tales either. But it is fun to play with the trivialities of these conundrums. Having some frivolity with a serious question seems to be (and IS) very often fair game on TORn.

Oh, how about just plain “game-like” if you don’t like “gamic”?

Grab a cookie from Riven Delve above. Sure she won't mind. Tongue




(This post was edited by Bracegirdle on Jan 11, 2:37pm)


noWizardme
Tol Eressea


Jan 11, 2:57pm

Post #22 of 22 (142 views)
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Quite so "these things are fun, and fun is good" (Dr. Seuss )// [In reply to] Can't Post

 

~~~~~~

"nowimë I am in the West, Furincurunir to the Dwarves (or at least, to their best friend) and by other names in other lands. Mostly they just say 'Oh no it's him - look busy!' "
Or "Hold off! unhand me, grey-beard loon!"

This year LOTR turns 60. The following image is my LOTR 60th anniversary party footer! You can get yours here: http://newboards.theonering.net/...i?post=762154#762154

 
 

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