# Adventures in Balrog MathFebruary 15, 2008 10:38 PM   Subscribe

Baby_Balrogs?
posted by shakespeherian at 10:42 PM on February 15, 2008

I'm against them!
posted by TwelveTwo at 10:44 PM on February 15, 2008

Also my nerdiness is extremely lacking. I was all about to point out that all of the math is irrelevant because we don't know what the mass of the planet is where all of this takes place, but then I realized that I didn't know what the planet is called in Middle-Earth, so I googled it so as to make my snark intelligent and suave. Apparently Lord of the Rings takes place on Earth, in the past. And I didn't know that.

D-, shakespeherian.
posted by shakespeherian at 10:52 PM on February 15, 2008

Oooh, it's not finished yet! I will subscribe for the thrilling conclusion.
posted by chrismear at 10:56 PM on February 15, 2008

From a rec.arts.books.tolkien posting dated 21 July 1995.

In an effort to compare the relative strengths of the Maiar, a recent poster to r.a.b.t. compared Sauron's strength to Gandalf's and the Balrog's by stating:

S > G and G = B implies B < S

It's an intriguing way of stating the problem. But Gandalf the Grey, who fought the Balrog, wasn't as powerful as Gandalf the White. Also remember that we're talking about a Sauron who has invested much of his native power in the Ring, which has weakened him greatly while he is not in possession of it; he is not as strong as he was with his original native power:

Gg < Gw

Sn = S + R

Sn > S

Now Gandalf was afraid of using the Ring, for fear it would conquer him; yet if he had used the Ring, he would have had enough power to defeat Sauron (Fellowship pp. 70-71 hardback):

Gg < R

Gg + R > S

But if the Balrog had arrived at the Bridge of Khazad-dum first it may have been possible that, though greatly weakened by Gandalf, it might have obtained the Ring. So, if the Balrog had been victorious,

Bv = B + R - Gg

would the Balrog have been able to overthrow a Sauron whose native power had been diminished by the loss of the Ring?:

B + R - Gg > Sn - R

And when Gandalf had returned from death, would he have assisted the Balrog, hoping that

(B + R - Gg) + Gw > Sn - R

then

Bv - 1/2(Sn-R) < Gw - 1/2(Sn-R) ?

Answers are due at the end of class next week. Be sure to show your proofs.
posted by Mr.Encyclopedia at 11:13 PM on February 15, 2008 [7 favorites]

you know what the real problem was? - gandalf didn't know the "safe word" and the balrog kept up with the whips and chains until the wizard was driven to slaying his master

this is why pre-agreed signals are so important, especially if you're going to have your s&m dates in some funky scary dungeon
posted by pyramid termite at 11:19 PM on February 15, 2008 [2 favorites]

It seems like an awful lot of trouble to measure the Balrog's CdA and mass when we have a perfectly good human also falling down the shaft at terminal velocity.
We have at least two good data points.

1. Gandalf can catch up to the balrog in full 'tuck' position, and
2. Gandalf does not fall away from the balrog when he is below it(while fighting)

This means that the balrog will be falling at a rate between the max and min terminal velocities of a robe laden human. terminal velocity at full tuck is ~200mph and terminal velocity of one of those wing suits is apparently ~60mph. normal min terminal velocity is ~110mph. Since Gandalf has a robe and not a wing suit, I'll say his terminal velocity is ~90mph or 132 ft/s.

v=at so time to reach terminal velocity is t=v/a
I'll cheat here and say his average acceleration is 1/2g or 17 ft/s/s
so time to accelerate is 7.75s
distance traveled in that time is at2 or 1021ft

the rest of the 104 seconds is at terminal velocity, 132 ft/s
so
d=1021ft+132 ft/s*(104s-7.75s)=13726ft=2.6miles=4.2 miles which is certainly feasible.

I think I remember a comment in the commentary where they say how long the tunnel actually is, because they did have to model it. but I've forgotten what it was
posted by TheJoven at 11:32 PM on February 15, 2008 [1 favorite]

BAD! Bad blogger! Do not type out URLs as un-clickable un-copyable text within images!
posted by XMLicious at 11:35 PM on February 15, 2008

The mass of Middle Earth isn't the same as Earth, though - it's a bit more, since the Undying Lands were shot off into space at the end of the mythic ages. No, seriously.
posted by nicolas léonard sadi carnot at 11:46 PM on February 15, 2008 [1 favorite]

The mass of Middle Earth isn't the same as Earth, though - it's a bit more, since the Undying Lands were shot off into space at the end of the mythic ages. No, seriously.

Now is probably a good time to admit that I don't care about LOTR, despite being in most other ways a perfectly acceptable dweeb.
posted by shakespeherian at 11:50 PM on February 15, 2008

The bending of the world occurred in 3319 S.A. while Gandalf and the Balrog fought in 3019 T.A.

THE MATH IS CORRECT.

Christ, the ignorance about history on this website astounds me.
posted by TheOnlyCoolTim at 12:23 AM on February 16, 2008 [15 favorites]

And to think I once wrote a writeup on Everything2, on the node titled "What is the Earth's carrying capacity?", in which I tried to figure it out in terms of if our planet was a D&D 3rd edition monster.

To think I thought that proved that I was a geek.
posted by JHarris at 1:31 AM on February 16, 2008

Seriously Tim? So what, the boats everyone got on at the end of LOTR were sealed against the vacuum and had ion thrusters or something?
posted by nicolas léonard sadi carnot at 2:05 AM on February 16, 2008

Just doing a quick calculation in my head the answer of 43 tonnes or 110 tonnes for a lava Balrog seems off by an order of magnitude.

Assuming Earth-like conditions the Balrog is roughly 3 times taller than Gandalf giving a volume of 27 times that of Gandalf's and lets round that up to 30. Now lets assume that Gandalf has a mass of 100 kilograms (probably less but it's a nice round number so stick with 100).

If Balrog is of similar density then it has a mass of 30 x 100kg = 3 tonnes.

Or for a lava Balrog at 2.6 times the density of water then about 8 tonnes.
posted by electricinca at 3:48 AM on February 16, 2008

Just doing a quick calculation in my head the answer of 43 tonnes or 110 tonnes for a lava Balrog seems off by an order of magnitude.

I'm guessing those wings on the Balrog model are not even close to being in scale. They are going to way too thick and won't weigh as much as the rest of the balrog for their volume anyway since they are mostly skin and bone. 3 to 8 tonnes seems a lot more realistic to me as well. A Balrog is just a double size laza gorilla with wings really.
posted by public at 4:56 AM on February 16, 2008

Metafilter: just a double size lava gorilla with wings
(sorry)
posted by YAMWAK at 5:36 AM on February 16, 2008

There was a time when I was considered nerd-like. I took AP Physics. I had read LOTR. I played D&D. I thought I was set. How could I have been so wrong?
posted by ThusSpakeZarathustra at 5:41 AM on February 16, 2008

Probably you can use the wingspan/body length ratio of a vampire bat and estimate the balrog's height ... Why a vampire bat? Because other bat species aren't evil! Never suggest a balrog would eat bananas.
posted by ersatz at 6:10 AM on February 16, 2008

These are awesome.

This reminds me those movies were pretty good too. I don't want to own any DVDs, but I've always thought a LOTR box set would be my one soft spot. Instead I just get them every couple years from Netflix.

And I love the idea of a creature 'made of molten lava, with plates floating on top of it'.
posted by These Premises Are Alarmed at 6:23 AM on February 16, 2008

Seriously Tim? So what, the boats everyone got on at the end of LOTR were sealed against the vacuum and had ion thrusters or something?

They were able to travel metaphysically/mystically on the "Straight Road." It's all in the book.
posted by TheOnlyCoolTim at 6:26 AM on February 16, 2008

you know what the real problem was? - gandalf didn't know the "safe word"

Bah. Safewords are for fairies. And elves.
posted by rokusan at 6:51 AM on February 16, 2008

WTF, homunculus? It's not DONE YET.
posted by anotherpanacea at 6:52 AM on February 16, 2008

Balrog? But what about M. Bison?
posted by Servo5678 at 7:29 AM on February 16, 2008 [1 favorite]

nicolas léonard sadi carnot: "Seriously Tim? So what, the boats everyone got on at the end of LOTR were sealed against the vacuum and had ion thrusters or something?"

Maybe this wasn't spelled out clearly enough for you in the Silmarillion. The Valar are somewhat equivilent to gods. Their singing created the whole of Arda. Aulë was powerful enough to single-handedly create the dwarves, and he wasn't even the most powerful of them.

If gods want to be not physically part of the earth, but somehow allow boats to sail to them, they can.
posted by Plutor at 7:41 AM on February 16, 2008

This is silly. Type VI demons Balrogs are not made from lava. They are made from a spiritual substance that looks like lava, but is different. So all his mortal experimentation is for naught.
posted by moonbiter at 7:43 AM on February 16, 2008

Phenocrysts aren't plates of rock, they're crystals!

That's the one that bothered me... geology nerds in the house!
posted by Kattullus at 8:01 AM on February 16, 2008

It seems like an awful lot of trouble to measure the Balrog's CdA and mass when we have a perfectly good human also falling down the shaft at terminal velocity.

Gandalf may be many things, but he's certainly not human. For all the walking around he does, he demonstrates ample non-corporeality later on.
posted by lumensimus at 8:48 AM on February 16, 2008

Wouldn't an "ash" balrog be considerably less dense than a "lava" balrog?. After all, they are described as "shadow and flame" in both the movie and the book. The flame could just as easily be a burning embers/ashy substance as it could be lava.
posted by fraxil at 8:50 AM on February 16, 2008

And a styrofoam balrog would be even less dense than that!
posted by Plutor at 9:20 AM on February 16, 2008

WTF, homunculus? It's not DONE YET.

Tune in next week, same balrog time, same balrog channel.
posted by homunculus at 10:04 AM on February 16, 2008

"Seriously Tim? So what, the boats everyone got on at the end of LOTR were sealed against the vacuum and had ion thrusters or something?"

Actually, the boats sailed out a few hundred miles, and then the crews torched them. Creepy.
posted by Mr. President Dr. Steve Elvis America at 2:35 PM on February 16, 2008

This is truly awesome but I think the premise that ordinary physics applies to Istari and Valaraukar is flawed. Plus we don't really even know if balrogs are entirely physical or somewhat ethereal, and whether they had literal wings or not. Tolkien's descriptions vary.

Seriously Tim? So what, the boats everyone got on at the end of LOTR were sealed against the vacuum and had ion thrusters or something?

With a few notable exceptions, generally only the Elves can travel the Straight Road to the Undying Lands (Aman). In brief, when Bilbo and Frodo and company sail off into the distance and disappear at the end of the LOTR, it's not because they're far away from the continent (Middle-earth). It's because they're far away from the planet (Arda). Once upon a time, when the world was flat, the journey to Arda where the Valar are was a literal sailing across an ocean. But because the Valar withdrew from being part of the world in a literal way, they separated Aman and Arda. By the time LOTR occurs, the Valar are acting entirely indirectly through the wizards, and they are themselves located in another dimension. So yes, the boats are in a sense interdimensional travel.

Reading the Silmarillion really changes the perspective of some things in LOTR. Gandalf is sort of like a minor angel in disguise, and Sauron is sort of like a more powerful fallen angel who once served an even more powerful fallen archangel.
posted by Tehanu at 3:57 PM on February 16, 2008

Once upon a time, when the world was flat, the journey to Arda Aman where the Valar are
posted by Tehanu at 4:05 PM on February 16, 2008

Is now a good time to mention I've never been able to finish the Silmarillion? I tried three times. Put me to sleep. My stepfather once told me that a reviewer (or somesuch) described it as "a telephone book in elvish". I suppose I'll try again someday...
posted by adamdschneider at 7:56 PM on February 16, 2008

I loved the Silmarillion, for what it's worth.
posted by Kattullus at 9:42 PM on February 16, 2008

I loved it too. Yes, the pace is slower and more deliberate than LOTR; Tolkien didn't write it for publication, but as his own sort of myth-making.

I think the Silmarillion is a lot like Sir Thomas Mallory's King Arthur book. I read them both as winter bedtime reading; they do put you to sleep, but you get a good story in small instalments.
posted by Pallas Athena at 5:32 AM on February 17, 2008

So, are we to assume that the LOTR movies took place in real time then, 24-style? Because I've seen a lot of movies that show me two events occurring at the same time.

I'm sorry if movie time-bending destroys your nerdgasm.
posted by graventy at 7:51 AM on February 18, 2008

Is now a good time to mention I've never been able to finish the Silmarillion? I tried three times. Put me to sleep. My stepfather once told me that a reviewer (or somesuch) described it as "a telephone book in elvish". I suppose I'll try again someday...

It's not a novel, so I don't read it the same way I do something like LOTR. From what I recall (it's been years), it reads more like a collection of folklore or epic poems or mythology strung together by a good editor. If you wouldn't enjoy reading something like a book of folklore, then the Silmarillion probably will always put you to sleep.
posted by Tehanu at 8:50 PM on February 18, 2008

Just thought I'd drop by...
posted by Durin's Bane at 3:19 PM on February 22, 2008

Ai! Ai! A balrog! A balrog is come!
posted by Tehanu at 3:38 PM on February 22, 2008 [1 favorite]

Oh, wait. I'm a dragon. You're pretty evil though. I wonder who would win in a fight?
posted by Tehanu at 3:42 PM on February 22, 2008 [2 favorites]

posted by homunculus at 2:31 AM on February 23, 2008

OK, now I want to know which actresses who've worked for Joss Whedon blessed those cookies. It's very important.

But in the meantime I will totally take that recipe down because I love ginger snaps. And I will mourn for that quilt to have been taken-- those things are a ton of work to make, and this person is clearly awesomely clever too.

Cookies and a quilt almost make up for no balrog math. Almost.
posted by Tehanu at 2:48 PM on February 24, 2008

Balrogs are clearly made of dark matter, so the balrog didn't so much fall, as travel downward, in order to stay with the puny collection of baryonic matter named Gandalf.

It's all in the books, you just have to read between the lines a bit...
posted by blm at 10:50 PM on February 28, 2008

The Cross-Sectional Area of a Balrog
posted by homunculus at 10:17 PM on February 29, 2008

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