May I put to readers more knowledgeable than I a question posed to me by
my eight-year-old son that I was unable to answer.
At the Bridge of Khazad-Dum, when Gandalf faced the Balrog, it is described
as having a shadow about it "which reached out like two vast wings." A
little later, the Balrog steps on to the bridge, draws itself up to a great
height, and "its wings were spread from wall to wall." Can we take it from
this that the Balrog literally had wings, or was Tolkien merely referring
to the shadow about it?
Later, on the River Anduin after leaving Lorien, when the Company saw a great
winged creature in the night and Legolas brought it down with his bow
and arrow, Gimli said that it had reminded him of "the shadow in Moria
-- the shadow of the Balrog". But even from this it cannot be clearly
inferred that the Balrog did have wings.
So -- did the Balrog have wings? The question is, if it did, why did it not
use them to save itself from falling into the chasm? No mention was made
of its even flapping them: it simply "plunged down and vanished".
Now, looking at the relevant passages more closely, my conclusion is that
Tolkien was probably writing figuratively and that the Balrog did not
actually have wings; but is there another passage elsewhere in his writings
that is less ambiguous on this point?
---------------------------
Boon Lee
Dept of Economics
University of Wollongong
Wollongong, New South Wales
Australia.
I don't think JRRT drew any pictures of Blarogs; but it seems clear to
me that Balrogs in general don't have wings, and the "wings" mentioned
are, indeed, just the wings of shadow mentioned before.
My reason for confidence: Two different Baalrogs are defeated by being
cast down. Gandalf dropped one into the Chasm of Khazad-dum; and
Glorfindel defeated one in the mountains near Gondolin, when "both
fell to ruin in the abyss". I don't think JRRT would have had two
Balrogs defeated this way if they could fly.
--
Andrew Solovay
"But that was in another country;
and besides, the wench is dead." ---Marlowe
I don't know about Glorfindel's Balrog, but neither Gandalf nor
the Balrog of Moria were killed by the fall: they survived to
climb Durin's Stair. I don't think this proves that Gandalf had
wings, though.
--
Mike Pettersen, Ecole Normale Superieure
m...@physique.ens.fr
Perfect love casteth out fear.
In article <1vtmi9$d...@wampyr.cc.uow.edu.au> bo...@wampyr.cc.uow.edu.au (Boon Chye Lee) writes:
>
>At the Bridge of Khazad-Dum, when Gandalf faced the Balrog, it is described
>as having a shadow about it "which reached out like two vast wings." A
>little later, the Balrog steps on to the bridge, draws itself up to a great
>height, and "its wings were spread from wall to wall." Can we take it from
>this that the Balrog literally had wings, or was Tolkien merely referring
>to the shadow about it?
Oh no. The `Do Balrog's have Wings?' debate has reached r.a.b.t.
Well I suppose it was bound to happen sometime. We have had the
`Who/What was Tom Bombadil?', `Two Glorfindels or one?',
`Are Orcs immortal/irredemably evil?' debates. I suppose we'll
get onto `Did the Numenorians have Nuclear Weapons?' debate
soon. (This is due to a description of weapons that some people
think must be ICBMs, something about weapons that can cause
destruction from afar).
Andrew
>>>>> Tolkien comes right out and directly says that the Balrog has
wings.
Pg. 429 ....It stepped forward slowly onto the beidge, and suddenly it
drew itself up to a great height, and its wings were spread from wall
to wall.... (FotR)
Here many claim that JRRT did not mean wings but shadow, but he comes
right out and smacks us in the face with the information.
*Which one is it fellas*, is his word gospell, or is it open to
interpretation. If it is one or the other please stick with it.
It's kind of frustration to argue with people who switch horses
in midstream.
Well, gosh, I'd answer, buddy, but you're in my killfile, so I never
saw your post.
I did say "defeated", not killed...
Anyway, my point is, if Balrogs could fly, Gandalf wouldn't have
thought, "I know, I'll knock the bridge out from under him"; the
Balrog could simply flutter back up to the other side of the chasm.
And more to the point, if Balrogs could fly, JRRT wouldn't have-- on
two separate occasions-- had a fight with a Balrog end with the Balrog
being cast down from a high place. It just wouldn't make sense; why
should being "cast down" be a problem for a flying being?
All IMHO, of course. But it is IMWIHO (In My Well-Informed Humble
Opinion).
The other possibility is that Balrogs have wings, but they're
non-functional. But that would be silly.
Oh, and another point: Yes, the "wings" are referred to as tangible
things ("its wings were spread from wall to wall"). But then, the
Shadow of the Balrog is *also* referred to as a tangible thing ("Too
much it reminded me of the shadow in Moria-- the shadow of the
Balrog"). So I say that the "wings" mentioned are simply the "shadow
about [the Balrog]" that reached out "like two vast wings".
Come on, are you sure it is the same people arguing these two points?
There's a lot of people posting here, and not all agree on all points.
It is not surprising that you could have two viewpoints presented based
on different ways of interpreting the books.
In any event, I think you lessen the argument about Uruk-Hai by putting
it in that fashion. The reason goes beyond a lack of specific
notice by JRRT. But let's not drag that one into this discussion...
(Incidently, anyone consider that maybe that Balrog has wings, but
can't use them to fly? Also, given the size described for those wings,
you'd need a lot of space to use them to fly. Maybe more space than
was available in the fall from the bridge.)
JD> Come on, are you sure it is the same people arguing these two points?
JD> There's a lot of people posting here, and not all agree on all points.
JD> It is not surprising that you could have two viewpoints presented based
JD> on different ways of interpreting the books.
>>>>> I did my homework on this point. At least one individual definatly
qualifies and another is, or is real close. The rest fall generaly
into one of two camps; those who feel that what JRRT say goes and
nothing else will fly, and those who feel that some speculation is
necessary to find out what JRRT meant. In my opinion both are viable
arguments and I readily accept one or the other. I feel that these
two camps are mutualy exclusive.
JD> In any event, I think you lessen the argument about Uruk-Hai by putting
JD> it in that fashion. The reason goes beyond a lack of specific
JD> notice by JRRT. But let's not drag that one into this discussion...
>>>>> I don't think it does at all. If people argue from only one camp
then I stand a better chance of getting my point across. If I get
it from both sides then I can't nail down the oposing view, as it
keeps shifting its basis for argument.
What I am suprised you didn't nail me for is my utter lack of
diplomacy and tact.
JD> (Incidently, anyone consider that maybe that Balrog has wings, but
JD> can't use them to fly? Also, given the size described for those wings,
JD> you'd need a lot of space to use them to fly. Maybe more space than
JD> was available in the fall from the bridge.)
>>>>> I like the above explanation alot. I might also add that as the Balrog
plumeted down, it would probably repetedly smack into the sides of the
crevas and tumble.
Not to mention your atrocious grammar and spelling.
(Ancalagon? Glaurung? You guys are better at this than I am.)
>(Incidently, anyone consider that maybe that Balrog has wings, but
>can't use them to fly? Also, given the size described for those wings,
>you'd need a lot of space to use them to fly. Maybe more space than
>was available in the fall from the bridge.)
That thought had occurred to me. However, as I mentioned in my earlier
post, no mention was made of the Balrog's even flapping its wings. One
would expect that, had its wings been functional, it would instinctively
have attempted to use them.
>Later, on the River Anduin after leaving Lorien, when the Company saw a great
>winged creature in the night and Legolas brought it down with his bow
>and arrow, Gimli said that it had reminded him of "the shadow in Moria
>-- the shadow of the Balrog". But even from this it cannot be clearly
>inferred that the Balrog did have wings.
My impression is that the "shadow" refered to is the feeling of
dread that follows the Nazgul. Legolas shot down a nazgul-bird,
with a nazgul riding on it. As far as I know, it is not said anywhere
that belryg has a similar aura of fear around them, but I find it
very likely. How else does Gimli identify Durin's Bane? He has surely
never seen a balrog before.
Klaus O K
PS: if Sindarin plural of craban, Adan, and orch are crebain, Edain,
and yrch, plural of balrog must be belryg.
Well, Balrogs appear frequently in _The Silmarillion_; they
kill Feanor and Fingon, among others, and feature prominently in
the fall of Gondolin. Nowhere are they mentioned as having
wings or flying. I doubt that Sauron could or would have
fashioned wings for them if Morgoth couldn't or wouldn't.
I too once thought they had wings, because of the vivid
passage from _LOTR_. But once someone (hi Julian!) told me
about the debate, I went back and re-read the passage, and was
convinced that Tolkien was just referring to a dark aura that
surrounded him and stretched out *like* wings.
--Jamie.
ja...@cs.sfu.ca
"There be seven seen sorts, seventeen several sorts of divels on the
Moruna, and if the fancy took me I could name them all by rote."
What??? Of course the Balrogs have wings! In the passage quoted above,
it says, "It's wings were spread from wall to wall", _NOT_
"Some strange effect made it look as if there were wings spread wall to wall."
I think we can count on JRRT's sense of metaphor vs. direct writing
to steer us clear of such inane questions or observations.
Secondly, to refute the 'proof' cited above, of Balrogs being
cast down to a fiery end in a chasm or abyss,
I think you need to re-read Gandalf's depiction of the battle. The
Balrog _did_ survive the plunge, and both it and Gandalf raced back
up through the Mines of Moria via Durin's Stair, to the top of the
Silvertine, where Gandalf finally managed to off the sucker.
___________________________________________________________________________
GOD IS NO WHERE Bruce Robert Cordell
GOD IS NOW HERE cor...@shaman.nexagen.com
___________________________________________________________________________
The passages in the Silmarillion in which they zoom in to rescue
Morgoth from Ungoliant always seemed to me to be suggestive of
Balrogs flying to the rescue (though I do not remember whether
JRRT states that, and I am sans books at the moment). They were
certainly capable of fast movement, if not quite of flight.
[...]
>What??? Of course the Balrogs have wings! In the passage quoted above,
>it says, "It's wings were spread from wall to wall", _NOT_
>"Some strange effect made it look as if there were wings spread wall to wall."
>I think we can count on JRRT's sense of metaphor vs. direct writing
>to steer us clear of such inane questions or observations.
>Secondly, to refute the 'proof' cited above, of Balrogs being
>cast down to a fiery end in a chasm or abyss,
> I think you need to re-read Gandalf's depiction of the battle. The
>Balrog _did_ survive the plunge, and both it and Gandalf raced back
>up through the Mines of Moria via Durin's Stair, to the top of the
>Silvertine, where Gandalf finally managed to off the sucker.
*sigh* Of course the Balrog survived the fall, but so did Gandalf,
and if I recall correctly, they fell and hit water - not fatal. They're
both going to fall at the same speed *BUT* if the Balrog had wings,
why did it fall at all ? The fight with Gandalf is but one instance
of a Balrog being cast down, the other mentioned results in the Balrog
not surviving - perhaps because nothing lay underneath it to cushion the
fall. Maybe to satisfy everyone, the schools of thought on this could be
divded into "Balrogs don't have wings" and "Balrogs have useless wings"
(wings but they don't serve any practical purpose bar being spread from
wall to wall :). Anyone for the "Balrogs have useful wings" party ? :)
Darren
Scot
Yes, of course. The wings were useful, just not for flying. Belryg
used them for *swimming*.
(Bred in mockery of penguins, don't y'know...)
"With a terrible cry the Balrog fell forward, and its shadow plunged
down and vanished."
Next...
>>>>> The Balrog was big and it's wing span was probably huge. This would
imply that it need a large space to flap those wings, space it
probably isn't going to have. Now picture the Balrog falling in a
crevas, crashing into the sides, and tumbleing end over end due to
contact with the walls.
This mental picture doesn't conjure an environment where this big
winged beastie is going to see any use for those wings. Hammering
into the sides would probably just slow it down enough so it didn't
go splat when it hit the water. (hiting water at terminal velocity
is just like hitting concrete)
I believe that if they fell far enough for Gandalf to describe it
by saying, "Long I fell..." then they would have been killed by
the impact, even if they landed in water. I conclude either that
they used magic to slow their fall, or to protect themselves from
the impact; or else that the Balrog had wings, but was too distracted
by Gandalf's attacks to use them to do more than slow their coupled fall.
(Or perhaps, as someone else suggested, the chasm wasn't big enough
for it to spread its wings fully. The danger of saying that the Balrog
can't possibly have wings because then something else wouldn't have
happened... is that you can always find another explanation for the
something else.)
How deep is the chasm under Durin's Bridge? If it were 10 km deep,
and nothing retarded their fall,
it would have taken 45 seconds to hit bottom. If you're falling,
this might seem like forever. Is this long enough to qualify for
"Long I fell..."?
Actually, it's something of a plot weakness that Gandalf survives the
fall. It's a cheap trick to give your reader every evidence that
your character is dead, and then say, "Hah--but guess what! He
survived!" It's like bringing Spock back after Star Trek II, or
Darth Vader, after he disappears into the void at the end of the
first Star Wars. A cheap trick.
Indeed, Tolkien does it twice, because not only does
Gandalf survive the fall in contradiction to all the clues that
he gives the reader, but then he makes Gandalf really truly die, and then
he ressurects him!
I hope this isn't a spoiler for anyone... anyhow, after reading
the book 20 or 30 times, you're not disappointed that his
"death" is a phony surprise, when Gandalf comes back, because
of course you're expecting it, and it's a logical
part of the plot; but for a first time reader,
at least for me, it was a little bit of a let down. Anyone else
find that to be the case?
Maybe only SOME Balrogs have wings. Not all dragons had wings but no one
will deny that Smaug did.
--
- Bill Seurer Language and Compiler Development IBM Rochester, MN
Internet: BillS...@vnet.ibm.com America On-Line: BillS...@aol.com
>Next...
>--
>Andrew Solovay
Score one for Andrew. Guess it used the wings to glide down. Perhaps lack of
space to use them for flying. If the alredy "spread wall to wall" it would
be hard for a Balrog to use it's wings except in open sky.
Perhaps it was stunned...
(Ansd the Monty Python in me makes me add, "or restin' ... or pinin' for
the fjords")
--
Stan Brown, Oak Road Systems br...@Ncoast.ORG
Can't find FAQ lists? ftp to 'rtfm.mit.edu' and look in /pub/usenet
(or email me >>> with valid reply-to address <<< for instructions).
Or that wizards can survive hard impacts with the ground.
Or that wizards don't weigh much (after all, and eagle can carry them).
(yeah, I know this leads to the sparrow and cocconut question)
>If it were 10 km deep, and nothing retarded their fall, it would have
>taken 45 seconds to hit bottom. If you're falling, this might seem
>like forever. Is this long enough to qualify for "Long I fell..."?
This leads to the "wizards don't weigh much" explanation.
If wizards fall like feathers it would indeed take "Long" to fall 10 km.
Ron Mayer
ma...@orthanc.acuson.com
Hmm. Maybe Balrogs and/or Dragons fly using magic, and have wings for
more satisfying purposes than catering to Aerodynamic trivia; things
like (a) Looking Really Impressive; (b) Providing Neat Wind Effects for
Intimidating Peasants, (c) Suckering Archers into firing at unimportant
parts of their anatomy :-), and (d) As a convenient way of keeping
prying eyes at bay while examining their favourite treasure...
Besides, flapping like crazy would have been so undignified :-) :-)
--
+------------------------------------------------------------------+ |
| Jerry Cullingford #include <std.disclaimer> +44 442 230000 x3868| ,-|--
| j...@crosfield.co.uk j...@selune.demon.co.uk je...@shell.portal.com | \_|__
+-----(Work)--------------(Home)--------------(another alternate)--+ \___/
So its wings must be pretty big then. (Assuming it had them, which is how
I read the passage.)
So it's reasonable to expect that there may not have been enough room to
flap them as it fell down the chasm.
When I was at uni, the zoology department conducted strictly monitored
tests and established that an area at least 144 BTU's across was
required for an average-sized balrog to flap its wings. The shape of
the chasm was also important, and even more space was needed if a
wizard was falling at the same time.
Is this getting us anywhere? It seems like the original poster has made up
his mind anyway.
Not at all! Especially reading the story at about age 12 or
14 -- Gandalf's return is one of the great moments in the entire
book. Even now, I can get a sense of the thrill I had the first time
when he came back.
"Mithrandir!"
"Well met again I say to you, Legolas!"
(purely from memory, and I haven't read the books for at least 5
years)
For me, and being 12 years old (I think), it was the first
time I got the idea that the good guys might win this thing
after all.
A thrilling scene, and one of my favorites in a book of
many.
Jim Acker
jga...@neptune.gsfc.nasa.gov
I agree completely.
For the original poster: I think you're missing one _very_ important detail in
you assumptions: That Gandalf would be normally affected by physics.
Gandalf, Saruman, Radagast, Sauron and the Balrog were all MAIAR. Translation:
they were demigods. Sauron got throttled by the greatest hound ever to live and
got his butt kicked there and survived, then survived being at the epicenter of
one of the two biggest cataclysms in the Elves' history (The downfall of
Numenor), then proceeded to put much of his being into a ring and survived when
all his works and his being except for a minor shadow and the ring were
destroyed. Sauron and Gandalf are the same type of beings, albeit at opposite
ends of the spectrum.
If two demigods (Gandalf and the Balrog) fall down a hellishly deep hole,
they're still pretty likely to survive. You can't kill a Maia that easily. In
addition, Gandalf did 'die' in some context, as is evidenced by his being
'sent back' (presumably from Mandos or Valinor) in spirit and Gwaihir's
statement that he weighed less than he had on previous trips.
Just my 2 cents.
--
------------------------------>>>
Brian Landwehr
ta...@vax1.mankato.msus.edu
If the Balrog had tried to flap its wings on the way down surely they
would have just torn off! It's too heavy!
If by useful wings, you mean the aerodynamic lift-generating variety,
then surely a creature as heavy as a Balrog would not only need
wall-to-wall wings, but a 50 metre breastbone and pectorals to match. If
they did use their wings to fly, it must have been for steering, with
magic keeping them aloft.
Can any aerodynamics people give their opinions?
""\_ _/""
/"""\___/ \___/"""\
'"""\_ _/"""`
********************$$$$$********************
$ Fangy, Canadian Elk Society $
$ L o n g l i v e t h e M o o s e ! $
******* Chris <C.D.H...@uk.ac.bham> *******
>I believe that if they fell far enough for Gandalf to describe it
>by saying, "Long I fell..." then they would have been killed by
>the impact, even if they landed in water.
I don't think so .... As long as you hit the water "properly" (and the
water isn't too shallow :-> ), there shouldn't be a problem. Don't
high-divers reach a significant fraction of terminal velocity?
>How deep is the chasm under Durin's Bridge? If it were 10 km deep, and
>nothing retarded their fall, it would have taken 45 seconds to hit bottom.
A lot longer, I think, if you take air resistance into account.
>Actually, it's something of a plot weakness that Gandalf survives the
>fall. It's a cheap trick to give your reader every evidence that
>your character is dead, and then say, "Hah--but guess what! He
>survived!"
>Indeed, Tolkien does it twice, because not only does
>Gandalf survive the fall in contradiction to all the clues that
>he gives the reader, but then he makes Gandalf really truly die, and then
>he ressurects him!
But Gandalf was already "resurrected" before the other characters found out
all these details. The details of what happened to G between "The Bridge of
Khazad-Dum" and "The White Rider" isn't exactly relevant to the question of
whether this is a plot weakness. I would say yes, this is a cheap trick, but
it isn't two cheap tricks.
>... for a first time reader, at least for me, it was a little bit of a
>let down. Anyone else find that to be the case?
I guess I've already admitted that I did ....
Drin
--
^..^ / | Dan Peters | "There's too much craziness here - |
/_/\_____/ | | in 25 years I have used all the tears |
/\ /\ |pet...@physics.ubc.ca| in my eyes." |
/ \ / \ | | -Kansas |
I'm embarrassed to admit this, but I attempted to do the calculation
before I made the posting... "Assume a spherical Balrog."
Probably not a good approximation, especially if Balrogs have
wings. Is it really true that divers are near terminal velocity?
I, at least, wouldn't want to jump off a 10 meter platform...
Anyway how about another favourite bits thread? Mine include the parts where
Frodo claims he ring for himself , where the Lord of the Nazgul threatens
to take Eowyn/Dernhelm to the 'Houses of Lamentation' , and the council of
elrond.
Matt.
--
Matthew Woodford.....mjw@uk.ac.cov.cck.....No .sig quote at the mo'
Both the famous Acapulco cliff divers (approx. 70 feet), and
some exhibitions I've seen on WWSports, at Sea World ("High diving"
championships), sometimes to 200 feet, considerably exceed the
velocity acheived by 10-meter platform divers.
The problem is control -- if you enter the water at any
other than a knife-edge angle, the sudden drag can do serious damage
(not to mention a flat "belly-flop" impact = death). The divers generally
do a 1 1/2 pike so that they control the angular momentum they
impart on leaving the platform. In one competition, one of the
divers dislocated his shoulder on entry.
Jim Acker
jga...@neptune.gsfc.nasa.gov
Quite possible.
>Or that wizards don't weigh much (after all, and eagle can carry them).
> (yeah, I know this leads to the sparrow and cocconut question)
Nothing to do with it.
>
>
>>If it were 10 km deep, and nothing retarded their fall, it would have
>>taken 45 seconds to hit bottom. If you're falling, this might seem
>>like forever. Is this long enough to qualify for "Long I fell..."?
10km is easily enough to do nasty things upon hitting.
>
>This leads to the "wizards don't weigh much" explanation.
>If wizards fall like feathers it would indeed take "Long" to fall 10 km.
*cough*
Need I point out that gravitational acceleration has _nothing_ to do with
mass/weight, but constant? The only reasons feathers don't fall fast is their
high surface area.
The only reason why Gandalf would fall "like a feather" is if he has
a) A parachute. Doubtful.
b) Wings. Ditto.
c) Magic. Most likely explanation.
Of course, being a Maia, he could have been able to change into a bird or
something, though being Istari he wasn't allowed.
Or maybe he just held on to the Balrog, who used his wings to slow down? :-)
--
-Matt cro...@cs.colorado.edu
Mere anarchy is loosed upon the net!
And Gandalf doesn't have a larger surface area than a feather?
Gravitational acceleration is constant, but downward acceleration is not.
It is equal to the *total* force on Gandalf divided by his mass. So, with
air providing viscosity:
a = (gm-Bv)/m => a = g - Bv/m
where a is acceleration, m is mass, B is a viscosity term that takes into
account Gandalf's surface area and streamlining, v is his velocity, and g
is gravitational acceleration.
By the above equation, as Gandalf's mass decreases (and his surface area does
not), the velocity at which there is NO acceleration decreases also, so Gandalf
falls slower.
This isn't terribly relevant, but I've seen the "everything drops at the same
speed, except feathers" argument used too many times. Sorry.
(Admittedly, coming up with scientific violations in LOTR is shooting
fish in a barrel. To be fair, I know of nowhere where JRRT claimed
anything different. But doesn't that make it a bit silly to argue
about the physics of falling balrogs?)
>Ron Mayer writes:
>>This leads to the "wizards don't weigh much" explanation.
>>If wizards fall like feathers it would indeed take "Long" to fall 10 km.
>*cough*
>Need I point out that gravitational acceleration has _nothing_ to do with
>mass/weight, but constant? The only reasons feathers don't fall fast is their
>high surface area.
*BEEP!* Wrong, but thanks for playing. (Well, your first sentence is right,
but your second, and your implicit conclusion, are way out.)
Gandalf had a lot more surface area than a feather. So do you. If your
statement were correct, he or you would fall much more slowly than a feather,
regardless of weight. In fact weight makes a big difference.
Proof the that Balrog not only had wings, but feathered wings!
Ron Mayer
ma...@orthanc.acuson.com
*cough out a lung*
Since when does Gandalf loose mass in mid-air, now that is some quick
mass-loss plan, he let go of something big (hopefully you mean he let go
of the Balrog in his fall), or you are dealing with a different problem
(a leaking and falling water tank) {... :) ...}.
-- -----------------------------------
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# # ### #### ## # |---------------------------------
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----------------------------------- The abbrev. doesn't work
[many reasons for Gandalf surviving the fall deleted]
>The only reason why Gandalf would fall "like a feather" is if he has
>a) A parachute. Doubtful.
>b) Wings. Ditto.
>c) Magic. Most likely explanation.
>Of course, being a Maia, he could have been able to change into a bird or
>something, though being Istari he wasn't allowed.
>Or maybe he just held on to the Balrog, who used his wings to slow down? :-)
So obvious its painful: Perhaps Gandalf DIED and was reborn as GTW :0)
-Chris
--
======================================================================
Chris Goebel - Motorola Inc. Any opinions expressed here are my
Cellular Infrastructure Group own and should not in any way be
Arlington Hts, Il considered those of my wife.
>Wayne Crawford writes:
>>By the above equation, as Gandalf's mass decreases [...]
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^
>*cough out a lung*
> Since when does Gandalf loose mass in mid-air, now that is some quick
>mass-loss plan, he let go of something big (hopefully you mean he let go
>of the Balrog in his fall), or you are dealing with a different problem
>(a leaking and falling water tank) {... :) ...}.
I _hope_ this was just a bad attempt at humour. I'm feeling rather
humour-impaired at the moment, so I can't tell. I'll assume the worst.
\begin{rant}
*cough out both lungs*
You twit, he didn't mean "Gandalf's mass decreases" in a temporal sense,
he was just explaining how terminal velocity depends on mass.
\end{rant}
Drin
--
^..^ / | Dan Peters | Too long for haiku: |
/_/\_____/ | | Truly marvelous the proof |
/\ /\ | pet...@physics.ubc.ca | Of Fermat's Theorem. |
/ \ / \ | | (author unknown) |
No. He didn't die then. (Or at least he didn't say that he did.) When he
recounts the story to Aragorn, Legolas, and Gimli, he gives the following
sequence of events:
1) Fall into chasm with balrog
2) Hits water(?) at bottom
3) Follows/chases balrog up Endless Stair, from bottom-most dungeon to
topmost tower
4) Final battle with balrog outside topmost tower
5) "Casts down" balrog from tower
6) Death (or death-like state)
7) Resurrection (as Gandalf the White)
8) Transport by eagle to Lothlorien
Julian C. Lander
jcla...@mitre.org
>And Gandalf doesn't have a larger surface area than a feather?
>Gravitational acceleration is constant, but downward acceleration is not.
>It is equal to the *total* force on Gandalf divided by his mass. So, with
>air providing viscosity:
> a = (gm-Bv)/m => a = g - Bv/m
>where a is acceleration, m is mass, B is a viscosity term that takes into
>account Gandalf's surface area and streamlining, v is his velocity, and g
>is gravitational acceleration.
>By the above equation, as Gandalf's mass decreases (and his surface area does
>not), the velocity at which there is NO acceleration decreases also, so Gandalf
>falls slower.
>This isn't terribly relevant, but I've seen the "everything drops at the same
>speed, except feathers" argument used too many times. Sorry.
Also, all of this happened before Galileo's alleged experiment with the two
different size cannonballs, so that principle wasn't in effect yet.
BK
It's late at night, and my mind is a bit fuzzy, and it's been 15 years
since I studied such things, but anyway...
In Newtonian physics, there are two forces acting on Gandalf and
the Balrog, assuming they are passive in their fall:
- gravity
- air resistance
The nice experiments done by Galileo and others are always done at or
above the earth's surface. If you look a little "deeper" into how
gravity acts, there is an interesting effect when dealing with the
interior of a solid sphere (which to a reasonable approximation is
what the Earth is). As you get nearer to the CENTER of the sphere
(i.e., deeper in the earth), the net acceleration due to gravity
LESSENS. At the exact center, there is zero acceleration.
So, depending on what assumptions you want to make about the density
and composition of the atmosphere down there (cough, cough), you could
possibly make it work out such that Gandalf and the Balrog would
actually slow down, if they fell deep enough. (Remember, the stairway
back up was "endless", and the fact that the Balrog could not strike
a light at the bottom might be commentary on the air quality.)
Now, whereas the late Professor Tolkien was possibly not thinking
about such things when he devised the narrative, the real answer may
well be that both the combatants had just given ample demonstration
of ability to produce unexpected physical effects by supernatural
means, and could have performed other such feats to slow their fall.
--
...Richard S. Shuford | "Whoever digs a pit may fall into it; whoever
...shu...@cs.utk.edu | breaks through a wall may be bitten by a snake."
...Info-Stratus contact| Ecclesiastes 10:8 NIV