Aufero says:
As a side benefit of the process, you now have a balrog-to-teaspoon conversion formula. {in case you want to make balrog tea}
MadGastronomer says:
Would it be very, very mean of me to point out that the time you're using may not be accurate, since some of the scenes that take up that amount of time are in slow motion?
Frith Ra says:
At 1/72 scale he'd go nice with my model airplanes. I'll have to look into that sometime
Joshua says:
Yay! First Comment!
Ace Dreamer says:
Actually, seeing as you have a metric volume getting the mass of a balrog is pretty easy. If you assume a balrog has the same density as water (i.e. a specific gravity of 1) one litre has a mass of one kilogram, so your 43,000lt balrog has a mass of 43 tonnes.
Which is interesting, as I don't think a balrog was 'traditionally' considered to weigh more than a few tons...
Forger says:
Well if a Balrog has a volume of approximately 43000 Litres then he will weigh somewhere in the region of 43 tonnes since if you assume the Balrog's density is approximately equal to that of a human which is approximately equal to that of water (1 Litre = 1 Kilogram) then a full sized Balrog should weigh 43 Tonnes.
DrGaellon says:
Irony, darlin', I adore you. If I were straight, I'd propose. :D
Adam says:
Assuming the Balrog is only slightly more dense than a Human [i.e. has a density of 1 equal to water, humans are 0.95ish since they float] that is a 43 ton Balrog. Birds tend to be less dense to make flying easier [hollow bones and all]
Some Guy says:
It bothers me when people round off numbers in the middle of a calculation for no good reason. That was Lorenz’ mistake. In this case, using 5 instead of 4.929 gives a final result of 42923520 instead of 42314006.016, a difference of more than 1.4%. Also, according to GNU units, 23 tsp is 113.3652ml, not 113.367, which would make the more exact volume to be 42313.3341696 l, which, compared to 43000 l is a difference of about 1.6%.
Now, the real volume should more accurately be calculated as 23.5±0.5 tsp, giving 43233.18893568±919.85476608 l.
(I don’t know the accuracy of your 1/72 scale estimate, but that would need to be factored in as well.)
Something else which would throw the calculations off is that the thickness of the wings is probably not to scale because of fragility and manufacturing issues. Think about it: how thick would a leathery wing be? How thick is that plastic?
towr says:
For a creature not 4 times as large as a human, the volume you arrived at seems a bit large. I'd expect something around 4^3*100L~=6400L (give or take a factor 2).
Hazgarn says:
Irony, you are an obsessive nutjob. But this is why we love you to death :D
And damn, that is a sweet Balrog.
jtobako says:
Use dinosaur scaling-pick a part you CAN measure (like knee to ankle) and just use that measure to scale the whole thing.
I don't remember, did the balrog float when they hit the water and the flames went out?
JSW says:
You know, an easier way to determine the scale of the balrog from the movie stills would be to just measure one part of the body, rather than trying to account for pose. Just compare, say, the lower leg of the movie-balrog with your figure. Assuming the proportions are the same, that should allow you to scale the figure with a reasonable degree of accuracy.
Grant C. McCormick says:
For conversions, one American gallon is *EXACTLY* 231 in³ = 3785.411784 cm³ = 3.785411784 liters.
For the Imperial gallon: Per Wikipedia, "The Weights and Measures Act of 1985 switched [the Imperial gallon] to a gallon of exactly 4.546 09 L (approximately 277.4 cu in)."
The Canadian gallon fluctuates, but is currently at near-parity with the American gallon.
Also, there is a good possibility that the Balrog may be at the HO scale, defined to be 3.5 mm = 1 foot (one of the most crazy definitions I've ever seen). This is what many model trains, Matchbox cars, etc., are at, and is the ratio of 3.5/(12*25.4), or 1/87.085714. This is so you can have your Godzilla (or Balrog) stomping on a train while eating a Buick.
Daniel says:
Balrogs are reportedly made of shadow and fire, which I'd expect to be substantially less dense than water, although it's obviously hard to quantify exactly how much.
Sean says:
You know, now that you've got this nifty model, you could just *measure* its wind resistance; it's a pretty complex shape, and no approximation ("assume a spherical Balrog") will be very good. So build yourself a nice little vertical windtunnel, and measure the airspeed needed to keep it from falling. Easy -- the guys on Mythbusters do it all the time! ;-)
Anonymous says:
Isn't a balrog a creature consisting mainly of shadow and flame, though? I'd imagine the density of shadow and flame to be far off from that of a human.
Milo says:
Well, I tried to look up how thick bat bat wings are, but Google isn't cooperating. But! I did find http://dinobase.gly.bris.ac.uk/forum/viewtopic.php?pid=1164 mentioning "the thin nature of the pterosaur wing (perhaps one or at most two mm in a 3 m wingspan animal)", so I guess that's something. Also, pterosaurs are cool too. Still, the balrog's wings are obviously based on a bat's rather than a pterosaur's, plus the fact that pterosaurs are, well, extinct, and therefore hard to get accurate numbers about. Also, I have no idea how wing thickness would scale with size, and doubly so when the scaled-up creature isn't actually expected to fly. Umm, watch this space?
maryling says:
Psst - it's early February. There isn't any baseball yet ;-) (Unless you're a Mets fan and jizzing your pants over the Santana deal.)
Sam says:
I hope no actual Balrogs were harmed in course of this project?
CatCube says:
Some Guy: The final answer wouldn't be 43233.18893568±919.85476608, it would be 43000±1000. It's dishonest to report anything more than the thousands place in the answer since the measurement method is not going to be accurate to more than two significant figures.
sb says:
If the Balrog is that heavy, it will fall much faster than the wizard. But if they keep fighting until they land, the Balrog will have to spread its wings to slow its fall. I think you might want to focus on the falling wizard instead if you want to get at the depth of the mine.
Blastrogath says:
But you can't assume that the wizard was free falling, because he could be grappling or grappled by the balrog, who because of his wings can modify his drop speed at will by a significantly greater degree than a human can.
The Auld Grump says:
Errr, weight does not affect the speed of a falling object SB (ask both Galileo and Newton...). And in fact the increased surface area slows the balrog's fall, even leaving out the wings (as well you should).
Interesting to see that the balrog is now entirely plastic - the one I built and painted a few years ago was metal with plastic wings.
The Auld Grump, who really needs to dig out the trilogy....
Milo says:
Weight does not affect the speed of a falling object IN VACUUM. However, the calculation for falling-balrog-in-vacuum has already been made and we're now dealing with trying to figure out terminal velocity, where it does matter. (Imagine a feather and a horseshoe both approaching a sheet of paper at the same speed. Intuitively, the feather will probably not punch through while the horseshoe will. It's the same with "punching through" air resistance.)
Martin says:
Hmmmmmmmmm ... Creative Anachronism ??? Do you know about the Society for Creative Anachronism? www.sca.org ... in fact.
As to coloring, do you currently use a tablet or a mouse? Computer Geeks has tablets starting at $30 www.geeks.com/products_sc.asp?Cat=563
JP says:
43 tonnes sounds like a lot, but that's with water's density... but weren't balrogs made of "darkness and evil matter" or something like that???...in any of my books comes the density of such things, but I suppose that should be less than water...
jbrecken says:
Which one of those boys is going to say "peep" first?
The Auld Grump says:
Milo - I did mention surface area - which is what affects terminal velocity. In either event the balrog is not falling FASTER than the beardy guy with the pointy hat, but rather SLOWER.
As for the density of EVIL - watch Time Bandits - the density is roughly similar to that of a burned meatloaf.
The Auld Grump, two movies between which parallels should never be drawn....
Ceriona says:
I think the "fire and shadow" thing is a good point. However, does, "It's a being of fire and shadow" mean that that is what it is made of, or does it mean that those are it's elements (ie, fire, air, earth, water, light, shadow)?
sb says:
@auld grump: The terminal velocity is proportional to sqrt(m/sigma), where m is the object's mass and sigma is its cross section perpendicular to the fall. Assuming the balrog geometry of the figure, each wing is roughly as long as the balrog is tall (height h). Let's say it is also as wide. The maximal sigma is then 2 h^2 larger than its minimal sigma (folded wings). The minimal sigma is probably less than h^2, so you have a maximal cross section of 3 h^2. Assume the balrog is 10 m tall, then sqrt(m/sigma) ~= 12 sqrt(kg/m^2). The same ratio for a 100 kg human of height 2 m (assuming sigma = h^2 since he has no wings), is roughly 5 sqrt(kg/m^2).
A balrog of 43 t will fall more than twice as fast as a 100 kg wizard, even with wings fully extended.
Cortejo says:
you are so cool!
Anonymous says:
Maybe Gandalf was extremely massive?
Scott Jaqua says:
Toss yourself in a swimming pool. Now do you float or do you sink? It's going to be pretty close to one way or the other. Close enough so that it doesn't really mater. You are mostly water. So your mass is about that as the same volume of water. Now before someone says Reptiles are different, check out how a Galapagos Marine iguana dives. Too much mass and they couldn't swim. To little and they couldn't dive under water. So once again the mass has to be about the same as the water displaced.
Tamfang says:
It's a treat to find a few people who recognize significant figures.
Anonymous says:
The nerdness here, given the amount of energy it has, if harnessed, could power the entire planet for the next several years.
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