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TORn AMATEUR SYMPOSIUM Essay "The Physics of The Hobbit: Barrels out of Bond" by DwellerInDale
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TORn Amateur Symposium
Bree


Nov 14 2013, 5:19am

Post #1 of 60 (712 views)
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TORn AMATEUR SYMPOSIUM Essay "The Physics of The Hobbit: Barrels out of Bond" by DwellerInDale Can't Post


Welcome to November 2013 TORn Amateur Symposium, the second TAS!

We are very pleased to present the next essay for TAS2:

"The Physics of The Hobbit: Barrels out of Bond"


Abstract:


This essay presents an analysis of one of the most iconic scenes in The Hobbit, the escape from the dungeons of the Woodland Realm. Bilbo Baggins, using his magic ring, is able to steal the keys to the dungeon cells and free the Dwarves. The company then escape by being packed into wooden wine casks and floating down the river toward Laketown.

In Tolkien’s book, Bilbo packs each Dwarf into a wine barrel and seals the barrel with a lid. In The Desolation of Smaug, however, we know from previews that the barrels will be without lids, allowing us to see each of our characters as they negotiate the river and the rapids. This will undoubtedly produce a more visually exciting sequence than in the novel, but is it physically possible? Several members of TORn have criticized this scene on the basis of the physics. If the barrels have no lids, they argue, won’t they fill with water, causing them to sink and thus possibly drowning most of our main characters?

In Part One and Part Two of The Physics of The Hobbit I explained the basic physics of free fall, with and without air resistance. In this essay I will explain the basic physics of floating in water, including what happens to hollow objects when they fill with water. The concepts will then be applied to Barrels Out Of Bond.






To view the essay, please click on the link above.

Our authors have written essays and analyses that are concerned, in some way, with the legendarium of John Ronald Reuel Tolkien. These essays may be philosophic opinions, scientific theories, or analytical approaches to understanding or highlighting some facet of Tolkien's writings and world. These pieces are written with the goal of amateur scholarship at their core - thus inspiring our Symposium title. Authors may choose to include citations or footnotes, but they are by no means required. Keeping in mind the dual spirit of enjoyment and inquiry that we believe in (as much as we value cheer and song), and which is of paramount important to both the TAS team and our authors, we fully encourage discussion of the essays presented.We hope you enjoy it as much as we enjoy posting it. The TAS is open for discussion, and any comments, questions or thought you wish to share about this essay can be posted in this response to this thread.

We have quite a full schedule of essays - essays will posted approximately every other day. The full schedule can be found


here.

So please, go forth and enjoy all of the works we have posted for this 2013 November Session. The entire TAS Team, (Elaen32, DanielLB and Brethil), is both delighted and proud to present the essays our TAS members have crafted, relating their interests and skills to the world of JRRT that we all love; a world most intricately crafted, and one that "takes hold of us, and never let's go."



noWizardme
Tol Eressea


Nov 14 2013, 1:37pm

Post #2 of 60 (293 views)
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Well done Dweller in Dale, another excellent read! [In reply to] Can't Post

In The Hobbit, Bilbo (who as you r physics predicts, cannot manage to get stably ontop of the outside of an empty barrel) still spares a thought for his dwarves and whether he has got their barrel lids on tight enough. He's worried that, if the lids leak the barrels will sink, I suppose. But it seems like he needn't have worried on that account!

Disclaimers: The words of noWizardme may stand on their heads! I'm often wrong about things, and its fun to be taught more....

"nowimė 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!"


DwellerInDale
Rohan


Nov 14 2013, 2:27pm

Post #3 of 60 (285 views)
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Thanks [In reply to] Can't Post

Yes, I guess they didn't teach integral calculus in the Shire in those days! I wonder what J.R.R. Tolkien's understanding of the physics was?

I wish I'd had a bit more time to prepare the essay (very busy lately); I'd like to do an analysis of the stability of the situation where a Hobbit is spread-eagled on top of a barrel. Maybe the next rainy day...


In Reply To
In The Hobbit, Bilbo (who as you r physics predicts, cannot manage to get stably ontop of the outside of an empty barrel) still spares a thought for his dwarves and whether he has got their barrel lids on tight enough. He's worried that, if the lids leak the barrels will sink, I suppose. But it seems like he needn't have worried on that account!


Don't mess with my favorite female elf.









Rembrethil
Tol Eressea


Nov 14 2013, 2:32pm

Post #4 of 60 (266 views)
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Awesome!!! [In reply to] Can't Post

Good stuff DiD!! I can follow all your illustrations and totally get what you are saying. Way to make physics fun!!

Call me Rem. Rembrethil is a lot to type!!


DwellerInDale
Rohan


Nov 14 2013, 2:43pm

Post #5 of 60 (282 views)
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Thanks R [In reply to] Can't Post

Although I was a bit pressed for time with this one, it was great fun to do the analysis. I hear they may have the Dwarves go over a waterfall in DoS, so maybe there will need to be a sequel analyzing how possible that might be!

Don't mess with my favorite female elf.









Lightfoot
Rivendell


Nov 14 2013, 4:08pm

Post #6 of 60 (273 views)
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Well Bilbo would not have had to worry [In reply to] Can't Post

about sinking barrels per say - but if they leaked to badly the he would have to worry about drowned dwarves stuck in floating barrels!Frown Great piece Dweller in Dale! I enjoyed it all and would love to hear about the probability of surviving a waterfall while in open topped barrels.

Faithful servant yet master's bane,
Lightfoot's foal, swift Snowmane



The Grey Elf
Gondor


Nov 14 2013, 4:24pm

Post #7 of 60 (261 views)
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Fascinating article, Dweller, and so meticulously written and diagrammed [In reply to] Can't Post

Could you briefly address what may happen given that, in SPJ's movie, Bilbo is hanging on to the side of Nori's barrel? Logic would seem to suggest his weight, especially as his clothes became soaked, might be enough to pull over the barrel. Or would Nori, leaning in the opposite direction, be enough to keep it upright? Or, if I understand what you've put forth in your article, would Bilbo's buoyancy in the river be enough to make no difference to the stability of Nori's barrel?

Welcome more children to Middle Earth. Support The S.H.I.R.E. Project!


DwellerInDale
Rohan


Nov 14 2013, 4:37pm

Post #8 of 60 (254 views)
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Many variables in play... [In reply to] Can't Post

Thanks for the feedback! There are lots of variables here, so the outcome is difficult to predict. Bilbo could possibly capsize Nori's barrel if he isn't careful. It depends on how much water has accumulated in the barrel, how much Nori weighs and his position in the barrel, and how far over Bilbo pulls the barrel. Bilbo's own buoyancy, however, won't be much of a factor; it is a matter of the torque that Bilbo puts on the barrel and whether that is enough to tip the barrel past its critical angle. The best thing Bilbo could do would be to "hug" the barrel at or below the water line so as to minimize the distance between his center of gravity and the barrel's center. Nori could also, as you suggest, help by leaning, although there isn't a lot of room for him to do this.

Don't mess with my favorite female elf.









noWizardme
Tol Eressea


Nov 14 2013, 4:56pm

Post #9 of 60 (264 views)
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Drowning in the barrrels [In reply to] Can't Post


In Reply To
[Bilbo would not have to worry] about sinking barrels per say - but if they leaked to badly the he would have to worry about drowned dwarves stuck in floating barrels!Frown Great piece Dweller in Dale! I enjoyed it all and would love to hear about the probability of surviving a waterfall while in open topped barrels.

and now I'm stuck inside this quotes box...
I think it's touch and go re drowning anyway: I believe DiD's analysis suggested "Depending on the exact shape of the barrel, from 10 to 15 cm should be above the water line..." So that portion of the barrel presumably wouldn't be constantly flooded. So the dwarf has to keep his nose and mouth in that air space. Which sounds do-able But it could be a difficult ride - Bilbo has packed them in with straw etc. to try and avoid bruising. But feasibly that means the dwarf can't turn around inside the barrel. And the barrels are meant to roll and pitch around a fair bit. If it rolls so that the dwarf is head down, he's going to have to hold his breath until the barrel rights itself. If the barrel is side on for a while, the dwarf might be head underwater - or get repeatedly underwater if the barrel is rolling in the water. If the barrel's stable attitude is such that the dwarf is head-down, he'll certainly drown. It's presumably nearly totally dark inside the barrel, so little chance of judging when the air pocket is coming your way to take a breath.

I suppose the other issue is suffocation, if the air isn't exchanging enough with that outside.

Oh, and any dwarves with motion sickness are going rapidly to add to their problems....Unsure

So traveling lids off and dwarf semi-popped out seems a much safer option - though in the book the dwarves have to be sealed up while the elves hauling the barrels drop them into the river without realizing that the prisoners are escaping!

Amusingly, it may be that Tolkien was taking more liberties with physics than Peter Jackson & team are going to Wink

You know what we need here to try this out - The Mythbusters Laugh


Disclaimers: The words of noWizardme may stand on their heads! I'm often wrong about things, and its fun to be taught more....

"nowimė 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!"


Rembrethil
Tol Eressea


Nov 14 2013, 4:56pm

Post #10 of 60 (249 views)
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Well......... [In reply to] Can't Post

You have those people who went over Niagra. Possible? Maybe. Probable? No way!!

Call me Rem. Rembrethil is a lot to type!!


noWizardme
Tol Eressea


Nov 14 2013, 5:00pm

Post #11 of 60 (249 views)
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And there are still more variables... [In reply to] Can't Post

...to Bilbo hanging onto Nori's barrel, when one considers that they appear to be in a strong current. Bilbo+ barrel is going to be much less streamlined than barrel only: if he's not too busy just hanging on, maybe Bilbo could vary the amount of drag on him quite a lot in an attempt to keep things steady.

Disclaimers: The words of noWizardme may stand on their heads! I'm often wrong about things, and its fun to be taught more....

"nowimė 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!"


DwellerInDale
Rohan


Nov 14 2013, 5:05pm

Post #12 of 60 (255 views)
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Stuck Inside (Small Clarification) [In reply to] Can't Post

Note in the essay that the 10-15 cm is my estimate for the case where the barrels are completely filled with water. If the barrel is sealed but is leaking, the distance above the water line will be greater. Most of the preview shots from DoS suggest that the lidless barrels may only be half to three-quarters full. If we assume that the barrel is half full of water and that the Dwarves weigh about 40 kilos, this distance will double to about 30 cm.


In Reply To
and now I'm stuck inside this quotes box...
I think it's touch and go re drowning anyway: I believe DiD's analysis suggested "Depending on the exact shape of the barrel, from 10 to 15 cm should be above the water line..." So that portion of the barrel presumably wouldn't be constantly flooded. So the dwarf has to keep his nose and mouth in that air space. Which sounds do-able But it could be a difficult ride - Bilbo has packed them in with straw etc. to try and avoid bruising. But feasibly that means the dwarf can't turn around inside the barrel.


Don't mess with my favorite female elf.









The Grey Elf
Gondor


Nov 14 2013, 5:10pm

Post #13 of 60 (248 views)
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So, [In reply to] Can't Post

if I understand what you're suggesting, Bilbo's affect on the barrel's stability might be one thing if they were floating in still water, and another if in the active water that we see as it introduces the torque factor?

Knowing SPJ's imagination and his love of set pieces, I suspect we will be seeing poor flailing Bilbo being forced to shift from one barrel to another as they make their way down the river and more than one kind of amazing stunt will be staged what with elves and orcs in hot pursuit of the escaping dwarves. This could provide you with a wealth of material for you to do a follow up to this article, LOL, should you be so inclined ! Smile Dweller in Dale, Middlle-earth Mythbuster!

Welcome more children to Middle Earth. Support The S.H.I.R.E. Project!


noWizardme
Tol Eressea


Nov 14 2013, 5:17pm

Post #14 of 60 (242 views)
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Thanks for that ! [In reply to] Can't Post

Quite right- I'd forgotten that the dwarf starts dry in the barrel, and as long as the barrel is sealed (as per the book) it's only leakage which brings water in.

So the barrel rider should have a reasonable volume of air, and is left with some even in a terribly leaky barrel Violent agitation of the barrel might be a problem though- trying to breath in air , getting a lot of water mixed in with it, and choking.

Lids off, you'd expect more water to slop in, but the passenger can stick his head out (arrows permitting…)

No wonder they were grumpy when they got out!

Disclaimers: The words of noWizardme may stand on their heads! I'm often wrong about things, and its fun to be taught more....

"nowimė 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!"


Werde Spinner
Rohan


Nov 14 2013, 5:47pm

Post #15 of 60 (237 views)
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Awesome!!! [In reply to] Can't Post

I could follow the math perfectly and the diagrams really helped. It's truly amazing to see two of my favorite fields of geekery, mathematics and Tolkien, combined in such a satisfactory way. Great job, DiD!! Smile

I may or may not now be contemplating suggesting a viewing of DoS as extra credit for my physics class... Cool Laugh

"I had forgotten that. It is hard to be sure of anything among so many marvels. The world is all grown strange. Elf and Dwarf in company walk in our daily fields; and folk speak with the Lady of the Wood and yet live; and the Sword comes back to war that was broken in the long ages ere the fathers of our fathers rode into the Mark! How shall a man judge what to do in such times?"

"As he ever has judged. Good and ill have not changed since yesteryear; nor are they one thing among Elves and Dwarves and another among Men. It is a man's part to discern them, as much in the Golden Wood as in his own house."


Brethil
Half-elven


Nov 14 2013, 7:22pm

Post #16 of 60 (244 views)
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A feast for the senses Dweller! [In reply to] Can't Post

Another great read!

And the timing here is so perfect, I'm glad we have this to enjoy before seeing the film version, where we can go in with the ideas. Now I know I am going to spend a lot of time watching what Bilbo and Nori do with that shared barrel - wonder if there will be any close calls in tipping. And the idea of falls and other complications - I now hope there are, because then we have more factors to look forward to analyzing!

Is there a Tolkien topic that you have wanted to look into more deeply, and write about your thoughts on it? If so, we'd like to hear from you for the next TORn Amateur Symposium- coming in November. Happy writing!





elaen32
Gondor


Nov 14 2013, 9:16pm

Post #17 of 60 (222 views)
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As always.... [In reply to] Can't Post

I really enjoyed your analysis, DiD! Looking forward to the waterfall analysis- those poor dwarfs!! Maybe we also need some analyses on those Matrixwood Elves and their movements!!Evil That said, the aerodynamics of Smaug and dragons in general might be a good one too? Are you ready??AngelicEvil

One point- I would assume that the wood could absorb some water (especially if the barrels have not been varnished and caulked properly) and that would affect the overall mass? How significant could that be?


Is there a Tolkien topic that you have wanted to look into more deeply and write about your thoughts on it? If so, we'd like to hear from you for the next TORn Amateur Symposium- coming in November. Happy writing!



elaen32
Gondor


Nov 14 2013, 9:20pm

Post #18 of 60 (218 views)
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Yes.... [In reply to] Can't Post

I think I'm going to be watching the barrels scene in a different light, even taking into account Thorin's majestic, if soggy, piloting of his craft!! But seriously, I think it may help to know that these things are feasible. I switched off for a while during the goblin's sequence in AUJ, until I read DiD's analysis and I could appreciate the action a bit more!


Is there a Tolkien topic that you have wanted to look into more deeply and write about your thoughts on it? If so, we'd like to hear from you for the next TORn Amateur Symposium- coming in November. Happy writing!



Brethil
Half-elven


Nov 14 2013, 9:26pm

Post #19 of 60 (218 views)
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Interesting question Furincurunir [In reply to] Can't Post


In Reply To

In Reply To


I suppose the other issue is suffocation, if the air isn't exchanging enough with that outside.





Dweller's calculations give us a minimum of 15cm and approximately 30cm of space above the water line for gas to be present. The question of suffocation in a sealed barrel (as in carbon dioxide poisoning) I suppose would depend on the spaces between the barrel staves above the water line. I wonder if the danger would not increase incrementally with dry barrels becoming wet and the staves expanding to fill the gaps even more? Would enough CO2 be able to vent and be exchanged with atmospheric air? The danger ultimately would be drowning, because if the exhaled CO2 concentration in the space rose high enough narcosis followed by loss of consciousness and subsequent drowning would be the result.

Open barrels in this respect are certainly much safer!

Is there a Tolkien topic that you have wanted to look into more deeply, and write about your thoughts on it? If so, we'd like to hear from you for the next TORn Amateur Symposium- coming in November. Happy writing!





Brethil
Half-elven


Nov 14 2013, 9:42pm

Post #20 of 60 (211 views)
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I agree! I want to see all of this too... [In reply to] Can't Post


In Reply To
I really enjoyed your analysis, DiD! Looking forward to the waterfall analysis- those poor dwarfs!! Maybe we also need some analyses on those Matrixwood Elves and their movements!!Evil That said, the aerodynamics of Smaug and dragons in general might be a good one too? Are you ready??AngelicEvil

One point- I would assume that the wood could absorb some water (especially if the barrels have not been varnished and caulked properly) and that would affect the overall mass? How significant could that be?




Good question about the water absorption - I was wondering about it in relation to suffocation in a closed barrel but wasn't thinking in terms of overall mass.

Is there a Tolkien topic that you have wanted to look into more deeply, and write about your thoughts on it? If so, we'd like to hear from you for the next TORn Amateur Symposium- coming in November. Happy writing!





DanielLB
Immortal


Nov 14 2013, 10:26pm

Post #21 of 60 (222 views)
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Can't argue with the physics! [In reply to] Can't Post

Another great essay, thank you DwellerInDale. Smile

I wonder what else the Dwarves could have done to ensure the barrels didn't tilt. Oil has a density less than water ... they should have oiled themselves up. Sly

Without pulling out the book, do we know what trees grew in Mirkwood (or possibly around Laketown and Thranduil's Halls). Oak seems like a good approximation, but wooden Lignum Vitae barrels might have made it more difficult.

Smile



elaen32
Gondor


Nov 14 2013, 10:31pm

Post #22 of 60 (210 views)
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I must be losing the plot, but... [In reply to] Can't Post

the line "Bring wood and oil" just went through my mind on reading your post DanielCrazy Now THAT would be an interesting feasibility studyWink


Is there a Tolkien topic that you have wanted to look into more deeply and write about your thoughts on it? If so, we'd like to hear from you for the next TORn Amateur Symposium- coming in November. Happy writing!



DanielLB
Immortal


Nov 14 2013, 10:51pm

Post #23 of 60 (204 views)
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I imagine .... [In reply to] Can't Post


In Reply To
Yes, I guess they didn't teach integral calculus in the Shire in those days! I wonder what J.R.R. Tolkien's understanding of the physics was?


In Reply To

Tolkien knew a bit about everything (and anything!). And that includes the practical and theoretical sciences. Just reading the books gives that away - botany, meteorology (and climatology), astronomy, translation, theology, philosphy, biology ... the list really is endless.

He might not have been able to work out a Balrog's free fall, but he certainly understood the basic concepts of it. I don't doubt that. I use this quote a lot in my essay:


Quote
Despite being a faery-story, miles are miles, days are days, and weather is weather. Letter 210


And it's probably applicable here, as well.

Smile



Darkstone
Immortal


Nov 14 2013, 11:12pm

Post #24 of 60 (203 views)
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Probably ballistics at least. [In reply to] Can't Post


In Reply To
Yes, I guess they didn't teach integral calculus in the Shire in those days! I wonder what J.R.R. Tolkien's understanding of the physics was?


In officer training he doubtess received some instruction in ballistics. Probably more later since as battalion signaling officer he'd often be working closely with the Forward Observation Officer and his signallers in forward observation posts.

******************************************
“Indeed if fish had fish-lore and Wise-fish it is probable that the business of anglers would be very little hindered.”
-JRR Tolkien


Kim
Valinor


Nov 14 2013, 11:29pm

Post #25 of 60 (203 views)
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All I can say is [In reply to] Can't Post


In Reply To
... they should have oiled themselves up. Sly



Yes, yes they should. Evil

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