Math of Iron Throne

[Irbis]

Okay, something bugs me. This is TV series Iron Thone:



It's supposedly made from 1000 swords. Except, Martin himself said it looks pitifully small, making producers insert the line it's actually made from 200 swords. Here's how GRRM imagines it:



The problem? It makes no fucking sense whatsoever.

Let's see. There's about 2 kg of steel in good, big sword. It means thousand of them will weight about two tons. Volume of two tons of steel? ~0.25 m³. Volume of Iron Throne? When you look at it from the side and compare it to Ned, who is pretty tall, it's at least 2 m³. Making it 87.5% air (barely reasonable, there is bound to be a lot of gaps between swords, but it starts approaching foam densities). Even tiny 1 m³ estimate means 75% of it are empty spaces.

Now think about 200 swords. 2 kg per sword is actually overestimation, but let's keep it to be conservative. 400 kg of steel is plate 1x1 m, 5 cm thick. Look at that number and tell me with straight face you can make something approaching TV Throne that won't look like an eggshell.

As for the painting - that monstrosity has at least 20 m³ (actually looks like 50, but we're trying to be conservative). Let's assume superior Westerosi technology makes steel as good as aerogel, 98% air. The problem? 20 m³ of steel is 160 tons, 2% of it is still 3.2 tons. Meaning, you need 1600 swords minimum using NASA technology.

If we use 87.5% number from above, you need 40.000 swords. Again, using drastically optimistic weight, volume, and durability assumptions. Something that empty would leak light like a sieve, not dramatically block it. In fact, I tried to use realistic numbers, and come up with 1.2 million swords needed to make what GRRM dubs "good" Iron Trone.

Then there is the fact that surface flame welding just doesn't produce good connections, even with dragon flame. TV Throne is reasonable - interleaved swords with some used to reinforce and tie together the construction. It definitely could hold a human, and, seeing it's bottom heavy, would be stable. Painting one? I am sorry, that mess would disintegrate in seconds, raining swords all around and ending Targaryen dynasty right there.

Also, work time. 59 days? I am sorry, what they did for so long? Freshly forged all the swords? The throne looks like it took week, tops, with breaks, unless GRRM really says dragons can melt hundreds of tons of steel for two months straight so it could be worked upon. By Targaryen smiths, no less, seeing normal blacksmith would be cooked by that much steel heated to glow in seconds. Huh?

Conclusion: there is rule of cool, and there is Star Trek writers math literacy level (see also Wall, Harrenhall, and several other quite damning pieces for other examples).

[Purple]

Why must the throne made of swords be made exclusively out of swords? Why can we not assume that there is an actual iron throne underneath there that the swords are welded onto? That would make far more sense in terms of structure and yet would be impossible to discern for an observer if the swords are layered right on the outside.

[Elheru Aran]

...a good sword is 2 kg? No. 1 and change. You have to get into the really heavy ones to hit 2 kg, like big two-hand swords.

Take this one: http://www.kultofathena.com/product.asp ... 7%27+Sword

That's only around 1.8 kg, if Google's calculator is correct. Borderline, but as you can see, it's a big sword. No, your average normal-sized sword would only be around 1 to 1.5 kg, depending on size and how well it's made.

As for the Iron Throne... meh. It's a bit of piffle. Certainly they *say* it's made of swords, but I'd be okay with assuming some smart smith just stuck a few iron pillars in there to hold the whole shebang up and the sword thing is just Rule of Cool.

[Lord Revan]

tbh the throne (at least the TV one) could be largely hollow and still look like that

[Elheru Aran]

What's *really* silly about the Iron Throne (TV version) is you can see the hilt wraps on a lot of those swords. Leather and wood can survive dragon-fire? Must be some tough cows in Westeros...

[TheHammer]

What's *really* silly about the Iron Throne (TV version) is you can see the hilt wraps on a lot of those swords. Leather and wood can survive dragon-fire? Must be some tough cows in Westeros...

Well the idea that the throne was made entirely by melting swords via dragon-fire is probably more legend than reality. Even if it was partially created by dragons, there were no doubt blacksmiths that did the finishing sculpting to create the symmetrical look.

GRRM's imagining certainly looks like it could have been created from randomly melting swords.

[GuppyShark]

HBO's set designers probably have a pretty good idea how many 'swords' were used.

[Sea Skimmer]

Logical thing to do to me would be to weld pegs onto the swords in hidden locations, then use the pegs to pin some swords to others, and the rest onto a frame. Then use dragon fire and or whatever the hell some carefully placed wire to melt everything a tad to make it merely look like it was all fused together.

Both designs would easily allow that, and even if the giant one would still be very heavy it would hardly be beyond the limits of what a solid foundation could hold. You'd just have to assemble it on site, but like that would stop anyone crazy enough.

What's *really* silly about the Iron Throne (TV version) is you can see the hilt wraps on a lot of those swords. Leather and wood can survive dragon-fire? Must be some tough cows in Westeros...

They look grey though in that picture, couldn't that just be the result of making actual metal swords with sculpted metal hilts? I mean its only a matter of money, they don't need to be balanced for combat, and I think money need not apply to the logic of this very much.

[Simon_Jester]

If it's just about the number of swords, well, the minimalist figures for how many soldiers the Targaryens killed in their conquests almost have to run up to ten thousand or more, plus many other soldiers who surrendered on the field. The Field of Fire alone saw the Targaryens break an army of over fifty thousand men.

So they certainly would have had enough weapons to melt them down and make a throne out of them.

[LaCroix]

There was definitely a lot of refining work done, as there are stairs in the artwork leading to a seat.

It is pretty much necessary that the dragons heated up the heap to weld them,as there is no way to heat that monstrosity in a forge... And without a modern arc welder, a dragon is the second best thing.

They had a heap of swords and let the dragon spit fire on it, then more swords were thrown onto it, some properly placed, (e.g. for structural reasons, the stairs, and later, the seat), and the dragons did the welding in between the craftsmen arranging the stuff...

I can very well imagine the king sitting on his dragon, getting that idea to make this huge iron throne, and commanding his men to bring him more and more swords until that thing was done, while the embedded blacksmiths of his army were frantically trying to keep that thing from collapsing as the king laughed and drank.

[Elheru Aran]

What's *really* silly about the Iron Throne (TV version) is you can see the hilt wraps on a lot of those swords. Leather and wood can survive dragon-fire? Must be some tough cows in Westeros...

They look grey though in that picture, couldn't that just be the result of making actual metal swords with sculpted metal hilts? I mean its only a matter of money, they don't need to be balanced for combat, and I think money need not apply to the logic of this very much.

Sculpted metal hilts only really happen very late in IRL history-- Renaissance period or so-- because they'd throw off the weight of the sword just too much. Making swords *specifically* for the throne would defeat the narrative they were setting up and make them look like they were cheesing their way out of actually using a few thousand swords.

[Zixinus]

It could be argued that the hilt-bits were added to make the swords more recognizable (in-universe that is). They are already changing and modifying them for aesthetic purposes. They had the time and they clearly planned the whole thing.

A question: is it mentioned anywhere why the thing hasn't rusted away into nothingness by now?

I can very well imagine the king sitting on his dragon, getting that idea to make this huge iron throne, and commanding his men to bring him more and more swords until that thing was done, while the embedded blacksmiths of his army were frantically trying to keep that thing from collapsing as the king laughed and drank.

Actually, I imagine the whole process to be a "seemed like a great idea, is actually very tedious and boring". Remember, it took two months to make it happen. I actually imagine the king having difficulty controlling the dragons to spray fire in a specific location and amount, with a team of blacksmith with specialist tools struggling to piece the damn thing together piece-by-piece while having to constantly argue how to put it together to make it fit whatever aesthetic idea the king has.

[Elheru Aran]

A question: is it mentioned anywhere why the thing hasn't rusted away into nothingness by now?

*shrugs* Magic? Kings dropping greasy food all over the place during feasts? Generations of servants very carefully keeping it oiled? It's one of the biggest symbols of dominance over the Six Kingdoms. It also hasn't been there all that long-- only 300 years or so. We've got furniture and such still sitting around from far longer ago than that.

[Elheru Aran]

Missed the edit window, so here:



From: http://thomasguild.blogspot.cz/2013/02/ ... chair.html

A folding chair from the 1400s, so... oh... 600+ years, easy. And wood, at that. Even if it rusted, such a hulk of iron and steel (and quite possibly some Valyrian steel in there-- if they weren't smart enough to pick those out of the mess before wasting them on the throne-- unless they used them as structural components) would take a LONG time to be seriously damaged. Of course that depends somewhat upon local conditions at King's Landing... humidity and atmosphere can have an effect. Anyway, there's all kinds of reasons why the Iron Throne could have lasted 300ish years. Rust is the least of the concerns, honestly-- constructing a throne out of a pile of swords is quite another question...

[LaCroix]

It could be argued that the hilt-bits were added to make the swords more recognizable (in-universe that is). They are already changing and modifying them for aesthetic purposes. They had the time and they clearly planned the whole thing.

A question: is it mentioned anywhere why the thing hasn't rusted away into nothingness by now?

It's not unusual for hand-forged metal to be rust resistant, if not polished/ground. If steel is heated to welding heat and let cool, the outer layers are decarbonized/oxidized and create a black/grey layer that is surprisingly rust resistant - as it is already oxidized to hell and back. So if you leave these parts alone, and have them sheltered from the elements, like in a throne room, it is very likely that it will hold up for ages. Churches did display swords and parts of armor hung above the graves of some knights buried in shrines, and many of these are still pretty much in useable shape, just from being suspended in air inside the church for centuries.

So as long as they take care of the parts of the throne that are touched and stepped upon, the rest would hold up pretty much indefinitely.

[madd0ct0r]

Hell, even if it was outside in the rain having highway salts dumped on it over the winter the loss is measured in fractions of mm a year. Rust loss is often localised and looks worse then it is (because the rust is larger then the steel it replaced). There's thousands of hundred-150 year old iron/steel bridges around the UK.

As for throne volume, don't think about foam, think about loosely packed swords welded only where they touch each other. Like the dragon breathed them hot and a smith struck it with a hammer to spot weld it on.

If it was cast as a solid lump of iron, differential thermal cracking would have ripped it apart as it cooled.

[Irbis]

If it's just about the number of swords, well, the minimalist figures for how many soldiers the Targaryens killed in their conquests almost have to run up to ten thousand or more, plus many other soldiers who surrendered on the field. The Field of Fire alone saw the Targaryens break an army of over fifty thousand men.

Problem here: it was earlier medieval period. Even in current, late medieval period with 300 years of peace to build up weapon stocks, less than 10% of warriors uses swords. See force Tywin took to Castamere - nearly 4500 men, only 400-500 knights. Rest were bowmen, spearmen, axemen. Read, cheap levy infantry.

And that is in richest lands around - Dorne for example uses spears exclusively, so they both use "spears" as metonym for soldier, but their nobles use them too (see Prince Red Viper). 330 years earlier the issue had to be even worse, and I wouldn't be surprised if 1000 swords was gathered after literally scraping the bottom of the barrel.

...a good sword is 2 kg? No. 1 and change. You have to get into the really heavy ones to hit 2 kg, like big two-hand swords.

Um:

2 kg per sword is actually overestimation, but let's keep it to be conservative.

[...]

I tried to use realistic numbers, and come up with 1.2 million swords needed to make what GRRM dubs "good" Iron Trone.

That's exactly what I said? Besides, if we use 1kg, even show Throne jumps to 92% empty space?

A question: is it mentioned anywhere why the thing hasn't rusted away into nothingness by now?

For same reason why hundreds of years old artefacts left in the open didn't? You don't need magic, we did that in real life too.

As for throne volume, don't think about foam, think about loosely packed swords welded only where they touch each other.

Small issue here - when we approach figures like 85% empty, it means you need 6-7 swords worth of space between each blade. Since that is obviously not the case, you need even more empty space inside. At some point, this space grows so large its structural integrity begins to become a problem, especially after 300 years. Unless that dragon was very good in dedicated point spot welding.

[madd0ct0r]

weight of a sowrd as 2kg, density of iron as 7870kg/m3. gives a volume per sowrd of 0.000254m3, in a funny shape that dosen't stack neatly.

the throne is clearly not cast as a monolithic block. your assumption that it is 2m3 is over estimating it's volume hugely. Like a normal chair, I would expect the entire area under the seat to be hollow, and the 'solid' steel skirt and back to be maybe 5cm thick and 30% voids.

[Purple]

We all know no one is actually capable of building this thing entirely out of swords. From an engineering standpoint that just won't work. Even if the thing stands up to use, which is debatable you won't be able to construct it with any sort of shape or beauty.
What you need to do is first and foremost take a no thrills metal chair. Than you need to take a set of long metal girders and construct a skeleton for the throne. Than weld all that into place. Once that's done you attach cross beams and the like to serve as attachment points for swords and weld those into place. Than and only than you add the swords. If you did things right up to this point all you really need to do is have craftsmen position a later of swords and tie them down with rope. Than have the dragon melt them into place (conveniently burning the rope away) and repeat this for as many layers as you want.

[Irbis]

Remember, it took two months to make it happen. I actually imagine the king having difficulty controlling the dragons to spray fire in a specific location and amount, with a team of blacksmith with specialist tools struggling to piece the damn thing together piece-by-piece while having to constantly argue how to put it together to make it fit whatever aesthetic idea the king has.

You know, the image of Throne taking two months to make not because it was long or difficult job, but because main actor didn't wanted to cooperate and give too much or too little flame in wrong spots causing smiths to curse as they had to redo the whole work again and again is probably best explanation for "epic" construction time

Logical thing to do to me would be to weld pegs onto the swords in hidden locations, then use the pegs to pin some swords to others, and the rest onto a frame. Then use dragon fire and or whatever the hell some carefully placed wire to melt everything a tad to make it merely look like it was all fused together.

Ok. Let's assume there is a frame inside. It can't be too thin because Throne base is actually small pool of molten metal and if sword "cover" was too thin it wouldn't be a throne, but an ottoman. But that just highlights the issue I had in OP - if, despite thick sword layer, indicated by both thick back and heavy sides of seat, you had to use framing, it means even 1000 swords was no nearly enough.

This means GRRM supposed request to add "there is just 200 swords" line into TV series even more sad, as he goes for minimalism where one is not only not needed, but counter-productive. Hell, even casual counting of sword points in the back would produce close to hundred, and that's just visible from one side. Someone who insists there was just 200 swords in all simply can't count, IMHO.

Both designs would easily allow that, and even if the giant one would still be very heavy it would hardly be beyond the limits of what a solid foundation could hold. You'd just have to assemble it on site, but like that would stop anyone crazy enough.

With giant one, even if it was perfectly empty, you'd need at least tens, if not hundreds of thousands of swords, vastly more that seven kingdoms had back then. You'd also think it would be mentioned in grandiose legend of hot king defeated his enemies: "And then he gathered five dozen thousand swords, and cast them like a chaff unto fire". The fact it doesn't makes big throne impossible. You can't go around it with clever sword placement, even if you put a thousand swords into flat 2D plane they would be still smaller than this monstrosity.

Then, I am still very sceptical of big throne having any durability, even if they had the required colossal pile of swords. Even with pegs and some solder, we're talking about random open flame welding, something I very much doubt would hold tens of tons of steel together. You'd need visible big frame outside, one inside simply wouldn't have enough grip.

density of iron as 7870kg/m3

Steel is denser. 8 tons per m³ is good middle ballpark for easier calculation.

your assumption that it is 2m3 is over estimating it's volume hugely

What? If anything it's overly conservative. Block 1.4 x 1.4 x 1 m (if you fold back into base, though it's much, much thicker than your 5 cm estimate) comes to exactly 2 m³. Plus, as I noted in OP, even if there is 1 m³ empty space inside, Iron Throne with just 1 m³ volume will be 75% empty on top of that. It should be full of holes then, but it isn't.

[madd0ct0r]

steel, also known as iron with some carbon and other impurities in it, is denser then iron? oh dear.
Still, it's less then 2% difference, so let's take 8000kg/m3 as an easy number.

the volume is the kicker here.
looking at the photos of the show's one, there's clearly lots of small gaps along the lines of sowrds and between them and a honking big few holes in the front beneath the seat. I also agree with purple that there'd be an iron frame under it that the sowrds (some bent to shape) were strapped to.




Ok, so lets go with 10% voids in the 'solid' parts. That's a conservative underestimate. Don't believe? Stuff a jar with toothpicks and measure how much water you can still add.
lets say your estimate the of the throne back is 1.4m by 1.4m is correct. I count 6 layers of swords visible in it, and if each blade is 8mm thick, that gives us 48mm. Call it 50mm
(incidentally, I think the throne back is much thicker then 50mm, but that's it's mostly air between outer layers of blades. A good smith would have gone for a spaced arrangement for the same reason modern engineers do. Iron at the center of a beam does very little)
Volume of the back is 1.4by1.4by0.05 which is 0.098m3, or 784 kilos of steel.

Lets ignore the contribution of the underlying frame.

Lets say the seat of the throne is at 0.5m above the floor. Let's further say it's 0.5m square (larger then most seats).
The seat looks to be an interlacing of blades, so that's a 2 layers of blades, or 16mm. You want the max number of sowrds right? so lets round that up to 20mm.

The splayed out diagonals at each corner are a nice touch - it looks like a giant flat sheet was made of blades, it was placed on a rectangular stone the size of the seat, a second smaller one placed above to hold them in place and the dragon heated the lot until the steel sagged and folded like a cloth. There's some cool as shit chairs available that use a similar method, sans dragon: http://www.valentinagw.com/portfolio/th ... air-clear/

So let's say it was actually a big sheet of interlaced steel blades 1.5m by 1.5m and 20mm thick that make up the seat and sides of the throne.
Volume of that is 0.045m3, or 360 kg of steel blade.

Total weight = 784+360=1144kg
Take off 10% for the obvious voids and you have 1030 kg. Divide by 1.5 kg per sword (i'm not counting bits that'd get burnt off) and you get 685 swords.

Pare back my conservative assumptions and increase the % of voids to a realistic level of 20% or more and you might be able to get down to 200. Easily if you include an iron chair within the iron throne.

GRMM has no idea, but your starting volume was wildly wrong.

[Simon_Jester]

If it's just about the number of swords, well, the minimalist figures for how many soldiers the Targaryens killed in their conquests almost have to run up to ten thousand or more, plus many other soldiers who surrendered on the field. The Field of Fire alone saw the Targaryens break an army of over fifty thousand men.

Problem here: it was earlier medieval period. Even in current, late medieval period with 300 years of peace to build up weapon stocks, less than 10% of warriors uses swords. See force Tywin took to Castamere - nearly 4500 men, only 400-500 knights. Rest were bowmen, spearmen, axemen. Read, cheap levy infantry.

And that is in richest lands around - Dorne for example uses spears exclusively, so they both use "spears" as metonym for soldier, but their nobles use them too (see Prince Red Viper). 330 years earlier the issue had to be even worse, and I wouldn't be surprised if 1000 swords was gathered after literally scraping the bottom of the barrel.

[Rolls eyes]

OK, now you're gratuitously underestimating things to support a bad conclusion with made-up evidence.

While spears, maces, and so on were certainly common medieval weapons, it's not like "only the elite use swords." We have plenty of examples of low-status foot soldiers using swords in the novels and the TV show. So your ridiculous, farcical claim that after defeating the combined armies of a set of kingdoms that have fifty or a hundred thousand soldiers total (if not more), Aegon I would have 'at most' a thousand swords available is... well, ridiculous and farcical.

What, are you seriously saying that only two percent of soldiers in Westeros were armed with swords?

...a good sword is 2 kg? No. 1 and change. You have to get into the really heavy ones to hit 2 kg, like big two-hand swords.

Um:

2 kg per sword is actually overestimation, but let's keep it to be conservative.

[...]

I tried to use realistic numbers, and come up with 1.2 million swords needed to make what GRRM dubs "good" Iron Trone.

That's exactly what I said? Besides, if we use 1kg, even show Throne jumps to 92% empty space?

A chair is mostly empty space. Look at a chair some time. Notice how much empty space there is under the legs?

Also note that your figure of 1.2 million swords indicates that the Iron Throne would need to be made out of, oh, at least 1200 tons of steel. That's enough steel to make a couple of dozen battle tanks, enough steel to make a WWI destroyer (or two).

Given that steel has a density of around 8 kilograms per liter, that's 150 cubic meters of steel. A solid steel cube 5.22 meters on a side.

I would argue that that's grossly out of line with any reasonable estimate for the bulk of the Iron Throne, even if we go with the huge lopsided thing portrayed here.

I suggest you recheck your calculations.

[Zixinus]

On the bit of prices of medieval sword:



Short version: swords were like any other commodity, their prices and quantity fluctuated with the market. The best swords possible to make are always going to be only available to the elite, but there is still space for less-expensive good swords (say, made out of iron rather than steel) and old, usable swords being available.

Plus there is the fact that after the conclusion of a battle pretty much in all history, surviving soldiers would go out and loot dead enemies. Easily imaginable that more common soldiers would loot enemy blades. This wasn't a free-for-all, this was an organized effort that was one of the tasks of the leaders. Even then, there is bound to be decent swords to be given out for commoners.

[LaCroix]

Steel is denser. 8 tons per m³ is good middle ballpark for easier calculation.

I wouldn't think that it is still steel after being welded over and over again in dragon fire. Medival swords have been examined and did usually have an average carbon content of around 0.4 %, equivalent to C40, but with lots of impurities and uneven distribution, some parts as low as 0.25%. After repeated uncontrolled heating to welding temperature and the resulting spark firework as the carbon ignites, you can pretty much assume that each of those blades is now either mild steel or wrought iron.

[Eleas]

Plus, if you lived during the Hansa age, there was always the option to buy a fighting-knife (which could easily be the length of a sword). It would still be a knife and thus far less durable in combat, but if you didn't have the means to get a proper sword, a fighting-knife would do you, and it could be priced at a fraction of what a sword would cost.