[OB] Dimensions of Urithiru

[Jofwu]

4 hours ago, 17th Splinter said:

@jofwu that looks great! But what do the different colors mean? 

Different levels of stress. Just shared for the pretty factor. The model isn't good enough to share actual numbers and their implications. In particular, its showing von Mises stress, which I don't believe is accurate for stone. .

[17th Splinter]

3 minutes ago, jofwu said:

Different levels of stress. Just shared for the pretty factor. The model isn't good enough to share actual numbers and their implications. In particular, its showing von Mises stress, which I don't believe is accurate for stone. .

Okay. Cool

[ccstat]

This new quote from ch 15 helps a bit with the floor height question.

Quote

Radiant stood in what felt like a very stiff pose, Blade held before herself in two hands. She’d only scraped Pattern on the ceiling two or three times; fortunately, most of the rooms in Urithiru had high ceilings.

Shallan is shorter than our Alethi mains, but with Roshar's 0.7g everyone is going to be tall. Let's pretend she's 5'5" (165 cm), which is just above average for women in the USA. Pattern is "a long, thin weapon nearly as tall as she was." This means that at full extension, arms above her head, the sword would not reach higher than 3.7m, which makes that the upper limit if she's managed to scratch the ceiling a few times. It won't be much less than that if she and Adolin are both able to swing swords around mostly unimpeded.

Her room sounds typical of Urithiru, so I think we could peg the interior height as ~3.5m. Add 1m(?) for the ceiling. It sounds to me like the original guess of 4.5 is probably close. 

The OP was edited previously too adjust that up to 5.5. I'll probably revert that change if there are no objections/alternative arguments.

[+ElephantEarwax]

On 9/25/2017 at 4:10 PM, 17th Splinter said:

I think that it could be possible now that we know more about Urithiru. If Nohadon came from the side with the ring of oathgates it might have been possible. We don't know if the is a sheer cliff on every side

But in one of the first chapters they had to lower the baskets to the storms, so it seems like they had to over a cliff.

[17th Splinter]

34 minutes ago, ElephantEarwax said:

But in one of the first chapters they had to lower the baskets to the storms, so it seems like they had to over a cliff.

We know that the back side is on a cliff. So it is probably easier to lower them of that one side instead of going all the way to the other side then down a mountain to reach the storms

[Jofwu]

Bringing this back from the dead after a conversation on Discord tonight.

If you look closely on Shallan's sketch of Urithiru you'll notice a 3ish story tall Chasmfiend on the right side of the page to give a sense of scale. In Words of Radiance, Shallan was kind enough to draw a Chasmfiend with a human for scale. I could swear someone has pointed this out before, and maybe done the math, but I can't find it anywhere and I figure it should be documented somewhere. (like here) These are rough numbers obviously, but they should get us in the ballpark...

Calculating the Height

A chasmfiend is about 8 humans tall. If we figure a typical Rosharan male is about 6 feet tall that gives us a 48 foot tall chasmfiend.

Urithiru is about 68.5 chasmfiends tall. At 48 feet per chasmfiend that's 3,288 feet tall. That's right folks. Exactly 1 kilometer tall. Bravo to @ccstat (and everyone else who contributed) because this is exactly what we concluded in this thread.

That's 5.55 meters (18.2 feet) per floor by the way.

Balconies and Roof

Now the other views on this sheet are slightly different scales, so I had to do a few more comparisons between them. But here's what I came up with for the balconies, units in meters

First thing to highlight is that we misinterpreted Szeth's comments about balconies extending outward on each floor (or it was retconned). It's pretty clear that the face of each tier is relatively vertical.

Concerning the "balconies" for each tier... The final conclusion here (looking at the first post) was 50 meters per tier, which gives you 450 meters of extension from balconies. I'm getting 690, though of course that's with the lower balconies much larger than those at the top. Also worth pointing out that they seem to get a bit more narrow closer to the mountains on either side.

The "roof" has a radius of about 70 meters (diameter = 140m = 460 ft). Dalinar said it was about 100 [Rosharan] yards across. So we've got about 1.4 meters per Rosharan yard? That's 4.6 feet. Perhaps there are 5 Rosharan feet per Rosharan yard, which sounds like the kind of numbers they'd use. And then 10 inches per foot. That would make their inches about 10% longer, their feet 6% shorter, and their yards 50% longer than ours. (give or take, depending on the error in this whole process)

Oh, and not pictured here both the Oathgate platforms come to 200 meters across. This conflicts with the statement that they are "several hundred yards across", as they're only about 40% further across than the tower roof.

Farmland and living space

I measured square pixels for each floor on the plan view. These are particularly rough, but again it should give at least a sense of what's going on.

For total roof/balcony area, I'm getting 20.3 million square feet = 466 acres = 1.9 square km. Anyone know a thing or two about farming, because I sure don't. A quick Google search tells me the overall, worldwide average for humans is 0.5 acres of cropland per person. That's not good news for the Urithiru residents, because that suggests they can only support about 900 people... And that's assuming all of that area is for farming. (looks to me like there are buildings on much of it.) They've got more land to use outside the city. They can grow food in their balconies. I don't see how any of these would EVER been enough to make Urithiru self-sufficient though. Yikes.

In terms of overall space (roofs balconies plus interior space, at 18 floors per tier) I'm getting a little bit over 1 billion square feet = 24k acres = 97 square km. Burj Khalifa apparently has 3.6 million square feet of floor space, so Urithiru has about 290 times as much space. I'm also seeing that Burj Khalifa is designed for about 900 people to live in it. If we use the same ratio that would put a 260,000 cap on the population in terms of living space. I have no clue how much of that skyscraper is residential vs commercial, so I'm not sure how valid that comparison is. With Urithiru you're going to have a lot of space required for government/military, commercial, and even some light industrial work. But we're also dealing with different societies in different settings. I'm sure the Kholin barracks pack people in a lot tighter than fancy skyscraper apartments.

And that order of magnitude doesn't look completely unreasonable, right? If I'm off by a factor of four and it can fit a million people, that's London in 1800 (one of the biggest cities in the world at the time, I think) Seems like the Alethi are using most of the first two floors, right? Those account for 28% of the total area. In TWoK chapter 22 Dalinar comments that there are 150,000 troops together in all of the warcamps. So the total population of the warcamps was maybe 400,000? Is that reasonable? They took losses over the first two books, and only 8/10 highprinces moved into the tower. That would put the current population of the tower at about 300,000. If it can hold 1 million then they're using something on the order of 28%.

So when it comes to food they're in trouble. Living space will maybe work. Unless I'm missing something?

I'm ignoring the basement levels of the tower completely, of course.

Anything else that needs looking at?

[+Oltux72]

4 hours ago, Jofwu said:

So when it comes to food they're in trouble. Living space will maybe work. Unless I'm missing something?

I'm ignoring the basement levels of the tower completely, of course.

Anything else that needs looking at?

Water & sewage. You are looking at two thousand tons of water per day roughly. How many wells will they need?

[Karger]

Perhaps the stone had its density increased at the lower levels via soulcasting or Cohesion to make the tower hold itself up?

[+Oltux72]

1 hour ago, Karger said:

Perhaps the stone had its density increased at the lower levels via soulcasting or Cohesion to make the tower hold itself up?

That does not really help. It needs to be stronger, not heavier. Obviously there are mountains one kilometer high. The problem is that they are not hollow. Stone lacks in tensile strength. It would help if there were metal inside the rock.

[Calderis]

That's what the surge of Tension is for... 

[Karger]

This does imply that as a future plot point whatever is maintaining the tower's tension could be sabotaged and the entire tower could break

[Bookish Ocelot]

Given a necessity of 2000 tons of water per day, you get about 530,000 gallons. A hand pump can have an output of about 2 gallons per minute. But that assumes you're pumping really fast. In reality, it'd be around 1 gallon/minute. That's 530,000 minutes you'd need to spend pumping. You'd need 368 wells running nonstop in order to supply water. That's a lot. And a lot of time. But if you can get the rate to 2 gallons per minute, it becomes 184. If we assume Urithiru has really sophisticated pumps, with 10 gallons per minute, then you could run about 40 wells and have water left over. Anyone with knowledge on this subject please correct me. If we have an idea of water table depth that'd be helpful too. 

 

Side note: IIRC, there is a gemstone column in Urithiru mentioned in Oathbringer made of rubies, sapphires, emeralds, and garnets. These are the gems used to soulcast heat/fire, air, grain/plants, and water/non-oil respectively. 

[Wandering Investor]

1 hour ago, Karger said:

This does imply that as a future plot point whatever is maintaining the tower's tension could be sabotaged and the entire tower could break

More likely the surge of tension was used to modify the structure of the rocks, a one time change, enabling them to withstand the forces they're subjected to.

 Otherwise it would require a constant surge of fuel, which while I think it less likely, is possible and would represent a threat to the tower.

[Karger]

Just now, Wandering Investor said:

 Otherwise it would require a constant surge of fuel, which while I think it less likely, is possible and would represent a threat to the tower.

You are probably correct although watching a radiant try and keep it together by strength and stromlight would be awesome.

[Exthalion]

On 3/29/2019 at 4:08 PM, Wandering Investor said:

More likely the surge of tension was used to modify the structure of the rocks, a one time change, enabling them to withstand the forces they're subjected to.

 Otherwise it would require a constant surge of fuel, which while I think it less likely, is possible and would represent a threat to the tower.

Weren't their veins of gemstone that ran through the rock, presumably down to the storm level? Every highstorm might serve to recharge the thousands of tons of diffuse gem which could keep powering the infusion.

[Karger]

5 minutes ago, Exthalion said:

Weren't their veins of gemstone that ran through the rock, presumably down to the storm level? Every highstorm might serve to recharge the thousands of tons of diffuse gem which could keep powering the infusion.

And when Odium stops the highstorms in an attempt to crumple the tower stoneward Kadash shall keep it together by shear force of will!

[Wandering Investor]

35 minutes ago, Exthalion said:

Weren't their veins of gemstone that ran through the rock, presumably down to the storm level? Every highstorm might serve to recharge the thousands of tons of diffuse gem which could keep powering the infusion.

I believe the gemstone pillar is at highstorm level, but there is no apparent activation of the pillar and several effects of the tower remain in place (like pressure and temperature, possibly its ability to hold its own weight). So I'm not sure what the gemstone pillar actually does at this point. None of the characters make any comment to indicate there is stormlight in the gems. Renarin even attempts to push stormlight in and nothing happens.

[Jofwu]

I definitely tend to think the stone is modified by Surges to be stronger. There's a reason that mountain peaks do not typically exist with the slenderness of a skyscraper. There's a reason that kilometer high shear cliffs are very rare. Even if massive walls and clever arches can handle it's own weight, the wind forces on something at this altitude are going to be insane.

In other news...

I posted the above on Reddit as well and got the following response from Ben McSweeney (the artist behind these sketches):

Quote

If I recall rightly (it's in my notes somewhere) the height is 15' per level. Only a variance of 3', but it adds up. I feel like 17S did this same math a while back but it's probably buried by now. Could be worth digging up to compare notes though.

We do have numbers, I went to some pains to try and get the drawing to represent them correctly. Your estimates are a little high I think, and you might be discounting the amount of internal space given to non-residential function (giant elevator atrium, for instance), but I think you're in the right zone.

I'm not quite sure how those numbers fit, as I think 6 feet for the human was on the low side and this would imply an even shorter figure. Or I guess you could argue the size of the chasmfiend isn't 1:1, or... something...

In any case, Ben's word (assuming he remembers correctly) is more valid than my guessing.

15 feet as the story height would mean that all of the linear dimensions above should be 82% of what I gave, and all of the area measurements should be 68%.

[TheGhostInTheMachine]

This wob implies that roshar may have been created by cymatic vibrations, so it's not unreasonable to assume that the vibrational patterns created "perfect" structures (the dawncities).

Quote

Hoiditthroughthegrapevine [PENDING REVIEW]
So were the Dawncities, the ones based on cymatic patterns, created using a supercharged combinations of the surges of cohesion and illumination?Using cohesion to make the ground liquid and using illumination to create the frequency.
 
Brandon Sanderson [PENDING REVIEW]
You are theorizing in the right direction.

You also have to remember that much of roshar revolves around things being symmetrical. Sound waves, and waves in general have a really interesting structure and do interesting things when applied to sand-like materials.

 

My theory is that Urithiru (along with the other dawncities) is kind of like the king's drop. A perfect city, with the perfect alignment, made by supernatural forces harnessing the natural symmetry of the universe (cosmere), which allows Urithiru to have fun proportions that are just one the precipice of possibility.

 

Edited April 4, 2019 by TheGhostInTheMachine

[Calderis]

Which makes the fact that Urithiru is not symmetrical even weirder. 

[TheGhostInTheMachine]

Just now, Calderis said:

Which makes the fact that Urithiru is not symmetrical even weirder. 

Well, Kholinar is not exactly symmetrical. What I meant is more like it has a supernatural grace to it that allows it to achieve things that normal architechts couldn't.

 

My thinking is that everything in Urithiru works together, the shape of the tunnels, the layout, the types of rock, everything. Basically it comes together to make harmony (not the shard lol).

[Calderis]

My point is that the dawncities, Kholinar and the others, are a fully radial symmetrical pattern. Even if that has worn and been changed over time. 

Urithiru is not. It's half a circle. 

Edited April 4, 2019 by Calderis

[+Oltux72]

That suggests that the cities were made by fabrials controlled with cymatics. Urithiru housed living Surgebinders. They could use a utilitarian mode of thought to control their own surges.

[dvoraen]

On 3/30/2019 at 5:06 PM, Exthalion said:

Weren't their veins of gemstone that ran through the rock, presumably down to the storm level? Every highstorm might serve to recharge the thousands of tons of diffuse gem which could keep powering the infusion.

I suspect it will depend on the nature of the Sibling and the Cognitive reflection of the tower.  With ten Oathgate platforms, there is most likely those ten platforms sitting in the Cognitive Realm, but the gemstone pillar could partly exist in the Cognitive Realm in its own way as well, or the Sibling could exist in both the Physical and Cognitive and draw it from a Cognitive highstorm directly.

[EggArdent]

Its always amazing too me to look back and see how accurate people where before there was anything confirmed and I cant wait to read RoW and see if anybody in this thread theorized correctly, I'm especially looking forward to seeing what the pillar does and if it helps support the structure of the tower.