[OB] Dimensions of Urithiru

[king of nowhere]

With a volume of one third of cubic km, it's some 300 millions cubic meters. If we give everyone a room that is 10 square meters in size and 3 meters high (it must include walls and supports) then it can house 20 million people. that's not the whole roshar population, but it's a fair number.

As for supporting, the thickness of ceilings does nothing there, because the ceilings are not supporting the weight of the structure. In fact, you'll want them as thin as possible. What supports a structure like that are pillars and looad bearing walls. There must be enormous ones scattered around the structure. However, when building pyramid-like, you can go very high, provide you set a wide enough base. So urithiru looks like a building that can support itself easily. It has been calculated that, if there was the will and money to do so, we could make skyscrapers up to 20 km high with current technology, if we used a large enough base. We could also make a skyscraper going all the way to geostationary orbit, but the base would be about one third of the planet's surface. I read all  that stuff while reading about space elevators, but it's not directly on wikipedia's space elevator page, so I can't quote you an exact reference

[Ray7455]

Just a quick correction to your assumption about the size of the Oathgate platforms.  In Chapter 86 of Words of Radiance, during Dalinar's PoV

Quote

The plateau everyone was crowding onto was relatively small, by the scale of the Shattered Plains—but it was still several hundred yards across.

That makes it sound like it's around 300 yards across, meaning an area of about 70 thousand square yards, which gives each person a lot more space than the story makes it sound like they have.  It is possible, however, that because of everyone getting onto the plateau from the same spot, across a single bridge, they were not spreading out very well and sticking mainly to just one side of the platform, especially since no one would want to be near the edge in the middle of those storms.

[Ansalem]

1 hour ago, Ray7455 said:

Just a quick correction to your assumption about the size of the Oathgate platforms.  In Chapter 86 of Words of Radiance, during Dalinar's PoV

That makes it sound like it's around 300 yards across, meaning an area of about 70 thousand square yards, which gives each person a lot more space than the story makes it sound like they have.  It is possible, however, that because of everyone getting onto the plateau from the same spot, across a single bridge, they were not spreading out very well and sticking mainly to just one side of the platform, especially since no one would want to be near the edge in the middle of those storms.

I think they were definitely bunching up around the center, because remember they were thinking that it would be like a portal that you walk through in the middle that they were planning on rushing through.

[Overlord Jebus]

All the talk of the balconies at the top of each level stretching out further than the one below to provide sunlit balconies made me think each level actually overhung the one below it, getting thicker as it got closer to the top (As opposed to each getting thicker at the base).

I can't draw at the moment but might do later, but I always imagined it more like a stack plant pots with lids on, getting smaller near the top. Doesn't affect the height but would effect the width of the place massively.

[king of nowhere]

1 hour ago, overlordjebus said:

All the talk of the balconies at the top of each level stretching out further than the one below to provide sunlit balconies made me think each level actually overhung the one below it, getting thicker as it got closer to the top (As opposed to each getting thicker at the base).

I can't draw at the moment but might do later, but I always imagined it more like a stack plant pots with lids on, getting smaller near the top. Doesn't affect the height but would effect the width of the place massively.

If that was the case, the higher balconies would shade the lower ones. You would not gain any terrace space (wheter you go large above or below, the surface is the same) but it would be awfully inefficient. Not to mention the structural instability.

 

I think the image in the first post is a good approximation. Soomeone should show it to shallan

Edited September 18, 2017 by king of nowhere

[Overlord Jebus]

5 minutes ago, king of nowhere said:

If that was the case, the higher balconies would shade the lower ones. You would not gain any terrace space (wheter you go large above or below, the surface is the same) but it would be awfully inefficient. Not to mention the structural instability.

I thought this was why it specifically mentions the balconies are wider than the one above it.

Quote

 

each one beneath larger than the one above it to provide a sunlit balcony

 

So even though each level is wider at the top, the widest point on the balcony would not be as wide as the widest point on the balcony below it. 

And don't even get started on structural instability, that's a rabbit hole and a half.... 

Edited September 18, 2017 by overlordjebus

[Salkara]

Another interesting question about Urithuru (tangentially related to its dimensions) is its location. It's on a mountain on a planet without plate tectonics and where the continent drifts.

From my limited understanding of planetary forces, there shouldn't be a mountain this tall without plate tectonics, right? Additionally, do the mountains remain in the same place relative to the continent, or do they slowly move over millenia?

[king of nowhere]

3 hours ago, Salkara said:

Another interesting question about Urithuru (tangentially related to its dimensions) is its location. It's on a mountain on a planet without plate tectonics and where the continent drifts.

From my limited understanding of planetary forces, there shouldn't be a mountain this tall without plate tectonics, right? Additionally, do the mountains remain in the same place relative to the continent, or do they slowly move over millenia?

That's not the only mountain on roshar. Without plate tectonics, there should be no mountains at all. In fact, there should be no continent, just an endless ocean with a flat bottom.

Posible reasons are: roshar had plate tectonics but it stopped recently (in geological terms), possibly because the nucleus cooled down too much or some other reason like that.  Or a shard made roshar with mountains and everything else. considering how much shards shaped roshar, I'd be more prone to this explanation. Also considering that the shape of the land doesn't fit much with plate tectonics. In particular the mountains east of the horneater peaks and those west of shinovar don't fit much with normal orogenetic processes.

[Overlord Jebus]

Well, Adonalsium grew Roshar himself, so I imagine that's where the mountains came from.

I wonder, did he on purposely grow a mountain range that was above the storms or did it just turn out that way... Hmmm...

[ccstat he/him]

On 9/17/2017 at 5:33 PM, Ray7455 said:

Just a quick correction to your assumption about the size of the Oathgate platforms.  In Chapter 86 of Words of Radiance, during Dalinar's PoV

That makes it sound like it's around 300 yards across, meaning an area of about 70 thousand square yards, which gives each person a lot more space than the story makes it sound like they have.  

Thank you for that quote! I knew there was a description somewhere. If we assume 300 meters across, and 10 Oathgate platforms spaced evenly in a circle, the enclosed space is a minimum of 700 meters in diameter (measuring between the closest sides of opposing Oathgates), and the whole complex a minimum of 1300 meters in diameter. That requires the platforms to be barely separated from the ones adjacent to them. It scales up as you space them further apart.

On 9/18/2017 at 8:27 AM, overlordjebus said:

And don't even get started on structural instability, that's a rabbit hole and a half.... 

:-) Half the point of these speculations is to map that rabbit hole!

On 9/17/2017 at 10:38 AM, king of nowhere said:

As for supporting, the thickness of ceilings does nothing there, because the ceilings are not supporting the weight of the structure. In fact, you'll want them as thin as possible. What supports a structure like that are pillars and looad bearing walls. There must be enormous ones scattered around the structure. However, when building pyramid-like, you can go very high, provide you set a wide enough base. So urithiru looks like a building that can support itself easily

Good points. I was thinking about the ceilings functioning as horizontal beams to transfer force between the pillars, but that is only necessary if a LOT of the structure is hollow, and is probably a poor design decision using rock. I agree that it is safe to assume that there is sufficient rock in place to support itself pyramidally.

In light of this I think we could safely revise our ceiling height back down a bit. I'll wait to do that until we have another description, though.

[Jofwu he/him]

This is fantastic!

Is there anything in particular you're wondering about? I can do my best to help.

Unfortunately stone is not a common structural material. Particularly for something of this scale and particularly for anything besides walls. The strangest thing to me is the nature of the construction. It sounds like the whole thing is solid stone, as if the tower were carved rather than built. I have no idea off the top of my head how you would size a solid stone slab floor.

If it's as wide as you figure, I wouldn't be surprised if it can handle its own weight well enough. I was totally forgetting about the 0.7g. That helps a lot. To do some super basic calculations for walls we'd need to make a guess at what kind of rock we're dealing with. (i.e. numbers for the weight and compressive strength)

In general you probably don't need to worry about deep floors. You definitely wouldn't want load bearing walls to be supported in the middle of a slab. The offset of the outer wall should be manageable, and the walls support less weight there. Though I'm curious what kind of open spaces are inside. Take the cavernous area Adolin was at in chapter 2. What's going on with the roof there? I don't see how a stone slab can span dozens of meters.

The other amusing thing to me is the glass. It's a single 180 story pane of glass? Surely that's magic?

You mentioned fabrials... I know with some Surges we've seen the magic is time limited before it bleeds out. But I think it's possible tension and/or cohesion are different. And if nothing else, the tower could be soulcast in some way. So if all else fails we can say that the stone was soulcast into something with unnaturally high strength and/or light weight.

[Calderis he/him]

5 minutes ago, jofwu said:

Unfortunately stone is not a common structural material. Particularly for something of this scale and particularly for anything besides walls. The strangest thing to me is the nature of the construction. It sounds like the whole thing is solid stone, as if the tower were carved rather than built. I have no idea off the top of my head how you would size a solid stone slab floor.

Seeing as it's always apparently solid, I think the carved into the mountain itself by soulcasting the stone into smoke. 

Beyond that, I have nothing to add. All of the building experience I have is in piping systems. 

[Mulk he/him]

I'm of the opinion that it had to have been cast or created whole by Tanavast, with some detailing and personalizing left up to the Radiants.  Without heavy cranes and things of that sort, I think it would be VERY hard to create a tower like Urithiru without divine guidance and support.  Even with the use of Gravitation, Friction and the rest, it's hard to imagine a bunch of warriors suddenly being able to fine tune lashings to carry and place rock slabs weighing hundreds or thousands of tons with the precision needed to construct a tower in the fashion described.

To put it in perspective for today, the first 100-story+ building in Earth history was completed in ~1930 or so.  The oldest extant complete and LARGE structure in the world I would guess is the Great Pyramid in Giza - it's been guessed to be ~4500 years old.  We need to place that in the context of Roshar, for whom a year is approximately 1.1 Earth years according to the Coppermind wiki.  Thus, the Great Pyramid of Giza is almost as old as the time lag between Aharietam and the current Stormlight times.  As we know very little about how long the Heraldic Epochs lasted and whether Urithiru was built at the beginning or not...well, Urithiru could be anywhere from 15,000 years old (assuming 100 year lags between Desolations, which is as short as I dare make it) or as long as...perhaps 105,000 years old, if there is a 1,000 year lag between Desolations.  I'd submit it defies any human explanation for a human-contrived residence to survive anything like that long, particularly in light of the fact that it seems to be in no need of any sort of repairing.  Even if it's in a benign climate (as it seems to be), the erosion of years even without highstorms would suggest it should be ruinous, not completely whole.  If Urithiru is subject to freezing (and it should be given its relative altitude), well, that does a crap ton of damage over time.  Freezes if they are severe enough can break steel-reinforced concrete and cause trees to shatter spontaneously.

[Calderis he/him]

@Mulk which is why I think they didn't use any of those things. The mountain peak, in my mind, extended above where the tower is now, and they literally carved it out of the rock with soulcasting stone to smoke.

What is left is one solid piece with no joints at all. The interior was hollowed out of existing rock. 

[+Wax he/him]

1 hour ago, Calderis said:

@Mulk which is why I think they didn't use any of those things. The mountain peak, in my mind, extended above where the tower is now, and they literally carved it out of the rock with soulcasting stone to smoke.

What is left is one solid piece with no joints at all. The interior was hollowed out of existing rock. 

Agree... constructing something like that wouldn't be possible very easily.  As in the first post, the pyramids are shown to be tiny against this tower and Pyramids took 20+ years with a lot of slaves.

Soulcasting holes makes so much sense.

Each place got its own oathgate by elsecalling of places in full.

PS I think soulcasting plus bondsmith helped make it happen.

 

Edited September 22, 2017 by axcellence

[Mulk he/him]

I get that and it makes a certain amount of sense, explaining just about everything exceptional about it except for the lack of decay.  We don't know (at least if we do know, I haven't seen that information) when exactly the Recreance happened, but it was a long time ago, long enough that no one knows why it happened and if Urithiru was abandoned the whole time, it should be a mess.  Based on Honor's visions, I think Honor died sometime after that (no idea how long after, but I assume it was still a while ago), so maybe he kept things up until then. It could have been as recent as the time period right before Gavilar started having visions, or as far back as the day after the Recreance.

That leads to another possibility in my mind.  Did, by abandoning the Oathpact, the 9 unfaithful Heralds leave the way open for Odium to attack Honor and kill him?  Maybe his relative silence since then has more to do with the fact that he had to spend more effort fending off Odium's attempt on his life.  That part of the reason Taln lasted so long wasn't just that Odium took it easy on him - it was that Odium was spending all of his energy trying to finally get Honor out of the way, now that he had access to do so.  Therefore, the reason Taln finally broke to the point that he has a busted mind is he alone bore the full fury of Odium for however long it was after Honor died until he finally capitulated with no support from either the other nine or from Honor himself - as I would theorize part of the reason the Heralds could survive the torture is the direct support of Honor.  Maybe I should dump this in another thread...I can get a little stream of consciousness thing going when I start replying to something.

[BlackYeti he/him]

11 hours ago, Mulk said:

Urithiru could be anywhere from 15,000 years old (assuming 100 year lags between Desolations, which is as short as I dare make it) or as long as...perhaps 105,000 years old, if there is a 1,000 year lag between Desolations.

Even your smaller number is a massive overestimate. 

Quote

SHAWN M. HALVERSON (HTTPS://WWW.FACEBOOK.COM/GROUPS/270545169744383/PERMALINK/731811053617790/)

So I just got back from the book signing Brandon held today, I asked him about the time between each of the original 99 desolations.

BRANDON SANDERSON

It turns out that the number 99 in the stories was made up, and that there were much fewer of them. He also then stated that the cosmere runs along a 10,000 year gap and that Roshar falls right into the middle of the timeline. He ended with "That should give you a perspective of the timeline and events of the desolations". I figured that if anyone wanted to know a bit more of Roshar's history they might find this interesting.

 

source

So the time period from the Shattering to Mistborn Era 4 is 10,000 years.

The time from Aharietiam to The Way of Kings is ~5,000 years (4,500 years * 1.1 = 4,950 years). We know that the Stormlight Archive is currently running almost concurrently with Mistborn Era 2. 

Mistborn Era 2 is set ~300 years after Era 1. Era 3 is an unknown, but it's a much shorter period after Era 2. Let's assume 400 years between Era 1 and Era 3, and similar separation between Era 3 and Era 4. That puts Era 4 ~500 years after The Way of Kings.
Therefore the time from Aharietiam is ~5,500 years, and the time from the Shattering to Aharietiam is ~4,500 years.

From the Shattering we have to allow some time for humanity to find their way to the Tranquiline Halls and get settled in, then for Honour and Cultivation to arrive on Roshar. During which time Odium is taking out Devotion, Dominion, and Ambition. Let's say this period lasts for 500 years (probably an underestimate).

Then Odium shows up and drives humanity onto Roshar, and the Oathpact is formed.The Radiants have not yet been formed, so Urithiru probably doesn't exist yet, but let's say that Pailiah had a premonition that it would be needed (or something like that), and the Heralds built it right away.

This would mean that Urithiru is currently, at most, 9,000 years old. And it is probably a lot younger than that. I'll grant you that still makes it unbelievably ancient, but not in the tens (and certainly not in the hundreds) of millennia as you suggest.

[Mulk he/him]

was not aware of the WoB stating the 99 is made up.  Makes total sense.  As a relative newcomer to the Cosmere, I've not had time to sift through all of it or all of the multitudinous Brandon QA's and interviews.

[ccstat he/him]

So, with the quote @Ray7455 provided establishing that the oathgates are ~300m across, I generated a top-down view, including the tower of Urithiru and the oathgate complex. Given the numbers we've generated so far, the ring of oathgates has almost the same footprint on the mountain as the tower city does. That's not what I was picturing, but it's possible from the descriptions. (I've added this image to the OP.)

15 hours ago, jofwu said:

This is fantastic!

Is there anything in particular you're wondering about? I can do my best to help.

[...]

To do some super basic calculations for walls we'd need to make a guess at what kind of rock we're dealing with. (i.e. numbers for the weight and compressive strength)

In general you probably don't need to worry about deep floors...Though I'm curious what kind of open spaces are inside. Take the cavernous area Adolin was at in chapter 2. What's going on with the roof there? I don't see how a stone slab can span dozens of meters.

The other amusing thing to me is the glass. It's a single 180 story pane of glass? Surely that's magic?

Thanks! The main question that needs answering is the assumed height of each level. I know that in modern skyscrapers we fill the ceilings with air handling ducts, water pipes, other support machinery, etc. But with what amounts to a cavern with solid floors/ceilings, none of that will matter. So if we assume Rosharans are a bit taller than Earth humans due to living in 0.7g, how high would you guess each level has to be?

I ran some simple calculations assuming it was comparable strength/weight to granite, since that appeared to be the strongest rock type. But I was mostly using google and simple math, so I'd appreciate the input of someone who knows the appropriate factors to consider. 

I was sort-of assuming that Adolin's large cavern would have an arched or vaulted ceiling, with the appropriate angles/shape to not act as a simple slab. That's totally a guess, though. And yes, that full-length elevator window is unlikely, to say the least. Either the lightweavers/soulcasters worked together to simply make the rock transparent there, or I need to hire some Rosharan glaziers to do put some magical glass in my windows.

[Jofwu he/him]

2 hours ago, ccstat said:

Thanks! The main question that needs answering is the assumed height of each level. I know that in modern skyscrapers we fill the ceilings with air handling ducts, water pipes, other support machinery, etc. But with what amounts to a cavern with solid floors/ceilings, none of that will matter. So if we assume Rosharans are a bit taller than Earth humans due to living in 0.7g, how high would you guess each level has to be?

I ran some simple calculations assuming it was comparable strength/weight to granite, since that appeared to be the strongest rock type. But I was mostly using google and simple math, so I'd appreciate the input of someone who knows the appropriate factors to consider. 

I was sort-of assuming that Adolin's large cavern would have an arched or vaulted ceiling, with the appropriate angles/shape to not act as a simple slab. That's totally a guess, though. And yes, that full-length elevator window is unlikely, to say the least. Either the lightweavers/soulcasters worked together to simply make the rock transparent there, or I need to hire some Rosharan glaziers to do put some magical glass in my windows.

I can't add much to the conversation on required head space. My work is focused on industrial structures--not skyscrapers--and it's more of an architectural concern anyways. I agree with all of your assumptions there. I think 3.5m is plenty of room there.

I did some rough numbers on floor/ceiling thickness, and its easy to see why we don't use stone for this. It's not a material I'm familiar with, so I did some brief research. It sounds like 170 pcf is a reasonable weight to use for granite (120 at 0.7g). I also threw on 150 psf for loads on the floor. That's high for residential, but not unreasonable conservative I think. (Doesn't matter terribly anyways because the weight of the stone itself is more significant.) The other key number I dug up is a flexural strength of 1500 psi. What we're going to do is load up the floor slab and see how much stress it causes. We need it to be less than this number to physically work. Realistically, I think you'd want a safety factor of 3, meaning you don't exceed 500 psi.... But... For 1500 psi my calculations say you need 2 feet of stone to span just 5 feet, 5 feet of stone to span 10 feet, 10 feet of stone to span 15 feet, and basically exponentially worse from there. I saw one source saying the bending stress for granite can be up to 3 times higher than this, and the weight could be a little lower.. With those assumptions (and NO safety factor) you can span 20 feet with a bit less than 2 meters of stone. Slate looks like it can give a 25 ft span with 6 feet of rock (at its best, and with no safety factor). Now, this is all assuming a flat slab of rock spanning between opposite supporting walls. If we can thicken the floors near the walls (i.e. the ceiling drops a number of feet near opposite edges in the room below) then we can go further. But then you throw on a safety factor and we're still not in great shape. I'm personally not convinced it's very feasible unless the stone is enhanced in some way. Or unless the tower makes significant use of arches. Arches would go a long way, though I don't think there's been any mention of them so far?

Haven't had a chance yet to think about walls.

[ccstat he/him]

Thanks, @jofwu. Those numbers are really helpful for thinking through this, even if I don't know what to do with them yet. 

Just for fun, I threw together a mockup using this site. This helps me see the perspective a bit better, but I still think the other images do a better job of conveying scale.

Edited September 22, 2017 by ccstat

[yulerule]

I kept imagining the Oathgates surrounding the tower. Like 

 

I feel that also makes sense as it makes the Oathgates equidistant from the tower, thus not favoring any location.

Edited September 23, 2017 by yulerule

[ccstat he/him]

That's a possibility. There can't be any on the flat side, since that is apparently flush with a cliff, but they could be in a half-ring around the base.

The only description we have of the arrangement says "The field was ringed by ten columnar plateaus."  I can't say for sure if "ringed" suggests a circle or semicircle.

[yulerule]

To me, "ringed" suggests that they surround the tower, not that they are off away from it.

[ccstat he/him]

Yeah. The more I think about it, the more I agree with you. I'll modify the picture tomorrow.

The part that throws me off is that the oathgates are ringing the field in front of the tower. It sounds more natural to say that if they are in a circle around something, but if the whole plateau is considered "in front" and is used as a field, then your suggested arrangement makes more sense.

Edited September 23, 2017 by ccstat