Setting limits on the size of Roshar (the planet) and Roshar (the continent)

[Everstorm]

Hi,

 

While trying to uncover the secret location or Urithiru, I found myself totally at a loss about the size of Roshar and the relative distances between places. This is most probably because most characters so far have been confined in specific areas, and the book doesn't really deal with travel in the way some other books do (LotR, NotW, aSoIaF to name a few). So I decided to try and look for clues in the book which may help me set at least a few limits on the size of the planet and the continent.

 

The first and most solid clue that we have is the gravity on Roshar.

g_Roshar = 0.7 * g_Earth.. (I'm not sure where we know this from, since I've only been a fan for about a year, and it has been on the stormlight wiki for at least that long)

 

Now in a simplified model g is related to the size of the planet by the formula

g = G*M/R²  = G*d*V/R² = G*d*4*pi*R/3 where G is Newton's constant, d is the density of the planet and R its radius.

 

So constant multiplicative terms aside, the acceleration due to gravity should be proportional to d*R. If you look at the densities of the terrestrial planets in our solar system, most of them seem to have a pretty typical value, that of around 5.5 g/cm³ , If we assume Roshar to have the same density, then that would mean that its radius is 0.7 times that of Earth. However, I think Roshar is likely to be a tiny bit denser if anything, given that it seems to have a sandy or soily crust only on about a sixth of its area (Shinovar) and seems to be made of solid rock everywhere else (which is presumably denser). If it is denser, then that would mean that its radius is smaller than 0.7 times that of Earth. 

 

In any case, the point I'm trying to make is that we can safely say that Roshar has at max 0.7 times the radius of Earth. This would put its circumference at 28000 km. 

 

Our next, and to the best of my knowledge, only other clue about distances in Roshar is the following epigram  from WoK Ch 39.

 

“Within a heartbeat, Alezarv was there, crossing a distance that would have taken more than four months to travel by foot.”

 

So we know that there are two places on the Roshar continent that are far enough apart that it takes four months to travel by foot. Now one Rosharan year is 1.1 Earth years, and has 10 months. So 4 months would be about 0.4*1.1*365 earth days ~ 120 days. I assume if you're traveling on foot, you'll walk for at least 9-10 hours at a leisurely pace of 5 km/h. So that would make a total distance covered in 4 months of 120*5*10 =6000 km. Now this might seem like a small number compared to the circumference of 28000 km quoted above, but to put things in perspective, that is the approximate distance between Geneva and Mumbai. So that's at least  how wide Roshar (the continent) is in one dimension, assuming Alezarv whoever he was had to travel across the continent to get wherever he got to. 

 

The original motivation of this study was to check if Roshar the continent covers most of the planet, because that would put more weight into the idea that Urithiru was somewhere in Shinovar, and westward in the place nearest to honor is actually pretty near the Origin of Storms which is in the East. After all these calculations, I don't think I can say anything either way. Alezarv may have travelled within Alethela, in which case the continent could ver well span Roshar, or he could have crossed the entire breadth of Roshar in which case over half the planet is as yet unexplored in the novels. As they say in academia, no result is still a result, and while I may have been unsuccessful in pinpointing the location of Urithiru, at least we have a better idea of how big Roshar really is.

 

In case there is some more information available about this (WoB etc.) please let me know. I think both these questions (how big is the Rosharan continent in comparison to the planet, and how big is it in absolute terms) are really fascinating, so if any of you get a chance to ask Brandon, I'd be really grateful if you did!

 

 

[QuantumHarmonix he/him]

Couldn't you use the scale on the map of Alethkar to figure out the size of the continent?

[Aminar]

What unit does it use? Miles? KM? Something specifically Rosharan. The other side of things is the size of the shattered Planes. Bridge runs seem to take hours, with long bouts of running that don't make a lot of sense with the plateau sizes seen on the drawing.(Even if half the section seen has established bridges.

[Everstorm]

Couldn't you use the scale on the map of Alethkar to figure out the size of the continent?

 

As Aminar mentioned, that map doesn't have scales, nor have any standard units been mentioned in the book. They have their own system for months, weeks etc which is different from ours, so I don't know if we can assume if their miles are the same thing. Moreover, the (nice) thing about Roshar is that almost everything is in units of 10, and our miles are not defined that way, so it seems unlikely that they will be the same. 

[Aleksiel]

Guys, this is fictional. Don't obsess on every little detail. How big is the planet, what's the acceleration, the gravity... Really?! This isn't sci-fi.

 

First, let me apologize for being rude – it was not my intention, though I totally get when I reread my post that is does sound too harsh. I’m sorry.

 

Now, allow me clarify what I thought, but didn't write.

 

I think it’s nearly impossible to measure this, because there are too many assumptions needed for the calculation. When I wrote about the details, I was actually referring to the second part of the post where the math is based on one of the Heralds saying

 

 

crossing a distance that would have taken more than four months to travel by foot

 

 

We have no clue what distance an average rosharian is able to travel by foot per day. What is their average speed? Is it really 5 km/h? Most alethi are either soldiers or farmers, which means the average alethi is pretty build up with unknown height. Yes, there were some comparing between different nations’ height in the book, but we don’t know what that means. Is the average person 1.6 meters tall or rather 2.0? This changes very much the pace they will able to keep for hours. How much time does the average person need to rest? Are 5 hours of sleep enough or is it more like 10? This changes how much time per day they travel. And what does ‘4 months’ mean – is it more like 3.5 or is it just less than 5?

 

These are but details, yet they change all calculations and it’s nearly impossible to not get at least one of these wrong (because there simply isn't enough and precise data, which is what I meant when I wrote ‘this isn't sci-fi’).  I didn't mean to imply that it’s in any way wrong or whatever to do such calculations (after all, I was think what a chull's skeleton looks like and how crazy is that?), only that I think it’s highly improbable to get the distance even roughly right. 

 

Again, my apologize to anyone who felt offended. I hope now my opinion is clearer and contributes to the topic. 

Edited February 2, 2014 by Aleksiel

[Everstorm]

Don't obsess on every little detail. 

Allow me to quote JD (from Scrubs) on this one.

[Iredomi]

Guys, this is fictional. Don't obsess on every little detail. How big is the planet, what's the acceleration, the gravity... Really?! This isn't sci-fi.

I upvoted you just so I could neutralize the downvote you had been given. But comments like these are both unhelpful and unneeded. Especially on a site such as this. The forums should be a safe place to all where they can obsess however much they like over Brandon's works. I know you probably didn't mean to be as harsh as it seems but please ask yourself next time, "Is what I'm posting adding anything to the discussion ?" and act accordingly. Thank you.

[Morsk he/him]

The gravity on the planet could be very important. Can you have a normal earth atmosphere at 0.7 G? (edit: It seems you can. Venus has really high atmospheric pressure with less gravity than Earth. I don't know how that works.) I also find 500-day years suspicious, and wonder if the orbit is unnatural too. So things like this are very interesting.

Edited February 2, 2014 by Morsk

[Natans he/him]

The gravity on the planet could be very important. Can you have a normal earth atmosphere at 0.7 G? I don't know, but if you can't, Roshar's atmosphere is magic. (edit: As a bonus, it gives an explanation for why Atmospheric Pressure is a surge. I've always felt it was weird.) I also find 500-day years suspicious, and wonder if the orbit is unnatural too. I was trying to come up with a theory that the Weeping is the power of the Highstorms being diverted, once a year, to maintain whatever unnatural changes Honor and Cultivation made to keep the planet habitable. So things like this are very interesting.

 

It was a shard that created Roshar, wasn't? If so he kind had the power to mess around a bit, let's say making the planet take 500 days to orbit the sun just because he liked he multiples of 5. =)

[Morsk he/him]

It was a shard that created Roshar, wasn't? If so he kind had the power to mess around a bit, let's say making the planet take 500 days to orbit the sun just because he liked he multiples of 5. =)

There are limits though, if they still want humans to live on it. Spinning the planet faster will lower air pressure. Moving its orbit so it matches 500 days will change the climate. But with air pressure and gravity magic, they could put the planet anywhere, with any length days and years, and use magic to fix the side-effects.

[Aether he/him]

It was a shard that created Roshar, wasn't? If so he kind had the power to mess around a bit, let's say making the planet take 500 days to orbit the sun just because he liked he multiples of 5. =)

It was presumably Adonalsium, and not a particular Shard, that created the planets of the Cosmere:

 

Fire Arcadia

You have said before that all the planets had their names before the arrival of the Shards. Is Roshar the planet's name before the Shards arrived?

Brandon Sanderson

Yes.

FIRE ARCADIA

How do the Roshar natives know the name of the Cosmere?

BRANDON SANDERSON

RAFO

<source>

[PeterAhlstrom he/him]

Four Roshar months is 200 Roshar days. Also, the radius calculation doesn't look right to me at all.

 

But yes, we do think about this kind of thing.

 

You should see my equirectangular and azimuthal equidistant map projections. Except you won't, not anytime soon.

Edited February 2, 2014 by PeterAhlstrom

[+eveorjoy she/her]

Four Roshar months is 200 Roshar days. Also, the radius calculation doesn't look right to me at all.

 

But yes, we do think about this kind of thing.

 

You should see my equirectangular and azimuthal equidistant map projections. Except you won't, not anytime soon.

 

Will we get to someday?

[EvilKetchupCow he/him]

earth has about 8765.81 hours in a year. Roshar year is 1.1 times longer so 9642.391 hours.
500 days in a year so 19.284782 hours in a day.

If we assume that Roshar also has daylight half of the day that leaves 9.642391 hours of walking to do a day.

 

If we take out and hour to setup camp and hour to take camp down that puts us at 7.642391 walking hours a day.

 

It seems that the lower the gravity the slower we move as well(http://jp.physoc.org/content/528/3/657.full)

 I don't have a proper calculator with me to do the full calculation so I'm just going to go at 4.5 km/h for now.

so that is  7.642391*4.5=34.3907595 km a day. So that puts us at about 6878.1519 km in 4 months(with estimated speed)

or 7642.391 KM using 5 km/h.

 

If we assume .5 hours to setup camp and .5 hours to take camp down that is

7778.1519 km (at 4.5 km/h)

8642.391 (at  5 km/h)

Edited February 2, 2014 by EvilKetchupCow

[Everstorm]

Four Roshar months is 200 Roshar days. Also, the radius calculation doesn't look right to me at all.

 

But yes, we do think about this kind of thing.

 

You should see my equirectangular and azimuthal equidistant map projections. Except you won't, not anytime soon.

Thanks! I think I missed that piece of info. Could you tell me what's wrong with the radius calculation? I went over the calculation again, and I couldn't find anything wrong with it. I think everything other than the density and the volume (and thus the radius) is constant in the equations, so unless the density of Roshar is different from that of Earth the numbers should match. If I calculate the radius of the Moon by the same method (assuming gravity of the Moon to be a sixth of that on Earth), I get 

 

g_moon /(d_moon*R_moon) = gearth/(d_earth*R_earth)

 

0.16/ (0.6*R_moon) =  1/R_earth

R_moon = 0.16*5/3 = 0.27*R_earth= 1728 km.

 

Google gives a number of 1737 km. 

 

Is the density of Roshar different from that of Earth? Because that's the only reason I can think of why the numbers won't match. 

 

So, taking into account that 4 months = 200 days, Roshar is at least 10000 km in one direction. That's huge! It definitely covers half the planet, and might very well cover more of it! I would really love to see the equidistant and azimuthal map projections! Could you also confirm if the maps shown in the book are the maps of known Roshar or all of Roshar? 

[EvilKetchupCow he/him]

Could you also confirm if the maps shown in the book are the maps of known Roshar or all of Roshar? 

If we assume Hoid's story to Kaladin is true than the maps would be of known Roshar

Edited February 2, 2014 by EvilKetchupCow

[Everstorm]

If we assume Hoid's story to Kaladin is true than the maps would be of known Roshar

I don't remember this actually, could you remind me which chapter it is in?

[EvilKetchupCow he/him]

I don't remember this actually, could you remind me which chapter it is in?

I don't have the book with me, but I know it happens before the battle of the tower.

Basically a King builds a boat that can withstand highstorms and sends it off in search of what caused the desolation's. They land on an island near a whirlpool after taking damage.

[Everstorm]

Oh yeah now I remember. So unless the story is apocryphal, there definitely seems to be uncharted territory on Roshar.

 

[cem he/him]

Brandon actually talked about whether there were other landmasses on Roshar before.

 

http://www.theoryland.com/intvmain.php?i=977#63

FireArcadia
Does the world map in the Way of Kings show all of the landmasses of Roshar? Does that make the continent on Roshar a Pangaea-like supercontinent? And as I think about it, are there tectonic plates on Roshar?

Brandon Sanderson
It is a supercontinent. I won't say there is NOTHING out there, but (unlike Scadrial) there is not another full continent. Plate tectonics are not a factor on the supercontinent.

Edited February 2, 2014 by cem

[Epicrandom]

WoB is that Roshar is the only major landmass/continent, but other smaller islands certainly exist.

[TomR]

Okay, assuming you have a ratio of 2 different g's, and d is equal, you can assume the ratio of r will be the same as the ratio of g.  Higher if d is lower, lower if d is higher.  That's simple substitution, and it makes sense.  The only potential problem is interpreting the travel time:

 

I assume if you're traveling on foot, you'll walk for at least 9-10 hours at a leisurely pace of 5 km/h. So that would make a total distance covered in 4 months of 120*5*10 =6000 km. Now this might seem like a small number compared to the circumference of 28000 km quoted above, but to put things in perspective, that is the approximate distance between Geneva and Mumbai. So that's at least  how wide Roshar (the continent) is in one dimension, assuming Alezarv whoever he was had to travel across the continent to get wherever he got to. 

 

We live in a world of paved roads and interstates and machine transportation.  But pre-20th century Earth, and presumably Roshar, is a different beast.  

 

First, the travel may not be in one dimension; it's very unlikely that the destination would be e.g. directly west.  Instead, it'd probably be south- or northwest.  Let's assume the second city is southwest of the first.  Existing roads may not even follow the hypotenuse, so you'll have to go south, then west, then south, then west again.  Even the idea of two straight arms is optimistic, as roads are likely to curve around any big hills or waterways.  When the roads do leave you with no choice but to trudge up those hills, without machine transportation, that's slowing you down from your 5km/h.  Speaking of which, roads aren't paved, they'll be cobbled at best.  When they're plain dirt and stone, they can be uneven, or pitted, or washed out, so again, you may be going slower than 5km/h.  Finally, without modern infrastructure, there may not be as many roads in the first place, necessitating zigzagging.  For instance, with a city southwest of your starting point, the only roads available may take you farther south than you need to go, so you have to then go north again to make up for it.  

 

Plus, saying a trip requires four months of travel by foot doesn't necessarily mean travel every day.  Ask anyone who's hiked the Appalachian Trail or biked cross-country-- barring those trying to set records, you take breaks, or you break down.  That's not even taking into account the weather, which again without machine transportation is a bigger problem than on modern-day Earth.  And on Roshar especially, weather is a big deal.  Stormwardens are a recent thing, and if you're on foot you want to make sure you can take shelter from a Highstorm.  If there hasn't been a Highstorm for a while when you have a lot of open space coming up, you might wait around in a town another day or two for it to roll through just to make sure you have enough time to get to the next town safely.

 

All that's to say that the continent may not be 10,000km across.  But yes, it's still probably very big.  8,000-9,000km wouldn't surprise me.  However, I wouldn't think it covers most of the planet.  Just most of one hemisphere

Edited February 2, 2014 by TomR

[Everstorm]

I actually checked a few links before that post as to how long it took couriers in Ancient Egypt to travel some x distance and they actually went much faster than 50 km / day. For just general travelers, it was as much as 30 km/day. But I reasoned that if the speaker is actually making a comparison about how fast it takes a man to travel on foot he would definitely not be talking about the slowest denomination, but about the average (or the fastest), hence I decided to stick to 50 km/day (Also 5 km/hr is not really fast at all, it's more like an average speed). I think 30 would be a conservative estimate, and because an analogy isn't likely to be about the slowest possible speed, I think 50 is probably a good number too. 

 

I agree with your point that the travel is probably not in a straight line, but then, the journey that the speaker is talking about is also probably not coast to coast .

 

Also, I think my original calculation and EvilKetchupCow's calculation make much more sense than assuming 10 hours of travel in a 19 hour day, so around 6000-7000 is probably a better estimate.

[dyring]

hmm. Nasty marching that.

 

Remember my 40 km marches with full equipment in the military. That is not something you do without getting seriously tired. I doubt anyone would reach much higher then that. Atleast not unless you have set waypoints(inns or such) so you dont need to carry any supplies.

 

And just cause its say 400 km´s as the crow flies, that does not mean its just 400 km´s as you walk. roads are seldom perfectly straight, and there are hills up and down wich not only makes it harder, but adds distance too.

 

As for length of year and day, length of day might be an issue, to quick rotation would throw the atmosphere away, but its not that much faster then earth. I dont have the exact numbers but that sounds resonable.

 

Time around the sun is viable with any climate changes. Climate is mostly due to the tilt of the axle, wich roshar lack(so no major summer/winter temperature variations)

Time to rotate a lap around the sun, Im a tad tired here but unless I´m overlooking something, all you need to to is twiddle abit with the mass of the planet and the sun it revolves around, and you could speed up/slow down a planet in its orbit without needing to move it cloer or further away from the sun to add length to the year.

[QuantumHarmonix he/him]

As Aminar mentioned, that map doesn't have scales, nor have any standard units been mentioned in the book. They have their own system for months, weeks etc which is different from ours, so I don't know if we can assume if their miles are the same thing. Moreover, the (nice) thing about Roshar is that almost everything is in units of 10, and our miles are not defined that way, so it seems unlikely that they will be the same. 

I just noticed that the map scale doesn't have units. I wonder if that is a misprint or done on purpose to stop these types of calculations. Given the preference of the shards to make multiples of 10 I would probably assume it was supposed to be kilometers, but that is a big source for error.