I need help calculating the area of a region for my fantasy setting.

[S@tanicoaldo]

I need help calculating the area of a region for my Alice through the looking glass.

The thing about me is that I'm bad with numbers. Realy baaaad with numbers, like I can't calculate 6+7 on the fly.

I'm Dming a Alice through the looking glass game and for those who don't know Alice through the looking glass is all about chess.

In my setting there is a region where the red and white armies clash called "the eternal battlefield" it's basically a chess board between the two kingdoms.

A player of my group keep asking me what's the total area of the region and I really don't know how to calculate it.

Picture a chess board and now each square is about the size of the state of Arizona or another more square shaped state of the USA.

How large would the total area of the board be?
https://upload.wikimedia.org/wikipedia/commons/thumb/9/92/Map_of_USA_with_state_names_2.svg/440px-Map_of_USA_with_state_names_2.svg.png
https://cdn4.vectorstock.com/i/1000x1000/52/68/chess-board-without-chess-pieces-vector-1765268.jpg
Whould the size be too big? What would be a better size?

Also, the objective of the group is to become a queen by reaching the end of the board, how long would such trip take?

Thanks.

[factotum]

There are 64 squares on the board. If each square has the same area as Arizona, then the total board area is 7.3 million square miles; each square is approx. 337 miles across, so to get from one side of the board to the other (assuming you start in the middle of the second row, as a pawn normally would, and end in the middle of the last row) would be a journey of a smidgeon over 2000 miles. How long a trip of 2000 miles takes depends entirely on the method of transportation--if you're trying to *walk* that, then I'd say about a month and a half, assuming you're walking for 16 hours a day and only stop to sleep.

As for it that's too big, only you can answer that, since you created the world this is set in! For comparison, this chessboard is about twice the total area of the USA, which seems pretty darned large to me.

[Peelee]

As for it that's too big, only you can answer that, since you created the world this is set in! For comparison, this chessboard is about twice the total area of the USA, which seems pretty darned large to me.
Or roughly the size of the US and Canada.

Or a just about the size of Alaska and Russia.

Or just about the size of two and a half Australias.

Sorry, i just wondered how big some places were and found a few that also fit pretty close. It does seem to be a bit big, but maybe OP wants big.

[Bucky]

I think maybe you should calculate the other way around.

1) Declare how long it takes to walk across one square. You're the worldbuilder, so you can just decide this and make the rest of the numbers fit it.
2) Multiply that by marching speed (use the book rules, or 40 miles per day if there are none)
3) Square that to get the area of a square.
4) Multiply step 3 by 64 to get the whole area of the chessboard continent.

If you do step 1, the forum can handle the rest.

[Brother Oni]

How long a trip of 2000 miles takes depends entirely on the method of transportation--if you're trying to *walk* that, then I'd say about a month and a half, assuming you're walking for 16 hours a day and only stop to sleep.


2) Multiply that by marching speed (use the book rules, or 40 miles per day if there are none)

2000 miles in 6 weeks is 47.6 miles a day.

Those are some really high numbers considering you're walking over 1.5 marathons a day while carrying load. While I can see you keeping that pace for a few days, anything more than that is impractical without daily healing magic to heal up exhaustion and injuries.
While I agree a small group would travel faster than an army, it's not that much faster.

That said, if you want to assume that the heroes are at the peak of human performance and can travel rough terrain while loaded as easily as a athlete on a paved road, then the world ultramarathon record is 101.5 miles in 12 hours on road.

[jayem]

Or roughly the size of the US and Canada.

Or a just about the size of Alaska and Russia.

Or just about the size of two and a half Australias.

Sorry, i just wondered how big some places were and found a few that also fit pretty close. It does seem to be a bit big, but maybe OP wants big.

Which kind of makes sense, Arizona's what I think of as a 'average' sized state, and 64 is pretty close to 50. So you'd expect it to be about USA sized (rather than say Britain sized or World sized).

My idea of an average state is based on looking at the map which puts less weight on the smaller ones (I'm not sure what type of average it would be). And of course area goes as the square, so when I think Arizona's slightly on the big side but close enough. So not surprised by a factor of 2.

And similarly to take about 7 times the length of time it takes to cross Arizona.

[S@tanicoaldo]

Ok yeah, that's much too big, what would you guys suggest to make it more reasonable sized but still making each square fairly big?

[Grey_Wolf_c]

Ok yeah, that's much too big, what would you guys suggest to make it more reasonable sized but still making each square fairly big?

As said above, start from the conclusion and work backwards: how long do you want it to take for an army to cross from one side to the other? Or how many people you want involved? Or anything else that is of a practical nature to the story you want to craft. We can work backwards from that. Otherwise, I'm not sure how we can figure out what is "reasonable" to your story, I'm afraid.

GW

[Tvtyrant]

I would chime in that 20 miles is about how far people on foot in a sedentary society could go to regularly, 60 is as far as they are likely to go and come back home. With a cart 20 miles is a day and change, or a day on foot. Then you stay the night where you go and can head back on day 3. 60 miles is several days travel, stay there for a fortnite and come back.

The reason this is important is travel time dictates city locations. A big city-state has a 60 mile radius of territory (Athens, Sparta, Genoa, etc) and then territories accessible by water. A small city-state has closer to a 30 mile radius. These are the regional markets.

Big cities aren't regional markets but global ones, or administration centers. So if you have a village every 10 miles, a town every 30 miles, a small city every 120, and 1 big city per big region you basically peg down medieval and antiquities structure. Manors can be swapped for villages and castles for towns in fortress orientated areas.

[jayem]

To go down an order of magnitude, England is divided into between 40-80 counties. (these roughly correspond to a days easy travel, except as you get further out)

Arizona is divided into 15 (clearly the counties are bigger).
France gives both having about 16 "regions" (depending on time) and 96 departments.

So you could have an smaller intermediate stage with French/Low Countries/Germany/An expanded Switzerland. Or 2*2 block of states (Midwest for a bit larger, Mideast for a bit smaller).

Or for a bigger intermediary pick quarter of the US (there isn't really a simple bit of Europe the right size), and divide each state into 4 (half each way).

[halfeye]

So if you have a village every 10 miles, a town every 30 miles, a small city every 120, and 1 big city per big region you basically peg down medieval and antiquities structure. Manors can be swapped for villages and castles for towns in fortress orientated areas.

For England, this is seriously wrong. There are hamlets every mile or two or maybe in some cases three here. It probably varies somewhat in different regions, but it's what I remember from before I moved to a city.

Consider this region: Spoilered for large image. The black and white bits on the bottom and top edges are approximately miles but the ones along the sides seem to be something else. Thanks to Bohandas for spotting that.
https://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Chew_Valley_Map.png/1920px-Chew_Valley_Map.png

By No machine-readable author provided. SFC9394 assumed (based on copyright claims). - No machine-readable source provided. Own work assumed (based on copyright claims)., CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=914291

https://en.wikipedia.org/wiki/Chew_Valley

[Bohandas]

Are the squares euclidean?

[halfeye]

Are the squares euclidean?

Good catch, it seems the bottom and top are approximate miles, and the sides aren't. There is a scale in the key, but the font is tiny on my computer and difficult to read.

[Tvtyrant]

For England, this is seriously wrong. There are hamlets every mile or two or maybe in some cases three here. It probably varies somewhat in different regions, but it's what I remember from before I moved to a city.

Consider this region: Spoilered for large image. The black and white bits on the bottom and top edges are approximately miles but the ones along the sides seem to be something else. Thanks to Bohandas for spotting that.
https://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Chew_Valley_Map.png/1920px-Chew_Valley_Map.png

By No machine-readable author provided. SFC9394 assumed (based on copyright claims). - No machine-readable source provided. Own work assumed (based on copyright claims)., CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=914291

https://en.wikipedia.org/wiki/Chew_Valley

A Hamlet is not a village. There are 14 parishes in Chew Valley, which are administrative units built around village sized settlements.

A village is a settlement of at least 100 people, usually larger, where a hamlet is the next size up from a thorp.

[Peelee]

A Hamlet is not a village. There are 14 parishes in Chew Valley, which are administrative units built around village sized settlements.

A village is a settlement of at least 100 people, usually larger, where a hamlet is the next size up from a thorp.

You gave a definition for a village, then compared a Hamlet to a thorp with no way to relate either to a village. I am displeased with this geography lesson.

Also, I vote we make the OP's landmass a non-orientable surface and call it a day.

[Tvtyrant]

You gave a definition for a village, then compared a Hamlet to a thorp with no way to relate either to a village. I am displeased with this geography lesson.

Also, I vote we make the OP's landmass a non-orientable surface and call it a day.

Hamlet is a term that in England means a group of houses too small to have a church or any administrative purpose. It is a lot like a farming neighborhood, 6-7 houses put together. It used to also be built around a single purpose, so a mill, a manor or a lumberyard could all have a hamlet.

A thorp I had been led to believe is just a few houses, but it appears it is just a germanic phrase meaning Hamlet.

[Elanasaurus]

Then you stay the night where you go and can head back on day 3. 60 miles is several days travel, stay there for a fortnite and come back."Fortnite"! Someone's got video games on the brain!
:elan:

[factotum]

For England, this is seriously wrong. There are hamlets every mile or two or maybe in some cases three here. It probably varies somewhat in different regions, but it's what I remember from before I moved to a city.


It varies according to terrain. If you look at the Pennines you'll see that settlements are far further apart, mainly because they tend to follow the valleys and passes while the peaks and moors are left uninhabited.

[halfeye]

It varies according to terrain. If you look at the Pennines you'll see that settlements are far further apart, mainly because they tend to follow the valleys and passes while the peaks and moors are left uninhabited.

I wouldn't be in the least surprised if that's true, but 10 miles between nearest villages still seems far too far to me.

[Knaight]

Big cities aren't regional markets but global ones, or administration centers. So if you have a village every 10 miles, a town every 30 miles, a small city every 120, and 1 big city per big region you basically peg down medieval and antiquities structure. Manors can be swapped for villages and castles for towns in fortress orientated areas.

It really depends on the region - look at the distances between the Hellenic city states (several of which were big cities), and the nearest city state is often closer to 30 miles than 120. The Hanseatic League cities were also packed more tightly, as were the large Italian city states, as were the large Japanese towns, etc. Meanwhile the Arabian Peninsula was generally a lower density than this, as were the city-analogs in the Mongol empire, etc. Some places get settled much more tightly than others, with rough and forest heavy terrain likely to get settled a lot more densely than large steppes or plains, which are still likely to get more settled than deserts. On top of that coastlines are generally likely to get settled more densely with port cities.

[Tvtyrant]

It really depends on the region - look at the distances between the Hellenic city states (several of which were big cities), and the nearest city state is often closer to 30 miles than 120. The Hanseatic League cities were also packed more tightly, as were the large Italian city states, as were the large Japanese towns, etc. Meanwhile the Arabian Peninsula was generally a lower density than this, as were the city-analogs in the Mongol empire, etc. Some places get settled much more tightly than others, with rough and forest heavy terrain likely to get settled a lot more densely than large steppes or plains, which are still likely to get more settled than deserts. On top of that coastlines are generally likely to get settled more densely with port cities.
I don't disagree. There is going to be a lot of variation in practice, as well as differences in nomenclature (the part of that quote you took out includes me acknowledging that small city states in Greece had smaller catch basins).

For instance I would generally expect a few hundred miles between major cities, but sometimes it can be much less (Cairo and Alexandria) or much more (Constantinople to Kiev).