UPDATE The formula has changed as of the March 2011 patch, it is now
(city population * 1.1) + (capital population * .15) - 1
for each city connected to the capital, not including the capital.
- The Machu Pichu wonder increases the modifier by 20%, to
(city population * 1.3) + (capital population * .15) - 1
.
- Arabia increases the constant by 1, to
(city population * 1.1) + (capital population * .15)
(thanks WillfulWizard).
The economic overview also gives a far better explanation of how it is calculated - in other words, this question is now trivially solved by simply looking at that economic overview :)
Original answer below.
Okay, I did a bit more testing, and bwarner's answer is almost accurate:
Each city, excluding the capital, provides (city's population * 1.25) + 0.01
gold per turn. Owning the Machu Pichu wonder increases the modifier by 20%, to (population * 1.5) + 0.01
, for all the cities.
The capital does not provide any gold.
The 1.25 and 0.01 can be seen in the Assets\Gameplay\XML\GlobalDefines.xml
file:
<Row Name="TRADE_ROUTE_BASE_GOLD">
<Value>1</Value>
</Row>
<Row Name="TRADE_ROUTE_CAPITAL_POP_GOLD_MULTIPLIER">
<Value>0</Value>
</Row>
<Row Name="TRADE_ROUTE_CITY_POP_GOLD_MULTIPLIER">
<Value>125</Value>
</Row>
The economic overview also demonstrates these values.
I couldn't find any other factor which affects these values, and I checked different difficulty levels, different distances between cities, different city route type (road vs railroad, road/railroad vs harbor), different city health and whether it is occupied. Looks like it's solely the population.
It isn't as simple anymore. There's a number of things to think about
Initially your cities will only be able to access the tiles next to them. It will take a long time before your cities are generating enough culture on their own to add many tiles, unlike earlier civs where it was quite easy to boost to a full 2 square radius. So if you need a particular resource, you should either build next to it or be prepared to buy access to the tile.
Once a tile has been claimed, you can't "steal" it like in Civ 4 (except using the Great Artist in the base game, or Great General in the G&K expansion). So you want to make sure you establish your borders quickly before another Civ or city-state grabs those tiles.
Building additional cities causes increased unhappiness across your empire, and it also makes it more expensive to adopt social policies. So while spamming cities early will help you establish a large territory, it will penalize you in other ways.
So while the technical answer is that you maximize your potential territory without gaps or overlap by leaving 6 hexes between cities (since the maximum radius for a city is 3 hexes), I think you will find that blindly following that will be a sub-optimal strategy.
This is one of the systems in Civ 5 that is not necessarily more complicated, but certainly seems to be more strategic than it was in earlier civs.
Best Answer
There is no penalty for building a city far away, though it does pose some hardships in practice:
It takes longer to move troops from one city from the other, which can be critical at times.
Moving airplanes and missiles between them requires special naval units, unless you have friendly cities in the middle.
Creating a trade route between them can take longer and be more expensive, see this related question on road maintenance cost - though this can be mitigated if they are both coastal cities, or close to other coastal cities, as you can read in this question which explains the trade network.
It takes longer to get the settler there in the first place - those are turns wasted on moving a fragile settler around instead of starting a city.
It takes longer to move workers and great people from one city to another, meaning more turns in transit (while still paying unit maintenance costs) and less turns doing useful stuff.
If you try to build a spaceship, and you build the parts in distant cities, it takes longer to move them back and they must be carefully guarded - spaceship parts are very lucrative units to destroy.
I think point (1) is the most important one. I've had enough instances where my distant cities came under siege and I could not reinforce them in time; I now try to expend slowly, though I admit it's sometimes very hard to resist building a city when coming upon a great location.
Point (3) is also very important but can usually be mitigated by just covering the long distances with the help of coastal cities.