## Sparta 101: Doing the Math - coordinates, distances, travel speed and -duration

Understanding the SWOE (Sparta: War of Empires) map layout as well as its coordinate system is rather straightforward if one views this whole topic as an experiment in grade school Euclidian geometry. Remember geometry, that part of math wedged in with algebra which you were sure you would never again need as long as you live (unless you were prepping for calculus on the nerd-fasttrack :-)? Well, here it’s back to haunt you.

Map Layout

The SWOE map is plotted onto a coordinate grid, x-values running from left to right and y-values from top to bottom. The exact centre of the map is located at x=0 and y=0:

Note than both x and y values may be positive or negative depending on the direction. and y values increase from top to bottom, which takes a moment getting used to since classic charts and plots will most often have y increasing on an upward pointing axis, but that’s how it is).

Currently, the map extends some 2,000+ units in each direction, with new cities (a.k.a. new players) being added in the suburbs (go to “Map”, then “Regional Map” to get a better sense of where your city is located in respect to the map centre and the pantheons where the real action is :-).

All cities, emporia, Persian positions, capitals, and so on, will always show specific coordinates such as (1094, -623) with the first value being the x-, the second value the y-coordinate. By the way, when you see a coordinate x,y pair somewhere in this game, chances are it is clickable, for example in reports or at the top of personal messages, taking you to the selected target on the map.

Distances

All distances in SWOE are expressed in miles, each grid unit equal to one tenth of a mile. Had we two cities with the same y-coordinates for example, calculating the distance between these two would be trivially simple:

Subtract one x value from the other (in whatever order), then remove any minus sign and multiply by 10. In the above case the two cities are 3.393 units apart, therefore 339.3 miles distant. The trouble of course is that most locations do not do us the favour of being on the same x or y axis, but look rather something like this:

Pythagoras' theorem

It seems only fitting that we turn back to the old Greeks to solve our little problem. If you recall the Pythagorean theorem, it explains how to get the length of the hypotenuse (c) if we know the lengths of the other two sides (a, b) of a right triangle.

… which, as luck would have it, is exactly what we need to find the distance between two cities (or other locations):

Doing the Math

Let us first rename our parameters a bit to make it simpler:

… where x is the difference between source and target x values. y the difference between source and target y values and d the distance between the two points. Therefore:

x = x[1] - x[2] (where 1 is the source and 2 is the target location)

y = y[1] - y[2] (where 1 is the source and 2 is the target location)

Therefore d² = x² + y².

After removing any negative signs that might result, calculate the square root of d² , divide by 10 and you’ve got your distance in miles. If you are using a spreadsheet application such as Excel or Google Sheets, the formula would look something like this:

=SQRT(POWER(ABS(x[1] - x[2])) + POWER(ABS(y[1] - y[2])))/10

(here you can find a small Google Sheets example)

If we refer to the last example above, then the math would look like this:

Speed

Discovering the speed for galleys carrying troops, resources or agreements can be a bit tricky since the net speeds will always depend on boosts, academy scrolls, building upgrades, coalition membership and other variables, but it becomes simpler if one first differentiates between two basic types of transport:

- Transporting goods such as resources and agreements
- Transporting troops to a destination (as in raids, sieges or reinforcements)

Transporting goods

The base speed of a galley transporting goods is 48 mph. If we return to our example above, then that trip would be logged with a duration of 10:21:38 (497.3 at 48 mph). Later in the game, you will be able to build the lighthouse, allowing you to increase the speed of these galleys. At level 11 for example, the Lighthouse will add 22% to your base transport speed, which would now change our trip duration in the example above from 10:21:38 to 8:29:32 (497.3 mi. at 58.56 mph).

Transporting troops

Calculating the speed and duration of a troop transport relies on other parameters, mainly the unit speeds. Each unit has an assigned base speed, with stronger, more advanced units generally offering higher speeds than basic ones; check the penultimate value on the details sheet of any unit to see what it has to offer.

A swordsman for example has a base speed of 6 mph, a Carthaginian Horseman 30 mph. The speed of a mixed troop transport will always depend solely on the speed of the slowest unit, therefore sending 20 horsemen and 50 swordsmen will result in a speed of 6 mph.

Coalition Transports

Depending on the type of transport (troops or goods) there are many ways available to speed up these trips, such as studying academy scrolls and building a lighthouse, but that is a subject for a future post; the most important consideration when sending transports should be at least mentioned here: travels between members of the same coalition are increased by a factor of 24, therefore a trip which would commonly take 12 hours is cut down to half an hour, making trades, reinforcements and other transports possible, even if the coalition member is 600 miles away.

Hope this helped a bit, please comment if you have a question or have found an error.

Cheers