Speed (travel)

Each type of unit and each type of ship have a specific speed, defining the distance (islands) that the unit/ship can reach after traveling for 20 hours. Some units travel faster than others overland. A mixed group of units or ships travels at the speed of the slowest member. Gyrocopters are the fastest unit.

Ships have different speeds, too. Warships are slower than Cargo Ships.

__NOWYSIWYG__

Formulas
The folllowing formulas give the amount of time that is necessary for ships and / or units to reach it's destination. __NOWYSIWYG__

Basic
Time to travel (in minutes) = $${ \left \lfloor \frac{ 1,200 }{ \mbox{ speed } } \times \sqrt{ ( x_2 - x_1 ) ^ 2 + ( y_2 - y_1 ) ^ 2 } \right \rfloor }$$ or Time to travel (in seconds) = $${ \left \lfloor \frac{ 72,000 }{ \mbox{ speed } } \times \sqrt{ ( x_2 - x_1 ) ^ 2 + ( y_2 - y_1 ) ^ 2 } \right \rfloor }$$


 * Notes :
 * 1) This formula is what is best use when you 1st start the game and do not have any researches discovered that can increase your travel speed.
 * 2) The result value is in minutes and seconds respectively and on both cases the seconds part is always rounded up to the nearest whole number integer.
 * 3) In the game, it is assumed that each island has a mean diameter of half the distance between 2 islands (0.5). This means that any travel attempts between the cities on the same island has a mean distance of half the distance between 2 islands (0.5). __NOWYSIWYG__

Cargo Ships
The speed of a Cargo Ship is 60 islands in 20h, so the above formulas is simplified to:

$${ 20 \times \sqrt{ ( x_1 - x_2 ) ^ 2 + ( y_1 - y_2 ) ^ 2 } }$$ or $${ 1,200 \times \sqrt{ ( x_1 - x_2 ) ^ 2 + ( y_1 - y_2 ) ^ 2 } }$$ __NOWYSIWYG__

Examples
or $${ 1,200 \times \sqrt{ ( 30 - 30 ) ^ 2 + ( 31 - 30 ) ^ 2 } }$$  =   $${ 1,200 \times 1.0 }$$   =. or $${ 1,200 \times \sqrt{ ( 31 - 30 ) ^ 2 + ( 31 - 30 ) ^ 2 } }$$  =   $${ 1,200 \times \sqrt{ 2 } }$$   =   $${ 1,200 \times 1.41 }$$   =.
 * 1) If your Cargo Ship is going from 30:30 ( x1:y1 ) to 31:30 ( x2:y2 ) (Straight line) $${ 20 \times \sqrt{ ( 30 - 30 ) ^ 2 + ( 31 - 30 ) ^ 2 } }$$   =   $${ 20 \times 1.0 }$$   =.
 * 1) If your Cargo Ship is going from 30:30 ( x1:y1 ) to 31:31 ( x2:y2 ) (Diagonal) $${ 20 \times \sqrt{ ( 31 - 30 ) ^ 2 + ( 31 - 30 ) ^ 2 } }$$   =   $${ 20 \times \sqrt{ 2 } }$$   =   $${ 20 \times 1.41 }$$   =.

or $${ 0.5 \times 1,200}$$  =. __NOWYSIWYG__
 * Note :
 * A zero distance, means that the towns are on the same island and thus the mean diameter of the island is used (0.5). This gives a time travel for Cargo Ships of $${ 0.5 \times 20 }$$  =.

Advanced

 * $${ \left \lfloor \frac { Dist \times 72,000 } { ( Speed + \left [ Speed \times SE% \right ] + \left [ Speed \times SCALevel ~ ( only ~ ships ) \right] \times Gov% ) \times ( 1 + ( Pos% + Draft% ) + Triton ) } \right \rfloor}$$


 * Dist
 * The number of Island spaces (Euclidean diatance) you will be traveling ($${ \sqrt{ ( x_1 - x_2 ) ^ 2 + ( y_1 - y_2 ) ^ 2 } }$$) or 0.5 for on the same island movements.


 * Speed
 * See the individual units / ships to get their speed, indicated by this icon.


 * SE%
 * Special Event speed increase.


 * SCALevel
 * The level of the building Sea Chart Archive. Can be [0 through #.#] for [Levels 0 through 40].


 * Gov%
 * The government form Oligarchy can increase your speed by 10% or 1.10, otherwise, the speed will be the normal speed or 1.0.


 * Pos%
 * The percentage from the activation of the Miracle of Poseidon. Can be [0.0, 0.10, 0.30, 0.50, 0.70, 1.0] for level [0, 1, 2, 3, 4, 5].


 * Draft%
 * Can be [66.4%, 49.8%, 33.2%, 16.6%, 0%] based on the amount of cargo per merchant ship [100, 200, 300, 400, 500].


 * Triton
 * Can be [0, 1, 2, 3] for [+0%, +100%, +200%, +300%].


 * Notes :
 * 1) This is the most accurate formula to use after you have learned the researches that will increase your travel speed and thus reduce the travel duration.
 * 2) The result value is in seconds and is always rounded up to the nearest whole number integer. __NOWYSIWYG__