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Units and Armies have a certain number of Movement Points to spend each turn. An Army's Movement Point is equal to the lowest value from its Units. So Armies move at the speed of the slowest Unit they contain. Each Movement Point allows a Unit or an Army to cross a single Tile of open terrain. Difficult terrain costs more to cross, and some actions consume some or all of a Unit’s Movement Points.
Moving on Land[]
Rivers[]
Rivers consume all of a Unit’s remaining Movement Points to enter, and Units in Battles get a Combat Strength penalty while standing on a River Tile. This debuff is applied to either the Unit is attacking or defending. Moving up or down the same River, only costs 1Movement Point, regardless of the Terrain Type of the Tiles that are crossed. If a Road or District is built on top of a River Tile then the Unit no longer needs to spend its remaining Movement Points to enter it.
Roads[]
All roads set the movement cost of the terrain to 0.5, regardless of its type.
The first road infrastructure is unlocked with the Wheel technology. This technology automatically creates roads from each of your Cities to their immediately adjacent Outposts.
The road system can be extended with the Supply Lines technology in the Early Modern Era. This upgrade automatically creates roads between Outposts of your Empire.
After the Civil Engineering Technology Highway effect all roads only cost 50%Movement Points. (This effects is not shown on the in-game tooltips.)
Railroad[]
The Steam Engine technology in the Industrial Era unlocks the Train Station District, which can provide railroads between territories. To connect two neighbouring territories with rail, you need to build a Train Station in both territories. Then the Train Stations automatically generate rails towards neighbouring Train Stations. Rails allow travelling instantly from one Train Station to another at the cost of 1Movement Point. If another player's Army stands on one of the Train Stations or the connecting tracks, it blocks the movement through this station or track; the movement effects for the player's Units will be unavailable until the other Army moves away. Both peaceful and hostile player Units will block the movement effects.
Fortifications[]
Entering an enemy fortification will require the entering Unit to start its turn next to the walls, and the Unit must spend all of its Movement Points climbing over them. Mounted Units, like the Cavalry and the Heavy Cavalry Units, are unable to climb Fortifications. Inside the walls (between fortified tiles) the Units not suffering any movement penalties. To allow mounted Units to enter fortified tiles first the walls have to be breached by Siege Weapons or a bombard Unit.
Cliffs[]
Cliffs are impassable borders between two Tiles on account of the Elevation difference being greater than a single unit.
Moving in Water[]
Embarking / Disembarking[]
Units only can Embark on Naval Transport class ships. These types of Units replacing the land Units when they enter any water tiles. The Trade Expeditions is the first technology, which unlocks the first Naval Transport Unit, the Transport Galley. To Embark, or to Disembark, a Unit must not have spent any Movement Points this turn and doing so consumes all the Unit’s Movement Points. Embarking onto or Disembarking from a Harbor only costs 1Movement Point, however.