Turns are costed as follows:
– 45 degree turns by troops that are unmanoeuvrable or out of command range cost 4 AP except on bridges and in heavy fortification squares.
– Turns of between 46 and 90 degrees cost 8 AP
– Larger turns cost the unit’s full starting AP.
Any turn required to reach the chosen square in a Move order is costed similarly. Note that only the angle between the original facing and the line between the starting tile and the final position is taken into account, so that sometimes a unit can make multiple twists and turns along the way that are not costed. This is particularly true of AI units, which use a different route-finding algorithm taking into account terrain preferences.
The route they take may sometimes include multiple changes of direction, but as usual, only the overall angle between the original facing and the line between the starting tile and the final position is taken into account. This may appear to favor the AI, but in fact, they end up moving to the same final position that they would have reached using the direct route if they were a player unit.
All this means that most non-light foot troops cannot turn more than 45 degrees and also move in the same turn. Most non-light mounted troops can turn 90 degrees and still move a square or two, but use their entire movement allowance to turn 135 or 180 degrees.