Command: "To the right on the same ground, wheel!" Wheeling upon the center halves the amount of turning space required for the unit compared to other types of wheeling.  The wider the unit's frontage, the more space required for the wheel, especially for one other than wheeling upon the center.  Although that seems obvious to read, when on the field, enthusiasm and excitement (not to mention musket smoke) may distort the objective appraisal of space needed.

Sergeant Subtlelus says: A wheel can be used to turn the front a few or several degrees to face directly an enemy that may be approaching at an angle or already poised there.