Related topics:
Uncoordinated flight will effect all aircraft types, not just a Bearhawk. However because the Bearhawk has a remarkably powerful rudder these effects may be more noticeable.
Fuel System
Uncoordinated flight (ball not centered) can significantly impact the fuel system, resulting in uneven fuel burn from each tank, fuel transfer from one tank to another in the direction of the ball, and possibly fuel starvation. See the above links for more details.
Fuel Cap Vents
If trouble-shooting a fuel transfer or uneven fuel burn issue, be aware that a blocked fuel cap vent will exhibit similar symptoms.
Heavy Wing
One factor that may make it difficult to fly the aircraft with the ball centered is if it has a "Heavy Wing". This can be caused by mounting more hardware in one wing than the other, for example a Magnetometer, Landing Light etc. When weighing the aircraft, it may show up as more weight on one of the main wheels than the other and may be amplified due to the long arm if items are mounted outboard on the wing.
Steady Heading Side-slip
In the case with a heavy wing (or a rigging error), the ailerons may be continually deflected a small amount to keep the wings level. Due to more drag from the down-going aileron, when flying wings level there will be yaw to that side, known as a Steady Heading Side-slip. It may also result in continual fuel transfer if the ball is not centered, or a continual small change of heading.
Sight Gauges
Sight gauges need to be read with the ball centered. If the ball is not centered, the sight gauges may indicate uneven fuel quantities, even if the fuel tanks contain exactly the same quantity of fuel. This can lead to the pilot selecting what they perceive to be the fullest fuel tank in an attempt to balance fuel, and can lead to unintended consequences.
These effects are discussed in detail at the above links.
