Final answer:
The pilot must use vector analysis to combine the airplane's airspeed with the wind speed to determine the direction of bank necessary to compensate for crosswinds. They must adjust the heading to ensure the resultant groundspeed vector aligns with the runway. During banking, the lift force is manipulated to create a horizontal component that allows the plane to turn.
Step-by-step explanation:
To determine the direction of bank from an attitude while considering crosswinds, a pilot must use vector analysis to combine the velocity of the airplane relative to the air with the velocity of the wind. Firstly, one must establish a coordinate system with the x-axis parallel to the intended direction of travel (e.g., parallel to the runway). The plane's airspeed vector and wind speed vector are then drawn, taking into account their directions.
For a crosswind situation, the combination of the wind vector and the airplane's velocity vector relative to the air will create a resultant groundspeed vector. The pilot must adjust the plane's heading so that this groundspeed vector aligns with the runway direction. This often means the pilot has to aim the aircraft into the wind to some degree, a maneuver called 'crabbing.'
During a banked turn, the lift generated by the wings is separated into vertical and horizontal components. The lift force helps the airplane to turn, with the horizontal component providing the necessary centripetal force for the turn. The angle of bank is chosen to provide the required centripetal force for the desired turn radius and airspeed.
The consequent velocity vector will also indicate the appropriate angle (relative to north or another reference direction) the pilot must maintain. This angle is essential for counteracting the crosswind effect and will be different from the airplane's actual path over the ground. Ultimately, the aim is to reach a point where the airplane's ground track is parallel to the runway, securing a safe landing. Any last-minute adjustments will depend on wind variability and the need to align the aircraft wheels with the runway.