Directional Stability: Yaw Plane (Yaw Moment, N)
Directional stability can be compared to longitudinal stability but it occurs in the yaw plane (i. e., the XY plane about the Z-axis), as shown in Figure 12.4. By definition, the angle of sideslip, в, is positive when the free-stream velocity vector, V, relative to aircraft is from the right (i. e., the aircraft nose is to the left of the velocity). V has component aircraft velocities u along the X-axis and v along the Y-axis, subtending the sideslip angle в = tan-1(v/u).
The V-tail is subjected to an angle of incidence (в + a), where a is the sidewash angle generated by the wing vortices (like the downwash angle in longitudinal stability). Static stability criteria require that an increase in the sideslip angle, в, should generate a restoring moment, Cn, that is positive when turning the nose to the right. The moment curve slope of Cn is positive for stability. At zero в, there is no yawing moment (i. e., Cn = 0).
Yaw motion invariably couples with roll motion because neither is in the plane of symmetry. In yaw, the windward wing works more to create a lift increase while the lift decreases on the other wing, thereby generating a rolling moment. Therefore, a pure yaw motion is achieved by the use of compensating, opposite ailerons. The use of an aileron is discussed in the next section.