Wake Vortex Effects due to Horizontal Crossing at Any Angle

The effects of wake crossing at any horizontal angle, airspeed, and altitude are considered, focusing on crossing at cruise speeds at altitudes close to the tropopause. The roll effect is considered in two cases: 1) specification of the aileron deflection as a function of time that exactly compensates for the rolling moment induced on the crossing aircraft by the wake of the leading aircraft so that the crossing aircraft is undisturbed; and 2) in the case when the available roll control power is not sufficient to compensate completely for the wake induced rolling moment, the resulting roll rate and bank angle of the crossing aircraft are calculated as a function of time. The distinction between the two cases is made by a safe separating distance or safe separating time: beyond which, roll compensation 1) is possible; and below which, rolling motion 2) is unavoidable. Besides the roll acceleration, roll rate, and bank angle for the roll axis, the effects of wake crossing are also considered for the vertical axis, including the load factor, vertical velocity, and altitude change. The theory applies to any pair of aircraft and indicates the dependence on aircraft parameters, flight, and atmospheric conditions.