General Solution of the Wind Triangle Problem and the Critical Tailwind Angle

A general analytical solution of the navigational wind-triangle problem and the calculation of the critical tailwind angle are presented in this study among other findings. Any crosswind component will effectively create a headwind component on fixed course tracks. The meaning of a route track is lost with excessive crosswinds representing the bifurcation point between the possible and the impossible navigational solutions. Any wind of constant direction and speed will effectively reduce groundspeed and increase time-of-flight on closed-loop multi-segment flights. Effective wind track component consists, in general, of true and induced components. The average groundspeed of multiple-leg flights is a harmonic average. The critical tailwind angle measured from the positive true course (TC) direction will increase as the wind speed/true air speed (WS/TAS) ratio increases. The extreme case is when the wind correction angle is 90° in which case the airplane is oriented and flying perpendicular to the TC and the groundspeed (GS) is equal to TAS because of the true tailwind component. Relatively slow GA light airplanes could become very vulnerable to atmospheric wind effects as high WS/TAS conditions adversely affects flight safety. Atmospheric winds exert large influence on aircraft’s point-of-no-return, point-of equal time, and radius-of-action, which will also affect extended operations (ETOPS) operations and in-flight decisions. Extreme cases of adverse wind effects are not required to put flight operation at risk – even mild effects could suffice. Wind vectors have detrimental operational, economic, safety, and scheduling effects on flight operations