Of those obstacles with which nature confronts man in his use of the air as a medium of transportation, two are transcendent in importance—poor visibility that prevents him from seeing where he is going, and turbulent movement of the surrounding air that disturbs his vehicle and its flight path. To overcome these obstacles has always been and continues to be a major challenge to aviation. Poor visibility is associated with both darkness and weather, turbulence with weather alone. The former of these obstacles has to a great extent been overcome—modem navigation techniques permit blind flying with adequate safety for all but the critical phases of landing and take-off", and there is hope that the safety margins for these too will ultimately be acceptable.

The subject of this chapter is the second obstacle, turbulence. The motion of an aircraft in turbulence is akin to that of a ship on a rough sea, or an automobile on a rough road. It is subjected to buffeting by random external forces and as a result the attitude angles and trajectory experience random variations with time. The time scale and intensity of these responses are governed by the scale and intensity of the turbulence, as well as the speed and characteristics of the vehicle. Their effect is to produce fatigue in both the pilot and the structure, to endanger the structural integrity of the air­craft, to produce an uncomfortable, possibly even unacceptable, ride for

workload, fatigue, quality of ride

Fig. 13.1 Breakdown of the turbulence problem.

the passengers and cargo, and to impair the precise control of flight path needed for collision avoidance and safe landing.

To understand and analyze these responses, which is to provide the basis for ameliorating them, we dissect the total phenomenon into several parts, as illustrated in Fig. 13.1. The first is to describe the turbulence itself, the “output” of this description being the velocity field in which the airplane is immersed. Next, it is necessary to determine how these velocities result in aerodynamic forces and moments; these in turn become inputs to the mechanical/structural system whose mathematical modelling was the subject of Chapter 5. Finally, the motions and stresses that result serve to define the problems faced by the structure and the pilot. The diagram indicates that the pilot feeds back into the dynamic system via the controls—a feature that cannot be overlooked for realistic analysis. A study of all the problems embraced by the figure clearly spans the disciplines of meterology, aero­dynamics, vehicle and structural dynamics, metal fatigue, and human factors. We make no attempt here to go in depth into all of these! The aim of the following is to extend the mathematical models previously given to embrace a description of the turbulence and the inputs provided by it. This model then provides the tool for calculating the responses of interest for any design or operational problem.

Since turbulence is a random process that cannot be described by explicit functions of time, only a statistical, probabilistic approach can be taken. The basic random-process theory needed was presented in Secs. 2.6 and 3.4, and the following relies heavily on that material. In particular the role of input spectra in computing output spectra should be recalled at this point [see (3.4, 48 to 61)], and the role of output spectra in calculating response probabilities (Sec. 2.6).