RESPONSE TO ATMOSPHERIC TURBULENCE
The motion of an airplane, and the forces that act on it, as a consequence of the turbulent motion of the atmosphere, are very important for both design and operation. The associated mathematical problems are treated with the same general equations as given above. (uE, vE, we) then have to be sums of (u, v, w) and the velocity of the atmosphere at the CG, and additional complications arise from the fact that the relative wind varies, in general, from point to point on the airplane. This case is treated in depth in Chap. 13 of Etkin (1972) and in Etkin (1981).
A class of problems that has not received much attention in the past, but that is nevertheless both interesting and useful, is that in which some of the 12 variables usually regarded as dependent are prescribed in advance as functions of time. An equal number of equations must then be dropped in order to maintain a complete system. This is the kind of problem that occurs when we ask questions of the type “Given the airplane motion, what pilot action is required to produce it?” Such questions may be relevant to problems of control design and maneuvering loads.
The mathematical problem that results is generally simpler than those of stability and control. The equations to be solved are sometimes algebraic, sometimes differential. A decided advantage is the ability of this approach to cope with the nonlinear equations of large disturbances.
Another category is the mathematical problem that arises in flight testing when time records are available of some control variables and some of the 12 dependent variables. The question then is “What must the airplane parameters be to produce the measured response from the measured input?” (See Etkin, 1959, Chap. 11; AGARD 1991; Maine and Iliff, 1986.) This is an example of the important “plant identification” problem of system theory.