Transient loads occur in aeronautics either through airplane maneuver or through external excitations such as gusts and landing impacts. In general, the determination of the loading, as well as that of the response, requires the solution of the equations of motion of the aircraft.

In many dynamic-stress problems, of which the gust loads on aircraft structures is one, the time history of the external load assumes such a wide variety of shapes and magnitudes that any particular solution, derived with respect to a special load-time history, cannot characterize the whole situation. When an attempt is made to measure the external load-time history on an actual airplane flying through a turbulent atmos­phere, the statistical nature of the gust problem is revealed. How to derive from the experimental data on atmospheric turbulences the statistical information that is useful in airplane design is an interesting problem. How to predict, theoretically, the airplane responses (acceler­ation, inertia load, stresses, etc.) with respect to such statistical information of atmospheric turbulences is of practical importance.

Some mathematical concepts useful in the dynamic-stress analysis will be discussed in §8.1. The unit-step and uriit-impulse functions, the indicial admittance, complex impedance, Duhamel integral, etc., are briefly explained. The response of an airplane to a gust of specified profile is treated in § 8.2. From § 8.3 on, the statistical aspects of the dynamic – stress problems are considered. In § 8.4, the concepts of the mathe­matical probability and distribution functions are explained. In § 8.5, the question of choosing proper statistical averages to be measured and calculated is considered.

As an illustrative example, the problem of gust loading is discussed. In § 8.6, the mean square value of the response is calculated on the basis of the power spectrum of the excitation. The interpretation and use of such results are discussed in § 8.7.