Reply by the Authors to Bernard Etkin

Abstract

P ROFESSOR Etkin's Technical Comment is very insightful. It 1) identifies an ambiguous statement we made in the Introduction to our paper; 2) puts into sharper focus the potential usefulness of the SDG method; and 3) goes on to discuss some recent turbulence-simulation work at the University of Toronto. This reply addresses the first two items and then ties in some related work in the area of time-correlated gust loads recently conducted at NASA Langley. In the second paragraph of his Technical Comment, Professor Etkin states that our judgment regarding the PSD method (conventional random process analysis) is not strictly true. The judgment he is referring to is contained in the second paragraph of our Introduction and states that the PSD method is not capable of computing a set of physically-realizeable loads. Then, in his third and fourth paragraphs, Professor Etkin proves that, for linear systems subjected to a Gaussian input, such physically realizeable loads may, indeed, be computed. Professor Etkin is correct. Our statement is true, however, when interpreted in the following manner: For an airplane modeled as a linear system subjected to one-dimensional Gaussian atmospheric turbulence, assume that root-mean-square (RMS) values of shear force (SF) and bending moment (BM) are computed (using conventional random process analysis) at many locations along the span of the wing. The integral of this RMS SF distribution along the span from the wing tip to any inboard location yt in general, will not be equal to the RMS value of BM at y(. In this sense, the loads from a conventional random process analysis are not physically realizeable. Also in his second paragraph, Professor Etkin states that the main advantage SDG has over PSD is the ability of the former to use non-Gaussian turbulence inputs. J. G. Jones, the developer of the SDG method, has expressed the same thought when he says indirectly A principal objective of the SDG method is to cover, in a unified approach, the cases of encounters with relatively isolated severe to extreme gusts and flight in more extensive patches of continuous turbulence of generally less intensity. The patches of continuous turbulence referred to here are Gaussian, and it is for this condition that the SDG-PSD overlap has been shown to exist. For this condition, specific values of gust intensity parameter, UQ [Eq. (1) of Ref. 1], fractional exponent, k [Eq. (1) of Ref. 1], and amplitude reduction factors, p^ [Eqs. (4) and (5) of Ref. 1] are required. The Venn diagram in the following sketch depicts schematically the SDG-