Re-Computation of Numerical Results Contained in NACA Report No. 685

In an engineering note published in the Journal of Aircraft in the year 2000, Thomas A. Zeiler made generally known that some of the early works on aeroelastic flutter by Theodore Theodorsen and I.E. Garrick (NACA Report Nos. 496, 685, and 741) contained numerical errors in some of their numerical examples. Some of the plots containing numerical errors were later reproduced in two classic aeroelasticity texts (BAH and BA). Because these foundational papers and texts are often used in graduate courses on aeroelasticity, Zeiler recommended that an effort be undertaken to employ the computational resources available today (digital computers) to recompute the example problems in these early works and to publish the results to provide a complete and error-free set of numerical examples. This paper presents recomputed theoretical results contained in NACA Report No. 685 (NACA 685), Mechanism of Flutter, A Theoretical and Experimental Investigation of the Flutter Problem, by Theodore Theodorsen and I.E. Garrick. The recomputations were performed employing the solution method described in NACA 685, but using modern computational tools. With some exceptions, the magnitudes and trends of the original results were in good-to-excellent agreement with the recomputed results, a surprising but gratifying result considering that the NACA 685 results were computed by hand using pencil, paper, slide rules, and mechanical calculators called comptometers. Checks on the recomputations (about 25% were checked) were performed using the so-called -method of flutter solution. In all cases, including those where the original and recomputed results differed significantly, the checks were in excellent agreement with the recomputed results

Comparison of Theodorsen's Unsteady Aerodynamic Forces with Doublet Lattice Generalized Aerodynamic Forces

This paper identifies the unsteady aerodynamic forces and moments for a typical section contained in the NACA Report No. 496, "General Theory of Aerodynamic Instability and the Mechanism of Flutter," by Theodore Theodorsen. These quantities are named Theodorsen's aerodynamic forces (TAFs). The TAFs are compared to the generalized aerodynamic forces (GAFs) for a very high aspect ratio wing (AR = 20) at zero Mach number computed by the doublet lattice method. Agreement between TAFs and GAFs is very-good-to-excellent. The paper also reveals that simple proportionality relationships that are known to exist between the real parts of some GAFs and the imaginary parts of others also hold for the real and imaginary parts of the corresponding TAFs

Theodorsen's and Garrick's Computational Aeroelasticity, Revisited

No abstract availabl

Computation of maximum gust loads in nonlinear aircraft using a new method based on the matched filter approach and numerical optimization

Time-correlated gust loads are time histories of two or more load quantities due to the same disturbance time history. Time correlation provides knowledge of the value (magnitude and sign) of one load when another is maximum. At least two analysis methods have been identified that are capable of computing maximized time-correlated gust loads for linear aircraft. Both methods solve for the unit-energy gust profile (gust velocity as a function of time) that produces the maximum load at a given location on a linear airplane. Time-correlated gust loads are obtained by re-applying this gust profile to the airplane and computing multiple simultaneous load responses. Such time histories are physically realizable and may be applied to aircraft structures. Within the past several years there has been much interest in obtaining a practical analysis method which is capable of solving the analogous problem for nonlinear aircraft. Such an analysis method has been the focus of an international committee of gust loads specialists formed by the U.S. Federal Aviation Administration and was the topic of a panel discussion at the Gust and Buffet Loads session at the 1989 SDM Conference in Mobile, Alabama. The kinds of nonlinearities common on modern transport aircraft are indicated. The Statical Discrete Gust method is capable of being, but so far has not been, applied to nonlinear aircraft. To make the method practical for nonlinear applications, a search procedure is essential. Another method is based on Matched Filter Theory and, in its current form, is applicable to linear systems only. The purpose here is to present the status of an attempt to extend the matched filter approach to nonlinear systems. The extension uses Matched Filter Theory as a starting point and then employs a constrained optimization algorithm to attack the nonlinear problem

Flutter suppression control law synthesis for the Active Flexible Wing model

The Active Flexible Wing Project is a collaborative effort between the NASA Langley Research Center and Rockwell International. The objectives are the validation of methodologies associated with mathematical modeling, flutter suppression control law development and digital implementation of the control system for application to flexible aircraft. A flutter suppression control law synthesis for this project is described. The state-space mathematical model used for the synthesis included ten flexible modes, four control surface modes and rational function approximation of the doublet-lattice unsteady aerodynamics. The design steps involved developing the full-order optimal control laws, reducing the order of the control law, and optimizing the reduced-order control law in both the continuous and the discrete domains to minimize stochastic response. System robustness was improved using singular value constraints. An 8th order robust control law was designed to increase the symmetric flutter dynamic pressure by 100 percent. Preliminary results are provided and experiences gained are discussed

An Investigation of the Overlap Between the Statistical Discrete Gust and the Power Spectral Density Analysis Methods

The results of a NASA investigation of a claimed Overlap between two gust response analysis methods: the Statistical Discrete Gust (SDG) Method and the Power Spectral Density (PSD) Method are presented. The claim is that the ratio of an SDG response to the corresponding PSD response is 10.4. Analytical results presented for several different airplanes at several different flight conditions indicate that such an Overlap does appear to exist. However, the claim was not met precisely: a scatter of up to about 10 percent about the 10.4 factor can be expected

Recent activities within the Aeroservoelasticity Branch at the NASA Langley Research Center

The objective of research in aeroservoelasticity at the NASA Langley Research Center is to enhance the modeling, analysis, and multidisciplinary design methodologies for obtaining multifunction digital control systems for application to flexible flight vehicles. Recent accomplishments are discussed, and a status report on current activities within the Aeroservoelasticity Branch is presented. In the area of modeling, improvements to the Minimum-State Method of approximating unsteady aerodynamics are shown to provide precise, low-order aeroservoelastic models for design and simulation activities. Analytical methods based on Matched Filter Theory and Random Process Theory to provide efficient and direct predictions of the critical gust profile and the time-correlated gust loads for linear structural design considerations are also discussed. Two research projects leading towards improved design methodology are summarized. The first program is developing an integrated structure/control design capability based on hierarchical problem decomposition, multilevel optimization and analytical sensitivities. The second program provides procedures for obtaining low-order, robust digital control laws for aeroelastic applications. In terms of methodology validation and application the current activities associated with the Active Flexible Wing project are reviewed

A summary of the active flexible wing program

A summary of the NASA/Rockwell Active Flexible Wing Program is presented. Major elements of the program are presented. Key program accomplishments included single- and multiple-mode flutter suppression, load alleviation and load control during rapid roll maneuvers, and multi-input/multi-output multiple-function active controls tests above the open-loop flutter boundary

Control law parameterization for an aeroelastic wind-tunnel model equipped with an active roll control system and comparison with experiment

Nominal roll control laws were designed, implemented, and tested on an aeroelastically-scaled free-to-roll wind-tunnel model of an advanced fighter configuration. The tests were performed in the NASA Langley Transonic Dynamics Tunnel. A parametric study of the nominal roll control system was conducted. This parametric study determined possible control system gain variations which yielded identical closed-loop stability (roll mode pole location) and identical roll response but different maximum control-surface deflections. Comparison of analytical predictions with wind-tunnel results was generally very good

Re-Computation of Numerical Results Contained in NACA Report No. 496

An extensive examination of NACA Report No. 496 (NACA 496), "General Theory of Aerodynamic Instability and the Mechanism of Flutter," by Theodore Theodorsen, is described. The examination included checking equations and solution methods and recomputing interim quantities and all numerical examples in NACA 496. The checks revealed that NACA 496 contains computational shortcuts (time and effortsaving devices for engineers of the time) and clever artifices (employed in its solution methods), but, unfortunately, also contains numerous tripping points (aspects of NACA 496 that have the potential to cause confusion) and some errors. The recomputations were performed employing the methods and procedures described in NACA 496, but using modern computational tools. With some exceptions, the magnitudes and trends of the original results were in fairtoverygood agreement with the recomputed results. The exceptions included what are speculated to be computational errors in the original in some instances and transcription errors in the original in others. Independent flutter calculations were performed and, in all cases, including those where the original and recomputed results differed significantly, were in excellent agreement with the recomputed results. Appendix A contains NACA 496; Appendix B contains a Matlab(Reistered) program that performs the recomputation of results; Appendix C presents three alternate solution methods, with examples, for the twodegreeof-freedom solution method of NACA 496; Appendix D contains the threedegreeoffreedom solution method (outlined in NACA 496 but never implemented), with examples