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 𝑝𝑝-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.