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Aviation History
1932
1932 - 0571.PDF
June 17, 1932 Supplement to FLIGHT Edited by C. M. POULSEN June 17, 1932 CONTENTS The Estimation of Profile Drag. By W. R. Andrews, A.F.R.Ae.S. .. Torsion Calculations for a Rear Fuselage with Two or More " Unknowns." By H. Davies, B.A., A.F.R Ae.S Technical Literature— Summaries of N.A.G'.A. Technical Reports Page ll 4S THE ESTIMATION OF PROFILE DRAG. By W. R. ANDRKWS, A.F.R.Ae.S. In the following article Mr. W. E. Andrews, who is on the Technical Staff of A. V. Boe <fc Co., Ltd., Manchester, has analysed test data from the American Variable Density wind tunnel of the N.A.C.A., and has evolved certain empirical formula, which he has found, to give a closer approximation than any hitherto employed. The generalisation of k, llmx may, the author admits, be subject to errors, and the presentation may be by no means accurate, but ivith the information avail able it was the best he could do, and the results appear to give a reliable guide to the full-scale characteristics of any practical aerofoil. MANY attempts have been made to analvse Wind Tunnel Test data and produce generalised c urves for drag prediction. Most of these efforts have been based on tests carried out at low Reynolds Number, and have, as a conse quence, been handicapped by scale effect. A method has been developed (Reference 1) using the test results of the original Variable Density Tunnel of the American N.A.C.A. This tunnel, as then constructed, had certain irregularities of flow, and has since been redesigned to overcome this difficulty. The effect of this irregular flow upon the no-lift characteristics of the tested aerofoils was discussed in a previous article (Reference 2). It is inconceivable that irregularities can exist with out affecting the drag, and particularly the value of the lift coefficient at minimum drag. The tests on the three symmetrical aerofoils M.l, M.2 and M.3 (Reference 3) show that, as the thickness is increased, the minimum profile drag occurs at a more and more negative value of lift. It is obvious that for a symmetrical section the no-lift and point of minimum drag muft coincide, and invert ing the model should show up any error due to asym metry. For certain cambered sections the minimum profile 530 drag is also shown to occur at negative lift coefficient in these tests. This peculiarity of the original Variable Density Tunnel is partly responsible for the assumption made in Reference 1 that the minimum profile drag for all sections occurs at no-lift. The tests made in the redesigned tunnel (References 4, 5, 6, 7 and 8) show very great consistency, not only in the matter of minimum drag, but also in the no-lift conditions. The N.A.C.A. have designated the value of lift coeffi cient at minimum profile drag as the " Optimum.'" The same notation is used in this article, except that to comply with British notation K, of Ct opt is used in place opt It has been given by Glauert (Reference 9) that for an aerofoil having a centre line curved into the form of a circular arc the theoretical value of KL is given by "opt K, Vt 27ry (1) where y = the maximum rise of the centre line in terms of the chord. This, like all the theory so far developed, refers to very thin sections only. The latest tests suggest that the thickness of the profile modifies this relationship. For aerofoils having the same centre line the value of KL becomes smaller with increase in thickness. For purpose of comparison, Fig. 2 is included giving the values of KT for aerofoils discussed in R. & M. opt 946 and tested at atmospheric pressure. No indication is given here of any variation of KL , opt with thickness ratio, except perhaps to reverse that given by examination of the tests at full Reynolds Number. There are not sufficient points to provide conclusive evidence either way. It will be readily appreciated that the determination of the point of minimum profile drag by correction of tests at a finite aspect ratio is rather critical. A small change in the value of the induced drag coefficient and/ or the wind tunnel wall constraint correction will appre ciably affect KL opt' As an illustration, reference to Fig. 1 will show at once the variation in KL . for Sections 6509 and 4509 for an error of 0.005 K\ in the a T)
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