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Aviation History
1936
1936 - 1108.PDF
April 30, 1936 Supplement to (y 462a FLIGHT ENGINEERING SECTION w tii /Volume XII\ .,,. ,,„„ .No. 123 ^ No 4 1 11th \ear A^^il 30, 1936 MEAN AERODYNAMIC CENTRE and CHORD Analytical Formulae for the Co-ordinates of the Mean Aerodynamic Centre of a Wing and for the Length of the Mean Aerodynamic Chord By J R. CREAN, B.Sc.(Eng.) THE object of this paper is to deduce three simple analytical formulae giving the co-ordinates of the Mean Aerodynamic Centre (M.A.C.) and the length of the Mean Aerodynamic Chord in the case of a wing plan form whose inner portion is rectangular and cuter trapezoidal—this being the most important con temporary type and including the simple trapezoidal plan form as a special case. The position of the M.A.C. of a wing and the length of the M.A. Chord are important in the determination of the balancing loads of an aeroplane, also as a means of comparing the relative C.G. positions tor aircraft of varying wing plan form. The M.A.C, is defined as that point on a wing about which—for constant dynamic pressure—the moment of >e resultant air force is approximately constant at all angles of attack, and its location is defined by the co ordinates : V = KN- cy dy X = oJ KN c dy KN cXdy K N c dy ^'here (1) KM X = = semi-span. = normal force coefficient at a section. = the corresponding chord. = perpendicular distance of a section out board from the wing root. = ordinate of locus of the aerodynamic centre of the individual chords measured from TT the datum shown in Fig. i. Pitching re^ar<^ to the usual convention of expressing length "1 ,"10flents of an aerofoil in terms of the chord the °Un'ea " Aerodvnamic Chord may be defined as tude ot \\ Parameter entering the expression for the magni-e rooment of the resultant force. If, as will be assumed to be the case in the deduction of the corresponding formula, the moment coefficient about the aerodynamic centre of each individual chord is con stant over the semi-span, then the length of the Mean Aerodynamic Chord is given by : — Ps C = c2 dy • • •• o • • •• (2 J c . dy These three fundamental expressions may then be evaluated graphically for any plan form as described in Aeronautics Bulletin No. 26, 1934 (U.S. Dept. of Commerce) Paragraph 9, pages 14-16, from which publication the substance of the foregoing information has been extracted. Thi'- is, however, a somewhat cumbrous process, whilst on the other hand the formulae proposed enable the problem to be solved far more rapidly and directly in the case of the important class of plan form under discussion. In the deduction of the formulae for the co-ordinates of the Mean Aerodynamic Centre, the basic assumption will be made that KM is replaceable by KL — this being a very close approximation for all normal angles of attack. The lift loading, KLc/c0, (c0 = root chord) over the semi-
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