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Aviation History
1936
1936 - 1594.PDF
JUNE 18, 1936 39 THE AIRCRAFT ENGINEER SUPPLEMENT TO FLIGHT then, if we let \ „ = 4SV£Alt sin n 6 in the conventional manner. »rfcVA„ (2) I. and : m . d = MI 4SV2TA,, sin nB nb\T A, Then, the downwash at the general point y, due to " m • d " m , d = tan~ x 47r Vi — bj2 and the total downwash at the general point y, is given by the expression : 3 ^ Ti =V r—-—I tan-1 ——• -tan-1 sine? 4TT y+bji y—bj2\ ZltAHsmnB A0b\T i d d = V : • — tan-1 fan—1_ -tan-sin(9 8 rf (/" y+d/2 y—bJ2J The above expression gives the downwash as a function of the coefficients A0 and A„. The lift at any point is related to the downwash by the following expression : (4) |"~ = a0YC(a - W/V) where : BB = cos—1 b\i x S a0 = slope of lift curve in KL per radian for infinite A.R. V = forward velocity in feet per second C = chord of aerofoil in feet a = geometric angle of attack from zero lift W = downwash velocity at aerofoil in feet per second K, = British Absolute Coeff. p SV2 b = body span in feet. Since the_angle (a — W/V) will be small we may write : I = a„ VC sin (a - W/V) Therefore : (5) = a0VC sin a — a0VC(W/V) cos a considering : cos W/V = 1 sin W/V = W/V From equations (1) and (5), we may then write : 7T&A0 (6) —— = («0iC8 sin a, — a0aCa sin a„) — (a^CiW, cos a, — a0aC„Wa cos a„) where : subscript " i " denotes eddy and subscript " a " denotes autorotating. If we now write equation (6) at the point of discontinuity, substituting the values of downwash from equation (3), we obtain the first equation connecting the coefficients A0 and A,; as follows : (*H) (a0,C,cos a, — a0aCa cos a.)---o a ~^~i6d 'fl("c'cos a* = («0.C; sin a, a0oCo COS a„) aoaCa sin a„) - (a0,C, cos a - a0aCa cos aj V " — -^ sin Bv The other " n " equations relating A0 to the (A„)'s are obtained by equating the circulation as originally assumed to the circulation in terms of the downwash expression. These values are written for " « " values of 0. For the inboard portion between ± b\i, the expression is : /o i |— TrbVA0 (8a) I , = ° + 4SV2A,,sin nB = «oVA A0b Z„A„ sin nt sin 6 tan tan 8 d \ y + 6/2 5/ — 6/2/ For the outboard portion between " bjz " and " S " ; — bjz and — S, the expression (8a) becomes : (8b) |~ = 4SVi7Ansin nB Z„A„ sin nB — AoaVCa AJ> * ** sin 0 d tan d y + b/2 y — fc/2/_ This method has been applied to the Bumelli Model UB14-A, and four terms of the Fourier series seem to be sufficiently accurate. This means that equations (8) are written for the points : TT "Iff 77 77 2 8 48 This gives four equations with five unknown. A0, Aj, A3, A5, and Av The fifth equation between the five coefficients is equa tion (7). When the value of 8 falls within the body equa tion (8a) is used, and when the point 6 falls outside the body, equation (8b) is used. After the values of A0, Ax, A3, As, and A- are determined, the lift distribution may be plotted as follows : |~= 4SVZA,, sin nB = KLCV since the lift per foot is proportional to KLC we may plot (4S27A,, sin nB ) vs. (y) = — S cos 6. The integral under this curve is then taken to KL (wing area). If this is divided by the wing area, the value of KL is then obtained. SUMMARIES OF R. AND M.'s WIND TUNNEL TESTS OF HIGH PITCH AIRSCREWS. By C. N. H. Lock, M.A., H. Bateman, B.Sc., and H. L. Nixon, of the Aero dynamics Department, N.P.L. R. & M. No. 1673. (29 pages and 9 diagrams.) October 5, 1934. Price 2s net. In the tests on the original family of airscrews of 3ft. diameter (R. & M. 829)' we pitch diameter ratios of the principal series of screws (two- and four-bladers) were 0.3, 0.5, 0.7, 1.0 and 1.5, this range being considered adequate to cover all Practical requirements. After a lapse of 12 years, however, the pitch diameter ratios of "ill scale airscrews have increased almost to the limit of these tests and extreme values of 2.2 have l>een used. It was decided, therefore, that a further series of airscrews should be tested to extend the range of pitch values to 2.5. . I"he additional tests were made with the blades of P/D 1.5 rotated to the equivalent Pitch values 1.0, 1.25, 1.8, 2.2 and 2.5. Some of the tests on the low pitch screws Were made in a closed 7ft. tunnel, but the tests of the highest pitch screws were made in the new open jet tunnel No. 1 in order to use the higher maximum tunnel speed. ifiiis a comparison was obtained between observations in the closed and open jet "iimels for a number of airscrews, and these support the standard methods of cor- ection for tunnel interference. New apparatus was used including a new 15 h.p. "auction motor of 9in. diameter to drive the airscrew. The effect of the airscrew ooss was eliminated by using a cylindrical guard bodv of 0.27 airscrew diameters with wired nose and tail of sufficient length to give a uniform flow in the absence of the sntw' The tnrust readings were corrected by pressure plotting the airscrew boss th wihe recordcd thrust and torque coefficients refer to the exposed portions oj n " blades only. Instructions are given for correcting the performance data for H R. & M. 821) Experiments with a family of airscrews. «°ward and Bateman. Part I. Fage, Lock, the effect of interference when the screw is mounted on the fuselage of an actual aeroplane. The results show that the maximum thrust coefficient for the higher pitches is limited by the stalling of the blades so that after reaching a value of about 0.135 for the two-bladers and 0.26 for the four-bladers, the value of kr remains very roughly constant and independent of pitch for all smaller values of J. These values are however subject to a scale effect on maximum thrust coefficient of 5 to 10 per cent, for an increase of Reynold's number from 1.8 x 10s to 3 x 16*, but there is some evidence to suggest that the full scale values will not differ greatly from those of the model. The torque coefficient increases with increase of pitch at all working con ditions. The maximum efficiency for the two-bladers increases slightly from 88.4 per cent, at P/D 1.5 to an absolute maximum of 89.7 per cent, at a P/D rather less than 2.5. For the 4-bladers the corresponding figures are 81.8 and 86.8. THE LAMINAR BOUNDARY LAYER ON THE SURFACE OF A SPHERE IN A UNIFORM STREAM. BV S. Tomotika, D.Sc. Communicated by Professor G. I. Taylor, F.R.S. R. & M. No. 1678. (14 pages and 5 diagrams.) July 12, 1935. Price is. net. A preliminary study on the laminar boundary layer on the surface of a sphere is made, by starting from the momentum integral equation for the boundary layer on a body of revolution. For the velocity distribution just outside the boundary layer, two cases are considered ; in one case, the simple theoretical velocity distribution is employed, while, in the other, use is made of an experimental velocity distribution whicli has been obtained from a pressure distribution found experimentally in the case when the Reynolds number of the stream is below the critical Reynolds number of a sphere. In each case various quantities characteristic to the laminar boundary layer are discussed and ate shown by appropriate curves. (Other Summaries on page 44.)
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