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Aviation History
1932
1932 - 1086.PDF
78 SUPPLEMENT TO FLIGHT THE AIRCRAFT ENGINEER OCTOBER 27, 1932 enough to make up a typical case and work it out for himself. With this brief introduction the subject will be left. It is hoped that the extensions and further applications of the polar diagram outlined in the foregoing sections will induce readers to study and make the fullest use of this in genious method of beam analysis. then NOTES ON AIRSCREW-BODY INTERFERENCE By W. R. ANDREWS,* A.F.R.Ae.S. THE loss of overall thrust due to the combined effects of pressure gradient behind the airscrew and the slipstream over the body have been investigated by various experi menters. The exact significance of the results obtained do not appear to have been fully appreciated. The following notes are written to show how the results of the experiments can be used in synthetic estimates of aircraft performance. In all the tests the expressions for relative body drag are in the form of f1-*! + *! T„ (1) *•« where R„ = Drag in free air without airscrew present Rx = Drag with airscrew running T T = poV2D2 T = Thrust V = Forward speed D = Airscrew diameter and p and a have the usual significance. This includes both pressure gradient and slipstream effects. In a synthetic estimate of drag, " a " must equal 1*0 as the estimated drag of the parts is made for the case where the airscrew is present. In any case experiments show that as the body drag increases, the value of " flj" (in general) more nearly approaches unity. Writing "a" = 1-0, the increase in drag due to inter ference is then R, - R„ = R..6T, (2) Now for R0 we may write R0=KVp-a#V2 (3) where d = body diameter K,, = drag coefficient for body. Substituting 3 in 2 gives Rx _ R„ = 6K,, p arf2V2Tc Id \2 = W|)T. (4) If this amount is taken from the free air airscrew thrust the " net " thrust is obtained, viz., Net T = TF - (Rj - R0) = TF %>/. It has been shown (Ref. 1) that -"• + £' So that by substitution in (6) gives d\ Net T = T F If we write *:•,# = 1 - K,K,, 1) K, !J] • • 5) (6) (7) hKBSw where KB = Total parasite drag coefficient for aeroplane in free air h = Amount of KB affected by slipstream S„, = Wing area associated with KB, * Mr. Andrews is on the Technical Staff of A. V. Roe & Co., Ltd. Net T = TF K]«KBS„, D2 K 2< D (8) which includes the usual " Slip factor" KJ^KBS,,, D2_ suggested by Mr. Id and the pressure gradient factor K2 — R. McKinnon Wood. The " slip factor" has been in common use for some time, but the pressure-gradient effect seems to be neglected. The value of the pressure-gradient factor is expressed in R. & M. 1046 as an approximation : AR = i (d-J T. The mathematical solution for the slip factor is given in full, as uncertainty seems to exist as to how this result is obtained. Let forward speed = V- f.p.s. Let slipstream speed = V -f- v. By the vortex theory it has been shown that the ratio of inflow to outflow is 0-5, so that the velocity through the airscrew disc is V + $•«. The quantity of air passing per second is Q= p<r-a;-D2(V + H (9) Where x • D -2 = effective disc area of airscrew. The change in momentum is " v," so that the energy developed per second in the slipstream is T= p-a-x-TP-v (V + iv) ... (2V, + ^)= -^— (10) x • pa D2 The parasite drag affected by slipstream is R„ = /tKB- paS„.V2 (11) Similarly, R = A-KB- ptr-S,,.- (V + «)2 (12) Therefore the increase in drag due to slipstream is R - R„ = h-KB-p-a-Sw- [(V + vf - V2] = A-Ka-p-a-S,/ [2V-v + «*] Substituting for (2Ve + v") from (10) gives 2T R — R 0 = h • KB • S,„ • —-xD2 (13) which is similar to the slipstream loss included in equation (8), where 8 (14) x - This assumes the whole of the airscrew disc as being effective. The value of x is generally accepted as = 0 • 7 on the assumption that the middle third of the airscrew is ineffec tive. Thrust grading curves (Reference 2) show that generally the thrust reverses in value at about 0-25 to 0-3 the maximum radius of the airscrew, so that this assumption seems reasonable. Accepting this value for disc area gives K1 = 2-86 (15) In R. and M. 1030 (Reference 3), the effect of adding various excrescences to a streamline body has been investi gated. The excrescences have been added at different positions along the body. Since the size of the body has remained sensibly the same for all cases the pressure gradient effect will also be sensibly constant, so that the increase in drag from one case to another is due wholly to the slipstream speed over the body. 1008/
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