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Aviation History
1917
1917 - 0330.PDF
JjjGHT Consider the general efficiency formula, viz. :— 'h = 2.7T cyl.xi.f(x). sec Ax. (i —tan A. tan 7l). dx J»o. . \r \cyx.x3.f (x). sec Ax (tanvli + tan 7)) . dx in conjunction with that already established, viz. :— q.2.ir.x.(li J . sin Ax. [tan Ax — tan A] and therefore putting (b) <= cl.f(x), we get . sin Ax. [tan Ax — tan A] J v ' cj/^iV.C!- (i — tan A v tan 7l) whence, substituting for this function / (x) in the general efficiency formula, we get:—[ I 7\ *Mx+'~ 7- tan Ax. (tan Ax — tan A). dx r^ ) . (tan ^4,-VJ (tan fp I — tan .4,. tan 71 and now if we make (F,) and (VjVx) constant over the blade, which Mr. Lanchester defines as the condition for maximum efficiency, and (rB) equals zero, we get :— P 2.TT \x.dx x*.(V+ F, + 2.v.n.x. tan 71) . dx 2.v.n.x—tan 7l . (F + F,) and if tan y = o, then ij! - V/V + F,, thus reducing to the ordinary R. E. Froude formula. But in practice tan 7, is always greater than zero, and therefore, evaluating the above, we get :-^_".' di. (I — hr) tany' .[ 7r.ra.rf. - tan y,. (7+7,H3- (ir.».d.A-tan 7l. (F4 +^) 3] •- jr.nJJk.-tan 71. (7+7,) f 7^^ + 3- t»j 3- tanV 7" ge Where A = rojr, a fraction which is greater than zero in this case of discontinuous blade outline. Now consider the brake horse-power necessary to sustain a total weight of (W) lbs. in the air. The brake horse-power required at an axial speed upwards of (F) feet per second is given by 55°-->7i and therefore substituting for (j^) the value given from Mr. Low's "Rational" blade form, we get, making (F) equal to zero, H 8. V2-^- [/• tan and if tan 7l = o we get q = I 7,/7, = I 1.sec 2 7l][/+c,.cy1. tan7i] IF _ 5SOJ /A^i •= "442 x F. W. Lanchester's formula.So that, under similar ideal conditions— (tan 7l = o, q = 1, V2/V, = 1)we find that by making the inflow velocity constant over the blade we require only • 442 times the brake horse-powerrequired, to lift a given weight, as when using the " Rational" form of blade outline. APRIL 5, 1917. It is therefore obvious that for efficiency we require a blade form which is very wide near the boss and very narrow near the tips. Mr. Lanchester's condition of constant slip velocity is evidently an extremely sound one from the point of view of economy in brake horse-power/weight ratio. Returning then to the efficiency formula for an airscrew, having constant (F,) and (F2/Fi) values, we may estimate the brake horse-power required and the weight/brake horse-power possible under similar conditions to those assumed by Mr. F. W. Lanchester in his estimate already given, but taking into account the fact that in practice (tan 7jl) is always greater than zero, and hence we may expect a result similar to the one already given by Mr. F. W. Lanchester, but not so optimistic. This result is continued by an investigation of the analysis already established. However, owing to the fact that it is impossible to eliminate the factor (c,) from the expression for weight/brake horse-power ratio, an exact comparison between F. W. Lanchester's expression and the one obtained on this theory is impossible. It is also possible from the formulae for weight/brake horse- power already given to find the greater thrust possible with a given diameter propeller and given brake horse-power. We can write :—• W And putting . A.a W ~ in lb. ft. sec. units. we get W=(8-27).. ^/i- giving the equation required. Thus, with a screw of 8 ft. diameter and actuated byi b.h.p., the total thrust would be 41-7 lbs. with (Vn/Vi) equal to 1, and 33'08 lbs. with V^jVi) equal to zero. In the September number of Aeronautics, 1911, the follow-ing figures are given for two screws tested by Professor W. H. Pickering, of Harvard :— B.H.P. Diameter of Screw. Thrust.1 .. .. .. 1 12 feet 48 lbs. 2 .. .. 20 20 ,, 430 „ Applying the above formula for the two cases when (F2/Fi) is equal to 1 and when (F2/Fi) is equal to zero to the above figures, we get the thrust as calculated as given on the follow- ing table :— a 2 (1) 1 12 feet — 54-6 lbs. 43-3 lbs. 48 lbs. (2) 20 20 „ — 565 „ 448 „ 430 >. These results appear to indicate that the purely theoretical formula established from R. E. Froude's theory is not so hopelessly out of agreement with the facts as often happens to be the case when dealing with ideal conceptions of this kind. Further particulars regarding the form of Prof. Pickering's screws would have been interesting. The formula here given for thrust is really only a variation of the one proposed by Mr. F. W. Lanchester in his paper " A Contribution to the Theory of Propulsion and the Screw Propeller" (Institution of Naval Architects, March, 1915) 2 / 7-Awhere his coefficient (Q) has the value of : i + ( y'j as given in this paper. Probably a sufficiently approximate formula for the thrust delivered by a helicopter screw would be /F2\ • vj-1where (K) depends upon blade form and may have an extreme value of unity. A graph of (W) against (d) is given in Fig. 7, for [V.2IVX) = 1, (K) - 1, and (H) - 1. To be concluded.) Fire at Brussels Aerodrome. REPORTS received in Amsterdam from the Belgian border state that fire broke out on March 27th in a German military aerodrome at Berchem, near Brussels. Two Zeppelin sheds are said to have been destroyed, but both were empty ; a number of sheds containing Aviatik aeroplanes under repair were burned. The fire is said to have been started by three soldiers of the German garrison at Brussels. They disappeared when the fire broke out, probably deserting to Holland. 330
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