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Aviation History
1918
1918 - 0783.PDF
JULY II, 1918. efficient of detrimental resistance and R the total resistance to motion— (1) W- K,SVa. - - • (2) R = (K.S+A)V2. The coefficients Kr and Ky are determined from experience and given by the curves :— (3) Kv- F, (i). (4) Iv = F, (i). If H is the thrust of the screw of diameter D, turning at nrevolutions per second and absorbing an amount of work T, the velocity of propulsion being V, we have between thesequantities the following relations of similitude, verified at Anteuil's Laboratory and found true for values of «D varyingby 30 units :— (5) H - . • - (6 T=V ... •• • (7) •TD (8) • ....: (9) J8 =/ s (7)--a and /3 are represented as functions of 7 by experimental curves (Fig. 6) for a certain type of propeller. The N.P.L.represent the thrust coefficient as a function of 7 by writing :— II = 8H,.D*\T1 where 5 is the mass density of air and o is expressed in terms of H, by the relation :—- H = 8H,D*V> «= OM'D1, whence a—SH^*. If p is the efficiency, in terms of 7, of the whole power plant we have likewise :— -•o a7 5H,73 To return to our system of equations, we will have last of all a tenth, equation for expressing the fact that during horizontal flight the thrust of the screw H is equal to the total resistance to motion R :— (10) R= H. This system of 10 equations is soluble graphically withgreat ease. Suppose that there is, given the rptational speed M of the engine corresponding to the power T. By eliminating D equations (6) and (7) give us the relation : The curve (Fig. 6) enables us to construct the diagram nrepresenting the function — _ /, (7) for the type of pro- 7°peller chosen ; and as for each value of V equation (11) gives /5a single value of A we will also obtain with the aid of the 7diagram (Fig. 6) a single value of o. j3, and 7, which will enable us to calculate the corresponding values of H and D.To each value of V there corresponds consequently a single value of H. T. and D. We can then trace the curves repre-senting these new functions H -^(V), T - V,(V), and D -VS(V).Here the problem may be separated according to whether it is solved (a) by reference to the resistances, (b) by referenceto the powers, (c) by reference to the resistances per unit Weight, or (d) by the logarithmic diagram. (To be continued.) <$> SOME OUTSTANDING PROBLEMS IN AERONAUTICS. By Dr. DURAND. ; (Continued from page 751.) The Airscrew.WE shall now turn our attention for a few moments to one of the most intricate and hence one of the most interestingof the many problems presented to us by the aeronautic art, that of the airscrew or propeller. The function of the air-screw is, of course, to take the torque of the engine and to transform it into a propulsive thrust ; or otherwise to take thepower given by the engine to the crank shaft and transform it into driving or propulsive power for the. aeroplane. Theproblem is further complicated by the fact that, expressed in terms of a po%ver relation, it is not simply the question of anengine handing so much power over to the airscrew for the latter to transform into propulsive power. Instead, thepower which the engine itself can develop is dependent on the propeller and likewise on the aeroplane to which they areboth attached. We have here, in consequence, a series of complicated implicit relations, and from which the propulsivecharacteristics of the plane-propeller-engine combination take their origin. In fact, it must never for a moment be forgottenthat the moving aeroplane is in effect an aeroplane-motor- propeller combination and that no one of the three can bedetermined independent of the other two. Without entering into any d etailed discussion of this problem,it will be clear that the airscrew will exercise a controlling influence on the power which the engine can develop. Thus,it is evident that an aeronautic engine, in order to develop power, must be permitted to move its pistons, to revolve itscrank shaft, in other words, to make revolutions ; and other things equal, the power developed will vary difectly with therevolutions which can be realised. Again, it is easy to see that the size and amount of surface of the airscrew bladeswill present a controlling feature regarding the revolutions which can be realised. Thus, the airscrew may be enormouslyover size, too large in diameter and presenting a large and unwieldy surface to the air. Suppose this to be the case witha plane of size suited to the airscrew but not to the engine. That is, the engine is far too small for either airscrew or plane.In such case the engine simply will not be able to make its normal number of revolutions. It will be held down by theexcessive resistance to rotation presented under such circum- stances, and may thus develop far less than the normalpower which it is capable of under proper conditions. Many other combinations may occur which we cannot stop to discussor even to mention. Broadly speaking, the plane, the engine and the airscrew, as the propelling agent, form a most closelyknit combination, and each interacts in a more or less control- ling manner on the operation of the other two. In order even to make a start with the problem of theairscrew it is therefore necessary to assume conditions regard- ing both the plane and the engine. If these conditions, asassumed, are then realised in practice, and if the design has been well carried out, the anticipated results may be reached.If, on the other hand, the assumed conditions are not realised as regards the plane and the engine, then no matter how wellthe design of the airscrew may have been carried out, the anticipated results will not be realised. Hence, no matterhow good the airscrew may be by itself, no matter how carefully designed and constructed, no matter how faithfully it maybeable to realise the conditions for which it is designed, if these are not the conditions under which it is actually placed forservice, the results economic and otherwise will be unsatis- factory ; not necessarily by reason of any fault in the air-screw as such, but due simply to its lack of adaptation to the conditions of operation. An effective airscrew is thereforenot only one which is properly designed and constructed in itself, but also one which is permitted to operate under theconditions intended and contemplated in the design. All this is, of course, well known, and if I have taken thetime to repeat these well-known facts, it is the more clearly to bring to our minds at the present moment the fact that theairscrew represents not only a problem in itself, but also one of adaption to and of usage with the proper combinationof plane and of prime mover. The general problem of the airscrew is by no means, however, to be classed distinctivelyas outstanding. Instead, an enormous amount of work has been done on it, both theoretically and experimentally,and in its main features it has been brought fairly within the limits of a solved problem. There have been three modes ofapproach, briefly, as follows :—(1) The analysis, geometrically, of the blade of an airscrew into a series of elements, occupyingeach a narrow strip running across the blade from leading to following edge and making up, by their summation, the bladeas a whole. Each of these elements or strips is then considered as, in effect, a little elementary aerofoil and for which theusual aerodynamic characteristics are readily determined, either by direct experiment on a model, or by selection orinterpolation from and among the large amount of available data regarding such aerofoils which have already been sub-mitted to experimental investigation. With such data in hand relating to the series of elements going to make vip theblade, it is a matter of Simple computation to combine them in such manner as to represent the action of the blade as awhole, under the conditions assumed, and thus in general terms the problem is solved. (2) A law of similitude is assumed, 78l
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