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Aviation History
1917
1917 - 0274.PDF
l/uGHT MAKCH 22, 1917. X . THE SCREW PROPELLER IN AIR.* By M. A. S. RIACH. Introduction. AT the present time there does not appear to be any Really adequate theory -of the airscrew. The only theory that has been developed recently is the one given by Mr. F. W. Lan- chester in a paper to the Institution of Automobile Engineers in April, 1915. f This paper is, moreover, admittedly based on certain theoretical conceptions, and not directly upon aerofoil data obtained from wind channel tests. I have always believed in the possibility of successfully applying aerofoil data to propellers, and any method that attempted to co- ordinate the results of wind channel experiments on model aeroplane wings and on model airscrews appeared to me to be worthy of every encouragement. It was for these reasons that the so-called blade element method of propeller analysis, in the first instance enunciated by S. Drzewiecki and later developed by Mr. F. W. Lan- chester in his work " Aerial Flight," appeared to me to be a step in the desired direction, and the few experiments carried out at the National Physical Laboratory to test the accuracy of the theory, and as published in the Report of 1912—13, led me to believe that the method might with advantage be developed analytically so as to form a reasonably sound basis for the comparison of experimental results and to give to the designer a fairly clear outlook upon the subject. It has always appeared to me that, when testing any theory, how- ever empirical, a distinct advantage is obtained by first stating the whole of the premises, and, having got these clearly defined, to work out the results of the initial assumptions^to Fig. 1. their extreme logical conclusions. However approximate a theory may eventually turn out to be, it saves time in the long run to fully develop the theoretical aspect of the subject which is often capable of outlining new methods of attacking the problem, even when the original conceptions upon which the theory was based have been shown to possess no longer a sufficient degree of exactitude. As an example of this, I might quote the great importance of pitch-ratio upon efficiency in the design of airscrews, and it is difficult to see how such a conclusion could have been arrived at without the help of such analysis as that pro- posed. As a consequence I was led to investigate the subject from the point of view of the blade element theory, and the results so obtained are given in my book " Airscrews."! With the information now available upon the subject it lias been found that this method is not sufficiently accurate even for the comparatively " rough-and-ready " methods of commercial propeller design, where the employment of empirical correction factors has been found to be necessary, and although it will probably be found that the theory is still quite a good guide, and, if employed in conjunction with the correct correction factors, may usually be trusted to give quite sufficiently accurate results for the ordinary " hack " propellers demanded of the designer in commercial design work, yet, viewed from the much more rigid standpoint oi the degree of accuracy obtained in a laboratory experiment, it must be confessed that the method still leaves much to be desired. Many will probably remember Mr. A. R. Low's paper on "Airscrews " read before the Society in April, 1913. In the *"A paper read before the Aeronautical Society on March aist, 1917.t " The Screw Propeller," by F. W. Lanchester. April, 1915, I.A.E* I "Airscrews, by M. A. S. Riach. discussion which followed the reading of this paper, Mr. Handley Page pointed out that Mr. Low had dealt with the propeller problem from the point of view of what happens to the air as it passes across the blade, considered on the assump- tion that the blade elements were entering undisturbed and non-accelerating air, and that in reality it did not by any means follow that the lift coefficients and lift-drag ratios taken for the section as tested as an aerofoil in a wind channel would be identical with the results obtained when the section formed part of an airscrew blade revolving in a helical path and encountering disturbed air, and that in consequence the co- efficients would require modification to accord with practical results obtained. This, Mr. Page went on to say, really con- stituted the second half of the problem, and dealt with the question from the point of view of the slip stream on the basis of the Rankine or Froude theory. He expressed the opinion that there should be no antagonism between the two methods of design, bnt that they should rather be used in con- junction for the correct determination of all the constants of the propeller blade. It was with a view of co-ordinating these two methods of attacking the problem that led me some time ago to consider whether an advance might not be obtained by utilising both of these theories in an attempt to take into account certain factors ignored in both methods considered separately, and by which the determination of some of the empirical con-. stants used in practical design could be brought about, with the result of more closely co-ordinating theory and experj. Fig. 2. ment. Before entering upon a detailed discussion of the propeller theory given in this paper, I propose to commence with the formal presentation of the problem, as conceived by the majority of writers upon the subject, notably Rankine and R. E. Froude, and as given in standard text-books on the screw propeller of marine engineering practice. The subject is by no means a non-controversial one, the theory advanced by Mr. R. E. Froude in his papers read before the Institution of Naval Architects in 1889 and 1911 having been violently attacked by Prof. Henderson in the discussion of these two papers and in his own paper of 1910. General Analysis. Let:— V = the speed of advance of the screw relative to the un disturbed fluid. V + Vx — the speed of the fluid at the actuator disc relative to the screw. V + F, + F2 = the speed of the fluid after passing through the actuator relative to the screw. M — the mass per second of the fluid through the actuator. , Then, according to R. E. Froude, the thrust on the screw is equal to M . (Vi + F8), and the useful work done per second is equal to M . (F, + F2) . V, and the total work done per second is equal to M.(F1+F.,).<y+F1). and therefore the efficiency is given by _Z_, and also Vi/Vl ~ 1, K-f- V1 i.e., one-half the acceleration takes place in front, and one-half behind the actuator. 274
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