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Aviation History
1917
1917 - 0304.PDF
throughout, so that variation in (A,) is obtained by variationin (a,). "Then if we double the blade width, we halve the ordinates of curve (i), and since curve (2) remains constant throughout the result-ing values of (cy j and (a,) are smaller thanbefore. This increases (Ax) and probably also(tan 7J, but decreases (cyj), so that the newthrust value may be obtained in this mannerfor any given case. It will usually be foundthat, since (sec AJ has a value of nearly unity,the new value of the thrust will not be any-thing like double the old value, due todoubling the blade width. The percentageincrease in fact de- creases with increase inblade width, and* this result is, I believe, con-firmed by experiments on marine screws. Thereason for this loss of thrust, I contend, is dueto the higher inflow velocity (Fj) and consequently smaller angle of attack (a,). It may, it is true, be argued that if(F,) be increased, then the thrust must correspondingly increase, and in fact this is a necessary condition providingthat the ratio V»/V ) remains constant throughout. I shall endeavour to show, however, that the ratio (F2/F!)is by no means to be regarded as a remaining constant for changes in angle of attack (a^, and that for small or negativeangles of attack this ratio may conceivably become zero or even negative, depending upon the pressure distribution roundthe blade section at the angle of attack (a^ considered. Turning now to the efficiency of the element denoted by tan A tan (41 + 7,) it is evident that as the blade width is increased, both (Ax)and (yj) are increased, thus reducing the efficiency—a result again in accordance with experience of marine screws. Onthe other hand it is evident that the efficiency with wide blades may be considerably improved by increasing the chord angleof the blade (<p) so as to give to the angle of attack of the section a value corresponding to a minimum value of (71).In this case, therefore, the efficiency of the element is in- creased by increasing the so-called slip angle of the screw.This result is again in accordance with experiment on marine propellers. EXTENSION OF THE THEORY. We may, I think, roughly divide a propeller blade intothree parts, the boss, the tip and the centre forming the main portion of the blade. It is usual, I believe, when designingpropellers on the old aerofoil theory to choose for the sections an average aspect ratio of say six, and then to employ acorrection factor obtained by experiment in determining the blade widths along the blade. This process, however,seems to be open to objection from various sources. It is well known that the pressure distribution along the span of anyaerofoil, such as an aeroplane wing for instance, does not remain constant but varies from a maximum intensity inthe middle of the span to a minimum at the wing tips, and it is this fact of tip losses which makes the high aspect ratioaerofoil more economical than one of lower aspect ratio. The same consideration should apply to the blades of anairscrew, where each individual blade can be treated as a separate aerofoil, and where in consequence the end losses—in this case those of the boss and tip—must be taken into account in estimating the thrust, work and efficiency. The MARCH 29, 1917. boss conditions in this case may probably be ignored as beingvery small; the tip losses form, however, a fundamental link in the chain of analysis and in consequence require mostcareful consideration. The exact analogy between the pressure distribution alongthe span of an aerofoil considered as an aeroplane wing, and considered as a blade of a screw propeller, does not appear tobe immediately capable of demonstration. As a first estimate, however, I have assumed the maximum intensity ofpressure to occur at about the centre of the blade, i.e., at a radius of J diameter, and to fall off to a minimum value atthe boss and tip—that is, I consider the propeller blade as the equivalent of an aeroplane wing of infinite span revolvingabout one of its wing tips. Under these assumptions then it is possible to form some idea of the relative changes in liftand lift/drag which occur as we proceed along the blade from the boss to the tip. So that if, when analysing anyexisting airscrew, we apply the theory of inflow already enunciated under the conditions imposed by the pressuredistribution change considered above, we shall, I think, be in a position to form a fairly correct picture of the actual con-ditions under which the blades are working, and hence be in a position to estimate the probable values of the thrust, workand efficiency, with a much larger measure of success than by the older method in which such refinements as those outlinedhere are ignored. There is still the question of the values of the ratio (V^V^)to be allotted to the various sections along the blade of the airscrew, as it may be taken for granted, I think, that thisratio not only does not remain constant over the entire surface of the screw disc, but.that its numerical value mayusually be taken as considerably less than unity, and some- times even zero or negative. That values other than unity have been considered not onlypossible, but probable for this ratio by authorities on the marine screw propeller, may be gauged from the followingremarks by D. W. Taylor on the discussion of Mr. R. E. Froude's 1911 paper. Mr. D. W. Taylor said : " It is true that the experimentalcauses appear to indicate that the acceleration takes place mostly forward of the screw, and is not equally dividedbetween forward and aft, as deduced by Mr. Froude for his actuator. . . . This indication that with actual propellersthe greater portiqn of the fore and aft acceleration of the water takes place forward of the screw," &c. It appears to me in this connection not unreasonable toregard this (V^/V^ ratio as equal to the ratio of the lower and top pressures on an aerofoil section, and if this be appliedto all radii along the blade we are immediately in a position to analyse any given airscrew blade under any set of con-ditions. For instance, to take as an example the case of the section under the conditions when giving no thrust. Then dTx = L,. cos A1 — D].sin.41 = o 4- and .'. r~ ; •• tan 71 = cot A x and if (<p) is known, then we can solve for (a,), since known from the wind channel curve. But if = o, then F,. and hence either (Fj) is equal to zero or (V^/V^ is equal to minus unity. In the first case, there is no inflow, and in the second case the top pressure is numerically equal to the under surface pressure, but acts in an opposite direction, and in this case the angle of attack («i) of the section would be probably negative. Now. tests on aerofoils show that the pressure distribution at about (—20) is about the same numerically on top and bottom surfaces, but that the bottom surface pressures act in an opposite direction to the usual at positive angles of incidence. These facts appear to bear out the statement that (Fs/Fi) may have a negative value. (To be continued.) Air Work in the Advance. THE expert French commentator, writing on March 22nd, g said :—" Despite bad weather, there was considerable air1* activity in the zone of the enemy's retreat. French and British aviators furnished their general staffs with most valuable information, and successfully drove off many enemy machines. One of the aviators bagged was Prince Frederick Karl of Prussia." The correspondent of the Petit Journal, writing on March 19th, said that the British aeroplanes were doing remarkably good work in the pursuit. Mr. W. Beach Thomas, writing to the Daily Mail from theWar Correspondents' Headquarters in France on March 20th, said:—" Our airmen once again, as behind High Wood longago, saved a group of cavalry from destruction by their machine guns, and German airmen, who have been active,thought it worth while to dive and attack with machine-gun fire two staff officers bicycling forward for observation purposes."
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