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Aviation History
1923
1923 - 0185.PDF
APRIL 5, 1923 A DISCUSSION OF GERMAN AND ENGLISH METHODS OF COMPUTING AEROPLANE PERFORMANCE By F. RADCLIFFE, B.Sc. (Vic.) [OWING to the lack of uniformity in presenting the results of wind-tunnel experiments and other aerodynamic work, the student of aeronautics frequently finds himself baffled if and when he attempts to make a first-hand study of what has been accom- plished abroad. In France Eiffel introduced the system of plotting wing characteristics as a " polar " diagram, using the lift coefficient as ordinate and the drag coefficient as abscissa. Furthermore, the Eiffel coefficients have to be multiplied by 8 to make them equal to the " absolute " coefficients used in this country and—until recently-—in the United States. In Germany the polar diagram is also used, based upon those first employed by Lilienthal. Here, however, the " absolute " coefficient system has been adopted, but the coefficients have double the value of our absolute coefficients—due, as Mr. Radcliffe points out, to the fact that the Germans use J . pjg, while in this country we use pjg. Thus from the very outset the student is faced with a variety of " snags." Add to this the fact that he is reading the explanatory text in a language with which he is probably not familiar, and in which different symbols are used to denote the same thing (for instance, ky is used by Eiffel to denote the lift coefficient, while in this country it is now usual to denote this coefficient by £L, and in Germany by ca), and it will be seen that even in the most elementary things difficulties arise. When we come to the more complicated expressions the situation becomes even worse. We have therefore felt that the paper read by Mr. Radcliffe before the Students' section of the Royal Aeronautical Society some time ago deserves to be more widely known, and have decided to publish it in FLIGHT, in the hope that the paper will assist many who are now groping for an explanation of the often puzzling presentation of aerodynamic calculations in German aviation papers and text-books.—ED.] Introduction THE nineteenth century has been well termed the Age of Nationalism ; and historians tells us that the present century marks a new epoch—that of Internationalism. It is with the latter thought in my mind that I wish to emphasise the need for more concerted action in the realms of science. The recent advances made in our own particular branch of science—that of aeronautics—have been great; but, through very natural reasons, there has been a marked tendency for those advances to proceed along different paths, or, shall I say, by the utilisation of different forms of mechanism. This is seen very noticeably to be the case in the methods employed by the Germans and those employed by ourselves in the estimation of an aeroplane's performance. My object in writing these few notes is to set before you the outstanding points in the German method, showing you its good points and then its bad points, and comparing it with our own method. The time at my disposal is too short for me to outline the English method at any length, and all I can do is to put before you an actual example worked out according to the English method, and then afterwards to show you the same data utilised in the modified German method. From the outset let me say that the German methods I have been able to come across have all ignored " slip-stream " effect, and it is the taking into account of these effects that has caused me to speak of a " modified " German method. My chief aim will be to stimulate a wider, and shall I say an international, interest in aeronautics, which will lead us to study other people's views and mode of dealing with our everyday problems. I should like to express my very grateful thanks to the Blackburn Aeroplane Co., and in particular to the chief designer, Maj. F. A. Bumpus, for permission to use the Swift F " torpedoplane, as manufactured by them, as the basis for my examples. The Representation of the Characteristics of an Aerofoil In estimating the performance of an aeroplane by any method, the first requirement is a knowledge of the lift and drag of the aerofoil section we have chosen for the wings of our machine. ' The German method differs from ours. We are in the habit of plotting the lift (ky) and the drag (kx) of an aerofoil as two separate curves with the angle of inci- dence as abscissa. In addition to these we plot I./D (i.e., kyjkx) against the corresponding angles of incidence. . Thus, we have three curves which give the characteristics of a section. In the German method kv is plotted directly against kx as abscissa, giving us what is usually termed the " polar " diagram. Whilst we are speaking about the characteristics of an aerofoil, it ought to be mentioned that the German coeffi- cients are relatively double the value of ours, the general form of their equation being given by— F. = K\— . A.V '".- whereas ours is given by— F. = K'. — . A.V2 (1) (2) • E.g., the work by Prandtl, Glauert, etc.; vide " The Theoretical Rela-tionship for the Lift and Drag of an Aerofoil Structure," by H. Glauert, M.A., read before R.Ae.S. on November 30, 1922. If we use the " F.P.S." system of units in both equations, (1) and (2), we see that K. = 2K'. Let us digress for a moment or two and consider these two systems of absolute units, and put as general equations :— p = K — V2 2 German p = K'— V2 - English g (3) (4) where p = —, i.e., the intensity of pressure per square foot A (using the F.P.S. system of units). If we were to take a pitot tube for finding the pressure difference between air at rest and air with a velocity of V feet per second, .we know that by means of Bernoulli's theorem we have :— pThe pressure difference = p^p o= \ • - .V 2lbs. per sq. ft. (5) 8 where p1 = pressure of the air at a velocity of V ft. per sec. and pv = pressure of the air at rest. Hence, we see that the German expression is directly con- nected with the dynamical pressure of the air, whereas our expression of (p/£.V2) can only be interpreted as " twice the dynamical pressure." Furthermore, we see that the German choice is a natural choice of an expression, whereas ours is an artificial choice. This latter choice, however, is so universally used in this country that I shall not use the German expression even when working out a performance calculation after the German manner, as I do not think it would lead to greater lucidity. With these few remarks let us return to the representation of aerofoil characteristics. Now the term " angle of attack of an aerofoil " is merely a conventional term for the angle between the chord of the aerofoil and the direction of the air's velocity. Aerodyna- mically, it has no definite significance, for it depends on our definition of the chord of an aerofoil. The definition of the chord of an aerofoil is not clear in some cases, and in others breaks down completely. Consider a wing with wash-in and wash-out (i.e., a twisted aerofoil), or a system of planes where the chords are not parallel. Here the term " angle of attack " fails entirely. Thus, we see that in plotting the various coefficients against angles of attack we have no natural basis for comparing different systems of aerofoils. ky What we generally like is to have the ratio of — as large kx as possible, and the angle of attack interests us merely as a structural consideration. With the English system of two curves for ky and kx, there is not the same vividness as with the polar diagram. Recent researches* have shown that the lift of an aerofoil depends not on the angle of attack, but on the " circulation " of the air round the section. That is to say, the air flow round wings of the same section but of different plan form is the same for equal values of ky, and not necessarily for equal values of the angle of attack. Again, it has been found convenient to divide the drag of an aerofoil into two parts—one, due only to the plan form of the aerofoil and termed the " induced " drag, and, secondly, that due to the type of aerofoil section used, which has been 185
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