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Aviation History
1910
1910 - 0110.PDF
[/y£5i FEBRUARY 12, 191a. AERIAL PROPELLER5. BY A NAVAL CONSTRUCTOR. Continued from page 92.) CHAPTER III.—Water Propellers and Air Propellers Compared. THERE appears to be, at first, a decided difference between the action of the water propeller and the air propeller One is working in a practically incompressible fluid whilst the other is working in a compressible one. They present, however, the same problem to the designer of propellers. This was first pointed out and verified experimentally by Mr. A. W. Johns in a paper read before the Institution of Naval Architects, in 1904. The following will show in a general way why this is so :— Suppose we have a propeller of 8 ft. diameter working in an aeroplane and developing a thrust of 150 lbs. These are quite average figures. The area of such a propeller (two-bladed) would be about 6 sq. ft. The 150 lbs. is theresolved component of the pressure, on the propeller blade, in the direction of advance. The actual pressure, therefore, would be more than this. Say 240 lbs. at the outside. Thus the pressure per sq. ft. on the propeller blade would be —7—' = 40 lbs. Now atmospheric pressure is approximately 15 lbs. to the sq. inch, that is 15 x 144 = 2,160 lbs. per sq. ft. Thus the additional pressure of 40 lbs. to the sq. ft. would, by Boyle's law, compress the air very little. 40 The amount would be - > -7— = under 2 per cent. •2,160 + 40 r For all practical purposes in air-propeller design, therefore, we may take it that the air is an incompressible fluid. Thus the ratio of the thrust of a propeller working in air, and water, is the direct ratio of the density of the air to the density of the water. For air at the ordinary temperature and pressure this is about yig. Thus if we know the performance of a water-propeller, under certain conditions, we should be able to calculate for the air-propeller working under the same conditions. It is evident, therefore, that we can use the results of experiments on water-propellers for the purpose of designing air-propellers. CHAPTER IV.—Formulae for the Comparison of Model and Full'size Propellers. The generally accepted formula for getting the thrust of a propeller is T = K V2 D- where T is the thrust in lbs., V = velocity of the propeller forward in feet per second ; in the case of an aeroplane propeller this would be equal to the velocity of the aeroplane itself. D = diameter of the propeller in feet, and K is a con stant which is the same for all " similar" propellers ; by similar we mean that one is an exact counterpart of the other, but is made to a different scale. The propellers must, of course, be running at the same slip. Having found K by means of a model experiment we can apply it to the full-size propeller. The above equation is sometimes put in a different form. Thus, if s is the slip, R = revolutions per second, and/ = pitch of propeller in feet. Then from our definitions given previously we have, V = Rxj> (1 - s), hence T = K (1 - s) R2/D2. Throughout this book we shall use the formula T = K - V2D2. 1000 In the experiments the model is run at different slipsr and the thrust and efficiency calculated in each case. Curves are then plotted on squared paper showing the variation of thrust and efficiency with slip. These curves are given later for all propellers likely to- occur in practice, for two-bladed propellers. Now R. E. Froude, in his experiments, found that the relative thrusts given by propellers having two, three and four blades were as 650 : '865 : 1 ; the propeller in each case running at the same slip. The efficiency, however, does not alter appreciably,, except when blades of much higher disc area, i.e., wider blades, ratio than those already given are used. Hence if we wish to correct the following curves of thrust for three and four-bladed propellers we simply multiply by i"33 and 1*55 respectively. These are experimental results. From ordinary con siderations we should expect the above figures to be 1-5 and 20 respectively, but this is not so. Thus two two-bladed propellers working on different shafts will give about 30 per cent, more thrust than one four-bladed propeller having the same diameter and blade area; the efficiency, however, will be very nearly the same. CHAPTER V.—Information Required to Determine the Type of Propeller to be Used. Before it is possible to carry out the design of the' propeller or propellers for an aeroplane it is necessary to know two things :— 1. The thrust required of the propeller. 2. The speed of the aeroplane itself relative to still air. The aeroplane as constructed at present has only one speed relative to still air, and consequently it requires a certain definite thrust to keep it at this speed. If we increase the thrust above this amount the machine will rise higher in the air, and if we decrease the- thrust the machine will come to the ground. The speed of an aeroplane, and the thrust necessary for its flight, should be known to the designer, if the design has been scientifically carried out. Data obtained from a previous design which has flown are invaluable when a new design is in preparation. The following investigation of the action of the inclined plane, although not directly connected with propeller design itself, should be helpful in making a fair estimate for the quantities mentioned above. The surface is taken to be a plane, but the results are only very slightly different when applied to a surface with a slight camber on it. Suppose we have a perfectly frictionless plane surface, A, B, being forced through the air with a horizontal velocity V at an inclination 6 to the horizontal. Experiment shows that the normal pressure of the air on this surface up to 30° inclination to horizontal is given by P = c A V2 sin 0, where a is the. area of the plane surface and c is a constant determined by the experi ment. The force P can be resolved into a horizontal force, P sin 6, and a vertical force, P cos 6. The force P sin 0, necessary to push the plane through the air, is called the drift, « I) say. 106
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