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Aviation History
1910
1910 - 0367.PDF
MAY 14, 1910. g — gravity, A = disc area of propeller, v — slip stream velocity. If there is any discrepancy it must obviously lie in the value given to the disc area, for the other values are all actual quantities. It is here assumed that there is no appreciable rise in the density of the 1/QGHT] -tooo 2000 . "^ tf • I] ¥ ^•^— & z 1 8 2 1- 3 0 a 6 + *> 2 P 6 2. DISTANCE FROM A*IS OF ROTATION. (buMI Chart showing results of a test on an Asco propeller, 6 ft. 8 ins. B in diameter, pitch ratio ro, blade width (max.) 93 ins. The above curve indicates the velocity of the sMp stream at different distances from the axis of rotation as measured by an anemometer distant 3 ft. from the plane of the propeller, while the propeller itself is developing 55 lbs. thrust at 495 r.p.m. The maximum measured velocity exceeds the stated pitch speed. Tests taken on J. A. May's apparatus at the South-Western Polytechnic, April 6th, 1910. air as the result of compression, a fact that can be established one way or the other by a suitable investigation of the region in question. It does not necessarily follow that the effective cross sectional area of the slip stream is equal to the disc area of the propeller, but it is very important to know the relation ship between the two in connection with calculations. A direct measurement of the effective cross sectional area of the slip stream would probably be a difficult matter to ac complish, whereas it is quite possible that a series of static thrust tests might be the means of deducing a reasonably accurate coefficient of area that could be applied to all propellers of a certain type. Such coefficients would be of immense value in bringing about the agreement between theory and practice that is so very desirable. A Useful Formula. Taking the case of the fundamental formula T = mv = -P Ae* = ? - DV = I. - DW S 8 4 g' 4 where T = thrust, m — mass, v — slip stream velocity, p = density, g = gravity, A = disc area, D = propeller diameter, p = propeller geometric pitch, n — propeller revolutions per sec, and introducing coefficients of disc area (c\ and pitch q) as follows :— T = ?" i%W 8 4 2 the basis of a practical formula is obtained for the calculation of the thrust of propellers that have not been tested. Taking the case of a propeller in flight, we may express the slip stream v as a percentage (j>) of the flight speed V (feet/sec.) thus :— and, therefore, the above formula for thrust Chart showing becomes ratl° '*» blade T = p * ^DVV2 .8 4 which may be simplified to . • -.£ . T = «D»V2, where K is a constant, including in one term the values This form of the equation has many advantages. In the first place the thrust T, flight speed V, and diameter D, are always fundamental data in the design of any machine, which means to say that the required value of « is known in advance for any machine for the above equation. The Value of K. The problem of selecting a propeller thus resolves itself into finding the design that best satisfies the required value of K, i.e., has the highest efficiency when its K is the stated amount. The second advantage of the above form of the equation is that in making a test of a propeller (on a whirling table or in an artificial draught) the values of T, D, and V are obtained as direct readings, and, therefore, also produce values of K by direct calculation. The results of such a test would naturally first of all be set down in the form of a chart having the curve of thrust plotted to the co-ordinates of V and K, since for each value of V there is a value for K that can be obtained by direct simultaneous measurement. Bearing in mind, however, that the final results of the tests are required as a guide to the use of other propellers that have the same ratio of pitch to diameter but actually differ in size, it is obviously more convenient to express the flight speed V in terms of ihe pitch speed (/.».) or better still in terms of the apparent slip expressed as a percentage of p.n. Using such chart as a guide to which K is the index, it is a simple calculation to arrive at the requisite revolutions for a given flight speed and propeller diameter, both of which must be initially assumed in the design of any machine. If measurements of the torque on a propeller-shaft are made simultaneously with the other observations, a curve of efficiency in relation to thrust can be superimposed on the same chart, and thus the whole of the information required about a propeller is presented in a most convenient and intelligible form (see diagram). The constant, K, serves as an index to the conditions under which a propeller of given diameter and pitch must work in order to produce the required thrust at the stated flight speed. These conditions will differ for various forms of propeller, as shown by the difference between the curves obtained from different tests, but the index, K, is unaffected thereby. Any number of propeller chaits may be obtained, but the same value of K will be used as an index to each in order to ascertain which combines the qualities of highest efficiency and most con venient revolutions. jj -J h 3 1 r h Z I ' ' / • /' .' / ! s / / 0 i / NE T fl < y 1 ^ <l E« ^ •*>' we .< ^ t ps *2 - l^- 1 \ 2 i § Is ! \ .— i?'4 results of a test on an Asco propeller, 6 ft. 8 ins. in diameter, pitch width (max.) 10 ins. Tests taken on J. A. May's apparatus at the South-Western Polytechnic, April 18th, 1910. In practice, since K is such a very small number, it is convenient to work with values of K = (K X I,OOO). The advantage of having such a uniform basis as a common ground on which propellers could be compared and discussed the world over, is obvious; we hope the method described will meet 365
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