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Aviation History
1910
1910 - 0630.PDF
[fiWf] AUGUST 6, 1910. CAN WE FLY FASTER FOR L,KSS POWER? SUGGESTIONS FOR WINNING THE PART III. Conclusion.) IN the two preceding articles on this subject we have discussed the power required to propel cambered planes at different speeds and have suggested a method of calculating the lift that results from such impressed velocity. Throughout we have drawn attention to the angle of 50 as representing the condition of minimum resistance, and it is the purpose of the present article to show how that angle has been derived. It has already been explained that the determining factor in the calculation is an assumed coefficient and law of skin friction, and we purpose, therefore, discussing the question of skin friction forthwith. The most reliable data on the subject are to be found in the results of experiments conducted by Prof. A. F. Zahm, who established the relationship between skin friction and velocity in the following formula: R = "0000316/'9'iV1'85 (where R = skin friction in lbs./sq. ft. of double surface, /= length of surface, i.e., chord, V = flight speed m.p.h.) The above expression of the law of skin friction shows that the resistance due to this cause varies with the length of surface as well as with the velocity. As the length of service of an aeroplane is not very great, we have, for convenience, ignored this factor in the equation, which would, of course, have to be taken into account in calculations affecting the skin friction of a dirigible. Zahm's formula for skin friction is thus modified for the present purpose to the expression R = '0000316 V1"85. It will be observed that the index of V, which is 1*85, is approximately the square, and as it would be very convenient to assume that the skin friction is proportional to V2 it is worth while investigating the nature of the error of such an assumption in order to see how lar it is likely to affect calculations. In an accompany ing chart we have shown this difference by means of two graphs, one of which is plotted to represent Zahm's law, while the other is R08 Ibs/sqft •075 •07 065 •06 •055 •05 •045 •04 •055 03 •025 02 •015 -01 -005 "DAILY MAIL" £10,000 PRIZE. plotted to the V2 law by means of an assumed coefficient (•000018) that makes the results identical for a velocity of 40 miles an hour. This speed is in the order of that of modern aeroplanes. It will be noticed that the two graphs lie fairly close together up to a speed of 90 miles an hour, after which speed the discrepancy becomes more serious. It would seem, therefore, as if it is quite justifiable to assume the V2 law for skin friction as applying within the limits of the probable flight speeds of the immediate future. We may thus write R = -000018 V2. The importance of this assumption is due to the fact that the aerodynamic resistance, which constitutes the other part of the total resistance to flight, varies inversely as V2, and the consequence of assuming the V2 law for the skin friction is that it establishes a very simple condition for the minimum total resistance, which obtains when the resistance due to skin friction is equal to the resistance due to load. By the aid of Zahm's experiments, and the assumption of a suitable coefficient, we have been enabled to establish actual values for skin friction; it remains, therefore, to find an expression representing the aerodynamic resistance in flight, and here again it is necessary to make another assumption to the effect that the energy expended on the support of the load is entirely represented by the energy remaining in the deflected air stream, or wave as it might be called, that the aeroplane creates. Applying first principles to this assumption, we must work from the fundamental formula:—Energy (ft. lbs. per sec.) = \ mi?. Once again we will assume, as in the previous article, that the effective stratum of air deflected has a depth equal to the chord of the plane, whence we may write : m (per sec.) ?L//^=-?AV (where L = span, /=chord, V = flight-speed, p = density,g — gravity, A = area); for the velocity we will also.assume, as in the previous > IX It v7 /M // // r it /, it j 1 i // ' v'// // 1 R lb •25 •2 •15 1 •05 1-85 /saft V2^ ^r 5 •8, •7 - -65- •6 - -55 - 45 "4 i i 1 CHART SHOWING DIFFERENCE- BETV RESISTANCE* The Conslan /EEN s are:— R« OOOOOIBV2 R= Resistance Ibs/sq.ft. J y / / / / •* / / / / /' /' v> / X/"85 \P/ 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 ISO 200 MVH. 628
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