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Aviation History
1940
1940 - 0922.PDF
Italy's fighter squadrons, equipped with Fiat biplanes,persistently practise close-formation work. Here are C.R.32S in tight stepped-down " vies." dynamic resistance or " induced drag " may be calcu- lated as based on the mass of a cylindrical body of air of circular section whose diameter is equal to the span, in the following manner :— Let S be the span, and V be the velocity of flight; then the equivalent mass of air dealt with per second, which may be denoted by the symbol (mis) n- X 4 (I) where p is the density of the air. If W = the weight sustained, the downward velocity imparted to this mass of air per second, v = W/(m/s) (2) Then the work done per second = (w/s)^2 _ (m/s)W2 Wa 2 ~~ 2(w/s)2 ~~ 2(m/s) '' - " '" (3) Substituting for (mis) by eq. (1), 2W2 Work done per second = c,. .. .. (4)7rb Vp Since for any given flight velocity (V = const.) W and S are the only variables, equation (4) tells us that the work done in overcoming the induced drag varies as W2/S2. In order that no doubt shall exist as to the application • Absolute units are used throughout. MARCH 28, 1940 of this equation, a numerical example may be given. Let W = 31,000 pounds (approximately 14 tons), then 31,000 x 32.2 = 1,000,000 poundals. Let S = 100ft. Let V = 300ft./sec. p, air density (taken as at sea level) = .076 lb. per cu. ft. Then Foot-poundals per sec. = 2 x 1,000,000" = 2,800,000 3.14 x 10,000 x 300 x .076 = 87,000 foot-pounds per second. From this we derive the induced drag = 87,000/300 = 290 pounds, and the power necessary to overcome this = 87,000/550 = 158 h.p. This gives the induced drag/lift ratio = 290/31,000 or approximately one per. cent. This is, of course, only a part of the total drag, but it is the part with which we are now concerned. Having made clear by a numerical example the im- plication of equation (4), we may now return to our problem. Let it be supposed that two equal aeroplanes of identical weight and span are flying with their wings tips just touching (Fig. la). Then taken together their combined weight will be double that of a single machine. Also we may regard the total span as twice that of either machine singly. In order to make this more real the two planes may be regarded as definitely connected to form a single machine (Fig. ib). Then in equation (4) both W and S are increased in like ratio, so that W2/S2 has the same value for the combined machine as for the single machine, and the aerodynamic resistance or in- duced drag will be the same for the " twin," ib. as for the single ia. And the same will be true if we combine any number of machines in a similar manner as in Fig. 2a. The Span Load Distribution A pause for reflection is necessary at this juncture" There is a little discrepancy which becomes evident when the number of machines flying tip-to-tip becomes large ; the whole combined as a single machine in the manner illustrated (Figs, ia and ib) is not exact as representing the sum of the individual machines. Either the combination would have to be rigidly connected (structurally unified) in order to give the load grading proper to the combination, or we should have to postu- late that the centrally situated machines should be more heavily loaded than those on either flank. This would only be important if the combination shown in Fig. 2a were literally possible, which of course it is not. Still, the main result is unexpected. It would almost suggest an overwhelming advantage in favour of the large machine, which is contrary to experience, for although we are only dealing with that part of the drag known n* induced dnia the combined profile drag
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