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Aviation History
1920
1920 - 1213.PDF
NOVEMBER 25, 1920 since the new thrust divided by the new load W, gives thenew D/L, it is seen that TA T (35) and hence in order to determine the D/L for any new loading it is merely necessary to draw a tangent from ^/2 and the Pratio y read off on the original scale is the corresponding D value of the -y- required. m iK m •t — toon \ \ MOO \ tor Machine / fota//oodi 'is /jm \ \ - ' - — h — A — / i i i —i Af — 10 X 40 X Several interesting results appear from the values obtained. 1. The influence of wind on the L/D is greater for light loads than for heavy. A change in L/D from 8 • 43 to 5 • 90 is found for the 7,000-lb. machine as against a change from 8 43 to 7-60 for the 13,000-lb. machine, these values, corresponding to a change in head-wind speed of 50 miles per hour. 2. This influence still holds although much less noticeably for helping winds, the L/D changing from 8 43 to 8-30 for the light machine as against 8 43 to 8-34 for the heavy machine. 3. For any reasonable head wind that could be flown against in long-distance flight, the change in the L/D is small, running from 8 43 to 8-00 for the 7,000-lb. case to 8-43 to 8-25 for the 13,000-lb. case, these values corresponding to a head wind of o and 30 miles per hour, respectively. As practically it is difficult to fly at a given angle with mathematical accuracy the main result of these figures is to show that as the head winds increase in speed it is neces- sary to slightly diminish the flying angle ; exactly how much depending on a preliminary calculation as outlined above. The instructions to the pilot can be given in either of two ways : (a) Proper flying angles for any given wind. (b) Proper air speed for any given wind. A plot of the values of L/D against wind speeds for the three, loadings is shown in Fig. (11). These L/D values correspond to definite air speeds at a given altitude and definite angles of incidence which can also be placed upon the plot. Such a chart will give with sufficient exactness the proper flying angles for practical navigation under economical con- ditions. Range Formula including Effect of Winds ^ The time-weight equation (13) t = ^ - m.p / , SO /Or Fig. 10 This single curve is preferably ploted for some simple load such as 1,000 pounds or 10,000 pounds. The D/L's will then come out directly by dividing the power by the speed, and by changing the position of the decimal point. Example of Use of the One-Curve Method. In order to check the proposed method against the usual multicurve method, three P—V curves were plotted for the same machine with loads of 7,000 lbs., 10,000 lbs. and 13,000 lbs. respectively. The machine weighs 7,000 lbs. empty. These curves are shown in Fig. (10). The L/D's for various wind speeds were derived from them and compared with the L/D's taken from the 10,000-lb. curve using modified wind speeds as described above. The agreement is very satisfactory-, as shown in the table (6) below. When using the curve for a 7,000-lb. load the modified wind speeds corresponding to w are where V 7 = 1•195 w, and for a load of 13,000 lbs. they are "1 . : i j | t VA/M4r/0tf//V £\ —\W/rh /oading oncf' w/na'speecf | —• _._ "I — ! _ INS for machines hor/nt/ 1\ ! \ 1 \ \ \ \ J a l D 7 / V I 6 - •SO -w 0 Wind Speed mp h 40 SO Fig. 11 •0C3a o 5 rt « ftIll TABLE (6). a .5'i O oo -40 -20 o 10 20 30 40 5° 8-26 8-35 8-41 8-41 8-29 8-04 7-47 5 95 a o.t (7,000 lbs.) 8-31 8-37 8-43 8-43 8-31 803 7-45 5-90 -47-80 -23-9° 0 n-95 23-90 35-85 47-86 59-75 (10 ',000 lbs.) 8 8 8 8' 8- 8- 7' T •31 35 •44 41 32 •19 96 21 8 <-> w ft 8-358-38 8-43 8-41 8-41 8-25 8 04 7-62 9 qp (13,000 lbs.) 8-338-40 8-438-42 8-428-25 8-077-60 -35 06 -17-53o 8-77 J7-53 26-60 35-o6 4V82 is naturally unchanged, since for a given angle of incidence the time in which the fuel is consumed cannot depend on whether there is a wind or not. The time-distance equation must be modified. Since the ground distance is the important factor the wind modifies the range. If at any instant the air-speed is V and the wind speed vi, the ground speed is V - w, and in time dt a ground distance dS = (V - w)dt (36) will be covered. With an obvious substitution, this becomes W - dt — w dt and S == ~~7Z~ dt. 1215
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