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Aviation History
1911
1911 - 0403.PDF
MAY 6, 1911. iJX'!/ S^f W,ere °btained for the other friction-boards, ot Arables are oio'tted'nn ,reSPeCv1t,Ve'y- When ths Values fr™ *e hve tables are plotted on logarithmic cross-section paper thev eive hve separate straight lines, all having the same incline on is the one shown in tlg. 3, m which the sl -8?. This means that for all the velocities and lengths of surface employed in form"?-%$ Sk,n-f"Ctl0n/fts «P««?ed by an equatio'n "of the T fr - * '_.* ;T " (3)' a bemS a numerical constant, and v the wind speed. Hence if the net friction on each board is velodt any V y' n Can readi'y be comPuted for any other In practice the computations illustrated in Tables I and II were obviated, for all the tables, by a simple expedient. The observed anemometer readings and swing of the plane were plotted while the measurements were in progress, giving five straight lines, all of the same slope. Then a point was selected on each line representing a wind speed of 10 ft. per sec, and the corresponding friction per square foot of surface noted. From these values the numerical equations between F and v can at once be written. The observed values are given in the subjoined table :— TABLE III.—Skin-friction at 10 ft. per sec. for Various Lengths 0/ Surface. Length of friction board 2 4 8 12 16 Average friction, lbs. per sq. ft. 0-000524 0-000500 0-000475 0-000467 0-000457 Knowing, then, the friction at the same speed on five different boards, there remained to determine the law of its variation with length of surface. To that end, the values in Table III were plotted on logarithmic cross-section paper, as shown in Fig. 5. The result is a straight line whose equation is of the form, /= al,-°'m whence F =fi = a/'93. . . . (y), in which y is the average friction in pounds per square foot, and / is the length of surface in feet. At 1 ft. per sec. the coefficient is 0-00000778; hence at any speed, v feet a second, the average friction per square foot is /=• 0-00000778 ^*!im. . . (z/= ft. sec), /"=O-ooooi58/-°'07z;1'85. . . (v = m\. hr.) Assuming the two laws thus far derived to be true for the planes and wind speeds employed, we may readily express the total friction on a plane of any length from 2 ft. to 16 ft., moving at any speed from 5ft- to 40 ft. a second. Thus, by the last equation, the total friction, F, on a surface I ft. wide and 1 ft. long is F =/?o-ooooo778/'93wr85. . . (v — ft. sec.). F = 0-0000158l"Mvvm. . . (v = ra\. hr.) Of course this value of F must be doubled for a material plane of length, /, and width I ft., since a material plane has two sides. In order to facilitate the computation of skin-friction in practice, the following table has been derived from the equation /= 0-0000158/-°'07 w1'85. The friction for any intermediate velocity, or length of surface, may be found by interpolation. If the surface is of variable length, it may be divided into longitudinal strips, the force on each strip being the product of the area of the strip multiplied by the average friction for its particular length. Only the values in heavy type lie within the range of the experiments above described. TABLE IV.—Friction per sq.ft. for Various Speeds and Lengths oj Surface. Average Friction in lbs. per sq. ft. mi. hr. „ 5 0-000303 0-OOO289 0-OOO27S 0-000262 0-000250 o-000238 10 o-ooii2 0-00105 000101 0000967 0000922 0000878 15 0-00237 000226 000215 000205 000195 0-00186 20 000402 0-00384 000365 000349 000332 000317 25 o-00606 o-00579 000551 o-00527 0-00501 o- 00478 ?0 0-00850 0-00810 0-00772 0-00736 0-00701 0-00668 35 0-01130 0-0108 0-0103 0-0098 0-00932 o-c- 40 0-0145 0-0138 0-0132 0-0125 0-0125 50 0-0219 0-0209 0-0199 0-0190 0-0181 60 0-0307 0-0293 0-0279 0-0265 0-0253 0-0242 70 0-0407 0-0390 0-0370 0-0353 0-0337 0-0321 80 0-0522 0-0500 0-0474 0-0452 0-0431 0-0411 90 0-0650 0-0621 0-0590 0-0563 0-0536 o 0511 160 0-0792 o-o75S °-°7i9 °-°685 °'o652 ° °622 It may now be inquired what other circumstances alter the surface friction^ Perhaps the chief of these are the atmospheric changes of density and the unevenness of surface. \pM\ 0-0114 0-0172 No effort was made to determine the relation between the density and skin-friction of the air, partly for want of time, partly because, with the apparatus in hand, too great changes of density would be needed to reveal such relation accurately. Doubtless the friction increases with the density, since it is due to the inertia of the fluid near the friction surface. Of course, in steady motion at low velocity, such as studied by Maxwell, the conditions are different. He found that when one plane moved edgewise near and parallel to another plane, at a constant speed below ^th of an inch per •1 1 I I % MET 1 J \ ' ' "1 1 ( b • 10 u * » Fig. 5.—Relation between length and unit-friction at 10 ft. per sec. second, the friction is independent of the pressure and proportional to the absolute temperature for such atmospheric conditions as prevail near the earth's surface. Some measurements were made with the 4 ft. friction-board covered with various materials to observe the effect of quality of surface upon the tangential resistance. Practically the same friction was observed, whether the board was covered with dry varnish, or wet, sticky varnish, or sprinkled with water, or covered with calendered or uncalendered paper, or glazed cambric, or sheet zinc, or old Knglish drafting paper, which feels rough to the touch. But when the plane was covered with coarse buckram, having 16 meshes to the inch, the friction at 10 ft. a second was 10 to 15 per cent, greater than for the uncovered surface, and the friction increased as the velocity raised to the power 2-05, or approximately as the square of the speed. The fact that such a variety of materials exhibit practically the same friction seems to indicate that this is a shearing force between the swiftly gliding air and the comparatively stationary film adhering to the surface, or embedded in its pores. If, as seems to be true, there is much slipping, this means that the internal resistance of the air is less at the surface than at a sensible distance away. As the shearing strength of a gas is due to the interlacing of its molecules, owing to their rapid motion normal to the shearing-plane, it may be that the diminution of shear near a boundary surface is due to the dampening, within the film, of the component of molecule trans lation normal to the surface. To summarise the results attained thus far, it may be said that, within the ascribed limits of size and wind speed— i. The total resistance of all bodies of fixed size, shape and aspect is expressed by an equation of the form R = az>" .... (o), R being the resistance, v the wind speed, a, n, numerical constants. 2. For smooth planes of constant length and variable speed the tangential resistance may be written A' = ar rM .... (&). 3. For smooth planes of variable length, /, and constant width and speed the friction is R = al '*' . . . . (-y). 4. All even surfaces have approximately the same coefficient or skin-friction. 5. Uneven surfaces have a greater coefficient of skin-friction, and the resistance increases approximately as the square of the velocity. The equation A' = av" was found to express very accurately the resistance of all the shapes tested at speeds from 5 ft. to 40 ft. a second. For normal planes, spheres, cylinders, and blunt bodies generally, except very small ones, n equals 2, very approximately ; for thin, tapering bodies M may have any value from 2 to I -85 ; but in every case, if the form and aspect of the model remained fixed, a and u are found to remain practically invariable for all the speeds employed. This was manifested by plotting the speed and resistance on logarithmic cross-section paper and observing that the diagram was invariably a straight line for all the models tested. The statement cannot be true for a great range of speeds. (To be cone hided.) ® ® ® ® Flights as "Campaigns." IN spite of the special allowances granted to airmen, the French Minister of War appears to hold the opinion that their pay is still not sufficient, and so M. Berteaux intends to introduce shortly into the French Parliament a Bill providing for special payments t* certificated officers for cross-country flights, whMe the services of the aviators will count as "services in the field." On gaining his military certificate, each aviator will be credited with one "cam paign," while when he has flown a certain distance that will count as another "campaign," and so on. A certain number of "campaigns" render French officers eligible for the Legion of Honour, and thus these new rules would open the way for the airmen to obtain this distinction. 405
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