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Aviation History
1911
1911 - 0402.PDF
rtjcHT] Schaeffer and Budenberg tachometer; another assistant reao the deflection of the plane, while a third observed the differential pressure in the wind-shields by means of a manometer,, and the wind velocity as given by a pressure-tube anemometer or a Robinson cup anemometer. The duration of an experiment was usually about an hour and comprised ten differeni wind velocities. The following page from the laboratory note-book for January 30th, 1903, gives the results obtained after some skill had been acquired in using the various instruments. Similar observations had been taken in July, 1902, and this much of the present paper was communicated to the American Association for the Advance ment of Science in December, 1932. A few essential data may be prefaced : surface of plane between wind shields, 138*08 sq. ft. ; cross-section of plane, 202-1 sq. ins. ; weight, 58 lbs. ; i-in. swing of plane = o-296 lb. deflecting force ; 1 milligrame per square centimetre differential pressure in the wind shields equals 0-00287 lb. end-thrust on the plane ; mean tempera ture of experiment, 4-5° C. ; barometric pressure, 2974 ins. ; time, 3.30 to 4.30; weather, dry ; mouth of tunnel not screened. TABLE I.—Skin-friction on Plane Measuring 16 ft. x 4/I. xqins. e M B': • S * £ 1 J-1 &£ c u If iff* lbs. •000579 •000875 •001156 •00165 •00203 •00262 •00324 •00392 •00463 •00539 The force in the third column is computed from the observed •swing of the plane. Adding the end-thrust, since the differential pressure opposed the deflection of the plane, there results the actual skin-friction on the exposed surface. . Dividing by the area of the surface gives the values recorded in the. last column. The wind speed is computed from the pressure-tube readings by a theoretical formula, which has been carefully verified by a special series of experiments which were published in the Physical Review, December, 1903. The values of the wind velocity and skin-friction have been plotted on logarithmic cross-section paper, as shown in Fig. 3. MAY 6, 1911. Havintr fairly established the law of variation of the skin-friction with the air velocity, an effort was made to discover its variation w th the length of surface. A simpler method was then adopted which had been considered, but was discarded in the beginning as appearing hardly delicate enough to measure such extremely small forces as the friction was at first conceived to be. Planes were now constructed similar to those commonly used to determine the skin-friction of water. The first was a pine board 4 ft long 25-5 ins. wide, and 1 in. thick, carefully trued and var nished and suspended in the wind-tunnel, as usual, by steel wires o-ozs of an inch in diameter. It was provided with a 7-in. pine prow and stern, both of ogival form. These were held on by dowel-pins, as shown in Fig. 4, and each terminated in a sharp edge from the centre of which a steel pin protruded along stream see d o f F uQ .p.m. 150 200 250 303 35" 400 450 500 55° •600 win g ot Plane . in in. 0-27 0*41 o-54 0*76 o-95 1-19 i-45 1-74 2 "04 2-39 orceCau s Swing . fn ifferenti a Pressur e Shields . Q lbs. mg. sq. cm 0*080 0*121 o"i6o 0-225 0*277 0-352 0-428 o-5i5 0-603 0-701 o-o o-o 0*0 I -0 1*7 3'9 7-1 9-5 *V7 16-5 nd-thrus t Plane . W ressure-t u nemome t £-•••" . lbs. mg. sq. cm 0*0 0*0 0*0 0-003 0*005 O'OII 0*019 0*026 0-037 0-045 70 i°5 155 225 295 375 465 57o 670 815 'in d Spe e j-*» ft. sec. 11*11 13*63 16*16 19*46 22*30 25*14 28*0 •31-0 33*6 37*o S 1 | I 2 i 1 POUNDS PER j SQUARE 1 FOOT 1" r'i 1 "a I si 1 «, | 1 — S Fig. 3.—Relation between velocity and unit friction for 16-ft. plane. Their relation in this, as in subsequent experiments, is invariably expressed by a straight line—that is, by the relation, F=avn . . (a) in which /'is the total friction, v the wind speed, a, n, numerical -constants. The concrete relation obtained from the numerical values of table I is, for a plane 16 ft. long, f= 0-00000671 vvm .... (v = ft. sec.), /= 0*00001363-*'1'85 . . . . (v = mi. hr.), in which / is the average friction in pounds per square foot of surface, and v is the wind velocity in the units indicated within the parentheses. This relation was corroborated by later experiments in which no wind-shields were used. Fig. 4. -Skin-friction plane with sharp ends, suspended in wind-tunnel. between guides to steady the plane against wobbling. As the dowelling was carefully executed, straight planes of any length could be made by adding extra boards, the lengths most employed being 2, 4, 8, 12 and 16 ft. The method of using the planes to determine the surface-friction was as follows :—The total force was measured, at various velocities, using the prow and stern first on the 16-ft. board, then successively on the 12, 8, 4 and 2-ft. boards, and finally with nothing between them. Subtracting this last force from each of the others gave the friction on those five lengths. It may not be absolutely true that the end resistance was the same for each of' those. lengths, but the error of this assumption is regarded as very slight for several reasons : (I) The end resistance is but a small part of the total; (2) the stream lines are so slightly disturbed that the flow about the: ends must be practically the same in all cases ; (3) the results harmonise very well with those obtained by other methods. Tarjle II, taken from the laboratory note-book, exhibits the observed and computed values for the 2-ft. friction-board. The mouth of the tunnel was screened with cheese-cloth to steady the flow of the air, in order to obviate wobbling in so small a board. The velocity was thus reduced, it is true, but sufficient values are given to make a reliable diagram. The following data may be prefaced : Surface of the 2-ft. plane without prow and stern, 8*83 sq. ft. ; weight of plane with end pieces, 17 lbs.';" I-in. swing of plane = 0-0862 lb. wind force; barometric pressure, 29*80 ins. • mean temperature of experiment, 24*2° C. TABLE II.—Surface Friction by 24 ins. x 25*5 ins. Pine Board with Prow and Stern. •0 u a. O*) r.p.m 200 250 300 350 400 450 500 & ° V r<5 M .5 -r S '* *** g«o CO (I, in. lbs. o"05o 0*00431 o*oSo 0-00690 0*120 0*01034 0*158 0-01362 0-205 0-01767 0*260 0*02240 0*310 0*02586 O w i 0 0 s lbs. 0*00233 0*00365 0*00553 0*00734 0-00949 0-01188 0*01379 c 0 £ fc •jQ 9. Z H i. 0 5 E v a &&lt; lbs. mg.sq.cm 0*00198 0*00325 0*00481 0*00628 0*00818 0*01052 0*01207 22*8 37"o 58-0 78-5 103-5 132-0 i55'o f So i o-fcL, •si *a| M £ 5> •£ £w ft. sec. lbs. 6*38 0-000224 8-i2 0-000368 10-18 0-000545 n-8o o-ooo7io 13-52 0-000925 15-34 0-001188 16-61 0-001366 The third column gives the whole force on the friction-board with its prow, stern, and suspension wires. The fourth column gives the torce on the latter alone, which, deducted from the whole force, gives the friction on the sides of the 2 ft. length. Dividing this net tnction by i^, the area of the true friction surface, gives the values in the last column. 404
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