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Aviation History
1909
1909 - 0295.PDF
MAY 22, 1909. The lifting power of an aerofoildepends upon its sweep, i.e., the depth o£ the strata of air which itdisturbs. 10 boss of the propeller and not at the roots of the blade as might have^een expected, Lifting Power and Sweep. Reverting now to the preceding paragraph, the accuracy introduced into pressure-velocity equation by taking account of the value of the dipping front edge in the calculation, establishes the practical utility of the Newtonian method applied to the calculation of the lift of aerofoils. Air, by the Newtonian method, is regarded in principle as consisting of entirely disconnected molecules, which by being infinitely small, constitute an inviscid fluid. On this hypothesis the pressure-velocity equation becomes P = m v\n absolute units where m is the mass per second of the air particles which have been given a change in velocity = v. This change in velocity is determined by the angles of entry and trail, and as both are assumed l2 to be small, their equivalent sum in circular measure may be considered as representing v, in terms of the flight velocity itself. The mass dealt with by the aerofoil is less easily arrived at owing to the undefined sphere of its action; it affects a strata of air above and below its surface, the total depth of which — termed the sweep — may be shown to be a function of the area. Experiment suggests that the co - efficient o f sweep (K) is in the order of unity; that is to say, the depth of the strata may, for practical purposes, be taken as about equal to the fore and aft dimension of the aerofoil, from which the mass per second can be calculated accordingly. The experimental value of the sweep, as stated above, is demonstrated from the fact that a pair of superposed aerofoils (a biplane), do not appreciably interfere with one another, that is say, each exerts its full lifting value, when placed a distance apart, equal to the fore and aft dimension. The Tables, Sufficient has been said to show that there is very con- siderable interconnection between the factors that in- fluence aerofoil design, and pursuing the study of this side of the question to its natural conclusion results in establishing a series of constants to connect the opposite sides of the different equations. All these values are related to the aspect ratio («), as is shown in the accompanying table (Table II), which table, in addition, contains a series of angles of inclination (ft, trail) calculated for minimum resistance, that is to say, for a minimum gliding angle (7). The conditions of minimum resistance (x = y) have already been discussed, and it is of the utmost importance to bear in mind that the whole*basis of the table, and, in fact, the various theories associated with it, depend upon this hypothesis. Two of the constants, those relating to sweep (K), and to the ratio («) between the angles of entry (a) and trail (ft), are unknown, so values which are plausible in the light of theory and experimental evidence have been given. 297 TABLE II. Table of Constants and Angles. (Calculated for least resistance.) t, = -03 £ = -025 I = "O2 : E = -015 = -oi •68sJ2- •70 12- 71 ,2- 72 2- 72512- 73 ;2- 74 ,2 75 12- i6 1 27 1-03 38i-o64 48 I-TO j 551 62i < " I I in •4813-2 : 8-354i3-75 9 5914-14 10 12-9 731801 •12 •'4 •I75| •62 14-4 •6514-8 •6815-0 10-413-2 I3-5 14 11 12S•72 i6-o 12-8 14-7 68 :|i95!"75i6-8 1 inj ° 9-2;IO'8 IO JlI-2 io-8;n-6 10IO-2 i2-2|i2-i5ii3-5io-5 : 7 1 in IO'2 12 I2'8 1212-8 15 I13 1 in 12 7*6 13 ;7-9 14 18-1 I4-7J8-3 15-98-5 157 16-8 17-9 19-1 5 14410- o 15-8 11 -3 17-99-2 7 16-811-819 9-7 22 239 11 — Aspect ratio. C = Normal pressure constant ; PJQ — CpV" where P!l0 = normal pressure ; p = density of air ; V = velocity ft./secs. c — Oblique pressure constant; p /PJQ = r<3 where 0 is the angle of inclination. ^ K =• Sweep constant ; sweep = «A where A = area. Values given are merely plausible.£ = Angle ratio = o//3 where o = angle of entry, and B = angle of trail. Values given are merely plausible. P = Angle of trail for 7 = minimum. 7 = Gliding angle. S - Co-efficient of friction (by experiment). TABLE III.—Load Table. (Pterygoid Aerofoil.) Load (pounds) per Square Foot for Least Resistance. Values of "».":— 5 678 034 -037 136 -148 307^ '333 546 852! 23 ji 0146 |5'93 13 7'75 0 0 I 17- 20' 24S- 4148 54' 1 5 4 2 7 2530 35 40 60 70 80
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