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Aviation History
1915
1915 - 0234.PDF
dealt with almost without regard to considerations of theory, and has degenerated into empiricism pure and simple. For example, mouldings are made to "stock sections" and cut off to different lengths to determine the effect of change of aspect ratio ; or again, aerofoils of some definite camber are tested under unfair conditions, i.e., tho»e to which their particular camber is ill adapted, and in ferences are drawn a> to best values of pressure constant, &c, which are in no sense justified. The attempt is obviously that one condition only shall be changed at a time, but owing to lack of consideration the result is exactly the contrary. We are acquainted with many parallels in engineering practice. If one wishes to find the speed of maximum torque of an internal combustion engine, for example, to religiously change the one condition of speed would be, of course, absurd ; the ignition timing must follow the speed, and the carburettor may need several trial adjustments. Scores of similar examples could be quoted. The latter portion of the paper dealing with the quantitative treatment on vortex theory only purports to lie a sketch of a very promising development, and may be taken as an indication merely of the lines on which the author is at present at work. So far, the cases taken are those for which the main material for solution happens to be at hand ; it must not be imagined that the examples of vortex motion utilised have been selected for any other reason, also the results have in some cases been given without the whole of the reasoning or proofs on which they rest. Before the method can be considered complete, we require to possess the means of specifying our vortex distribution at will, and of solving the same to give the primary and second camber for all points along the span of the aeiofoil ; the author is at present engaged in endeavouring to find u practical solution to this general problem in such manner as will give the designer full control over his product—the difficulties do not appear to be insurmountable. APPENDIX I. This appendix will comprise a reprint of a note communicated by the author to the Advisory Committee for Aeronautics (May, 1914) concerning the influence of the " wash" of the aerofoil on the tail member of a flying machine as affecting stability. In this communication it is demonstrated that experiments made at the National Physical Laboratory to detect arid measure this effect give results in close agreement with the author's theoretical method of treatment a< based on vortex theory as given in his " Aerial Flight," Vol. II, pp. 99 el seq. APPENDIX II. The fotm of the degeneration of vortex rings and vortices generally is a matter of considerable interest. The author has observed that the degeneration is always accompanied by an access of fluid to the inner system of flow, the additional fluid entering the inner system in the vicinity of the axial line from behind. Thus, the theoretical shape of the surface of separation in an ordinary two-dimensional vortex pair is that given in Kig. 21 (A), the fluid in the inner system remains intact and unchanged to per petuity. In actuality it appears that the flow takes place as in Fig. 21 (B), a layer of fluid from the outer system after passing on either side of the combined vortex in stead of passing away symmetrically, in other words, returning to its original condition, is actually caught by the vor tex and enters it from the rear, becoming in due course the outermost layer of the inner system. The broad meaning of this, and, in fact, the proof of its necessity, is in reality very clear and simple. The impulse of the vortex is represented permanently in its momentum, and this is a quantity which do s not undergo diminution. The energy of the vortex, on the other hand, is being slowly eaten up internally owing to the fluid being imperfect, i.e., by the direct and indirect efforts of viscosity. Now, if a dynamic system loses energy under the condition of moment urn - constant, there must either be a redis tribution of the momentum between the different portions of the system tending to a state of uniform motion, or the system must acquire additional ma-s, for, momentum ///-• = const. = k and energy — w-3/2 = trJ2m. That is to say, mass must vary inversely as energy, hence as the energy of the vortex is dissipated, addition to the mass is Fig. 21. necessary. The alternative, that the velocity of the different portions of the vortex system tends to equalisation, may be, in some degree, also true, especially as due to a gradual increase in the diameter of the rotational core or cores, but there is obviously a limit to the extent to which this can take place. The increase of mass is clearly essential and the rate of increase would probably serve as a very close measure of the energy dissipated could measurements be made. The bearing of this on the problem of flight is that we are led to regard the trailing vortices almost as permanent; the distance separating their axes becomes greater and greater the "older" they become and the further their energy is dissipated, but the form of motion remains intact in all probability miles astern of a machine in flight. APPENDIX III. In considering the lateral force due to a cyclic system superposed on a motion of translation, the simplest conception to adopt is that the cyclic motion is due to an impulse applied in a direction- at right angles to the translation ; in the case of the aerofoil we imagine it to be applied to the surface represented by the track, of the advancing foil, that is to say, to a horizontal plane surface extending from the after edge of the foil indefinitely rearward : the direction of the impulse is of course downward. Now this impulse represents a certain quantity of momentum M per unit area of the surface over which it is applied, and if the aerofoil advance through the fluid by one unit distance the impulse surface- is extended by like amount, and for every unit span a quantity of momentum = M must be communicated to the air, hence the load sustained will be equal to the velocity of flight x span x M. This applies directly to the rudimentary case depicted in Fig. 19; when the vortex motion based on a distributed or multiple core (as is in practice invariably the case) the intensity of the impulse will vary over the length of the span in accordance with the distribution of the lines of velocity potential at the surface of gyration, and the form of the distribution requires integration to give the correspond ing solution. In order to carry out the author's present method (whatever the vortex system may be) two conjugate functions must be known ; firstly, the distribution of the stream function (the 1^ of the mathematician) over the surface of gyration on either hand of the axis of flight, as being the determining factor in the primary camber of the foil. Secondly, the velocity potential (the <p of the mathematician) as similarly distributed as determining the distribution of the momentum, and so also the secondary camber. APPENDIX IV. m/ = equivalent mass of air per second: v = velocity of downward discharge ; V — velocity of flight ; A = area of foil ; n = aspect ratio ; p = density of air; C = pressure constant (or lift coefficient) such that lift = CApV* (absolute units); Cw = pressure constant for normal plane, say = 065; | = coefficient of skin friction (double surface augmented coefficient in this case) ; x-Drift = direct aerofoil resistance ; y-Drift = aerodynamic resistance. Lift (= weight sustained) = m, x v. Energy , = mflP/2 . •. jy-Drift = mflpjz V y- Drift _ v ' Lift ~%V Now, on basis of § 11 (Fig. 17), m, = •KAr\pVj$, and lift = CApV- = m/v = irAnpVv/4, or CV = miv/4, or v — qCVjim. , , v v-Drift 2C Hence (1) becomes < -, ., = - Lift irn Where (as in R.A.F. 6) n = 6, this becomes C/3* = 0-to6 C (as plotted No. 2). Again, *-Drift = i,CmApF2 and Lift (as before) = CAp F2. . f-Drift _ ICW of 0-65S Lift C C For model (chord = 2£ in.) V — 30 ft./sec. I ~ 0-017.* x- Drift _ 0-017 x 0-65 _ Lift (1) (2) c For full size machine, ? = 0-0105.* q-Drift _ 0-0105 x 0-65 _ o-ou/C(as plotted No. 3). 0-oo68/C (as plotted No. 5). Lift C Condition of Least Resistance is x Drift = j'-Drift, or *^*> = 2C or C2 = o-$wlnCm. C irn Since o'$irCm, ordinarily speaking, lies within 2 or 3 per cent, of unity, we have approximately— C - ^£„. * Compare James Forrest Lecture, Inst.C.E. 1914, Appendix I. 234
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