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Aviation History
1919
1919 - 0013.PDF
JANUARY 2, 1919 PERFORMANCE OF AEROPLANES. By W. L. COWLEY, A.R.C.Sc, D.I.C., Wb IT is becoming increasingly evident that certain charac teristics of aeroplanes are of outstanding importance 111 relation to fitness for fighting. Whereas in the past it was considered an achievement if machines were strong enough structurally to withstand the stresses and strains brought into play during flight and at the same time to attain a speed of 90 to 100 m.p.h., recent experience has demon strated what important factors are excessively high speed, rapid climb, and ease and agility of manoeuvre. Whether or not the engine is to play a more or a less important part than the aerodynamic parts of the machine depends upon whether such questions as durability of flight enter into the calcula tions. It is ultimately, however, only by an analysis of the performance curves of machines in general, and of already built machines in particular, that the more important factors upon which these questions depend can be accurately deter- $0 90 JPEtD (M.P.H) mined. The power of putting up a short spurt at a critical moment in climbing, or manoeuvring rapidly in a small circle from one flight path to another, depends to a large extent on the thrust that can be developed in an emergency by the engine. The general problem of manceuvreability is clearly so wide and complicated, that it is proposed in the present article merely to analyse the performance of machines under certain steady conditions of flight, to determine the relations that exist between the horse-power that the engine and propeller develop, the rate of climb and the turning circle, and to find the conditions under which circular flight may be executed with the greatest rapidity. A corresponding analysis for spiral flight will also be given. In Fig. 1 is plotted the air resistance at various speeds at ground level for a given machine. The product of each REV5. fxr /VUN. ordinate of curve 1 by the corresponding velocity gives the power required at ground level to overcome the resistance. Sc„ and H. LEVY, M.A., B.Sc, F.R.S.E. (curve 3). The difference between the ordinates of these two horse-power curves for any speed furnishes a measure of the horse-power available for climb, &c. The upper point of intersection determines the maximum speed of horizontal flight. Performance curves describing the characteristics of the machine at various speeds are usually plotted, as above, on the assumption that the atmosphere is of unifotm density, but the fact that the air forces and the propeller thrust depend directly on the density of the air indicates clearly that the performance curves will not be complete unless allowance is made for variations 111 this quantity. The mere fact that at a height of 10,000 It., a not uncommon flying altitude, the density p has already dropped to 0-7 of its value at the earth's surface, is a sufficiently clear indication that alterations in the performance curves due to this cause are of considerable importance. The air forces are proportional to pVa, and since at higher altitudes for a given angle of attack the same lift, viz., pAL£VJ, must be maintained, a comparison between per formance curves at various levels must be made at corre sponding values of p~V*. It will therefore be convenient to plot the quantities concerned on a V *Jp base, where p is assumed unity at ground level. On this base the resistance curve of a machine will not change with altitude. This is not so, however, with the horse-power curves. In the case of the horse-power required to overcome the drag, the latter quantity was multiplied by the corresponding velocity. To obtain this horse-power curve, therefore, on a V -/p base, each original horse-power must now be divided by -v'p, so that the ordinates are accordingly all increased. Since at the higher altitudes the velocity of flight must be increased to maintain the lift, the propeller will of necessity be working at a higher slip, and the thrust will drop unless the revolutions be increased proportionately to give the same thrust and slip. At the same time the energy given to the engine will have fallen, on account of the smaller mass of air taken up by the cylinder at each stroke for these lower densities, and therefore the horse-power delivered up will fall off for the same revolutions, approximately as the density. In Fig. 2 is plotted horse-power available from engine at ground level against engine revolutions (curve 1). Curve 2, representing the engine horse-power at a height where the density is p, is derived by multiplying each ordinate of 1 by p. The system of curves 3, 4, and 5, giving the propeller torque horse-power against revolutions at various constant speeds, intersect curve 2 at X, Y, Z, &c, and accordingly fix the torque horse-power, forward velocity and revolutions. From these and the factors of the propeller the efficiency is, of course, at once obtained, and by multiplying the latter by the torque horse-power the thrust horse-power corresponding to that height is derived. This is now plotted on a Y Vp base in Fig. 3. The horse-power required to drive the machine is immediately calculable and plotted in Fig. 3 on a Vv'p base by multiplying the ordinate of the horse-power curve at ground level by V(i/p). Once more the horse-power available for further climb at each speed and the greatest minimum speed of flight can be derived. It is manifest that as the density diminishes these curves include a constantly decreasing area until ultimately a point is reached at which the maximum and minimum speeds of flight coincide, and there is no horse-power available for further climb. This determines the highest altitude to which this machine can ascend. This height is usually FIG. 3. termed the ceiling. It can be further increased by special treatment of the engine—for example, by supplying it with r-..^» .v-^^^v. ",. 6n.uim revu LU uvcituuie me icsisituice. ncctLiucni; ui xne engine—ior example, oy supplying it wit 11 This (curve 2) is plotted in Fig. 1 in the same diagram as oxygen underpressure. The effect of variation in density with the maximum horse-power available from the propeller height appears therefore to be the prime lactor in imposing 13
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