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Aviation History
1909
1909 - 0291.PDF
MAY 22, 1909. supported upon a stream of air projected upwards from a jet. It can be shown mathematically that if skin-friction be neglected all the forces which at any instant can possibly operate upon the sphere have each and all of them their vectors directed to its centre, when it is obviously impossible for the body under such circumstances to rotate. Now skin-friction in respect to a sphere would be represented by a tangential force, so that if skin-friction exists in the system described, the irrotational state will no longer result, since it requires but a tangential com- ponent to establish rotation about any arbitrary axis. The sphere is placed in the jet,* which is inclined now to the left, and now to the right, and the sphere, it will be observed, rotates in one direction and then in the other. Thus, by a simple little experiment, can skin-friction be demonstrated, and it only remains to put a practical value upon its co-efficient. Values of the Skin-Friction Co-Efficient (£). Although it is so easy to demonstrate that skin-friction exists, it is less simple, not to say a matter of great difficulty, to accurately establish definite figures for its co-efficient (£), that is to say, to express it as the decimal fraction of the resistance which would be encountered by the same plane moving normally i.e., face-on) instead of " edge-on/' By means of delicate tests, however, the following figures have been obtained :— 1. For smooth planes on a few square inches area at low velocities of about 10 ft. per sec, £ = "02 to "025. 2. For larger planes of from ^ to 1^ sq. ft. in area, moving about 20 to 30 ft. per sec, I = '009 to '015. From these figures it will be observed that skin-friction, so far from being negligible, becomes a dominating factor in flight, where it accounts for much of the resist- ance, and maintains its high order by neutralising the effect of high speed on power. The precise relationship between the co-efficient and the velocity is an investigation of an extremely interesting character, but for the moment it is unnecessary to do more than make a statement to the effect that for all practical purposes the resistance due to skin-friction may be regarded as proportional to V3. . x- ^; How to Reduce the Co-Efficient. In investigating the problem of skin-friction, theory leads to the conclusion that its nature must be that of micro-turbulance between the surface of the body in flight and the contacting fluid. It is not alone a matter of viscosity, for if it were it would not vary as V3,f as it has been found to do in practice. In order to reduce the resistance which it creates, the only way is to use surfaces which are as smooth as possible. :,.,, Head Resistance. Allied to skin-friction is that of direct resistance due to head resistance, which results in creating eddies by setting up surfaces of discontinuity in the wake. The only known way of avoiding this loss of power is to use smooth contours of ichthyoid or fish-like form, so that the resultant stream-line flow of the fluid shall keep it in touch with the surface of the body. There is no mathematical equation for a stream-line shape of body, but nature in the form of fishes, and man in his experi- ments with submarines and projectiles, has evolved suitable shapes for specified practical purposes. In parenthesis, it is worth mentioning that if real fluids possessed the properties of the Newtonian medium of theory, which by hypothesis has no viscosity, any shape of body, however rugged, would be of stream-line form and would meet with no resistance under this heading in flight. By employing bodies of ichthyoid or fish-shaped form'the air streams embrace the walls, whereas square ends and sharp angles cause a presence of dead water andincrease the resistance. Aerodynamic Resistance. Having arrived at this point it is now necessary to revert to that other aspect of the problem which has to do with the statement that the horse-power diminishes- with the speed of flight. It is not, as has already been stated, a complete solution in itself, owing to the fact that it ignores skin-friction. There is, in addition to the skin-friction and that other direct resistance already discussed, a resistance (y) of aerodynamic kind, which results from the supporting of the machine in flight. In this case it can be proved that neglecting skin-friction and edge effect, which have already been taken into account separately, the resistance in the line of flight varies as the angle of inclination (/3) * Mr. Lanchester performed this experiment at a lecture in Birmingham, but was unable to repeat it in London owing to the absence of necessary apparatus. t See Lanchester's Aerodynamics, Chapter II. The aerodynamic resistance encountered by a plane in flight is proportional to the load carried, W, multiplied by theangle of inclination, jj. of the plane multiplied by the weight (VV) sustained.* The weight supported is sensibly equal to the normal reaction ( P3 ) upon the plane, which in turn can be shown to be proportional to the angle of the plane (for small angles) and to VI It follows, therefore, that, if the weight is constant, the angle of inclination is itself inversely proportional to the square of the velocity, and, as the resistance is proportional to the angle, then the resistance consequently bears the same inverse, V2, relationship to the speed, whence also, of course, the power required for a given weight sustained on a given area varies inversely as the velocity of flight. * See Lanchester's Aerodynamics, p. 226. 293
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