Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/285

applicable.^[1] The result is that the aeroplane shows results far better than theory would indicate unless a diminished value of $\xi$ be employed in the equation.

The probable explanation of this anomaly is to be found in the supposition that for the angles investigated the flow is of the Rayleigh-Kirchhoff type, as illustrated diagrammatically in Fig. 98 ($a$), the result being that the effect of skin friction is only felt on the one face of the plane instead of on both faces, as would be the case if the flow were conformable, and consequently the apparent value of $\xi$ is only about half its real value.

There is a serious but not insuperable difficulty attached to the foregoing explanation. It would appear that since the “dead water” is itself subject to a tangential drag at its free surfaces, and since, as a whole, it has no influence to keep it in position other than the reaction of the aeroplane itself, this frictional drag must be transmitted to the aeroplane, and so in some way take the place of the missing skin friction.

On examining the matter in greater detail, it is evident that the form of the dead water region is determined primarily by the dynamics of the live stream, and if the fluid be supposed frictionless the dead water will extend indefinitely rearward, and its pressure will throughout be uniform. If now we take into account the effects of viscosity there will be a frictional or viscous drag acting tangentially at the surface of discontinuity between the dead water and the live stream, and referring to Fig. 114, it is evident that the cumulative effect of this drag will be to create a pressure gradient, the pressure at $A$ being less than that at $B$, and that at $B$ less than that at $C$, and so on. In consequence of this pressure difference the dead water will become

1. The results so far obtained by the author on the value of $\xi$ by different methods are not altogether in harmony. Since writing this and the following sections (§§ 182, 183, and 184), certain experiments made with a new instrument, the aerodynamic balance (Ch. X.), seem to indicate that the conclusions here formulated may require qualifying; the results at present available, however, are not conclusive, and it has been thought best to present the argument in its original form.

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