Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/204

§ 132 it has been shown by Allen (§ 35 et seq.), that where the $$V^2$$ law rigidly applies the resistance is entirely independent of viscosity, a result that would appear to be highly improbable.

It has been proved from the behaviour of projectiles in flight that the $$V^2$$ law breaks down when the velocity of sound is approached, and without doubt this applies also to an aeroplane when a similar velocity is reached. The defect that manifests itself at these high velocities is that the pressure becomes considerably greater than the law would indicate, or as it may be expressed, the value of the index increases, the expression being written: $$P = k\ V^n .$$ On the other hand, at very low velocities at which the influence of viscosity makes itself felt the law becomes modified in the opposite direction, the value of the index diminishes.

It is probable that in actuality these two influences correct one another over a fairly wide range, so that the $$V^2$$ law may become a far closer approximation than would otherwise be the case.

§ 133. Quantitative Data of the Normal Plane.—The following are the generally accepted data of the Normal Plane, the authority being stated where known:—

Wind Pressure.—$$P = k\ V^2$$ where the constant $$k = .0023, P$$ is in pounds per square foot, and $$V$$ feet per second.

The value of $$k$$ given is that usually accepted, and will be found in the majority of text-books, also in the “Encyclopaedia Britannica” under the article on “Wind.” Molesworth, in his “Pocket Book,” gives the figure .002288, but his authority is not disclosed, neither are particulars given of the method by which accuracy has been obtained to so many places of decimals.

Still Air Data.—Form of expression and units as before. Hutton is quoted as giving $$k = .0017.$$ This result at the time of his experiments (1787–8) must be considered quite remarkable, in view of the fact that one of the most recent