In a series of experiments to determine the skin-friction of surfaces moving tangentially in sea water. Froude found that an increase in area is not accompanied by a proportionate increase in resistance; he also found that the index connecting resistance and velocity is in general less than 2, the mean result of several experiments giving 1.92. Colonel Beaufoy, also experimenting in sea water, gives the value 1.7 to 1.8.
Dines, experimenting in the open air, obtained results that have some interest from the present standpoint. In spite of some conflicting evidence, it would, in the main, appear that, under the conditions of experiment, the V2 law is a very close approximation to the truth. In this Dines agrees with the previous experiments of Newton. Hutton, and others, and with the contemporary work of Langley.
It is to be inferred that in cases of direct resistance the Stokes (R ∝ V) and Allen (R ∝V1.5) stages are confined to bodies of very small size and very low velocity. The bodies employed by Dines varied from some few square inches to some few square feet area.
Allen's work in connection with the present subject is of the greatest moment. The present application of dimensional theory is largely due to him as also its experimental verification. His investigations principally relate to spherical bodies of very small dimensions, and demonstrate positively that which has been already inferred negatively, i.e., the small size and low velocities belonging to the Stokes and Allen stages of the characteristic curve.
§ 47. Froude's Experiments.—Owing to the condition of constant geometrical form not having been complied with in these experiments, some doubt exists as to the exactitude of the theory in its application. The planes employed differed in length alone, and it is evident that the skin-friction on a long narrow plane moving endwise will be less proportionately than one of more nearly square proportions, and consequently the effect of
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