Waves and ripples in water, air, and æther

by Sir J. A. Fleming

Briefly it may be said that there are three causes, and only three, for the resistance which we feel and have to overcome when we attempt to drag a boat or ship through the water. These are: First, skin friction, due to the friction between the ship-surface and the water; secondly, eddy-resistance, due to the energy lost or taken up in making water eddies; and thirdly, wave-resistance, due to energy taken up in making surface-waves. The skin friction and the eddy-resistance both arise from the fact that water is not a perfect fluid. The wave-resistance arises, as we shall show, from the unavoidable formation of waves by the motion of the boat through the water.

In the case of a wholly submerged body, like a fish, the only resistance it has to overcome is due to the first two causes. The fish, progressing through the water wholly under the surface, makes no waves, but the water adheres to its skin, and there is friction between them as he moves. Also he creates eddies in the water, which require energy to produce them, and whenever mechanical work has to be done, as energy drawn off from a moving body, this implies the existence of a resistance to its motion which has to be overcome.

Accordingly Nature, economical on all occasions in energy expenditure, has fashioned the fish so as to reduce the power it has to expend in moving through water as much as possible. The fish has a smooth slippery skin. (We say “as slippery as an eel.”) It is not covered either with fur or feathers, but with shiny scales, so as to reduce to a minimum the skin friction. The fish also is regular and smooth in outline. It has no long ears, square shoulders, or projecting limbs or organs, which by giving it an irregular outline, would tend to produce eddies in the water as it moves along. Hence, when we wish to design a body to move quickly under the water, we must imitate in these respects the structure of a fish. Accordingly, a Whitehead torpedo, that deadly instrument employed in naval warfare, is made smooth and fish-shaped, and a submarine boat is made cigar-shaped and as smooth as possible, for the same reason.

If the floating object is partly above the surface, yet nevertheless, as far as concerns the portion submerged, there is skin friction, and the production of eddy-resistance. Hence, in the construction of a racing-yacht, the greatest care has to be taken to make its surface below water of polished metal or varnished wood, or other very smooth material, to diminish as far as possible the skin friction. In the case of bodies as regular in outline as a ship or fish, the proportion of the driving power taken up in making eddies in the water is not large, and we may, without sensible error, say that in their case the whole resistance to motion is comprised under the two heads of skin friction and wave-making resistance. The proportion which these two causes bear to each other will depend upon the nature of the surface of the body which moves over the water, and its shape and speed.

At this point we may pause to notice that, if we could obtain a perfect fluid in practice, it would be found that an object of any shape wholly submerged in the fluid could be moved about in any way without experiencing the least resistance. This theoretical deduction is, at first sight, so opposed to ordinary preconceived notions on the subject, that it deserves a little attention. It is difficult, as already remarked, for most people who have not carefully studied the subject, to rid their minds of the idea that there is a resistance to the motion of a solid through a liquid arising from the effort required to push the liquid out of the way. But this notion is, as already explained, entirely erroneous.

In the light of the stream-line theory of liquid motion, it is easy to prove, however, the truth of the above statement.

Let us begin by supposing that a solid body of regular and symmetrical shape, say of an oval form ([see Fig. 30]), is moved through a fluid destitute of all stickiness or viscosity, which therefore does not adhere to the solid. Then, if the solid is wholly submerged in this fluid, the mutual action of the liquid and the solid will be the same, whether we suppose the liquid to be at rest and the solid to move through it, or the solid body to be at rest and the liquid to flow past it.

Fig. 30.—Stream-lines round an ovoid.