Fig. 33.—Echelon waves made by a model yacht.
On looking at a boy’s model yacht in motion on the water, the same system of waves will be seen; and on looking at any real yacht or steamer in motion on smooth water, they are quite easily identified ([see Fig. 33]).
Fig. 34.
The complete explanation of the formation of these bow or echelon waves is difficult to follow, but in a general way their formation can be thus explained: Suppose we have a flat piece of wood, which is held upright in water, and to which we give a sudden push. We shall notice that, in consequence of the inertia of the liquid, it starts a wave which travels away at a certain speed over the surface of the water. The sudden movement of the wood elevates the water just in front of it, and this displacement forms the crest of a wave which is then handed on or propagated along the surrounding water-surface. If two pieces of wood are fastened together obliquely, as in [Fig. 34], and held in water partly submerged, we shall find that when this wood is suddenly thrust forward like a wedge, it starts two oblique waves which move off parallel to the inclined wooden sides. The bows of a ship, roughly speaking, form such a wedge.
Hence, if we consider this wedge or the bows of a ship to be placed in still water and then pushed suddenly forward, they will start two inclined waves, which will move off parallel to themselves.
If we then consider the wedge to leap forward and repeat the process, two more inclined waves will be formed in front of the first; and again we may suppose the process repeated, and a third pair of waves formed. The different positions of the ship’s bows are shown in the diagram at 1, 2, and 3 in [Fig. 35]; and c, e, and f are the three corresponding sets of echeloned waves. For the sake of simplicity, the waves are shown on one side only. If, then, we imagine the ship to move uniformly forwards, its bows are always producing new inclined waves, which move with it, and it is always, so to speak, leaving the old ones behind. All these echelon waves produced by the bow of the ship are included within two sloping lines which each make with the direction of the ship’s line of movement, an angle of 19° 28´.[16] This angle can be thus set off: Draw a circle ([see Fig. 36]), and produce the diameter BC of this circle for a distance, CA, equal to its own length. From the end A of the produced diameter draw a pair of lines, AD, AD′, called tangents, to touch the circle. Then each of these lines will make an angle of 19° 28´ with the diameter. If we suppose a ship-to be placed at the point marked A in the diagram ([see Fig. 36]), all the echelon waves it makes will be included within these lines AD, AD′.
Fig. 35.