These waves move with the yacht. If the ship is a long one, then each of these waves gives rise to a wave-train; and on looking at a long ship in motion, it will be seen that, in addition to the inclined bow wave-system, there is a series of waves which are seen in profile against the hull.
When a ship goes at a very high speed, as in the case of torpedo-boat destroyers, the bow of the vessel is generally forced right up on to the top of the front transverse waves, and the boat moves along with its nose entirely out of water ([see Fig. 39]). In fact, the boat is, so to speak, always going uphill, with its bows resting on the side of a wave which advances with it, and its stern followed by another wave, whilst behind it is left a continually lengthening trail of waves, which are produced by those which move with the boat.
Fig. 39.
The best way to see all these different groups of ship-waves is to tow a rather large model ship without masts or sails—in fact, a mere hulk—over smooth water in a canal or lake. Let one person carry a rather long pole, to the end of which a string is tied; and by means of the string let the model ship be pulled through the water. Let this person run along the banks of the canal or lake, and tow the ship steadily through the water as far as possible at a constant speed. Let another person, provided with a hand camera, be rowed in a boat after the model, and keep a few yards behind. The second observer will be able to photograph the system of ship-waves made by the model, and secure various photographs when the model ship is towed at different rates. The echelon and transverse waves should then be clearly visible, and if the water is smooth and the light good, it is not difficult to secure many useful photographs.
By throwing bits of bread to ducks and swans disporting themselves on still water, they also may be induced to take active exercise in the right direction, and expose themselves and the waves or ripples that they make to the lens of a hand camera or pocket kodak. From a collection of snap-shot photographs of these objects the young investigator will learn much about the form of the waves made by ships, and will see that they are a necessary accompaniment of the movement of every floating object on water. By conducting experiments of the above kind under such conditions as will enable the exact speed of the model to be determined, and the resistance it experiences in moving through the water, information has been accumulated of the utmost value to shipbuilders.
Our scientific knowledge of the laws of ship-resistance we owe chiefly to the labours of two great engineers, Mr. Scott Russell and Mr. William Froude. Mr. Froude’s work was begun privately at Torquay about the year 1870, and was subsequently continued by him for the British Admiralty. Mr. Froude was the first to show the value and utility of experiments made with model ships dragged through the water. He constructed at Torquay an experiment tank about 200 feet in length, which was a sort of covered swimming-bath, and he employed for his experiments model ships made of wood or paraffin wax, the latter being chosen because the model could be so easily cut to the desired shape, and all the chips and the model itself could be melted up and used over again for subsequent experiments. Without detailing in historic order his discoveries, suffice it to say that, as the outcome of his work, Mr. Froude was able to state two very important laws which relate to the relative resistance experienced when two models of different sizes are dragged through the water at different speeds.
The first of these relates to what is called the “corresponding speeds.” Suppose we have a real ship 250 feet long, and we make an exact model of this ship 10 feet long, then the ship is twenty-five times longer than the model. Mr. Froude’s law of corresponding speeds is as follows:—
If the above model and the ship are both made to move over still water, the ship going five times as fast as the model, the system of waves made by the model will exactly reproduce on a smaller scale the system of waves made by the ship. In other words, if we were to take a couple of photographs, one of the ship going at 20 miles an hour, and one of the model one twenty-fifth of its size going at 4 miles an hour, and reduce the two photographs to the same size, they would be exactly alike in every detail.
Expressed in more precise language, the first law of Froude is as follows: When a ship and a model of it move through smooth water at such speeds that the speed of the ship is to the speed of the model as the square root of the length of the ship is to the square root of the length of the model, then these speeds are called “corresponding speeds.” At corresponding speeds the wave-making power of the model resembles that of the ship on a reduced scale. If we call L and l the lengths of the ship and the model, and S and s the speeds of the ship and the model, then we have—