Fig. 43.
The key to a correct comprehension of this ship wave-system is to be found in the fact explained in Chapter I., that a group of water waves on an indefinitely extended water surface advances at half the speed of a single wave. It has already been shown that when a single wave-disturbance is made upon water it gradually develops itself into a group of waves. The single wave when created causes a disturbance on water which extends both forwards and backwards. As the wave moves forward the wave-disturbance is always growing in front and dying away behind, and the wave-group therefore moves forward, but the centre or limits of the group move with only half the velocity of a single wave.
Now consider the ship originally at B ([see Fig. 36]), and let us suppose the ship to make a small jerk forward. This operation is like plunging a stone into the water, and it starts a wave-system. But if the ship moves forward with a uniform speed, by the time the ship has reached the point A, the end of the wave-group will have reached a point C, such that C is halfway between B and A. The movement of the ship, however, originates a group of waves, and the velocity of a wave on water is dependent upon its wave-length, as already explained, so that the greater the wave-length the greater the velocity. Hence the conditions that determine the form of the wave-system round the ship are: (1) that the head of the procession goes forward with the speed of the ship; (2) that there is an end or limit to the transverse system of waves behind, which moves forward with half the speed of the ship; (3) the inclination of the wave at any point to the direction of motion of the ship must be such that its velocity, in its own direction, is consistent with the wave-length at that place. These general conditions determine the form of the wave-group as shown in [Fig. 37]; but the detailed predetermination of the exact form of the oblique and rear wave cannot be made without the employment of mathematical reasoning of a somewhat advanced character.
For the purposes of the general reader it will be sufficient to note that this procession of ever-extending waves, which lengthens backwards behind a ship, requires energy to produce it. This energy must be supplied from the ship, and the wave-production constitutes therefore a cause of resistance to motion which is felt and has to be overcome in keeping the speed of the ship constant.
In close connection with this subject is the fine investigation made about the year 1834 by another eminent engineer, Mr. Scott Russell, on the motion of canal-boats. His researches were communicated to the Royal Society of Edinburgh. It has already been explained that when a wave is started in a canal, the wave-length being large compared with the depth of the canal, then the velocity of the long wave is the same as that attained by a stone in falling through air a distance equal to half the depth of the canal. Scott Russell made the interesting discovery that it is only when the speed of a canal-boat is less than that of a long wave in the canal that the boat leaves behind it a procession of waves. The position of the boat is then on the rearward side of the first wave. As already mentioned, the boat leaves behind it a trail of waves, and the rear of this procession travels forward at half the speed of the boat. If the speed of the boat is greater than that of the longest free wave in that canal, it cannot make any procession of waves, and then there would be no system of ever-lengthening waves behind it, but only one wave or hummock travelling along under the boat. Lord Kelvin describes, in his lecture on “Ship Waves,”[21] how this important discovery was in fact made by a horse. The horse belonged to one William Houston, and its daily duty was to drag a canal-boat on the Glasgow and Ardrossan Canal. On one occasion the horse took fright and galloped off, and Houston, being an observant man, noticed that when once the horse had attained a certain speed the tractive resistance evidently became lessened, and the boat was dragged along more easily and without wash behind it. Accordingly, he started a system of light canal-boats—or fly-boats, as they were called—each 60 feet long, and drawn by two horses at 7, 8, or 9 miles an hour. The horses were whipped up and made to gallop, and soon dragged the boat up on to the top of its own wave, whereupon it went along much more easily, and without a system of stern waves.
Mr. Scott Russell instituted a searching investigation into this effect in 1837 at the bridge of Hermiston, on the Forth and Clyde Canal, at a place where there was a straight run of 1500 feet. The depth of the canal water was 4 to 5 feet, and the speed of the long wave was accordingly 12 feet per second, or 8 miles an hour.
Experiments were made, amongst others, with a boat called Raith, the weight of which was 10,239 lbs., or 5 tons. This boat was towed along the canal, and the “pull” on the tow-rope measured by means of an instrument called a dynamometer. It was found by Mr. Scott Russell that the pull or force required to drag the boat did not increase with the speed regularly, but fell off in a marked manner when the speed of the boat reached 9 miles per hour. This is shown by the following table:—
| Scott Russell’s Experiments on Canal-boats. | ||||
| Tractive force in pounds applied to boat. | Speed of boat in miles per hour. | |||
| 112 | 4·72 | |||
| 261 | 5·92 | |||
| 275 | 6·19 | |||
| 250 | 9·04 | |||
| 269 | 10·48 | |||
For another boat-weighing 12,579 lbs., or 6 tons, the results obtained in the same manner were as follows:—
| Tractive force in pounds. | Speed in miles per hour. | |||
| 250 | 6·19 | |||
| 500 | 7·57 | |||
| 400 | 8·52 | |||
| 280 | 9·04 | |||