Over the water-surface is arranged a pair of rails, on which runs a light carriage or platform. This carriage is drawn along by a rope attached to a steam-engine, which moves at a very uniform rate, and its speed can be exactly ascertained and automatically recorded. This moving carriage has a rod or lever depending from it, to which the model ship is attached. The pull on this rod is exactly registered on a moving strip of paper by very delicate recording mechanism. The experiment is conducted by placing the model at one end of the tank, and taking a run at known and constant speed to the other end. The experimentalist is thus able to discover the total resistance which it is necessary to overcome in pushing the model ship at a certain known speed through the water. The immersed surface of the model being measured and the necessary calculations made, he can then deduct from the total resistance the resistance due to skin friction, and the residue gives the resistance due to wave-making. Suppose, then, that the experiment has been performed with a model of a ship yet to be built, the run being taken at a “corresponding speed.” The observations will give the wave-making resistance of the model, and from Mr. Froude’s second law the wave-making resistance of the real ship is predicted. Adding to this the calculated skin-friction resistance of the real ship, we have the predetermined actual total ship-resistance at the stated speed. For the sake of giving precision to these ideas, it may be well to give an outline of the calculations for a real ship, as given in a pamphlet by Mr. Archibald Denny.[19]

The tank at the Leven shipyard, constructed by Messrs. Denny Bros. for their own experiments, is 300 feet long, 22 feet wide, and 10 feet deep, and contains 1500 tons of fresh water. At each end are two shallower parts which serve as docks for ballasting and trimming models. As an example of the use of the tank in predicting the power required to drive a ship of certain design through the water, Mr. A. Denny gives the following figures: The ship to be built was 240 feet in length, and from the drawings a model was constructed 12 feet in length, or one-twentieth the size.

It was then required to predetermine the power required to drive the ship through the water at a speed of 13¹⁄₂ knots. A knot, be it remarked, is a speed or velocity of 1 nautical mile an hour, or 6080 feet per hour. It will be seen that this is not far from 100 feet per minute.

By Froude’s first law, the corresponding speed for the 12-foot model is therefore⁠—

The model was accordingly dragged through the tank at a speed of nearly 5 feet per second, and, after deducting from the total observed pull the resistance due to the calculated skin friction of the model, it was found that the resistance to the motion of the model at this speed due to wave-making was 1·08 lb. Hence, by Froude’s second law, the wave-making resistance of the ship was predetermined to be⁠—

The last fraction ⁴⁰⁄₃₉ is a correcting factor in passing from fresh water to salt water.

The surface of the proposed ship was 10,280 square feet, and the skin friction was known to be 1·01 lb. per square foot at a speed of 13·5 knots. Hence the total skin resistance of the ship would be⁠—

Adding to this, the 8850 lbs. for wave-making resistance, we have a total resistance of 19,470 lbs. predetermined as the total pressure required to be overcome in moving the ship at a speed of 13·5 knots. Hence, since 1 horse-power is defined to be a power which overcomes a resistance of 33,000 lbs. moved 1 foot per minute, it is easy to see that 19,470 lbs. overcome at a rate of 13·5 knots represents a power of⁠—

But now, in the case of a screw-driven steamer, a part of the power is lost in merely churning up the water, and a part in internal frictional losses in the engine and screw-shaft.

It is not far from the truth to say that 50 per cent. of the applied engine-power is lost in useless water-churning. Hence, for the above steamer, an actual power of at least 1600 H.P. would have to be applied to the screw-shaft. To allow, however, for the loss of power in friction, and to allow a margin for emergencies, it would be usual to provide for such a steamer engines of at least 3000 indicated horse-power.

Each shipbuilder has, however, at call a mass of data which enable him, from actual measured mile trials, to determine the rates between the calculated driving horse-power and the indicated horse-power of the engines, and so enable him, in the light of experience, to provide in any new ship the exact amount of steam-power necessary to produce the required speed. As an instance of how accurately this can be done by the aid of the tank experiments, Mr. A. Denny gives an example drawn from experience in building the well-known paddle-steamers Princess Josephine and Princess Henriette for the Belgian Government Dover to Ostend fast mail-steamer service.

The speed guaranteed before the boats were built was 20¹⁄₂ knots. The estimate was made for 21 knots, and the actual results of trials on the measured mile, when the ships were built, showed that each did 21·1 knots on prolonged and severe test.

The reader, therefore, cannot fail to see how important are these methods, laws, and researches of Mr. Froude.

The above-described process for testing models is being continually conducted in the case of all new battleships and cruisers for the British Navy, and also is pursued by the naval constructors of other nations. In connection with the extensive programme of battleship construction which has been carried out of late years, Sir William White, the late eminent Chief Director of Naval Construction, states that it is not too much to say that these methods of investigation and experiment have placed in the hands of the naval architect an instrument of immense power for guiding him safely and preventing costly mistakes. Sir William White has declared that it would have been impossible to proceed with the same certainty in battleship design, were it not for the aid afforded by these methods.

Mr. Froude was not content, however, with experiments made with models. He ascertained by actual trials the total force required to drive an actual ship through the water at various speeds, and obtained from other experiments valuable data which showed the proportion in which the total resistance offered to the ship was divided between the skin friction and the wave-making resistance.

Then he made experiments on a ship of 1157 tons, viz. H.M.S. Greyhound. This vessel was towed by another vessel of 3078 tons, viz. H.M.S. Active, by means of a tow-rope and a dynamometer, which enabled the exact “pull” on this hawser to be ascertained when the Greyhound was towed at certain speeds. The following are some of the results obtained:⁠—

It will be seen that the total resistance increases very rapidly with the speed, varying in a higher ratio than the square of the speed.

In addition, the indicated horse-power of the engine of the Greyhound was taken when being self-driven at the above speeds, and it was found that only 45 per cent. of the indicated horse-power of the engines was used in propelling the ship, the remaining 55 per cent. being wasted in engine and shaft friction and in useless churning of the water by the screw.

It is an important thing to know how this total resistance is divided between skin friction and wave-making resistance.

Mr. R. E. Froude has kindly furnished the author, through the intermediation of Sir William White, with some figures obtained from experiments at Haslar, showing the proportion of the whole ship-resistance which is due to skin friction for various classes of ships going at certain speeds.

The above table gives the percentage which the skin friction forms of the total resistance, and the remainder is, of course, wave-making and eddy-resistance.

The curves shown in Fig. 41 (taken, by kind permission of the editor, from an article by Mr. E. H. Tennyson-D’Eyncourt, in Cassier’s Magazine for November, 1901) give, in a diagrammatic form, an idea of the manner in which the two principal sources of ship-resistance vary with the speed.

It will be seen that when a ship is going at a relatively slow speed, the greater portion of the whole resistance is due to skin friction, but when going at a high speed, the greater portion of the resistance is due to wave-making. Hence the moral is that ships and boats intended to move at a high speed must be so fashioned as to reduce to a minimum the wave-making power. In general, the naval architect has to consider many other matters besides speed. In battleship design he has to consider stability, power of carrying guns and armour, and various other qualities. In passenger-steamers he has to take into consideration capacity for passengers and freight, also steadiness and sea-going qualities; and all these things limit and control the design. There is one class of vessel, however, in which everything is sacrificed to speed, and that is in racing-yachts. Hence, in the design of a racing-yacht, the architect has most scope for considerations which bear chiefly upon the removal of all limitations to speed. A little examination, therefore, of the evolution of the modern racing-yacht shows how the principles we have endeavoured to explain have had full sway in determining the present form of such boats.

Attention has chiefly been directed to this matter in connection with the international yacht race for the possession of the America Cup.

In 1851 a yacht named the America crossed the Atlantic and made her appearance at Cowes to compete for a cup given by the Royal Yacht Squadron. Up to that time British yachts had been designed with full bluff bows and a tapering run aft. These boats were good sea-boats, but their wave and eddy making powers were considerable. The America was constructed with very fine lines and a sharp bow, and was a great advance on existing types of yacht. In the race which ensued the America won the cup, and carried it off to the United States.

Since that date there has been an intermittent but steady effort on the part of British yachtsmen to recover the trophy, so far, however, without success.

In a very interesting article in Harmsworth’s Magazine, in 1901, Mr. E. Goodwin has traced the gradual evolution of the modern yacht, such as Shamrock II. or the Columbia, from the America.

No doubt the methods of “measurement” in force at the time, or the dimensions which determine whether the boat can enter for the Cup race or not, have had some influence in settling the shape. The reader, however, will see, on comparing the outlines of some of the competing yachts as shown in Fig. 42, [20] that there has been a gradual tendency to reduce the underwater surface as much as possible, and also to remove the wave-making tendency by overhanging the bows. The only rule now in force restricting the yacht size for the Cup race is that it must not be more than 90 feet in length when measured on the water-line. In order that the yacht may have stability, and be able to carry a large sail-surface, it must have a certain depth of immersed hull. This is essential also to prevent the boat from making leeway when sailing with the wind abeam. But consistently with this object, the two great aims of the yacht-builder are, first, to reduce as much as possible the skin friction by making the yacht-surface smooth and highly polished. Thus modern racing-yachts are not always built of wood, but very often of some metal, such as bronze, steel, or aluminium alloys, which admit of a very high polish. This hull-surface is burnished as much as possible before the race, to reduce to a minimum the skin friction. Then in the second place, the designer aims at fashioning the form of the bow of the yacht so as to reduce as much as possible its wave-making qualities. A fine type of modern yacht glides through the water with hardly any perceptible bow wave at moderate speeds.

Thus the following extract from the Chicago Recorder of September 4, 1901, respecting Sir Thomas Lipton’s yacht, Shamrock II., during her trials for the Cup race, shows how marked a feature this is in the case of a yacht of the best modern type:⁠—

We may say, therefore, that the ideal form of yacht is one which would travel through the water without making any wave at all at bow or stern. This condition can, however, only be reached approximately, but the clear recognition of the principle has enabled yachts to be designed with vastly greater speed powers than in the old days of bluff bows and tapering bodies.

Before passing away from the subject of waves made by ships, it is desirable to refer a little more in detail to the complicated wave-system made by a ship in motion. This has been most carefully elucidated by Lord Kelvin, who, in this as in so many other matters, is our great teacher. Lord Kelvin has shown that if a small floating body is towed through the water at a uniform speed, it originates a system of waves, each one of which is of the form shown in Fig. 43. The whole system of waves formed is represented in Fig. 37, where the position of the ship or moving object is at the point marked A.

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:⁠—

For another boat-weighing 12,579 lbs., or 6 tons, the results obtained in the same manner were as follows:⁠—

This last experiment shows, in a very remarkable manner, the way in which the force required to drag the boat falls off as the critical speed of 9 miles an hour is reached.

Here, then, we have the outlines of the proof first given by Mr. Scott Russell, that the tractive force undergoes a sudden diminution when the speed of the boat in a canal approximates to or just exceeds that of the long wave in that particular depth of water. If passenger traffic on canals had not been destroyed by the advent of railways, we should, no doubt, have seen extensive applications of the principle discovered so curiously by the aid of an alarmed horse, and so skilfully investigated by a celebrated engineer.

The whole theory of the trail of waves made by a canal-boat is only comprehensible if it is clearly seen that a water-surface wave has a certain velocity determined by its wave-length. If the wave-speed is small, the waves are short. As the speed increases the waves get longer. Or the matter may be put in another way. We may say that just as a pendulum has a certain rate of vibration depending on its length, so a water wave has a certain frequency, and therefore, a certain speed of propagation dependent upon the wave-length, or shortest distance from one wave-crest to the next. When a boat moves along a canal the waves it makes move with it, and the first wave of all moves with the speed of the boat. Hence the wave-length must accommodate itself to that speed. As the speed of the boat increases towards that of the free “long wave,” the wave-length gets greater and greater, and when the boat-speed is equal to that acquired by a heavy body, say a stone in falling through half the depth of the canal, then there is only one wave, and the boat rides up on that one. The next wave is practically so far behind that it is non-existent, and the boat ceases to be followed by any trail of waves, or “wash.”