The primary work of an experimental model basin is the estimation, with reasonable accuracy, of the resistance and horse-power of full-sized ships from experiments with small and inexpensive models. The first experimental model basin was built nearly forty years ago by Mr. William Froude in his garden near Torquay, England. It was soon taken over by the Admiralty. The second was built by an enterprising firm of Clyde shipbuilders at Dumbarton, Scotland, a little more than twenty years ago. During the last ten years the number of model basins has increased rapidly. Besides England, there are now government basins in Italy, Russia, the United States, Germany, and France, and there are private basins iIi England, Germany, and the United States. In the United States the government basin at Washington began work in 1899. There is a private basin at the University of Michigan, and at Cornell University a canal used for hydraulic experiments is also used, to some extent, for experiments with models of ships and propellers. Existing basins are from 300 to 550 feet long, from 20 to 45 feet wide, and from 8 to 14 feet deep. All of these experimental basins rely upon the principles first enunciated and applied in practice to vessels by Mr. William Froude. The law of Comparison, or Froude's law, as it is frequently called, teaches us that certain resistances of ships and models 11t corresponding speeds vary directly as their displacements. That is to say, at speeds proportional to the square roots of any similar linear dimensions (preferably length), resistances which obey Froude's law are directly as the displacements or as the cubes of similar linear dimensions. Mr. Froude demonstrated conclusively the value of his methods by showing that the actual resistance of a full-sized ship— the English naval vessel “Greyhound"— as determined by towing her, agreed very closely with resistance estimated by his methods from the resistance of a smll model. There are three main components of the resistance of a ship, viz., the skin friction, or the resistance due to the rubbing of the water on the surface; the eddy resistance, or resistance due to the formation of eddies, such as those behind stern-posts, struts, etc.; and the wave- making resistance, or the resistance due to the creation of waves as the ship advances through the water. The first and the third of these elements are the more important in practice. The eddy resistance in properly designed ships is not great, and for prac- ' tical purposes is classed with the wave- making resistance, the two combined forming what is often called the residuary resistance. It is the residuary resistance to which the law of comparison is applied directly. The skin friction does not follow the law of comparison, but, fortunately, it can be estimated with reasonable approach to accuracy for both model and ship. The quantities that have to be dealt with in model experiments are small, and it is necessary that the models be constructed with accuracy and tested by a reliable apparatus with much care. The majority of model basins use paraffin wax in the construction of models, following the practice originally established by Mr. Froude. Paraffin cannot be made to stand the summer heat of Washington without inadmissible change of form, so that at the United States basin wood is used as material for the models. This is more expensive, but, otherwise, has everything in its favor. It enables models 20 feet in length to be regularly used, while with paraffin from 12 to 14 feet is the greatest practicable length. Whether of paraffin or wood, a model must represent accurately to scale the under-water body of its corresponding ship and have a thoroughly smooth surface. At the Washington basin the principal shaping of the models is done by machinery, finishing touches being put on by hand. When preparing for testing, the model is carefully weighted in the water to the exact displacement and trim corresponding to the full-sized ship, and then towed at various speeds, through recording dynamo- metric apparatus, from a carriage which runs back Fig. 1.-Curves of Resistance and Change of Level of Model. Length, 20 Feet; Breadth, 2.076 Feet; Draft, 0.863 Feet; Displacement, 1,694 Pounds. Fig. t.-Speed of Ship About 18.5 Knots. Cumparison of Wave Profile Fore and Aft Estimated from Model Runs with That Observed on Trials of Shi". Fig. 3.—Curves of Effective Horse-Power for Ship of 40,000 Tons Displacement, 800 Feet Long and 0 5.5, 0.60, and 0.6.5 Cylindrical Coefficient. SIMPLE EXPLANATION OF MODEL BASIN METHODS. and forth, and is arranged so that it can tow models at a large number of speeds, the speed of each run being accurately determined and recorded. At the Washington basin electricity was used for the first time to drive the towing carriage. This feature has been copied in all basins of later date. The recorded resistances are plotted as ordinates above the speeds, thus giving a number of spots through which a fair average curve is drawn, giving the total resistance of the model. Fig. 1 shows from an actual model test a number of spots and the resistance curve RR drawn through them. The model represented a collier with a long parallel middle body and was tested to a corresponding speed higher than such a vessel could obtain in service. Its resistance curve shows up well the “humps” and “hollows” which are due to the fact that at some speeds the waves caused by the bow accentuate those caused by the stern, giving a “hump,” while at other speeds the waves from the bow partially neutralize those at the stern, causing a “hollow.” The curves in Fig. 1 showing the change of level of bow and stern are typical. In practically every case, vessels of normal types settle bodily both forward and aft, as speed increases, with but little change of trim until, at a critical speed, which is in knots about 1.15 the square root of the length in feet (5.25 knots for a 20- foot model), the bow begins to rise sharply and the stern to settle sharply. Not many actual ships are fast enough to reach this critical speed. The displacement, wetted surface, and all other necessary quantities in connection with the model having been calculated in advance, the first step in the reduction of the results is to plot a curve such as FF in Fig. 1, which, being the frictional resistance of a plane 20 feet long and having the same surface as the model, is taken as representing the fric- tional resistance of the model. It is important that the surface be taken as 20 feet long, because it has been found by numerous experiments that the coefficient of friction of a smooth plane surface in water varies with the length; the greater the length the smaller the coefficient of friction. The index or power of the speed according to which the friction varies also changes somewhat with the length; but for lengths such as those of actual ships the index is practically constant at 1.83. The intercepts in Fig. 1 between the curves RR and FF give the residuary resistance. The application of the law of comparison to this residuary resistance is comparatively simple. Thus, at 4 knots model speed the residuary resistance is 7.73 pounds. Suppose the 20-foot model represents a ship 500 feet long. Then the linear ratio between model and ship is 25. The displacements are as the cubc of the linear ratio, or as 15,625. Corresponding speeds will be as V 25, or ship speed will be 5 times model speed. The residuary resistance of the ship in fresh water would be, then, 15,625 x 7.73, or, in round numbers, 120,800 pounds at 5x4 = 20 knots. As a general thing, however, while model results are obtained in fresh water, we wish to know the resistance of a ship in salt water. All resistances are taken to vary as the density of the water, which is an ample approximation. So, to obtain the resistance of the ship in salt water, we multiply 120,800 pounds by the ratio between fresh and salt water, which is 1.026. Thus we determine the residuary resistance of the ship in spit water to be 123,900 pounds. We need still to calculate its frictional resistance. We know, by calculation, its wetted surface, and for the coefficient of friction we use Froude's or Tideman's frictional coefficients, obtained from experiments with plane surfaces many years ago, and which, ii may be remarked, have been confirmed by such experiments as have been made on the subject at the United States model basin. But some experiments on large and long planes, with snrfaces such as commonly presented by ships' bottoms, towed at high speeds, would be of great value. The coefficients in use are deduced from experiments with smooth planes of comparatively small dimensions and towed at comparatively low speeds. Actual ships' bottoms are seldom as smooth as pir.nes are made, and their dimensions are much greater- than the planes hitherto tested. The needed investigation. however, would have to be car- continued on page 420.)

This article was originally published with the title "Simple Explanation of Model Basin Methods" in Scientific American 97, 23, 418 (December 1907)

doi:10.1038/scientificamerican12071907-418