All those masses of water which receive a horizontal acceleration from the keel run counter, on the contrary, to the propulsive stress, and it becomes of interest, therefore, to bring them to a minimum. The vertical stress is limited by the weight of the boat, and, theoretically, with an infinite degree of speed, the boat would graze the water without being able to enter it.
The annexed diagram (Fig. 1) shows the form that calculation has led Mr. Pictet to. The sides of the boat are two planes parallel with its axis, and perfectly vertical. The keel (properly so called) is formed by the joining of the two vertical planes. The surface thus formed is a parabola whose apex is in front, the maximum ordinate behind, and the concavity directed toward the bottom of the water. The stern is a vertical plane intersecting at right angles the two lateral faces and the parabolic curve, which thus terminates in a sharp edge. The prow of the boat is connected with the apex of the parabola by a curve whose concavity is directed upward.
Fig. 4.--Diagram of the variations in the power as a
function of the speed.
When we trace the curve of the tractive stresses in a boat thus constructed, by putting the speeds in abscisses and the tractive stresses in ordinates, we obtain a curve (Fig. 2) which shows that the same tractive stress applied to a boat may give it three different speeds, M, M', and M'', only two of which, M and M'', are stable.
Experimental verifications of this study have been partially realized (thanks to the financial aid of a number of persons who are interested in the question) through the construction of a boat (Fig. 1) by the Geneva Society for the Construction of Physical Instruments. The vessel is 20.25 m. in length at the water line, has an everywhere equal width of 3.9 m., and a length of 16 m. from the stern to the apex of the parabola of the keel. The bottom of the boat is nearly absolutely flat. The keel, which is 30 centimeters in width, contains the shaft of the screw. The boiler, which is designed for running at twelve atmospheres, furnishes steam to a two cylinder engine, which may be run at will, either the two cylinders separately, or as a compound engine. The bronze screw is 1.3 m. in diameter, and has a pitch of 2.5 m. The vessel has two rudders, one in front for slight speeds, and the other at the stern. At rest, the total displacement is 52,300 kilogrammes. This weight far exceeds what was first expected, by reason of the superthickness given the iron plates of the vertical sides, of the supplementary cross bracing, and of the superposition of the netting necessary to resist the flexion of the whole. On another hand, the tractive stress of the screw, which should reach about 4,000 kilogrammes, has never been able to exceed 1,800, because of the numerous imperfections in the engine. It became necessary, therefore, to steady the vessel by having her towed by the Winkelried, which was chartered for such a purpose, to the General Navigation Company. It became possible to thus carry on observations on speeds up to 27 kilometers per hour.
Fig. 3 shows how the tractive stress varies with each speed in a theoretic case (dotted curve) in which the stress is proportional to the square of the speed, in Madame Rothschild's boat, the Gitana (curve E), and in the Pictet high speed vessel (curve B).
The Gitana was tried with speeds varying between 0 and 4 kilometers. The corresponding tractive stresses have been reduced to the same transverse section as in the Pictet model in order to render the observations comparable. At slight speeds, and up to 19.5 kilometers per hour, the Gitana, which is the sharper, runs easier and requires a slighter tractive stress. At such a speed there is an equality; but, beyond this, the Pictet boat presents the greater advantages, and, at a speed of 27 kilometers, requires a stress about half less than does the Gitana. Such results explain themselves when we reflect that at these great speeds the Gitana sinks to such a degree that the afterside planks are at the level of the water, while the Pictet model rises simultaneously fore and aft, thus considerably diminishing the submerged section.
With low or moderate speeds there is a perceptible equality between the theoretic curve and the curve of the fast boat; but, starting from 16 kilometers, the stress diminishes. The greater does the speed become, the more considerable is the diminution in stress; and, starting from a certain speed, the rise of the boat is such as to diminish its absolute tractive stress--a fact of prime importance established by theory and confirmed by experiment.
The curves in Fig. 4 show the power in horses necessary to effect progression at different speeds. The curve, A, has reference to an ordinary boat that preserves its water lines constant, and the curve, B, to a swift boat of the same tonnage. Up to 16 kilometers, the swift vessel presents no advantage; but beyond that speed, the advantage becomes marked, and, at a speed of 27 kilometers, the power to be expended is no more than half that which corresponds to the same speed for an ordinary boat.