FIG. 1. PICTET'S HIGH SPEED BOAT.
A. Lateral View. B. Plan. C. Section of the boiler room. D. Section of the cabin.
Mr. Pictet proposed the problem to himself in a different manner, and as follows:
Determine by analysis, and verify experimentally, what form of keel will allow of the quickest and most economical carriage of a given weight of merchandise on water.
We know that for a given transverse or midship section, the tractive stress necessary for the progression of the ship is proportional to the square of the velocity; and the motive power, as a consequence, to the cube of such velocity.
Fig. 2.--Diagram of tractive stresses at different speeds.
The friction of water against the polished surfaces of the vessel's sides has not as yet been directly measured, but some indirect experiments permit us to consider the resistances due thereto as small. The entire power expended for the progress of the vessel is, then, utilized solely in displacing certain masses of water and in giving them a certain amount of acceleration. The masses of water set in motion depend upon the surface submerged, and their acceleration depends upon the speed of the vessel. Mr. Pictet has studied a form of vessel in which the greatest part possible of the masses of water set in motion shall be given a vertical acceleration, and the smallest part possible a horizontal one; and this is the reason why: All those masses of water which shall receive a vertical acceleration from the keel will tend to move downward and produce a vertical reaction in an upward direction applied to the very surface that gives rise to the motion. Such reaction will have the effect of changing the level of the floating body; of lifting it while relieving it of a weight exactly equal to the value of the vertical thrust; and of diminishing the midship section, and, consequently, the motive power.
Fig. 3.--Diagram of variations in tractive stresses and
tonnage taken as a function of the speed.