It is now nearly a year ago since we announced to our readers the
researches that had been undertaken by the learned physicist, Raoul
Pictet, in order to demonstrate theoretically and practically the forms
that are required for a fast-sailing vessel, and since we pointed out
how great an interest is connected with the question, while at the same
time promising to revert to the subject at some opportune moment. We
shall now keep our promise by making known a work that Mr. Pictet has
just published in the _Archives Physiques et Naturelles_, of Geneva,
in which he gives the first results of his labors, and which we shall
analyze rapidly, neglecting in doing so the somewhat dry mathematical
part of the article.
For a given tonnage and identical tractive stresses, the greater or less
sharpness of the fore and aft part of the keel allows boats to attain
different speeds, the sharper lines corresponding to the highest speeds,
but, in practice, considerably diminishing the weight of freight capable
of being carried by the boat.
[Illustration: 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.
[Illustration: 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.
[Illustration: Fig. 3.--Diagram of variations in tractive stresses and
tonnage taken as a function of the speed.]
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.
[Illustration: 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.
The water escapes in a thin and even sheet as soon as the tractive
stress exceeds 2,000 kilogrammes; and the intensity and size of
the eddies from the boat sensibly diminish in measure as the speed
increases.
The interesting experiments made by Mr. Pictet seem, then to clearly
establish the fact that the forms deduced by calculation are favorable
to high speeds, and will permit of realizing, in the future, important
saving in the power expended, and, consequently, in the fuel (much less
of which will need to be carried), in order to perform a given passage
within a given length of time. Thus is explained the great interest that
attaches to Mr. Pictet's labors, and the desire that we have to soon be
able to make known the results obtained with such great speeds, not when
the boat is towed, but when its propulsion is effected through its
own helix actuated by its own engine, which, up to the present,
unfortunately, has through its defects been powerless to furnish the
necessary amount of power for the purpose.--_La Nature_.
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