Apparatus and Means for ascertaining by Laboratory Experiments the Behaviour of Ships on Waves.
Year: 1899

page_text: PROVISIONAL SPECIFICATION.
Apparatus and Means for ascertaining by Laboratory Experiments
the Behaviour of Ships on Waves.
I, GIOACCHINO Russo, Naval Architect, of the Royal Italian Navy, and Member of
the Institution of Naval Architects, of Rome, Italy, do hereby declare the nature
of this invention to be as follows:-
My invention relates to an experimental reproduction of the rolling movements of
ships among waves, by means of pendular bodies, each of which is so arranged as to
represent, on a small scale, the rolling motion of a given ship; such pendular bodies
are supported by a mechanical apparatus, whose motion is so contrived, as to exercise
on them the same action that the motion of the sea exercises on ships.
My mechanical experiments, produced on a small scale, have for their object the
solution of a problem of naval architecture, which lies in the following terms: to
ascertain what oscillations a given ship will perform, when set rolling passively broad-
side-on, in the different conditions of wave motion that she may meet.
These experiments relate both to existing ships and to ships about to be built, in
which case they serve to ascertain beforehand their more or less degree of steadiness,
as well as to demonstrate the influence of the different elements on which their
rolling depends, such as statical stability, fluid resistance, moment of inertia etc.; con-
sequently they render it possible to find the best arrangement of these elements,
having regard to the rolling properties of the ship.
The invention, which has been patented in Italy on an application dated 3rd July
1898, and in France on an application dated 29th December 1898, comprises:
wave motion oscillo-
1. The construction of an apparatus that I have named a
graph," although in reality it is, like the wave, a generator of oscillations; it is
intended to produce, when acting on pendular bodies whose description is given here-
after, the same mechanical conditions (on a small scale) which the motion of the sea
produces on rolling ships.
2. The construction of pendulum shaped bodies, which I call "navipendulums,"
and which are so made as to represent, for any given ship, the mechanical properties
which come into play in her transverse oscillatory movements.
3. The combination, made according to my method, of a wave motion oscillograph
and a navipendulum for experiments on rolling for any given ship, whatever may be
the dimensions that one may wish to assign to the wave.
Figs. 1 and 2, Sheet 1, show the shape I give to a navipendulum.
A tubular rod A B, strong but very light, is provided with two heavy, disc-shaped
bobs H, H, which are fixed at any required position along the said rod by means of
small friction collars D. A central piece or hub E, hollow for lightness, is secured
to the rod A B, and serves to support two steel blades, F, F, whose lower edges are
thinned down and shaped after a line ff whose geometrical properties I will define
hereafter. The navipendulum thus composed can be placed on a flat plate LL having
a hole in its centre, and can be made to rest with its two blades upon two perfectly
straight and parallel grooved bars. Upon these conditions it can oscillate like
a pendulum whilst rolling on its supporting base.

page_text: .
The navipendulum may, however, bave various other shapes; for instance, the
rod may be arranged horizontally, instead of vertically; instead of the two blades
that determine a cylindrical rolling surface, there may be a solid cylindrical surface.
The essential properties that form the special characteristics of a navipendulum are
the following-
=
1. The line ff (Fig. 1 Sheet 1) represents on a proportional scale y chosen
arbitrarily as regards lengths (for instance y 1/10 or y1/15) a line ƒƒ peculiar
to the hull, to be represented. In Fig. 1, Sheet 1, I have shown the section of the
ship and the navipendulum drawn to the same scale.
The line ff is, as regards the hull, a parallel curve to the curve C C, which is
defined in the theory of the ship as the curve of the centres of buoyancy for all
transverse inclinations corresponding to the given displacement.
One may say thus, that the curve ff is one of the involutes of the metacentric
evolute m.
Among the infinite number of involutes the curve ff is chosen, so as not to be
too far removed from the centre of gravity G, and so as to be convex as far as that
angle of inclination, which one may consider as the extreme angle which the ship
will never exceed when rolling; although not a very essential condition, it is
advisable, that the curve ff should be as near as possible to the point G.
y
2. The relative positions of the line ff and of the centre of gravity G in the
navipendulum are regulated so as to be similar to the relative positions of the line ff
and of the centre of gravity G in the ship, always in the ratio of similitude fixed
for the lengths. (In the case of Fig. 1, Sheet 1, the ratio of similitude is supposed
to be equal to the unit, and the lines F F and the points G of the ship and of the
navipendulum coinciding).
In order to fulfil this condition, it is enough, to fix the two weights H H in their
correct positions along the rod. It is then evident, that the arm of the couple of
statical stability, for any inclination, is in the ratio of y to the arm of the corre-
sponding couple of the ship; consequently if z be the ratio between the arbitrary
weight of the navipendulum and the displacement of the ship, the mechanical
moments of the couples of stability are in the ratio y xz, the mechanical works
required to incline the navipendulum and the ship to any angle are also in the
ratio y x 2.
3. Whilst fulfilling the above mentioned condition, the two weights H H are
sufficiently removed from the centre of gravity, to produce a period of oscillation of
the navipendulum which bears a determined ratio to the period of oscillation of the
ship in still water.
Assuming as above y to be the ratio of similitude for lengths, the ratio of similitude
for the periods of oscillation must ✓y. It arises from the well-known principle of
the mechanical similitude established by Newton.
In order to determine the period of oscillation of the ship in still water, for a ship
to be constructed, one must first calculate the real moment of inertia, then on the
basis of this element construct a model of the ship, then experiment in the usual
way, on a small scale, the transverse oscillations of the model in still water, as is
commonly done by naval architects.
From these experiments there can be obtained also the extinction curve of
amplitudes; now this result is indispensable in order to be able to complete the
composition of the navipendulum. It is necessary, that the navipendulum should
have the same extinction curve as the ship. This result may be obtained by making
passive forces of different sorts react on the navipendulum, for example a frictional
resistance on the supporting plane, or else the resistance of the air, by adding
suitably proportioned vanes to the rods A, B. The system that I prefer is the
following:
A block of wood D (Fig. 3, Sheet 1), or of any other light and easily shaped material,
is secured to the rod, with its upper cylindrical surface shaped according to a certain
dissecting line m, n. A leather belt CC is stretch above the block D in contact with
it, and parallel to the supporting plane B, B. As the navipendulum rolls, the block D

page_text: rubs continually against the belt, which produces a frictional resistance, more or less
great, according as the block D, in its motion, exercises a greater or less pressure on
the belt, raising it more or less from its original straight direction. Everything
depends on the shape of the line m, n; now this line cannot be determined
theoretically, but must be determined practically by a process of "trial and error
starting from small inclinations.
"
After experimenting from 4° to 1° and finding that the extinction of amplitudes
follows the preestablished law, one proceeds to try from 6° to 4°, making the necessary
corrections, then from 8° to 6°, and so on.
The desired curve of extinction of the ship is thus given to the navipendulum
without difficulty.
Under these conditions, the resisting couple, formed by the frictional resistance
against the belt and the frictional resistance between the blades of the navipendulum
and their supporting base, will absorb during an oscillation of a certain duration the
same quantity of mechanical work as the resistance of the water opposes to the rolling
of the ship.
Then all the conditions of geometrical, cinematical and dynamical similitude are
fulfilled, as far as they affect the angles of inclination of the ship in her rolling, and
the navipendulum is ready to be applied in the manner which is the principal subject
of my invention.
H
My wave motion oscillograph is based on the fundamental principles of the theory
of the trochoidal wave. It is known, that a molecule of liquid having a wave-like
motion, forming part of a trochoidal surface whose length is L and height H, revolves
with a constant speed in a circular path. The radius of the described circle is = 2°
The time required for a complete rotation is equal to the period of the wave, and is
expressed thus T
L, where and 9 have the values ordinarily given to them
in mechanics. It is further known, that the perpendicular drawn from the molecule,
in all its positions, to the trochoidal surface of which it forins part, passes always
through an absolutely fixed point; this point lies on the perpendicular from the
centre of the circular path, at a distance R, given by the following expression:
R =
L
2π'
=
✓2π
These are the theoretical principles, on which my apparatus is based. If we
consider a set of molecules resting on the trochoidal surface all round any particular
molecule, and if, in consideration of their small extension, we assume these molecules
to form a material indeformable plane or sheet, then the three conditions that
giver, T, R are sufficient to completely determine the movement of the material
plane.
It is further conceivable, that the same motion may be reproduced on a small
scale by mechanical means. It is precisely this movement, that my oscillograph is
designed to realise.
It is to be noted, that the mechanical movement thus produced possesses still a
characteristic property of the wave motion; a property which plays a very important
part in the rolling of ships on a wave.
The direction of the apparent weight or of the virtual upright, at any point of the
wave, is always according to the perpendicular through this point to the trochoidal
surface. This property depends on the combination of the action of gravity with
that of centrifugal force. Since the conditions of mechanical similitude are fulfilled,
this same property is verified in the oscillograph.
Supposing, for example, that in the centre of the material plane there exists a
little cavity, containing a small liquid mass, this latter will remain at rest with
respect to the plane, in the same way, as if the plane were horizontal and at rest.
Again, supposing that a body of small dimensions were resting on the plane of the
oscillograph, whilst in movement, its conditions of equilibrium would be the same, as

page_text: if the plane were horizontal and at rest. In order to have the conditions of similitude
fulfilled, if the ratio y is adopted for the lengths, it follows, that the ratio for time
must bey, just as for the navipendulums.
The principal parts of my wave motion oscillograph are. described in the following
"description and illustrated by Sheet 2 and 3 of the accompanying drawings. The
plate of the oscillograph, having two grooved bars, can turn on the axis C-C (Figs. 1
and 3, Sheet 2); the bottom lines of the grooves in which the navipendulum must be
placed are in the same plane, as the axis C C, Sheet 2.
Figs. 2, 4 and 5 of Sheet 3 show in detail the plate of the oscillograph, consisting of a
cast steel bracket revolving round a front pin C C by means of two ball bearing rings,
thus obtaining easiness and accuracy of movement. The pin C C, (Fig. 2 Sheet 3)
itself revolves round the fixed axis 0-0 (Figs. 1 and 2, Sheet 2), so that its points
describe a circumference having a radius, round the fixed axis 0 0.
The pin C C (Figs. 1 and 2, Sheet 3) is supported by a steel arm B, which is secured
by 4 bolts to the cross piece A A, which is in one piece with the axle 00. The
arm B can be moved along the crosspiece A A (after unscrewing the four bolts) by
means of a screw spindle f, until it occupies its correct position in relation to the
geometrical axis 00. On causing the shaft 0 0 to revolve, the geometric axis CC
of the pin and of the plane a revolves also; the duration of a revolution must be
Ty, assuming T to be the period of the wave, and y the ratio of similitude adopted
for lengths. In order to fulfil the other condition, viz., that a line perpendicular to
the plane a must always pass through a point. placed at a fixed height above the
axis 0-0, there is a second axis 0, 0₁ (Fig. 1 Sheet 2) parallel to the first, and
having also, like the first, a cross-piece A, A, and an arm B₁. The plate a--b (Fig. 4,
Sheet 3) is regulated in its movement by a rod k, secured by two bolts to the
extremities of the muff-shaped hub g h of the plane a b, and in a direction parallel to
that of the same plane.
The rod k k is known in Figs. 1 and 2 of Sheet 2. It has a hollow circular section
(tubular) for the greater part of its length; only at its lower extremity it bas a solid
elliptical section (Fig. 4, Sheet 3) for greater solidity.
Fig. 6, Sheet 3 shows the connection between the rod and the coupling. The
rod k k passes always through a coupling L₁ (Fig. 1 Sheet 2) fixed to the end of the
upper arm B, described above.
The coupling L₁, shown in detail in Fig. 7, Sheet 3, is free to turn on a horizontal
axis C, C, (Fig. 1, Sheet 2) placed at a certain distance r₁n from the fixed axis O₁ O₁.
As the two crosspieces A A, A, A₁, and the arms B₁ B₁ always remain parallel iu
their movement of rotation, it follows, that the geometrical axis of the rod kk (Fig. 2
Sheet 2) is pointing constantly to a certain point, not shown in the drawing, but
which is situated on the vertical of the point 0, at a distance R which is given by
R 00.
the equation
=3
1° 7'--7°1
By means of this proportion the radius ₁ namely, the
position of the arm B, along the crosspiece A₁ A₁ can be regulated, so as to fulfil the
condition of the wave R
L
2TT
which for the oscillograph becomes R
Vy.L
=
2πT
It
is now clearly seen that, by the contrivances above described, the motion of a set of
molecules partaking of the trochoidal surface of a wave, and assumed to form a
material indeformable plane or sheet, reproduced on the small scale y arbitrarily
1
chosen (for instance y =
Y
=
10' 15'
etc.).
As it is necessary, to have a recording apparatus to register the angles of inclination,
made both by the normal to the wave, and by the axis to the navipendulum in respect.
of the true vertical, during the whole duration of an experiment, I have arranged a
small board (Fig. 3, Sheet 2 and Fig. 2, Sheet 3) indicated by the letters p, q,?, s
above the coupling or hub gh. This board is carried by an articulated frame fixed to
its lower face and so designed, as to allow the plate to revolve round the axis CC.
This object is attained by having two collars, forming part of the frame, and two

page_text: cylindrical grooves formed in the coupling or hub g h (see Figs. 2, 4, 13, of Sheet 3;
and Fig. 1 Sheet 2). The plate p q r 8, whilst following the circular movement of the
axis CC, when the apparatus is at work, must however remain constantly horizontal,
and to accomplish this, one of the two collars is secured to a rod j, (Fig. 13,
Sheet 3, and Fig. 1 Sheet 2) which remains constantly vertical; in fact, there is a
third axis O, parallel to the two others 00₁, carrying a crosspiece A, A, an arm B₂and
a small sleeve coupling or boss 1, exactly like the axis O₁, only that the arm B, is
always in the saine place on the crosspiece A,, as the arm B on the crosspiece "A;
that is to say the axis C, C, is at a distance r from the axis O, O, and consequently
the two axes C C, C, C, are always in the same vertical plane to each other. Thus
the rod jj remains constantly vertical and the plate p q r s horizontal.
I have yet
1
to describe the organs for obtaining a simultaneous and parallel movement of the
three principal shafts of the apparatus, the indicator for ascertaining the regularity
of the speed and the recording apparatus.
The motive power is supplied to the apparatus by a small electric motor E (Figs.
1, 2, 3, Sheet 2) situated on a separate bed plate, so as to avoid any vibrations
affecting the oscillograph; the speed of the motor may vary from 500 to 1000 revolu-
tions per minute. The movement is transmitted from the shaft of the motor to the
shaft G by gearing, which reduces the speed to.
Between the shaft G and a secondary shaft P of the oscillograph the power is
transmitted by two conical stepped pulleys; by this means three different ratios of
speed, 1, 2, are obtained.
Besides the shafts O, O₁, O,, there are two other intermediate shafts S, T; all five
have 5 straight toothed wheels, with small helical teeth, so as to insure greater
accuracy and regularity of movement; the wheel S¹ (Fig. 2 Sheet 2) gears simul-
taneously into the two wheels O₂, O₁₁; the latter transmits motion to the wheel 0,1
by means of the wheel T¹. By this arrangement the three principal wheels 0¹,0₁¹, O₂¹
turn in the same direction and in perfect unison with each other.
It is easy to see that their speed can be made to vary from a minimum of 10
revolutions to a maximum of 80 revolutions per minute.
The framework of the apparatus consists of a lower cast-iron sole plate and two side
frames united by bolts; the two side frames are joined together by bolted crosspieces,
as shown,
In order to be sure, that the speed of rotation remains exactly constant during the
whole of the experiment (T revolutions per minute) I have adopted a Valessie
indicator (w in Figs. 2 and 3 of Sheet 2).
The properties of this apparatus are well known; it receives its motion from the
machine, whose speed is to be verified; by means of a variable train of small tooth
wheels, this indicator can be arranged for 512 different speeds; when it has been
arranged for a certain fixed speed, if the machine that drives it maintains exactly its
desired speed, one sees the pointer of a dial occupy apparently a fixed position (see
Fig. 3 Sheet 2); if on the contrary the speed of the machine undergoes any variation,
one sees the pointer move either to one side or the other, according as there is an
increase or decrease in the speed. I use a Valessie indicator having a clock whose
pointer makes one revolution in 30 seconds; I connect it, with the apparatus by
means of a small shaft and conical gearing t (Figs. 1, 2 and 3 Sheet 2) which increases
the speed in the ratio 2, 3: 1; the 512 different speeds which the indicator can be
arranged to verify, are from 9.5 to 77.25 revolutions per minute; they form a
geometrical progression, whose ratio is (31) *, that is to say
30
241
240
nearly between the
two extreme limits, there can always be found the most convenient combination,
whose error can never surpass
1
of its value.
480
During the working of the oscillograph it is necessary, that someone should con-
stantly observe the indicator, having at hand a small wheel for gradually introducing
a variable resistance into the circuit of the motor (v in Figure 2 Sheet II).
As the working of the oscillograph is in itself very regular and all the parts have a

page_text: rotary movement, there is no difficulty in maintaining a constant speed, when the
motor has been set going at the correct number of revolutions.
29
It is useful to provide counter-weights, secured to the wheels 01, 0¹, 0¹, to
balance the weights whose centres of gravity lie outside the line of their axes.
The observer can easily detect an error of above or below the required
1
200
speed; his attention should be directed to keep the pointer constantly at the spot it
marks, rather than to bring it back to the point from which it started.
The registering apparatus is represented by x in Figs. 1, 2, 3 of Sheet 2 and more
in detail in Figs. 8 to 12 of Sheet 3; Figs. 2 and 13 of the same sheet show parts
that refer to the same apparatus.
A paper strip 35 centimetres wide receives the impressions of 5 recording pencils.
The strip is drawn along by a drum A driven by clockwork D (Figs. 8, 9, 12); a
heavy roller E gives to the strip the necessary adhesion to the drum A. The paper
strip, which winds itself off a cylinder B, where it is kept in tension by two springs,
winds itself finally on the drum C, driven by a pair of pulleys and a flexible cord,
which receives its motion from the axis A as shown on the right of Figs. 8 and 9;
when the paper strip rolled on the drum B forms a layer of sufficient thickness, there
takes place a slipping of the cord on the pulleys; which however, is of no consequence
provided that the tension be not excessive.
There are, as I have said above, five recording pencils; one near the centre (a in
Fig. 9) is moved by an electro-magnet, in communication with a chronograph seconds
watch which is not represented in the drawings.
The other pencils are placed two on each side; the two pencils bb1 are for
recording the angles made by a line perpendicular to the wave with the vertical;"
the other two cc¹ for recording the angles made by a line perpendicular to the
navipendulum also with the vertical.
The pencil b moves horizontally along a straight line, and its distances from the
middle position are proportional to the angles to be measured; the pencil 6¹ being
fixed in an invariable position serves to give a continuous trace of the mean position ; so
that when the plate ab is horizontal, the two pencils b b¹, coincide perfectly. If the plate
is inclined at a certain angle, it causes the small sector e (Fig. 2, Sheet 3) moveable
with its centre round the axis C C, to describe the same angles; now the sector e is
connected to the other sector e¹ by a small rod (Fig 13, Sheet 3), so as to form a
sort of parallelogram, and to always incline it parallel to the other; a thin metal
riband stretched along the rims of the two sectors follows their movement, winding
itself off one sector on to the other; it is this band (Fig. 13) which carries the
recording pencil b; so that this pencil runs constantly along a generating line
of the drum, and deviates from the middle line proportionally to the angles of
inclination. The dimensions of the pieces are so calculated, that a deviation of
1.5 millimetres corresponds to one degree of inclination.
For moving the pencil c, that marks the line of the inclinations of the navipen-
dulum, there is a similar arrangement, as shown by Fig. 13, Sheet 3. From Fig. 2,
Sheet 3, it will be seen, that the two small sectors ei are fixed to the same axis,
carried by the plate p g; this axis coincides exactly with the axis CC of the oscillo-
graph. The sector e is connected with the bracket plate by a tail prolonged
downwards and having its extremity passing into an aperture in the plate; the
sector i is moved by a rod l, which must keep parallel to the rod of the navipendulum.
The latter in its oscillatory movements finds itself by necessity at variable distances
from the rod l, the more so, because after any prolonged experiment it may happen
that the entire navipendulum be slightly out of its initial middle position. In order
that the navipendulum, whilst having all its movements free, may always communi-
cate its movement to the rod 1, and keep it constantly parallel to its own axis.
I have arranged a combination of links which might be called a "hinge-jointed
prism," and which is fixed to the rod of the navipendulum: one of its sides is always
parallel to the rod of the navipendulum, but free to vary its distance from the navi-

page_text: to represent the statical and dynamical conditions of ships, for inclinations in any
directions.
Dated this 2nd day of February 1899
GIOACCHINO RUSSO.
By Fairfax & Wetter,
Agents.
Apparatus and Means for ascertaining by Laboratory Experiments
the Behaviour of Ships on Waves.
I, GIOACCHINO Russo, Naval Architect, of the Royal Italian Navy, and Member of
the Institution of Naval Architects, of Rome, Italy, do hereby declare the nature of
this invention and in what manner the same is to be performed, to be particularly
described and ascertained in and by the following statement:-
Its
My invention relates to appliances for experimentally reproducing oscillatory
movements, similar, on a small scale, to those of ships rolling among waves.
object is the solution of a problem of naval architecture lying in the following terms:
to ascertain what oscillations a given ship will perform, when set rolling passively,
broadside on, in a given condition of sea, namely, when exposed to the passage of
waves of a given length, height and period, following each other in regular succession.
The experiments are made by means of pendular bodies, each of which is so
arranged as to represent, on a small scale, the rolling motion of a given ship; such
pendular bodies are supported by a mechanical apparatus, whose motion produces on
them the same effect as the wave produces on ships.
The experiments may relate both to existing ships and to ships building or
projected, so as to ascertain beforehand their greater or smaller degree of steadiness,
as well as to prove the influence of the different elements which concur in their
rolling, viz., statical stability, fluid resistance, moment of inertia, etc. Consequently
it will become possible to find the best proportions or relations of these elements in
regard to the rolling properties of the ship.
This invention, which has been patented in Italy on an application dated
the 3rd July 1898 and in France on an application dated the 29th December 1898,
comprises:
1. The construction of pendulum-shaped bodies A B (Figs. 1 and 2, Sheet 1) of the
drawings filed with the Provisional Specification) which I call navipendulums,
whose description I will hereafter give, and by means of which any given ship may
be represented as regards her transverse oscillatory movements. A navipendulum is
a body quite different from the ship it is intended to represent, but, as it will appear
from the following description, its oscillations are similar (in the mechanical sense
of the word) to those of the ship, which it is intended to represent. When supported
by a fixed horizontal plate LL, as shown in Figs. 1, and 2, Sheet 1, its oscillations
are similar to those of the ship in still water.
2. The construction of an apparatus that I have named wave motion oscillograph
(Figs. 1, 2, and 3, Sheet 2), and the essential part of which is a plate L, serving as a
supporting base to the navipendulum. During the experiments while the latter is
moving, the plate L has also a peculiar rotary and oscillating motion, the nature of
which will hereafter be explained. In other words, the plate gives to the
navipendulum a periodically oscillating support, in the same way as a ship receives a
periodically variable support from a regular succession of waves.
I shall begin by describing firstly the shape and construction of a navipendulum

page_text: and the principles of naval architecture upon which its construction is based.
Then I shall describe the wave motion oscillograph and its use in combination
with a navipendulum.
A navipendulum (Figs. 1 and 2, Sheet 1) is composed of a tubular rod or shaft A B
provided with two heavy disc-shaped bobs HH; these may be fixed at any required
position along the shaft by means of small clamping rings or collars D. A central
piece E is secured to the rod A B, and serves to support two steel blades FF, the
lower edges of which are bevelled like knife edges and shaped to a line, whose
geometrical properties I will hereafter describe.
Under
The navipendulum composed as described is placed on a level plate L L, with its
two blades resting upon two perfectly straight and parallel grooved bars.
these conditions it can oscillate like a pendulum, whilst rolling on its supported
base.
In order that the oscillations of a navipendulum may be similar to the oscillations
of a given ship, according to Newton's well known principle of mechanical similitude,
it is necessary to proceed on the following principles:
1. Fig. 1, Sheet 1, represents the midship section of a given ship; CC is the curve
of the centres of buoyancy for all the transverse inclinations corresponding to her
displacement. An infinite number of curves may be traced parallel to the curve CC,
all having the same perpendiculars in the corresponding points, and all having a
common evolute mo (defined in naval architecture as the metacentric evolute of the
ship). Of this infinite number of curves parallel to C C, a curve ff is chosen, so. as
not to be too far removed from the centre of gravity G of the ship. It is not a very
essential condition, but it is advisable that the curve ff be as near as possible to the
point G. Now the curve ff, drawn on a scale of proportions y arbitrarily chosen
etc.) constitutes the line according to which the edges of the
1
(e.g. y= or y =
10
1
15
steel blades F F of the navipendulum must be shaped.
2. The position of the centre of gravity of the navipendulum must be regulated
(by fixing the two weights H H in their correct positions along the rod, in such a
way that its distance from the centre of the curve ff will be equal to the correspond-
ing distance measured on the ship, multiplied by the ratio of similitude y. With
reference to the well known properties of the curve of centres of buoyancy, it is then
evident that the arm of the couple of stability, for any inclination of the navipendulum,
is in the ratio y to the arm of the couple of stability of the ship for the same angle of
inclination.
3. Whilst fulfilling the above-mentioned condition, the weights H H are sufficiently
removed from the centre of gravity to ensure that the period of oscillation of the
navipendulum will bear a given ratio to the period of oscillation of the ship in still
water.
Assuming, as we have done, y to be the ratio of similitude for lengths, the ratio
of similitude for the periods of oscillation must be ✓. For instance, if the navi-
pendulum represents a given ship on the reduced scale its period of oscillation
16'
must be of the period of oscillation of the ship in still water.
We must observe, that if the subject under examination is a ship not yet built,
but only projected, then the period of oscillation in still water may be easily known,
either by calculation or by having recourse to model experiments (Froude's
method).
The correct position of the hobs H, H along the tubular rod A B is ascertained by
experiments, no graduated scale being necessary along the rod. To obtain the
correct position of the centre of gravity, I make use of a sort of balance, on which
the navipendulum, removed from the oscillograph, is arranged horizontally, in the
same conditions, as the beam of an ordinary balance. These experiments are
repeated, as long as it is necessary to obtain, not only that the centre of gravity is
R

page_text: brought in its correct position (as stated above), but also, that the period of oscilla-
tion, ascertained on the plate of the oscillograph at rest, attains its correct value
indicated above.
4. Finally, to complete the composition of a navipendulum, it is necessary, to add
some contrivances, which will enable it to have the same extinction curve, as the ship
it is intended to represent. In other words, the gradual increase of the amplitude of
oscillations, when starting from a given angle of inclination, should be identical for
the ship and for her navipendulum. This result may be obtained by causing various
kinds of passive forces to act on her navipendulum, for example, a frictional resistance
on the supporting plane, or the resistance of the air, obtained by adding to the
rod A B suitably proportioned vanes. The system that I prefer is the following:-:
A block of wood D (Fig. 3, Sheet 1) or of any other light and easily shaped material
is secured to the rod, with its upper cylindrical surface shaped according to a certain
section line m n. A leather belt CA CA is stretched above the block D in contact with
it, and parallel to the supporting plane B B. As the navipendulum rolls, the block D
rubs continually against the belt, producing a frictional resistance, greater or smaller
according to the greater or smaller pressure that the block D in its motion exercises
on the belt, raising it more or less from its original straight position.
The decrease of amplitudes depends on the shape of the line m n; .now this line
cannot be determined theoretically, but inust be determined practically by a process
of "trial and error" starting from small inclinations.
After experimenting from 4° to 1° and finding that the extinction of amplitudes
follows the pre-established law, one should proceed to try from 6° to 4°, making the
necessary corrections to the block D; then from 8° to 6°, and so on.
The desired curve of extinction for the navipendulum is then found without
difficulty.
Under these conditions, the resisting couple, formed by the frictional resistance
against the belt and the frictional resistance between the blades of the navipendulum
and their supporting base, will absorb during an oscillation of a certain amplitude, the
same quantity of mechanical work, that the resistance of the water absorbs during
the rolling of the ship for the same amplitude.
No theoretical correlation or empirical rule can be given between the friction of the
leather and the resistance of the oscillations of the ship. The important point is,
that the ship and the navipendulum should have the same extinction of oscillations.
Now, the extinction of oscillations of the ship in still water is a datum, either obtained
from the real ship, or from her model; so that the problem is reduced to the
empirical determination of the shape of the block D, to obtain the same decrease of
amplitudes or the same extinction.
f.
Then all the conditions of geometrical and dynamical similitude are fulfilled, as far
as they affect the angles of inclination of the ship in her rolling, and the navipendulum
is ready to be applied in combination with the oscillograph for experiments
concerning the rolling among-waves.
H
My wave motion oscillograph is based on the fundamental principles of the theory
of the trochoidal wave. It is known, that a particle of liquid having a wavelike
motion and forming part of a trochoidal surface, whose length is I, and height H,
revolves with a constant speed in a circular path, the radius of which is " = The
2'
time required for a complete rotation is equal to the period of the wave and is
expressed by T
L, where and g have the values ordinarily given to them
===
√2
g
in mechanics. It is further known, that the perpendicular drawn from any given
particle, in all its positions, to the trochoidal surface of which. it forms part, always
passes through an absolutely fixed point; this point lies on the vertical drawn from
the centre of the circular path, at a height R, given by the following expression:
L

page_text: These are the theoretical principles, on which my apparatus is based.
If, instead of considering a single particle lying on the trochoidal surface, we
consider a set of particles rigidly connected and forming a small thin raft, the notion
of this raft will be completely determined by the known height, length and period of
the wave, and its motion may be reproduced by mechanical means, independently of the
water which surrounds this raft. It is also conceivable, that the same motion may
easily be reproduced by mechanical means on a smaller scale, always according to the
principle of mechanical similitude.
2πT
=
A
In fact, if we consider for instance a wave whose height is 20 feet and length
500 feet, evidently its period (depending on the length) must. be 9.76 seconds.
small raft floating on this wave should revolve in a circular path, having a radius
of 10 feet, with a constant angular speed corresponding to one revolution at each
period of 9.76 seconds. Moreover, the perpendicular to the raft (namely to the wave
surface) drawn through its centre, would constantly pass, during the motion, through
a point lying on the vertical of the centre of the circular path at a
height R
80 feet. These conditions are sufficient to enable us to reproduce
the motion of the raft by mechanical means, if we suppose it freed from the action
of the surrounding water, and subject to a mechanical apparatus sustaining it and
possessing a suitably contrived motion. Moreover, it is evident also, that we can
produce the same motion of the raft on a small scale of similitude, for instance, on
the reduced scale y
The raft in question, which we' must suppose very small,
must then be made to revolve in a circular path having a radius of 7 inches
(of 10 feet) with a constant angular speed corresponding to one revolution for each
period of 2.44 seconds (namely 976 √y). During the motion, the raft must be
maintained in all its positions, with the perpendicular to its surface constantly
directed towards a point situated on the vertical of the centre of the circular path, at
a height of 5 feet (namely 80 x y).
1
16'
.
My oscillograph has been designed to realise a motion of the nature above described.
The plate L of the mechanism (Fig. 2, Sheet 2) represents the raft or a portion of
wave surface, rendered rigid and material, while the object of my apparatus is to
impart to this plate the desired motion, and all necessary arrangements are provided
for setting the apparatus so as to reproduce any given wave (between certain limits)
on any desired scale.
Before describing the construction of my wave motion oscillograph, it is necessary
to point out, that the plate L, while following the above-said wave-like notion,
possesses, from a dynamical point of view, a characteristic property, which plays a very
important part in the rolling of ships on waves.
The direction of the apparent weight, or of the virtual upright at any point of the
wave, is always according to the perpendicular through this point to the trochoidal
surface.
This property depends on the combination of the action of gravity with that of
centrifugal force. Since the conditions of mechanical similitude are fulfilled, the
same property is realised in the oscillograph.
Supposing, for example, that in the centre of the plate L. there exists a small
cavity, containing a small liquid mass, this latter will remain at rest with respect to
the plate, in the same way as if the plate were horizontal and at rest.
Again supposing that a body of small dimensions was resting on the plate of the
oscillograph whilst in movement, its conditions of equilibrium would be the same, as
if the plate were horizontal and at rest. Of course, to have the conditions of simili-
tude fulfilled, if the ratio y is adapted for the lengths, the ratio for times must be √y,
just as for the navipendulum. The principal parts of my wave motion oscillograph
are described in the following specification and are shown on Sheets 2 and 3.
The plate L of the oscillograph, having two grooved bars, can turn round the
axis C¹³ (Figs. 1 and 2, Sheet 2); the bottom lines of the grooves in which the

page_text: navipendulum must be placed, are in the same, plane, as the axis C C¹, as shown in
Fig. 2.
Figs. 2, 4 and 5, Sheet 3, show in detail the plate 1 of the oscillograph. The
grooved bars shown in these figures have double grooves, while in Fig. 2, Sheet 1, the
grooves are single. Only one pair of grooves is required, but I prefer to make bars
with two pairs of grooves, so that the inner pair of grooves can be used for small
navipendulums, and the outer pair for large navipendulums. The plate L. consists of
a cast steel bracket revolving around a front pin C₁ C₁, by means of two ball bearing
rings to obtain the desired ease and accuracy of motion.
The pin C C (Fig. 2, Sheet 3) itself revolves round the fixed axis OO (Fig. 1,
Sheet 2), so that all its points describe a circumference having a radius around the
fixed axis O O. It may be useful to point out that Figs. 1 and 2, Sheet 3, represent
the axis C C of the pin as coinciding with the axis 00; in reality however, during
the experiments, the two axes are at a certain distance apart, as shown in Fig. 1,
Sheet 2.
The pin C C (Figs. 1 and 2, Sheet 3) is supported by a steel arm B, which is
secured by four bolts to the cross-piece A A, and the latter is rigidly connected with
the axle Ŏ O. The arm B may be shifted along the cross-piece AA (after unscrewing
the four bolts) by means of a screw spindle f, until it occupies its correct position in
relation to the geometrical axis of the shaft 00. On causing the shaft 0 0 to
revolve, the geometrical axis of the pin C¹C" and the plate a, b, rotates also, the
duration of a revolution must be, as above stated, Ty, assuming T to be the
period of the wave and y the ratio of similitude adopted for lengths. In order to
fulfil the other conditions, viz., that the perpendicular to the plate ao bo, must always
pass through a point placed at a fixed height above the axis 0 0, there is a second
axle 0, 0, (Fig. 1, Sheet 2) parallel to the first, and. having also, like the first, a cross-
piece A, A, and an arm B₁. The plate a, b, (Fig. 4, Sheet 3) is regulated in its
movements by a rod, secured by two bolts to the extremity of the muff shaped
hub g h cf the plate a, b, and in direction perpendicular to that of the plate surface.
The guide rod k is shown in Figs. 1 and 2, Sheet 2. It is tubular with circular cross
section for the greater part of its length; only at its lower extremity it has a solid
elliptical section (Fig. 4, Sheet 3) for greater solidity. Fig. 6, Sheet 3, shows the
connection between the guide bar and the sleeve gh. During the motion of the
apparatus, the guide bar will determine the inclinations of the plate a, b, because
the rod always passes through a sleeve L, (Fig. 1, Sheet 2) fixed at the end of the
upper arm B, described above. The sleeve I₁, shown in detail in Fig. 7, Sheet 3, is
free to turn round an horizontal axis C₁ C₁ (Fig. 1, Sheet 2) placed at a certain dis-
tance <from the fixed axis O₁ C₁, being the distance of the pin C¹ C¹ from the
axis 0 0.
As the two cross pieces A A, A, A₁ and the arms B B, always remain parallel with
each other during their movement of rotation, it follows that the geometrical axis of
the rod k (Fig. 2, Sheet 2) is constantly passing through a certain point, not shown
in the drawing, but which is situated vertically above the axis at a distance R which
is given by the proportion, R: r = 00- By means of this proportion, the
rádius 7, that is to say the position of the arm B, along the crosspiece A, A₁, may be
regulated so to fulfil the condition of the wave R which for the oscillograph
becomes R
=
yL
2πT
L
==
2πT'
It will be clear now that by the contrivances described above, the motion of a set
of liquid particles, situated on the surface of a wave, and assumed to form a material
indeformable plane or sheet (raft) is reproduced on the small scale y arbitrarily chosen.

page_text: of the navipendulum, during the entire duration of an experiment, I have arranged
a small board (Fig. 3, Sheet 2, and Fig. 2, Sheet 3) indicated by the letters p, q, s,
above the sleeve g h. This board is supported by a pivotal frame fixed to its lower
face, and so designed as to allow the plate to revolve round the axis C¹ C¹; this object
is attained by means of two collars forming part of the frame, and two annular
grooves formed on the sleeve g h (Figs. 2, 4, 13 of Sheet 3, and Fig. 1 of Sheet 2).
The plate p, q, z, s, whilst following the circular movement of the axis C¹C¹, when
the apparatus is at work, must however remain quite horizontal; to accomplish
this, one of the two collars is secured to a rod j (Fig. 13, Sheet 3, and Figs. 1, 2,
Sheet 2) which remains constantly vertical. In fact, there is a third axle O₂, parallel
to the two others 0 0₁, which carries a crosspiece A₂ A₂, an arm B₂, and a small
sleeve L, exactly like the axle O₁, only that the arm B₂ always occupies the same
place on the crosspiece A, which the arm B occupies on the crosspiece A; that is to
say, the axis C₂ C₂ is at a distance "2 from the axis O, O, and consequently the
two axes C¹ C¹ and C₂ C₁ are always in one vertical plane. Thus the rod j j remains
constantly vertical and the plane p, q, 2, 8, horizontal.
I have yet to describe the devices for obtaining a simultaneous and parallel motion
of the three principal shafts of the apparatus, the indicator for ascertaining regularity
of speed, and the recording apparatus.
Motive power is supplied to the apparatus by a small electric motor E (Figs. 1, 2, 3,
Sheet 2) situated on a separate bed plate, so as to prevent any vibrations from
affecting the oscillograph; the speed of the motor may vary from 500 to 1000
revolutions per minute. Motion is transmitted from the shaft of the motor to the
shaft G by gearing, which reduces the speed to
5*
Between the shaft G and a secondary shaft P of the oscillograph the power is
transmitted by two conically stepped pulleys H H¹; by this means three different
ratios of speed, 1, 2 are obtained. For regulating the tension of the belt, known
regulating devices may be employed.
2
Besides the shafts 0 0, O₂, there are two other intermediate shafts ST; all five
have wheels, with small helical teeth so as to ensure great certainty and regularity of
motion; the wheel S¹ gears simultaneously into the two wheels 0¹, and O¹; the
latter transmits the motion to the wheel 01 by means of the wheel T. By this
arrangement the three principal wheels 01 01, 0¹, turn in the same direction and in
perfect unison with each other.
2
By means of the transmitting gear described above the speed may be made
to vary from a minimum of 10 revolutions to a maximum of 80 revolutions per
minute.
The framework of the apparatus consists of a lower cast iron sole plate and two side
frames or standards connected by bolts; the two side frames are joined together
by bolted cross stays and diagonals. Figs. 2 and 14 Sheet 3, show in detail one of
the bearings of the principal shaft.
In order to be sure, that the speed of rotation remains during the whole of the
experiment exactly what is required (T revolutions per minute), I have adopted a
speed indicator of Valessie's system indicated in Figs. 2 and 3, Sheet 2 by the
letter W.
The properties of this apparatus are well known; it receives its motion from the
machine whose speed is to be observed; by means of a variable train of small tooth
wheels, this indicator may be arranged for 512 different speeds; when it has been
arranged for a certain fixed speed, if the machine which drives it maintains exactly
its desired speed, one sees the pointer of a dial occupy a fixed position (see Fig. 3,
Sheet 2); if, on the contrary, the speed of the machine undergoes any variation, the
pointer will be seen to move either to one side or the other, according as there is an
increase or a decrease in the speed. I use a Valessie indicator having a clockwork
whose pointer makes one revolution in 30 seconds; I connect it with the apparatus
by means of a small shaft and bevel gearing (Fig. 2, Sheet 2) which increases the
speed in the ratio of 2.3 to 1; the 512 different speeds which the indicator can be
t

page_text: his attention should be directed to keep the pointer constantly at the spot it marks,
rather than to bring it back to the point from which it has first started.
The registering apparatus is represented by x in Figs. 1, 2, and 3, Sheet 2, and
more in detail in Figs. 8 to 12, Sheet 3; the same apparatus is shown also in Figs. 2
and 12, Sheet 3.
A paper strip 35 centimetres wide, receives the impressions of 5 recording pencils.
The strip is drawn along by a drum A, driven by clockwork D. (Figs. 8, 9 and 12);
a heavy roller E, produces the necessary adhesion between the strip and the
drum A. The paper strip, which is drawn off a cylinder B₁, where it is kept in
tension by two springs, winds itself finally on the drum Co, which is driven from
the axle of the drum A, by a pair of pulleys and a flexible cord, as shown on Figs. 8
and 9. When the paper strip on the drum B, forms a coil of a certain thickness, there
takes place a slipping of the cord on the pulleys; which however has no evil consequences,
provided that the tension be not excessive.
There are, as I have said before, five recording pencils; one near the centre
(a in Fig. 9) is controlled by an electro-magnet, in communication with a chrono-
graph seconds watch, not shown by the drawings.
The other pencils, are placed two on each side; the two pencils b b are for
recording the angles made by the perpendicular to the wave with the vertical; the
other two cc for recording the angles made by the perpendicular to the navi-
pendulum, also with the vertical.
The pencil b moves horizontally along a straight line and its deviations from the
middle position are proportional to the angles to be measured; the pencil 6', being
fixed in an invariable position, serves to give a continuous trace of the mean
position; so that when the plate a, b, is horizontal, the two pencils bb1 coincide
perfectly. If the plate is inclined at a certain angle, it causes the small sector e
(Fig. 2, Sheet 3), having its pivotal centre in the axis c¹ c¹, to describe the same
angle; now this sector is connected to another sector e¹ by a small rod f (Fig. 13,
Sheet 3), so as to form a sort of parallelogram and to always incline this sector ei
parallel to c. A. thin metal riband, stretched along the rims of the two sectors,
follows their movement, winding itself off one sector on to the other; This band
(Fig. 13) carries the recording peneil 6 mentioned above; so that this pencil runs
constantly along a generating line of the drum, and deviates from the middle line
proportionally to the angles of inclination. The dimensions of the parts are so
calculated that a deviation of 1, 5 mm. corresponds to one degree of inclination.
For moving the pencil c, that marks the inclination of the navipendulumn, there
is a similar arrangement as shown by Fig. 13, Sheet 3; from Fig. 2, Sheet 3, it will
be seen, that the two small sectors ei are pivoted on the same axis CC of the
oscillograph. The sector e is connected to the bracket plate by a tail-piece prolonged
downward and extending with its extremity into a rectangular aperture of the plate;

page_text: the sector is controlled by a rod 1, which must keep parallel to the rod of the
navipendulum. The latter, in its oscillatory movements finds itself of necessity at
variable distances from the rod 1, the more so, because after prolonged experiments,
it may happen that the entire navipendulum be slightly out of its initial middle
position. In order, that the navipendulum, whilst having all its movements free,
may always cominunicate its movements to the rod and keep it constantly parallel
to its own axis. I have arranged a combination of lines or pivotal pieces, which
might be called a "link prism" and which is fixed to the rod of the navipendulum:
one of its sides is always parallel to the rod of the navipendulum, but always free
to vary its distance from the navipendulum in any direction (within certain limits).
This side is tubular, and the rod passes through it.
As the navipendulum has to set in motion the rod 1, the sectors, and the
pencil c, it will have to overcome a small frictional resistance; but as artificial
resistances must be inserted for other reasons, this friction is no drawback; it is
sufficient that the regulation of the frictional resistance intended to obtain a
certain extinction, be made after the navipendulum has been set in its place on the
oscillograph.
I have not made a detailed drawing of the link prism, as its form can be seen
sufficiently in the general arrangement (Figs. 1 and 3, Sheet 2). The diagram
given by the recording apparatus contains five lines: one, near the centre, traced
by the electro-magnet, is an indented or zig-zag line, showing time (seconds and
half-seconds); two other lines, one on the right and the other on the left, are
straight lines, which serve as a basis for measuring the amplitudes; the last two
lines, traced by the pencils b c give the amplitudes (in relation to the vertical)
of the inclinations of the perpendicular to the wave line and of the axis of
the navipendulum; these amplitudes are represented by the ordinates of the two
winding curves measured from the corresponding base lines, considering the times
as abscissae. The inclination of the navipendulum to the perpendicular of the wave
line may be ascertained from the differences of the ordinates.
The application of my oscillograph in combination with the navipendulums,
founded on the theoretical study of the rolling of ships among waves, and the results
of my experiments lead to the following conclusions
1. If the navipendulum of a given ship is supposed to be made on a scale y,
and the oscillograph is set to represent on the same scale a continuous series
of waves of given dimensions, the oscillations of the navipendulum mounted on
the plate of the oscillograph will generally be the same, as those which could
be observed if the actual ship were exposed, broadside-on, to the passage of a
continuous series of real waves of the size assumed in the experiments. Then the
diagram produced by the registering apparatus will give the solution of the problem
of naval architecture stated at the beginning of this specification.
2. The correspondence between the real case and the experiments, as stated above,
is no longer quite accurate, if the size of the waves taken into consideration is
below a certain limit, in comparison with the dimensions of the ship. But whenever
this happens, the experiments will also very approximately give the desired results,
on condition that the oscillograph, instead of being set to represent the actual wave,
will be set to represent a fictitious wave. This last must have the same length and
period as the given wave, but its height must be somewhat less. The most
convenient height of the fictitious wave has to be determined, in each case, on the
basis of analytical researches concerning the action of weight, buoyancy and inertia
forces acting upon the ship in all the positions she assumes during the wave's
progress, and the inclinations she may have in each position. When experiments
are made on fictitious waves, the strictly useful indications to be gathered from the
diagram are the amplitudes of rolling of the navipendulum from the perpendicular
of the wave; such an element will be equal, with great approximation, to the
corresponding element of the real case.
Lastly I observe that up to the present, 1 have referred to a navipendulum capable
only of transverse inclination or movement, but its cylindrical rolling surface may

page_text: :
be replaced by a curved convex surface parallel to the surface of the centres of
buoyancy, and its moment of inertia may be so proportioned, as to enable it to
represent the statical and dynamical conditions of ships. for inclinations in any
.direction.
Having now particularly described and ascertained the nature of the said inven-
tion and in what manner the same is to be performed, I declare that what I
claim is
1. A navipendulum or pendular body adapted to embody and demonstrate on a
reduced scale, when resting on a plane, the mechanical properties of floating ships,
as regards their stability and transverse oscillations, substantially as described and
illustrated by the drawings.
2. A wave motion oscillograph or apparatus adapted to impart to a material plane,
a motion similar to that which would be imparted to the same by a regular
succession of waves, substantially as described and illustrated by the drawings.
3. The combination of a navipendulum with a wave motion oscillograph and
accessories, to reproduce and record on a small scale, the oscillatory motions of ships
: on waves, substantially as described and for the purpose specified.
FAIRFAX & WETTER,
Agents, 37 and 39, Essex Street, Strand, London.
FAIRFAX & WETTER,
Agents, 37 and 39, Essex Street, Strand, London.