Improvements in Wave Motors.
Year: 1897

page_text: Date of Application, 8th Apr., 1897-Accepted, 15th May, 1897
Improvements in Wave Motors.
We, ALBERT WILLIAM STAIL, Naval Constructor of U.S. Navy, of Navy
Yard, Norfolk, in the County of Norfolk, and State of Virginia, and FRANCES
BRYAN GATEWOOD, Inventor, residing at 2149 Florida Avenue, Washington,
in the County of Washington, and District of Columbia, United States of
America, 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 :-
In order that others may understand and apply this invention for utilizing the
power of waves, it will be necessary before referring to the mechanism and methods
employed, to describe and explain the physical conditions attendant on such wave
motion and the relation of these methods thereto.
While the motion of ocean waves in nature is usually quite complex in character,
there is a certain simple typical form of such motion to which, or to combinations
of which, all ocean waves approximate more or less closely. This form is known
as "trochoidal wave" motion, and it is by combinations of this simple wave with
others of the same general type that nearly all the complicated motions of the sea
are produced. Ocean waves in general thus usually consist of one principal series
of trochoidal waves, modified and influenced by other series of somewhat similar
but smaller waves of various lengths and directions; and the conclusions to be
derived from the study of simple trochoidal waves apply substantially for our
purposes to ocean waves in general.
The trochoidal wave is so called from its surface profile, which is the curve
known as the "trochoid." From the conditions governing the formation and pro-
pagation of the trochoidal wave the following general properties and characteristics
of its internal structure and movement have been mathematically deduced, and
such deductions have been verified by actual observation and experiment.
Each individual particle of water in a trochoidal wave moves in an elliptical
orbit whose major axis is horizontal and the plane of which is vertical and
perpendicular to the wave ridge or crest, the motion of the particle in the upper
portion of its orbit being in the direction of advance or propagation of the wave
itself and in the lower portion of its orbit in the opposite direction. The
eccentricity of these ellipses depends on the relation between the length of the
wave and the total depth of the water. As this depth of water increases in
proportion to the length of the wave the eccentricity of the ellipses becomes less,
and they finally become circles when the total depth of water becomes infinite.
Practically they cannot he distinguished from circles when the depth of water
exceeds about one-half the length of the wave. On the other hand, as the total
depth of the water becomes less the eccentricity of the ellipses increases, their
horizontal axes becoming much greater than their vertical axes as the water
becomes very shallow.
In any given wave all the particles which were originally in the same vertical
straight line while the water was at rest describe their respective orbits in the
same time and occupy the same phase in these orbits at the same instant; but the
orbits themselves become smaller as the distance of the respective particles below
the surface increases. In the case of the deep-water wave with circular orbits the
circles thus decrease in diameter with increase of depth of the respective particles.
ΓΓ

page_text: In the case of the shallow-water wave with elliptical orbits the ellipses also
decrease in size with increase of depth, but their focal distance remains constant.
Their vertical minor axes therefore decrease faster than their horizontal major
axes, thus rendering the ellipses flatter, as well as smaller, with increased depth of
particles. At the bottom the vertical axis disappears entirely and the particles
there move in horizontal straight lines whose length is equal to the focal distance
of the elliptical orbits of the higher particles. It is to be noted that the above is
strictly true only for a perfect liquid with a horizontal and frictionless bottom.
Practically the motion is somewhat modified by the actual slope and roughness of
the latter and by the viscosity of the water.
The horizontal component of the motion of a particle at any specified depth is
equal to the diameter of the respective orbit circle of the major axis of the
respective orbit ellipse, as the case may be, and is thus not the same at all depths,
but is less as the particle considered is farther from the surface. Hence it follows
that a set of particles originally in the same vertical straight line when the water
is at rest does not remain in a vertical line during the passage of the wave, so that
the line connecting a set of such particles, while vertical and straight in still water,
becomes distorted, as well as displaced, during the passage of the wave, its upper
portion moving farther and more rapidly than its lower portion.
This invention relates to utilizing the power developed by these movements in
accordance with the principles above set forth and further explained in the
accompanying drawings, in which-
Figure 1 is a diagram taken on a vertical plane, showing graphically the structure
and movement of a deep-water wave as above explained.
Figs. 2 and 3 are diagrams taken on a vertical plane, showing graphically the
motion during the forward and backward vibration, respectively, of the line
connecting an originally vertical set of particles in the deep-water wave of Fig. 1.
Fig. 4 is a diagram taken on a vertical plane, showing graphically the structure
and movement of a shallow-water wave as above explained.
Figs. 5 and 6 are diagrams taken on a vertical plane, showing graphically the
motion during the forward and backward vibration, respectively, of the line
connecting an originally vertical set of particles in the shallow-water wave of
Fig. 4.
Fig. 7 shows a vane suspended from points above the surface of the water in
such a manner as to permit it to move in general conformance with the motion of
the distorted verticals above referred to, the rotation of the vane about its horizontal
axis being independently regulated to cause it to approximate to their general
direction.
Similar letters of reference on the different figures indicate corresponding
elements or parts.
a a a is the
Referring to Fig. 1, the line A A is the original still-water level.
profile of the assumed deep-water wave, and the dotted line above, A A, is the
center line of the orbit circles for the surface particles. The circular orbits of
some of these particles are shown dotted, the position of the orbit radius in each case
showing the phase of the respective particle. Similar elements are shown for virtual
subsurfaces at successively equal depths below the surface, thus illustrating the
gradual decrease in motion with increasing depth below the surface. The
lines bede, &c., are the originally vertical straight lines connecting a set o
particles in still water, previously referred to, which become displaced and dis
torted during the passage of the wave. In the particular phase represented by
Fig. 1 they occupy the position b¹ c¹ d'e¹, &c.; and during the passage of on
complete wave each such originally vertical line passes by a continuous motion
through the positions and shapes shown in the diagram and through all inter
mediate positions and shapes. Each such originally vertical line moves as a whol
in alternately opposite directions, its upper end having the greater and more rapi
motion and always curving toward the nearest wave crest, be the same approaching
or receding, the line, as a whole, passing through a vertical phase at the passag

page_text: of each successive crest and trough of the wave across such line. Considering any
such distorted vertical then, its extreme positions are evidently found by drawing
curves passing through and connecting the ends of the horizontal diameters of the
orbit circles at different depths, as shown in Figs. 2 and 3, the line passing from
one of its extreme positions to the other, with its upper end describing the upper
half of the surface orbit circle during the forward vibration, Fig. 2, and the lower
half of the surface orbit circle during the backward vibration, Fig. 3. Thus the
entire area swept over by each such vertical during the forward vibration is that
shown hatched in Fig. 2, having for its upper boundary the upper half of the orbit
circle, while the area swept over by each such vertical during the backward
vibration is that shown hatched in Fig. 3, being a somewhat similar figure, but
having for its upper boundary a curve practically agreeing with the lower half of
the surface orbit circle.
By substituting for the orbit circles in Figs. 1, 2, and 3 the orbit ellipses
corresponding to any particular shallow-water wave we obtain the corresponding
diagrams, Figs. 4, 5, and 6, the main practical difference being a diminution in the
maximum curvature of the distorted verticals, accompanied by an increase in their
translation or displacements as a whole.
Considering in Fig. 1 or Fig. 4 a theoretical surface which was originally in
still water a vertical plane perpendicular to the direction of advance of the assumed
wave, such surface during the passage of the wave will move in alternately opposite
directions, but its upper end will have the greater and more rapid motion, curving
in alternately opposite directions toward the nearest wave crest. The surface as
a whole will during the forward vibration sweep through a volume whose section
is shown by the hatched portion of Fig. 2 or Fig. 5, as the case may be, and
during the backward vibration a volume whose section is shown by the hatched
portion of Fig. 3 or Fig. 6. If we conceive this theoretical surface to be replaced
by an extremely thin and flexible metallic vane, the latter will evidently during
the passage of each wave be subjected to a similar displacement as a whole in
alternately opposite directions and to a bending in alternately opposite directions
toward the nearest wave crest. If such vane be placed in still water and caused
by suitable mechanism to assume and pass through all successive positions and
shapes of a distorted vertical corresponding to any particular trochoidal deep or
shallow water wave, a certain expenditure of power will be required and the corre-
sponding wave will be produced. Conversely, it follows that by means of suitable
mechanism a certain amount of power can be derived from a vane of this kind,
which by the passage of a wave is caused to undergo the motions described.
Should such vane be made rigid instead of flexible, it would still have approxi-
mately the same motion of translation as the flexible vane, but instead of bending
in detail to conform to the exact shape of the distorted verticals it would slant as
a whole toward the nearest wave crest, taking at any instant the average direction
of their curvature along its length. While a flexible vane would theoretically be
best as interfering least with the normal structure and movement of the wave, yet
the increased complexity in mechanism required would more than counterbalance
the gain in power, so that for practical purposes a rigid vane is to be preferred.
Such vane should, in general, be made as light and thin as is consistent with proper
strength and rigidity and should extend from somewhat above the surface of the
water to near the bottom. It is also to be noted that the above description of the
movements of the wave applies strictly only to the more or less regular swell
outside the breakers, and it is in these waves outside the breakers that for greatest
efficiency such vane with its mechanism should be located.
The preferable method of suspending the vane B in any actual ease depends on
the depth of the water and on the range of variation in the usual magnitude and
direction of the waves.
When, as is usually the case, the water is so shallow in proportion to the length
of the wave that the orbits of the particles are quite elliptical, in which case there
s considerable horizontal motion at the bottom, the vane is preferably suspended

page_text: from above at a point of its length near the mean height of the center of
pressure.
For any given depth of water the curvature of the distorted verticals, as well as
their translation or displacement as a whole, depend on the dimensions of the wave,
and for any given wave the curvature and the translation of such distorted verticals,
bear a definite proportion to each other. These two motions can be computed or
determined experimentally for any particular contour of bottom, depth of water,
and size of wave; and the vane can by suitable mechanism be caused to rotate
about a horizontal axis while undergoing the motion of translation imparted to it
by the wave, this motion of rotation being regulated to bear at all times the proper
proportion to the motion of translation.
In Fig. 7, aaa is the wave profile, and B is a vane of the kind just referred to.
To the vane B are rigidly secured the crank-arms U and V, each of which is
supported by and pivoted to another crank f and g, respectively, the latter being
supported and pivoted at the points and k. By means of this mechanism any
translation or displacement of the vane B as a whole is accompanied by a
proportionate rotation of the same about the axis O, the proper ratio between these
two motions for any particular series of waves being secured by suitably adjusting
the distance between the bearings and k by means of the screws n and s.
power due to both translation and rotation is taken off by the cranks fand g and
transmitted by connecting-rods at their upper ends, or by any other equivalent
method, to suitable pumping or other mechanism for utilizing or storing this
power.
The
In order to adjust the vane B about a vertical axis to suit the direction of the
waves, a turn-table T is provided, which, by suitable mechanism, is turned and
adjusted to any desired position and properly secured after adjustment. This
turn-table T supports and carries with it the bearings and k, the screws n and s,
the vane B, and all other necessary parts. This turn-table T may be dispensed
with when the contour of the coast or other influences cause a practically constant
direction of the waves.
CD, &c., are firmly-braced structures supporting the platforms or floors E
and F, the turn-table T, and the vane B. On the platforms or floors E and F or
within the structures C D, &c., can be placed the pumping or other mechanism for
transmitting, utilizing, or storing the power derived from the waves by means of
the vane B and the mechanism for adjusting and securing the turn-table T.
The energy of the forward vibration of the distorted verticals is greater than
that of their backward vibration, and the vane will thus not vibrate equally in both
directions if the same resistance is opposed to it during both vibrations. The
proper and regular working of the vane can be insured either by opposing
a suitable smaller effective resistance to the motion of the vane during the
backward than during the forward vibration, or by opposing to the forward
vibration of the vane, in addition to the equal effective resistance opposing both
vibrations, a suitable additional resistance so arranged as to yield up during the
backward vibration the potential energy thereby stored up during the forward
vibration. The former method simply requires that the amount of power derived
from the vane on the forward and backward vibrations, respectively, is to be
adjusted to correspond to the normal energy of the distorted verticals during these
respective vibrations. The latter method is most simply carried out by the raising
of a free weight or the extension or compression of a spring during the forward
vibration, the potential energy of which is then allowed to assist the backward
vibration. The irregularity of the vibrations which would be induced by a current
can be rectified in a similar manner.
Having now particularly described and ascertained the nature of our said inven-
tion, and in what manner the same is to be performed, we declare that what
we claim is:-
1. In a wave-motor, the vane B, suspended, as shown in Fig. 7, at some point

page_text: along its length conformable to the depth of water and the motion of the distorted
verticals of wave motion, as hereinabove explained; the crank-arms U and V
rigidly connected to the vane B; the cranks ƒ and g, pivotally connected to the
cranks U and V and provided with bearings and k; the screws n and s for
adjusting the distance between the bearings 1 and k, so as to cause a certain
predetermined ratio to exist between the rotation of the vane B and its translation
or displacement as a whole; all arranged and operating substantially in the manner
and for the purposes herein set forth and specified.
2. A wave-motor, comprising a turn-table T, the bearings and k, the screws n
and s, the crank-arms U and V, the cranks f and g and the vane B suspended as
shown in Fig. 7; all arranged and operating substantially in the manner and for
the purposes herein set forth and specified.
Deted this 8th day of April 1897.
WHEATLEY & MACKENZIE,
40 Chancery Lane, London, W.C., Agents.