WAVES AND RIPPLES MADE BY SHIPS.
It is impossible for the most careless spectator to look at a
steam-vessel making her way along a lake, a boy’s boat skimming across
a pond, or even a duck paddling on a stream, without noticing that the
moving body is accompanied in all cases by a trail of waves or ripples,
which diverge from it and extend behind. In the case of a steamer there
is an additional irregular wave-motion of the water caused by the
paddle-wheels or screw, which churn it up, and leave a line of rough
water in the steamer’s wake. This, however, is not included in the true
ship-wave effect now to be discussed. We can best observe the proper
ship-wave disturbance of the water in the case of a yacht running
freely before the wind when the sea is fairly smooth. The study of
these ship-waves has led to most important and practical improvements
in the art of ship-designing and shipbuilding, and no treatment of the
subject of waves and ripples on water would be complete in which all
mention of ship-waves was omitted.
In order that we may explain the manner in which these waves are
formed, and their effect upon the motion of the ship, and the power
required to move it forward, we must begin by a little discussion of
some fundamental facts concerning liquids in motion.
Every one is aware that certain liquids are, as we say _sticky_, or, to
use the scientific term, _viscous_. A request to mention sticky liquids
would call up the names of such fluids as tar, treacle, gum-water,
glycerine, and honey. Very few people would think of including pure
water, far less spirits of wine, in a list of sticky, or viscous
liquids; and yet it is quite easy to show by experiment that even these
fluids possess some degree of stickiness, or viscosity. An illustration
may be afforded as follows: We provide several very large glass tubes,
nearly filled respectively with quicksilver, water, alcohol, glycerine,
and oil. A small space is left in each tube containing a little air,
and the tubes are closed by corks. If we suddenly turn all the tubes
upside down, these bubbles of air begin to climb up from the bottom
of the tube to the top. We notice that in the quicksilver tube it
arrives at the top in a second or two, in the water tube it takes a
little longer, in the oil tube longer still, and in the tube filled
with glycerine it is quite a minute or more before the bubble of air
has completed its journey up the tube. This experiment, properly
interpreted, shows us that water possesses in some degree the quality
of viscosity. It can, however, be more forcibly proved by another
experiment.
To a whirling-table is fixed a glass vessel half full of water. On this
water a round disc of wood, to which is attached a long wire carrying
a paper flag, is made to float. If we set the basin of water slowly
in rotation, at first the paper flag does not move. The basin rotates
without setting the contained water in rotation, and so to speak slips
round it. Presently, however, the flag begins to turn slowly, and
this shows us that the water has been gradually set in rotation. This
happens because the water sticks slightly to the inner surface of the
basin, and the layers of water likewise stick to one another. Hence,
as the glass vessel slides round the water it gradually forces the
outer layer of water to move with it, and this again the inner layers
of water one by one, until at last the floating block of wood partakes
of the motion, and the basin and its contents turn round as one mass.
This effect could not take place unless the water possessed some degree
of viscosity, and also unless so-called _skin friction_ existed between
the inside of a glass vessel and the water it contains.
We may say, however, at once that no real liquid with which we are
acquainted is entirely destitute of stickiness, or viscosity. We can
nevertheless imagine a liquid absolutely free from any trace of this
property, and this hypothetical substance is called a _perfect fluid_.
It is clear that this ideal perfect liquid must necessarily differ in
several important respects from any real fluid, such as water, and some
of these differences we proceed to examine. We must point out that in
any liquid there may be two kinds of motion, one called _irrotational_
motion, and the other called _rotational_ or _vortex_ motion.
Consider any mass of water, such as a river, in motion in any way;
we may in imagination fix our attention upon some small portion of
it, which at any instant we will consider to be of a spherical shape.
If, as this sphere of liquid moves along embedded in the rest of the
liquid, it is turning round an axis in any direction as well as being
distorted in shape, the motion of that part of the fluid is called
_rotational_. If, however, our little sphere of liquid is merely being
stretched or pulled into an ovoid or ellipsoidal shape without any
rotation or spinning motion, then the motion of the liquid is said to
be _irrotational_. We might compare these small portions of the liquid
to a crowd of people moving along a street. If each person moves in
such a way as always to keep his face in the same direction, that
movement would be an irrotational movement. If, however, they were to
move like couples dancing in a ball-room, not only moving along but
turning round, their motion would be called rotational. Examples of
rotational, or vortex motion are seen whenever we empty a wash-basin by
pulling up the plug. We see the water swirl round, or rotate, forming
what is called an _eddy_, or whirlpool. Also eddies are seen near the
margin of a swiftly flowing river, since the water is set in rotation
by friction against objects on the banks. Eddies are likewise created
when two streams of water flow over each other with different speeds. A
beautiful instance of this may be viewed at an interesting place a mile
or two out of the city of Geneva. The Rhone, a rapid river, emerges
as a clear blue stream from the Lake of Geneva. At a point called
_Junction d’eaux_ it meets the river Arve, a more sluggish and turbid
glacier stream, and the two then run together in the same channel.
The waters of the Rhone and Arve do not at once mix, but the line of
separation is marked by a series of whirlpools or eddies set up by the
flow of the rapid Rhone water against the slower Arve water in contact
with it.
Again, it is impossible to move a solid body through a liquid without
setting up eddy-motion. The movement of an oar through the water, or
even of a teaspoon through tea, is seen to be accompanied by little
whirls which detach themselves from the oar or spoon, and are really
the ends of vortices set up in the liquid. The two facts to notice
particularly are that the production of eddies in liquids always
involves the expenditure of energy, or, in mechanical language, it
necessitates _doing work_. To set in rotation a mass of any liquid
requires the delivery to it of _energy_, just as is the case when a
heavy wheel is made to rotate or a heavy train set in movement. This
energy must be supplied by or absorbed from the moving solid or liquid
which creates the eddies.
In the next place, we must note that eddies or vortices set up in an
imperfect fluid, such as water, are ultimately destroyed by fluid
friction. Their energy is frittered down into heat, and a mass of water
in which eddies have been created by moving through it a paddle, is
warmer after the eddies have subsided than before. It is obvious, from
what has been said, that if a really perfect fluid did exist, it would
be impossible by mechanical means to make eddies in it; but if they
were created, they would continue for ever, and have something of the
permanence of material substances.
[Illustration: FIG. 27.—The production of a vortex ring in air.]
A vortex motion in water may be either a terminated vortex, in which
case its ends are on the surface, and are seen as eddies, or whirls;
or it may be an endless vortex, in which case it is called a _vortex
ring_. Such a ring is very easily made in the air as follows: A cubical
wooden box about 18 inches in the side has a hole 6 inches in diameter
made in the bottom (see Fig. 27). The open top of the box is covered
tightly with elastic cloth. The box is then filled with the white
vapour of ammonium chloride, by leading into it at the same time dry
hydrochloric acid gas and dry ammonia gas. When quite full of dense
white fumes, we give the cloth cover of the box a sharp blow with the
fist, and from the round hole a white smoke ring leaps out and slides
through the air. The experiment may be made on a smaller scale by
using a cardboard box and filling it with the smoke of brown paper or
tobacco.[13] If we look closely at the smoke ring as it glides through
the air, we shall see that the motion of the air or smoke particles
composing the ring is like that of an indiarubber umbrella-ring fitted
tightly on a round ruler and pushed along. The ring turns itself
continually over and over, the rotation being round the circular ring
axis line. This rotatory motion is set up by the friction of the
smoky air against the edge of the hole in the box, as the puff of air
emerges from it when the back of the box is thumped. A simple but
striking experiment may be made without filling the box with smoke.
Place a lighted candle at a few feet away from the opening of the
above-described box, and strike the back. An invisible vortex ring of
air is formed and blows out the candle as it passes over it. Although
it is quite easy to make a rotational motion in an imperfect fluid, and
in fact difficult not to do it, yet of late years a very interesting
and valuable discovery has been made by Professor Hele-Shaw, of a
method of creating and rendering visible a motion in an imperfect
liquid like water, which is irrotational. This discovery was that, if
water is made to flow in a thin sheet between two plates, say of flat
glass, not more than a fiftieth of an inch or so apart, the motion of
the water is exactly that of a perfect fluid, and is irrotational. No
matter what objects may be placed in the path of the water, it then
flows round them just as if all fluid friction or viscosity was absent.
This interesting fact can be shown by means of an apparatus designed
by Professor Hele-Shaw.[14] Two glass plates are held in a frame, and
separated by a very small distance. By means of an inlet-pipe water
is caused to flow between the plates. A metal block pierced with
small holes is attached to the end of one plate, and this serves to
introduce several small jets of coloured water into the main sheet. In
constructing the apparatus great care has to be exercised to make the
holes in the above-mentioned block very small (not more than ¹⁄₁₀₀ inch
in diameter) and placed exactly at the right slope.
The main water inlet-pipe is connected by a rubber tube with a cistern
of water placed about 4 feet above the level of the apparatus. The
frame and glass plates are held vertically in the field of an optical
lantern so as to project an image of the plates upon the screen. The
side inlet-pipe leading to the pierced metal block is connected to
another reservoir of water, coloured purple with permanganate of potash
(Condy’s fluid), and the flow of both streams of water controlled
by taps. The clear water is first allowed to flow down between the
plates, so as to exclude all air-bubbles, and create a thin film of
flowing water between two glass plates. The jets of coloured water are
then introduced, and, after a little adjustment, we shall see that the
coloured water flows down in narrow, parallel streams, not mixing with
the clear water, and not showing any trace of eddies. The regularity of
these streams of coloured water, and their sharp definition, shows that
the liquid flow between the plates is altogether irrotational.
The lines marked out by the coloured water are called _stream-lines_,
and they cut up the whole space into uniform _tubes of flow_. The
characteristic of this flow of liquid is that the clear water in the
space between two coloured streams of water never passes over into an
adjacent tube. Hence we can divide up the whole sheet of liquid into
tubular spaces called tubes of flow, by lines called stream-lines.
If now we dismount the apparatus and place between the glass a thin
piece of indiarubber sheet—cut, say, into the shape of a ship, and of
such thickness that it fills up the space between the glass plates—we
shall be able to observe how the water flows round such an obstacle.
If the air is first driven out by the flow of the clear water, and then
if the jets of coloured water are introduced, we see that the lines of
liquid flow are delineated by coloured streams or narrow bands, and
that these stream-lines bend round and enclose the obstructing object.
The space all round the ship-shaped solid body is thus cut up into
tubes of flow by stream-lines, but these tubes of flow are now no
longer straight, and no longer of equal width at all points.
They are narrower opposite the middle part of the obstruction than near
either end.
[Illustration: FIG. 28.]
At this point we must make a digression to explain a fundamental law
concerning fluid flow in tubes. Suppose we have a uniform horizontal
metal tube, through which water is flowing (see Fig. 28). At various
points along the tube let vertical glass pipes be inserted to act as
gauge or pressure-tubes. Then when the fluid flows along the horizontal
pipe it will stand up a certain height in each pressure-tube, and this
height will be a measure of the pressure in the horizontal pipe at the
point where the pressure-tube is inserted. We shall notice that when
the water flows in the horizontal pipe, the water in the gauge-pipes
stands at different heights, indicating a _fall in pressure_ along the
horizontal pipe. We also notice that a line joining the tops of all the
liquid columns in the pressure-pipes is a straight, sloping line, which
is called the _hydraulic gradient_. This experiment proves to us that
when fluid flows along a uniform-sectioned pipe there is a uniform fall
or decrease in pressure along the pipe. The force which is driving the
liquid along the horizontal pipe is measured by the difference between
the pressures at its extreme ends, and the same is true of any selected
length of the horizontal pipe.
It will also be clear that, since water is not compressible to any but
the very slightest extent, the quantity of water, reckoned, say in
gallons, which passes per minute across any section of the pipe must be
the same.
[Illustration: FIG. 29.]
In the next place, suppose we cause water to flow through a tube which
is narrower in some places than in others (see Fig. 29). It will be
readily admitted that in this tube also the same quantity of water will
flow across every section, wide or narrow, of the tube. If, however,
we ask—Where, in this case, will there be the greatest pressure? it
is certain that most persons would reply—In the narrow portions of
the tube. They would think that the water-particles passing through
the tube resemble a crowd of people passing along a street which is
constricted in some places like the Strand. The crowd would be most
tightly squeezed together, and the pressure of people would therefore
be greater, in the narrow portions of the street. In the case of the
water flowing through the tube of variable section this, however, is
not the case. So far from the pressure being greatest in the narrow
portions of the tube, it can be shown experimentally that it is
precisely at those places it is least.
This can be demonstrated by the tube shown in Fig. 29. If water is
allowed to flow through a tube constricted in some places, and provided
with glass gauge-pipes at various points to indicate the pressure in
the pipe at those places, it is found that the pressure, as indicated
by the height of the water in the gauge-glasses at the narrow parts of
the tube, is less than that which it would have at those places if the
tube were of uniform section and length, and passed the same quantity
of water. We can formulate this fact under a general law which controls
fluid motion also in other cases, viz. that _where the velocity of the
liquid is greatest, there the pressure is least_. It is evident, since
the tube is wider in some places than in others, and as a practically
incompressible liquid is being passed through it, that the speed of the
liquid must be greater in the narrow portions of the tube than in the
wider ones. But experiment shows that after allowing for what may be
called the proper hydraulic gradient of the tube, the pressure is least
in those places, viz. the constricted portions, where the velocity of
the liquid is greatest. This general principle is of wide application
in the science of hydraulics, and it serves to enable us to interpret
aright many perplexing facts met with in physics.
We can, in the next place, gather together the various facts concerning
fluid flow which have been explained above, and apply them to elucidate
the problems raised by the passage through water of a ship or a fish.
Let us consider, in the first place, a body totally submerged, such as
a fish, a torpedo or a submarine boat, and discuss the question why a
resistance is experienced when an attempt is made to drag or push such
a body through water. The old-fashioned notion was that the water has
to be pushed out of the way to make room for the fish to move forward,
and also has to be sucked in to fill up the cavity left behind. Most
persons who have not been instructed in the subject, perhaps even now
have the idea that this so-called “head resistance” is the chief cause
of the resistance experienced when we make a body of any shape move
through water. A common assumption is also that the object of making
a ship’s bows sharp is that they may cut into the water like a wedge,
and more easily push it out of the way. Scientific investigation has,
however, shown that both of these notions are erroneous. The resistance
felt in pulling or pushing a boat through the water is not due to
resistance offered by the water in virtue of its inertia. No part of
this resistance arises from the exertion required to displace the water
or push it out of the way.
The Schoolmen of the Middle Ages used to discuss the question how it
was that a fish could move through the water. They said the fish could
not move until the water got out of the way, and the water could not
get out of the way until the fish moved. This and similar perplexities
were not removed until the true theory of the motion of a solid through
a liquid had been developed.
Briefly it may be said that there are three causes, and only three,
for the resistance which we feel and have to overcome when we
attempt to drag a boat or ship through the water. These are: First,
_skin friction_, due to the friction between the ship-surface and
the water; secondly, _eddy-resistance_, due to the energy lost or
taken up in making water eddies; and thirdly, _wave-resistance_, due
to energy taken up in making surface-waves. The skin friction and
the eddy-resistance both arise from the fact that water is not a
perfect fluid. The wave-resistance arises, as we shall show, from the
unavoidable formation of waves by the motion of the boat through the
water.
In the case of a wholly submerged body, like a fish, the only
resistance it has to overcome is due to the first two causes. The
fish, progressing through the water wholly under the surface, makes no
waves, but the water adheres to its skin, and there is friction between
them as he moves. Also he creates eddies in the water, which require
energy to produce them, and whenever mechanical work has to be done, as
energy drawn off from a moving body, this implies the existence of a
resistance to its motion which has to be overcome.
Accordingly Nature, economical on all occasions in energy expenditure,
has fashioned the fish so as to reduce the power it has to expend
in moving through water as much as possible. The fish has a smooth
slippery skin. (We say “as slippery as an eel.”) It is not covered
either with fur or feathers, but with shiny scales, so as to reduce to
a minimum the skin friction. The fish also is regular and smooth in
outline. It has no long ears, square shoulders, or projecting limbs or
organs, which by giving it an irregular outline, would tend to produce
eddies in the water as it moves along. Hence, when we wish to design a
body to move quickly under the water, we must imitate in these respects
the structure of a fish. Accordingly, a Whitehead torpedo, that deadly
instrument employed in naval warfare, is made smooth and fish-shaped,
and a submarine boat is made cigar-shaped and as smooth as possible,
for the same reason.
If the floating object is partly above the surface, yet nevertheless,
as far as concerns the portion submerged, there is skin friction, and
the production of eddy-resistance. Hence, in the construction of a
racing-yacht, the greatest care has to be taken to make its surface
below water of polished metal or varnished wood, or other very smooth
material, to diminish as far as possible the skin friction. In the case
of bodies as regular in outline as a ship or fish, the proportion of
the driving power taken up in making eddies in the water is not large,
and we may, without sensible error, say that in their case the whole
resistance to motion is comprised under the two heads of skin friction
and wave-making resistance. The proportion which these two causes bear
to each other will depend upon the nature of the surface of the body
which moves over the water, and its shape and speed.
At this point we may pause to notice that, if we could obtain a
perfect fluid in practice, it would be found that an object of any
shape wholly submerged in the fluid could be moved about in any way
without experiencing the least resistance. This theoretical deduction
is, at first sight, so opposed to ordinary preconceived notions on
the subject, that it deserves a little attention. It is difficult, as
already remarked, for most people who have not carefully studied the
subject, to rid their minds of the idea that there is a resistance to
the motion of a solid through a liquid arising from the effort required
to push the liquid out of the way. But this notion is, as already
explained, entirely erroneous.
In the light of the stream-line theory of liquid motion, it is easy to
prove, however, the truth of the above statement.
Let us begin by supposing that a solid body of regular and symmetrical
shape, say of an oval form (see Fig. 30), is moved through a fluid
destitute of all stickiness or viscosity, which therefore does not
adhere to the solid. Then, if the solid is wholly submerged in this
fluid, the mutual action of the liquid and the solid will be the same,
whether we suppose the liquid to be at rest and the solid to move
through it, or the solid body to be at rest and the liquid to flow past
it.
[Illustration: FIG. 30.—Stream-lines round an ovoid.]
[Illustration: FIG. 31.—Tube of flow in a liquid.]
If, then, we suppose the perfect fluid to flow round the obstacle,
it will distribute itself in a certain manner, and its motion can be
delineated by stream-lines. There will be no eddies or rotations,
because the liquid is by assumption perfect. Consider now any two
adjacent stream-lines (see Fig. 31). These define a tube of flow,
represented by the shaded portion, which is narrower in the middle
than at the ends. Hence the liquid, which we shall suppose also to be
incompressible, must flow faster when going past the middle of the
obstacle where the stream-tubes are narrow, than at the ends where the
stream-tubes are wider.
By the principle already explained, it will be clear that the pressure
of the fluid will therefore be less in the narrow portion of the
stream-tube, and from the perfect symmetry of the stream-lines it is
evident there will be greater and equal pressures at the two ends of
the immersed solid. The flow of the liquid past the solid subjects it,
in fact, to a number of equal and balanced pressures at the two ends
which exactly equilibrate each other. It is not quite so easy to see
at once that if the solid body is not symmetrical in shape the same
thing is true, but it can be established by a strict line of reasoning.
The result is to show that when a solid of _any_ shape is immersed in
a perfect liquid, it cannot be moved by the liquid flowing past it,
and correspondingly would not require any force to move it against and
through the liquid. In short, there is no resistance to the motion of
a solid of any shape when pulled through a perfect or frictionless
liquid. When dealing with real liquids not entirely free from
viscosity, such resistance as does exist is due, as already mentioned,
to skin friction and eddy formation. In the next place, leaving the
consideration of the movement of wholly submerged bodies through
liquids whether perfect or imperfect, we shall proceed to discuss the
important question of the resistance offered by water to the motion
through it of a floating object, such as a ship or swan. We have in
this case to take into consideration the wave-making properties of the
floating solid.
We have already pointed out that to make a wave on water requires an
expenditure of energy or the performance of mechanical work. If a
wave is made and travels away over water, it carries with it energy,
and hence it can only be created if we have a store of energy to draw
upon. If we suppose that skin friction is absent, and that the ship
floats upon a perfect fluid, it would nevertheless be true that, if the
moving object creates waves, it will thereby reduce its own movement
and require the application of force to it to keep it going. We may say
therefore that if any floating object creates waves on a liquid over
which it moves, these waves rob the floating body of some of its energy
of motion. The creation of the waves will bring it to rest in time,
unless it is continually urged forward by some external and impressed
force, and wave-generation is a reason for a part at least of the
resistance we experience when we attempt to push it along.
Accordingly, one element in the problem of designing a ship is that of
finding a form which will make as little wave-disturbance as possible
in moving over the liquid. It is comparatively easy to find a shape
for a floating solid which shall make a considerable wave-disturbance
on the water when it is pulled over it, but it is not quite so easy to
design a shape which will not make waves, or make but very small ones.
If we look carefully at a yacht gliding along before a fresh breeze on
a sea or lake surface which is not much ruffled by other waves, it is
possible to discover that a ship, when going through the water, creates
_four distinct systems of waves_. Two of these are very easy to see,
and two are more difficult to identify. These wave-systems are called
respectively the oblique bow and stern waves, and the transverse and
rear waves. We shall examine each system in turn.
The most important and easily observed of the four sets of waves is
the oblique bow wave. It is most easily seen when a boy’s boat skims
over the surface of a pond, and readily observed whenever we see a duck
paddling along on the water. Let any one look, for instance, at a duck
swimming on a pond. He will see two trains of little waves or ripples,
which are inclined at an angle to the direction of the duck’s line of
motion. Both trains are made up of a number of short waves, each of
which extends beyond or overlaps its neighbour (see Fig. 32).
[Illustration: FIG. 32.—Echelon waves made by a duck.]
Hence, from a common French word, these waves have been called _echelon
waves_,[15] and we shall so speak of them.
[Illustration: FIG. 33.—Echelon waves made by a model yacht.]
On looking at a boy’s model yacht in motion on the water, the same
system of waves will be seen; and on looking at any real yacht or
steamer in motion on smooth water, they are quite easily identified
(see Fig. 33).
The complete explanation of the formation of these bow or echelon waves
is difficult to follow, but in a general way their formation can be
thus explained: Suppose we have a flat piece of wood, which is held
upright in water, and to which we give a sudden push. We shall notice
that, in consequence of the inertia of the liquid, it starts a wave
which travels away at a certain speed over the surface of the water.
The sudden movement of the wood elevates the water just in front of it,
and this displacement forms the crest of a wave which is then handed
on or propagated along the surrounding water-surface. If two pieces
of wood are fastened together obliquely, as in Fig. 34, and held in
water partly submerged, we shall find that when this wood is suddenly
thrust forward like a wedge, it starts two oblique waves which move
off parallel to the inclined wooden sides. The bows of a ship, roughly
speaking, form such a wedge.
[Illustration: FIG. 34.]
Hence, if we consider this wedge or the bows of a ship to be placed
in still water and then pushed suddenly forward, they will start two
inclined waves, which will move off parallel to themselves.
If we then consider the wedge to leap forward and repeat the process,
two more inclined waves will be formed in front of the first; and
again we may suppose the process repeated, and a third pair of waves
formed. The different positions of the ship’s bows are shown in the
diagram at 1, 2, and 3 in Fig. 35; and _c_, _e_, and _f_ are the three
corresponding sets of echeloned waves. For the sake of simplicity, the
waves are shown on one side only. If, then, we imagine the ship to move
uniformly forwards, its bows are always producing new inclined waves,
which move with it, and it is always, so to speak, leaving the old ones
behind. All these echelon waves produced by the bow of the ship are
included within two sloping lines which each make with the direction of
the ship’s line of movement, an angle of 19° 28´.[16] This angle can be
thus set off: Draw a circle (see Fig. 36), and produce the diameter BC
of this circle for a distance, CA, equal to its own length. From the
end A of the produced diameter draw a pair of lines, AD, AD′, called
tangents, to touch the circle. Then each of these lines will make an
angle of 19° 28´ with the diameter. If we suppose a ship-to be placed
at the point marked A in the diagram (see Fig. 36), all the echelon
waves it makes will be included within these lines AD, AD′.
[Illustration: FIG. 35.]
Moreover, the angle of the lines will not alter, whether the ship goes
fast or slow. This is easily seen in the case of a duck swimming on a
lake. Throw bits of bread to a duck so as to induce it to swim faster
or slower, and notice the system of inclined or echelon ripples made by
the duck’s body as it swims. It will be seen that the angle at which
the two lines, including both the trains of echelon ripples meet each
other is not altered as the duck changes its speed.
[Illustration: FIG. 36.]
This echelon system of inclined waves is really only a part of a system
of waves which is completed by a transverse group in the rear of the
vessel. A drawing has been given by Lord Kelvin, in his lecture on
“Ship Waves,” of the complete system of these waves, part of which is
as represented by the firm lines in Fig. 37. This complete system is
difficult to see in the case of a real ship moving over the water. The
inclined rear system of waves can sometimes be well seen from the deck
of a lake steamer, such as those on the large Swiss or Italian lakes,
and may sometimes be photographed in a snap-shot taken of a boy’s yacht
skimming along on a pond.
[Illustration: FIG. 37.]
In addition to the inclined bow waves, there is a similar system
produced by the stern of a vessel, which is, however, much more
difficult to detect. The other two wave-systems produced by a ship are
generally called the transverse waves. There is a system of waves whose
crest-lines are at right angles to the ship, and they may be seen in
profile against the side of any ship or yacht as it moves along. These
transverse waves are really due to the unequal pressures resulting from
the distribution of the stream-lines delineating the movement of the
water past the ship.
If we return again to the consideration of the flow of a perfect fluid
round an ovoid body, it will be remembered that it was shown that, in
consequence of the fact that the stream-lines are wider apart near
the bow and stern than they are opposite the middle part of the body,
the pressure in the fluid was greater near the bow and stern than at
the middle. When a body is not wholly submerged, but floats on the
surface as does a ship, these excess pressures at the bow and stern
reveal themselves by forcing up the water-surface opposite the ends of
the vessel and lowering it opposite the middle. This may be seen on
looking at any yacht in profile as it sails. The yacht appears to rest
on two cross-waves, one at the bow and one at the stern, and midships
the water is depressed (see Fig. 38).
[Illustration: FIG. 38.]
These waves move with the yacht. If the ship is a long one, then each
of these waves gives rise to a wave-train; and on looking at a long
ship in motion, it will be seen that, in addition to the inclined bow
wave-system, there is a series of waves which are seen in profile
against the hull.
[Illustration: FIG. 39.]
When a ship goes at a very high speed, as in the case of torpedo-boat
destroyers, the bow of the vessel is generally forced right up on to
the top of the front transverse waves, and the boat moves along with
its nose entirely out of water (see Fig. 39). In fact, the boat is, so
to speak, always going uphill, with its bows resting on the side of a
wave which advances with it, and its stern followed by another wave,
whilst behind it is left a continually lengthening trail of waves,
which are produced by those which move with the boat.
The best way to see all these different groups of ship-waves is to
tow a rather large model ship without masts or sails—in fact, a mere
hulk—over smooth water in a canal or lake. Let one person carry a
rather long pole, to the end of which a string is tied; and by means
of the string let the model ship be pulled through the water. Let this
person run along the banks of the canal or lake, and tow the ship
steadily through the water as far as possible at a constant speed. Let
another person, provided with a hand camera, be rowed in a boat after
the model, and keep a few yards behind. The second observer will be
able to photograph the system of ship-waves made by the model, and
secure various photographs when the model ship is towed at different
rates. The echelon and transverse waves should then be clearly visible,
and if the water is smooth and the light good, it is not difficult to
secure many useful photographs.
By throwing bits of bread to ducks and swans disporting themselves
on still water, they also may be induced to take active exercise in
the right direction, and expose themselves and the waves or ripples
that they make to the lens of a hand camera or pocket kodak. From
a collection of snap-shot photographs of these objects the young
investigator will learn much about the form of the waves made by ships,
and will see that they are a necessary accompaniment of the movement of
every floating object on water. By conducting experiments of the above
kind under such conditions as will enable the exact speed of the model
to be determined, and the resistance it experiences in moving through
the water, information has been accumulated of the utmost value to
shipbuilders.
Our scientific knowledge of the laws of ship-resistance we owe chiefly
to the labours of two great engineers, Mr. Scott Russell and Mr.
William Froude. Mr. Froude’s work was begun privately at Torquay about
the year 1870, and was subsequently continued by him for the British
Admiralty. Mr. Froude was the first to show the value and utility
of experiments made with model ships dragged through the water. He
constructed at Torquay an experiment tank about 200 feet in length,
which was a sort of covered swimming-bath, and he employed for his
experiments model ships made of wood or paraffin wax, the latter being
chosen because the model could be so easily cut to the desired shape,
and all the chips and the model itself could be melted up and used over
again for subsequent experiments. Without detailing in historic order
his discoveries, suffice it to say that, as the outcome of his work,
Mr. Froude was able to state two very important laws which relate to
the relative resistance experienced when two models of different sizes
are dragged through the water at different speeds.
The first of these relates to what is called the “_corresponding
speeds_.” Suppose we have a real ship 250 feet long, and we make an
exact model of this ship 10 feet long, then the ship is twenty-five
times longer than the model. Mr. Froude’s law of corresponding speeds
is as follows:—
If the above model and the ship are both made to move over still water,
the ship going five times as fast as the model, the system of waves
made by the model will exactly reproduce on a smaller scale the system
of waves made by the ship. In other words, if we were to take a couple
of photographs, one of the ship going at 20 miles an hour, and one
of the model one twenty-fifth of its size going at 4 miles an hour,
and reduce the two photographs to the same size, they would be exactly
alike in every detail.
Expressed in more precise language, the first law of Froude is as
follows: When a ship and a model of it move through smooth water at
such speeds that the speed of the ship is to the speed of the model
as the square root of the length of the ship is to the square root of
the length of the model, then these speeds are called “_corresponding
speeds_.” At corresponding speeds the wave-making power of the model
resembles that of the ship on a reduced scale. If we call _L_ and _l_
the lengths of the ship and the model, and _S_ and _s_ the speeds of
the ship and the model, then we have—
_S_/_s_ = √(_L_/_l_)
where _S_ and _s_ are called corresponding speeds.
Mr. Froude then established a second law of equal importance, relating
to that part of the whole resistance due to wave-making experienced
by a ship and a model, or by two models when moving at corresponding
speeds.
Mr. Froude’s second law is as follows: If a ship and a model are moving
at “corresponding speeds,” then the resistances to motion due to
wave-making are proportional to the cube of their lengths. To employ
the example given above, let the ship be 250 feet long and the model
10 feet long, then, as we have seen, the corresponding speeds are as
5 to 1, since the lengths are as 25 to 1. If, therefore, the ship is
made to move at 20 miles an hour, and the model at 4 miles an hour,
the resistance experienced by the ship due to wave-making is to that
experienced by the model as the cube of 25 is to the cube of 1, or in
ratio of 15,625 to 1. In symbols the second law may be expressed thus:
Let _R_ be the resistance due to wave-making experienced by the ship,
and _r_ that of the model when moving at corresponding speeds, and let
_L_ and _l_ be their lengths as before; then—
_R_/_r_ = _L_^3/_l_^3
Before these laws could be applied in the design of real ships, it
was necessary to make experiments to ascertain the skin friction of
different kinds of surfaces when moving through water at various speeds.
Mr. Froude’s experiments on this point were very extensive. For
example, he showed that the skin friction of a clean copper surface
such as forms the sheathing of a ship may be taken to be about one
quarter of a pound per square foot of wetted surface when moving at 600
feet a minute. This is equivalent to saying that a surface of 4 square
feet of copper moved through water at the rate of 10 feet a second
experiences a resisting force equal to the weight of 1 lb. due entirely
to skin friction. Very roughly speaking, this skin resistance increases
as the square of the speed.[17] Thus at 20 feet per second the skin
friction of a surface of 4 square feet of copper would be 4 lbs., and
at 30 feet per second it would be 9 lbs. Any roughness of the copper
surface, however, greatly increases the skin friction, and in the case
of a ship the accumulation of barnacles on the copper sheathing has
an immense effect in lowering the speed of the vessel by increasing
the skin friction. Hence the necessity for periodically cleaning the
ship’s bottom by scraping off these clinging growths of seaweed and
barnacles.
Mr. Froude also made many experiments on surfaces of paraffin wax,
because of this material his ship models were made. It may suffice to
say that the skin friction in this case, in fresh water, is such that
a surface of 6 square feet of paraffin wax, moving at a speed of 400
feet per minute, would experience resistance equal to the weight of 1
lb. There are, however, certain corrections which have to be applied
in practice to these rules, depending upon the length of the immersed
surface. The mean speed of the water past the model or ship-surface
depends on the form of the stream-lines next to it, and it has already
been shown that the velocity of the water next to the ship is not the
same at all points of the ship-surface. It is greater near the centre
than at the ends. Hence the longer the model, the less is the mean
resistance per square foot of wetted surface due to skin friction when
the model is moved at some constant speed through the water.
The above explanations will, however, be sufficient to enable the
reader to understand in a general way the problem to be solved in
designing a ship, especially one intended to be moved by steam-power.
If a shipbuilder accepts a contract to build a steamer—say a
passenger-steamer for cross-Channel services—he is put under obligation
to provide a ship capable of travelling at a stated speed. Thus, for
instance, he may undertake to guarantee that the steamer shall be able
to do 20 knots in smooth water. In order to fulfil this contract he
must be able to ascertain beforehand what engine-power to provide.
For, if the engine-power is insufficient, he may fail to carry out his
contract, and the ship may be returned on his hands. Or if he goes to
the opposite extreme and supplies too large a margin of power, he may
lose money on the job, or else he may again violate his contract by
providing an engine and boiler too extravagant in fuel.
It is in solving the above kind of practical problem that Mr. Froude’s
methods of experimenting with models in a tank are of such immense
value. The first thing that the naval architect does in designing a
ship is to prepare a series of drawings, showing the form of the hull
of the vessel. From these drawings a model is constructed exactly to
scale. In England, following Mr. Froude’s practice, these models are
usually made of paraffin wax, about 12 or 14 feet long and 1 inch
in thickness. In the United States wood is used. These models are
constructed with elaborate care and by the aid of special machinery,
and are generally 10 or 12 feet in length, and some proper fraction
of the length of the real vessel they represent. The models are then
placed in a tank and experiments are made, the object of which is to
ascertain the force or “pull” required to drag the model through the
water at various speeds.
The tank belonging to the British Admiralty is at Haslar, Gosport,
near Portsmouth, and the experiments are now conducted there by Mr. E.
Edmund Froude, who continues the scientific work and investigations
of his distinguished father, Mr. William Froude. This Admiralty tank
at Haslar is 400 feet in length. The well-known firm of shipbuilders,
Messrs. Denny Bros., of Dumbarton, Scotland, have also a private
experimental tank of the same kind. The Government of the United States
of America have a similar tank at Washington, the Italian Government
have one at Spezzia, and the Russian Admiralty has also made one. These
tanks resemble large swimming-baths, which are roofed over (see Fig.
40).
[Illustration: FIG. 40.—An experimental tank for testing ship models
(Washington).[18]]
Over the water-surface is arranged a pair of rails, on which runs a
light carriage or platform. This carriage is drawn along by a rope
attached to a steam-engine, which moves at a very uniform rate, and
its speed can be exactly ascertained and automatically recorded. This
moving carriage has a rod or lever depending from it, to which the
model ship is attached. The pull on this rod is exactly registered on
a moving strip of paper by very delicate recording mechanism. The
experiment is conducted by placing the model at one end of the tank,
and taking a run at known and constant speed to the other end. The
experimentalist is thus able to discover the total resistance which
it is necessary to overcome in pushing the model ship at a certain
known speed through the water. The immersed surface of the model being
measured and the necessary calculations made, he can then deduct from
the total resistance the resistance due to skin friction, and the
residue gives the resistance due to wave-making. Suppose, then, that
the experiment has been performed with a model of a ship yet to be
built, the run being taken at a “corresponding speed.” The observations
will give the wave-making resistance of the model, and from Mr.
Froude’s second law the wave-making resistance of the real ship is
predicted. Adding to this the calculated skin-friction resistance of
the real ship, we have the predetermined actual total ship-resistance
at the stated speed. For the sake of giving precision to these ideas,
it may be well to give an outline of the calculations for a real ship,
as given in a pamphlet by Mr. Archibald Denny.[19]
The tank at the Leven shipyard, constructed by Messrs. Denny Bros.
for their own experiments, is 300 feet long, 22 feet wide, and 10
feet deep, and contains 1500 tons of fresh water. At each end are
two shallower parts which serve as docks for ballasting and trimming
models. As an example of the use of the tank in predicting the power
required to drive a ship of certain design through the water, Mr. A.
Denny gives the following figures: The ship to be built was 240 feet
in length, and from the drawings a model was constructed 12 feet in
length, or one-twentieth the size.
It was then required to predetermine the power required to drive
the ship through the water at a speed of 13¹⁄₂ knots. A knot, be it
remarked, is a speed or velocity of 1 nautical mile an hour, or 6080
feet per hour. It will be seen that this is not far from 100 feet per
minute.
By Froude’s first law, the corresponding speed for the 12-foot model is
therefore—
13¹⁄₂ × 6080/60 × √(12/240) = 306 feet per minute
The model was accordingly dragged through the tank at a speed of nearly
5 feet per second, and, after deducting from the total observed pull
the resistance due to the calculated skin friction of the model, it
was found that the resistance to the motion of the model at this speed
due to wave-making was 1·08 lb. Hence, by Froude’s second law, the
wave-making resistance of the ship was predetermined to be—
1·08 × (240/12)^3 × 40/39 = 8850 lbs.
The last fraction 40/39 is a correcting factor in passing from fresh
water to salt water.
The surface of the proposed ship was 10,280 square feet, and the skin
friction was known to be 1·01 lb. per square foot at a speed of 13·5
knots. Hence the total skin resistance of the ship would be—
10,280 × 1·01 × 40/39 = 10,620 lbs.
Adding to this, the 8850 lbs. for wave-making resistance, we have a
total resistance of 19,470 lbs. predetermined as the total pressure
required to be overcome in moving the ship at a speed of 13·5 knots.
Hence, since 1 horse-power is defined to be a power which overcomes
a resistance of 33,000 lbs. moved 1 foot per minute, it is easy to
see that 19,470 lbs. overcome at a rate of 13·5 knots represents a
power of—
(19,470 × 13·5 × 6080)/(33,000 × 60) = 810 horse-power
But now, in the case of a screw-driven steamer, a part of the power is
lost in merely churning up the water, and a part in internal frictional
losses in the engine and screw-shaft.
It is not far from the truth to say that 50 per cent. of the applied
engine-power is lost in useless water-churning. Hence, for the above
steamer, an actual power of at least 1600 H.P. would have to be
applied to the screw-shaft. To allow, however, for the loss of power
in friction, and to allow a margin for emergencies, it would be usual
to provide for such a steamer engines of at least 3000 _indicated_
horse-power.
Each shipbuilder has, however, at call a mass of data which enable him,
from actual measured mile trials, to determine the rates between the
calculated driving horse-power and the indicated horse-power of the
engines, and so enable him, in the light of experience, to provide in
any new ship the exact amount of steam-power necessary to produce the
required speed. As an instance of how accurately this can be done by
the aid of the tank experiments, Mr. A. Denny gives an example drawn
from experience in building the well-known paddle-steamers _Princess
Josephine_ and _Princess Henriette_ for the Belgian Government Dover to
Ostend fast mail-steamer service.
The speed guaranteed before the boats were built was 20¹⁄₂ knots. The
estimate was made for 21 knots, and the actual results of trials on the
measured mile, when the ships were built, showed that each did 21·1
knots on prolonged and severe test.
The reader, therefore, cannot fail to see how important are these
methods, laws, and researches of Mr. Froude.
The above-described process for testing models is being continually
conducted in the case of all new battleships and cruisers for the
British Navy, and also is pursued by the naval constructors of other
nations. In connection with the extensive programme of battleship
construction which has been carried out of late years, Sir William
White, the late eminent Chief Director of Naval Construction, states
that it is not too much to say that these methods of investigation
and experiment have placed in the hands of the naval architect an
instrument of immense power for guiding him safely and preventing
costly mistakes. Sir William White has declared that it would have been
impossible to proceed with the same certainty in battleship design,
were it not for the aid afforded by these methods.
Mr. Froude was not content, however, with experiments made with models.
He ascertained by actual trials the total force required to drive an
actual ship through the water at various speeds, and obtained from
other experiments valuable data which showed the proportion in which
the total resistance offered to the ship was divided between the skin
friction and the wave-making resistance.
Then he made experiments on a ship of 1157 tons, viz. H.M.S.
_Greyhound_. This vessel was towed by another vessel of 3078 tons,
viz. H.M.S. _Active_, by means of a tow-rope and a dynamometer, which
enabled the exact “pull” on this hawser to be ascertained when the
_Greyhound_ was towed at certain speeds. The following are some of the
results obtained:—
Speed in knots Strain in tons
of H.M.S. _Greyhound_. on towing-rope.
4 knots 0·6 tons
6 ” 1·4 ”
8 ” 2·5 ”
10 ” 4·7 ”
12 ” 9·0 ”
It will be seen that the total resistance increases very rapidly with
the speed, varying in a higher ratio than the square of the speed.
In addition, the indicated horse-power of the engine of the _Greyhound_
was taken when being self-driven at the above speeds, and it was found
that only 45 per cent. of the indicated horse-power of the engines was
used in propelling the ship, the remaining 55 per cent. being wasted in
engine and shaft friction and in useless churning of the water by the
screw.
It is an important thing to know how this total resistance is divided
between skin friction and wave-making resistance.
Mr. R. E. Froude has kindly furnished the author, through the
intermediation of Sir William White, with some figures obtained
from experiments at Haslar, showing the proportion of the whole
ship-resistance which is due to skin friction for various classes of
ships going at certain speeds.
At full speed. At 10 knots.
Battleships 55 per cent. 79 per cent.
Cruisers 55 ” 84 ”
Torpedo-boat destroyers 43 ” 80 ”
The above table gives the percentage which the skin friction forms of
the total resistance, and the remainder is, of course, wave-making and
eddy-resistance.
The curves shown in Fig. 41 (taken, by kind permission of the editor,
from an article by Mr. E. H. Tennyson-D’Eyncourt, in _Cassier’s
Magazine_ for November, 1901) give, in a diagrammatic form, an idea of
the manner in which the two principal sources of ship-resistance vary
with the speed.
[Illustration: FIG. 41.—(Reproduced, by permission, from _Cassier’s
Magazine_.)]
It will be seen that when a ship is going at a relatively slow speed,
the greater portion of the whole resistance is due to skin friction,
but when going at a high speed, the greater portion of the resistance
is due to wave-making. Hence the moral is that ships and boats intended
to move at a high speed must be so fashioned as to reduce to a
minimum the wave-making power. In general, the naval architect has
to consider many other matters besides speed. In battleship design
he has to consider stability, power of carrying guns and armour, and
various other qualities. In passenger-steamers he has to take into
consideration capacity for passengers and freight, also steadiness
and sea-going qualities; and all these things limit and control the
design. There is one class of vessel, however, in which everything is
sacrificed to speed, and that is in racing-yachts. Hence, in the design
of a racing-yacht, the architect has most scope for considerations
which bear chiefly upon the removal of all limitations to speed.
A little examination, therefore, of the evolution of the modern
racing-yacht shows how the principles we have endeavoured to explain
have had full sway in determining the present form of such boats.
Attention has chiefly been directed to this matter in connection with
the international yacht race for the possession of the America Cup.
In 1851 a yacht named the _America_ crossed the Atlantic and made her
appearance at Cowes to compete for a cup given by the Royal Yacht
Squadron. Up to that time British yachts had been designed with full
bluff bows and a tapering run aft. These boats were good sea-boats,
but their wave and eddy making powers were considerable. The _America_
was constructed with very fine lines and a sharp bow, and was a great
advance on existing types of yacht. In the race which ensued the
_America_ won the cup, and carried it off to the United States.
Since that date there has been an intermittent but steady effort on
the part of British yachtsmen to recover the trophy, so far, however,
without success.
[Illustration:
AMERICA, 1851.
VIGILANT, 1893.
PURITAN, 1885.
DEFENDER, 1895.
VOLUNTEER, 1887.
COLUMBIA, 1899.
United States yachts entered for the America Cup race, 1851–1899.
(FIG. 42.)]
[Illustration:
GENESTA, 1885.
VALKYRIE III., 1895.
THISTLE, 1887.
SHAMROCK, 1899.
VALKYRIE II., 1893.
SHAMROCK II., 1901.
FIG. 42.—British yachts entered for the America Cup race, 1885–1901.]
In a very interesting article in _Harmsworth’s Magazine_, in 1901, Mr.
E. Goodwin has traced the gradual evolution of the modern yacht, such
as _Shamrock II._ or the _Columbia_, from the _America_.
No doubt the methods of “measurement” in force at the time, or the
dimensions which determine whether the boat can enter for the Cup race
or not, have had some influence in settling the shape. The reader,
however, will see, on comparing the outlines of some of the competing
yachts as shown in Fig. 42,[20] that there has been a gradual tendency
to reduce the underwater surface as much as possible, and also to
remove the wave-making tendency by overhanging the bows. The only
rule now in force restricting the yacht size for the Cup race is
that it must not be more than 90 feet in length when measured on the
water-line. In order that the yacht may have stability, and be able to
carry a large sail-surface, it must have a certain depth of immersed
hull. This is essential also to prevent the boat from making leeway
when sailing with the wind abeam. But consistently with this object,
the two great aims of the yacht-builder are, _first_, to reduce as
much as possible the skin friction by making the yacht-surface smooth
and highly polished. Thus modern racing-yachts are not always built of
wood, but very often of some metal, such as bronze, steel, or aluminium
alloys, which admit of a very high polish. This hull-surface is
burnished as much as possible before the race, to reduce to a minimum
the skin friction. Then in the _second_ place, the designer aims at
fashioning the form of the bow of the yacht so as to reduce as much as
possible its wave-making qualities. A fine type of modern yacht glides
through the water with hardly any perceptible bow wave at moderate
speeds.
Thus the following extract from the _Chicago Recorder_ of September 4,
1901, respecting Sir Thomas Lipton’s yacht, _Shamrock II._, during her
trials for the Cup race, shows how marked a feature this is in the case
of a yacht of the best modern type:—
“With her owner, designer, builder, manager, and sailmaker on board,
the yacht _Shamrock II._ sailed her seventh trial race to-day off
Sandy Hook. Although at times there was not more than a three-knot
air, at no time did the yacht act sluggishly.
“She slipped through the water at an amazingly good rate under the
influence of her great mainsail and light sails. The water was
smooth, but even when pressed to a speed of 9 knots _the yacht made a
very small wave at the bow_, and left an absolutely clean wake.”
We may say, therefore, that the ideal form of yacht is one which would
travel through the water without making any wave at all at bow or
stern. This condition can, however, only be reached approximately,
but the clear recognition of the principle has enabled yachts to be
designed with vastly greater speed powers than in the old days of bluff
bows and tapering bodies.
Before passing away from the subject of waves made by ships, it
is desirable to refer a little more in detail to the complicated
wave-system made by a ship in motion. This has been most carefully
elucidated by Lord Kelvin, who, in this as in so many other matters, is
our great teacher. Lord Kelvin has shown that if a small floating body
is towed through the water at a uniform speed, it originates a system
of waves, each one of which is of the form shown in Fig. 43. The whole
system of waves formed is represented in Fig. 37, where the position
of the ship or moving object is at the point marked A.
The key to a correct comprehension of this ship wave-system is to
be found in the fact explained in Chapter I., that a group of water
waves on an indefinitely extended water surface advances at half the
speed of a single wave. It has already been shown that when a single
wave-disturbance is made upon water it gradually develops itself into
a group of waves. The single wave when created causes a disturbance
on water which extends both forwards and backwards. As the wave moves
forward the wave-disturbance is always growing in front and dying away
behind, and the _wave-group_ therefore moves forward, but the centre or
limits of the group move with only half the velocity of a single wave.
[Illustration: FIG. 43.]
Now consider the ship originally at B (see Fig. 36), and let us suppose
the ship to make a small jerk forward. This operation is like plunging
a stone into the water, and it starts a wave-system. But if the ship
moves forward with a uniform speed, by the time the ship has reached
the point A, the end of the wave-group will have reached a point C,
such that C is halfway between B and A. The movement of the ship,
however, originates a group of waves, and the velocity of a wave on
water is dependent upon its wave-length, as already explained, so
that the greater the wave-length the greater the velocity. Hence the
conditions that determine the form of the wave-system round the ship
are: (1) that the head of the procession goes forward with the speed of
the ship; (2) that there is an end or limit to the transverse system
of waves behind, which moves forward with half the speed of the ship;
(3) the inclination of the wave at any point to the direction of motion
of the ship must be such that its velocity, in its own direction, is
consistent with the wave-length at that place. These general conditions
determine the form of the wave-group as shown in Fig. 37; but the
detailed predetermination of the exact form of the oblique and rear
wave cannot be made without the employment of mathematical reasoning of
a somewhat advanced character.
For the purposes of the general reader it will be sufficient to note
that this procession of ever-extending waves, which lengthens backwards
behind a ship, requires energy to produce it. This energy must be
supplied from the ship, and the wave-production constitutes therefore a
cause of resistance to motion which is felt and has to be overcome in
keeping the speed of the ship constant.
In close connection with this subject is the fine investigation made
about the year 1834 by another eminent engineer, Mr. Scott Russell,
on the motion of canal-boats. His researches were communicated to
the Royal Society of Edinburgh. It has already been explained that
when a wave is started in a canal, the wave-length being large
compared with the depth of the canal, then the velocity of the long
wave is the same as that attained by a stone in falling through air a
distance equal to half the depth of the canal. Scott Russell made the
interesting discovery that it is only when the speed of a canal-boat
is _less_ than that of a long wave in the canal that the boat leaves
behind it a procession of waves. The position of the boat is then on
the rearward side of the first wave. As already mentioned, the boat
leaves behind it a trail of waves, and the rear of this procession
travels forward at half the speed of the boat. If the speed of the
boat is greater than that of the longest free wave in that canal, it
cannot make any procession of waves, and then there would be no system
of ever-lengthening waves behind it, but only one wave or hummock
travelling along under the boat. Lord Kelvin describes, in his lecture
on “Ship Waves,”[21] how this important discovery was in fact made by
a horse. The horse belonged to one William Houston, and its daily duty
was to drag a canal-boat on the Glasgow and Ardrossan Canal. On one
occasion the horse took fright and galloped off, and Houston, being
an observant man, noticed that when once the horse had attained a
certain speed the tractive resistance evidently became lessened, and
the boat was dragged along more easily and without _wash_ behind it.
Accordingly, he started a system of light canal-boats—or _fly-boats_,
as they were called—each 60 feet long, and drawn by two horses at 7, 8,
or 9 miles an hour. The horses were whipped up and made to gallop, and
soon dragged the boat up on to the top of its own wave, whereupon it
went along much more easily, and without a system of stern waves.
Mr. Scott Russell instituted a searching investigation into this effect
in 1837 at the bridge of Hermiston, on the Forth and Clyde Canal, at
a place where there was a straight run of 1500 feet. The depth of
the canal water was 4 to 5 feet, and the speed of the long wave was
accordingly 12 feet per second, or 8 miles an hour.
Experiments were made, amongst others, with a boat called _Raith_, the
weight of which was 10,239 lbs., or 5 tons. This boat was towed along
the canal, and the “pull” on the tow-rope measured by means of an
instrument called a dynamometer. It was found by Mr. Scott Russell that
the pull or force required to drag the boat did not increase with the
speed regularly, but fell off in a marked manner when the speed of the
boat reached 9 miles per hour. This is shown by the following table:—
SCOTT RUSSELL’S EXPERIMENTS ON CANAL-BOATS.
Tractive force in pounds Speed of boat in miles
applied to boat. per hour.
112 4·72
261 5·92
275 6·19
250 9·04
269 10·48
For another boat-weighing 12,579 lbs., or 6 tons, the results obtained
in the same manner were as follows:—
Tractive force in pounds. Speed in miles per hour.
250 6·19
500 7·57
400 8·52
280 9·04
This last experiment shows, in a very remarkable manner, the way in
which the force required to drag the boat falls off as the critical
speed of 9 miles an hour is reached.
Here, then, we have the outlines of the proof first given by Mr. Scott
Russell, that the tractive force undergoes a sudden diminution when the
speed of the boat in a canal approximates to or just exceeds that of
the long wave in that particular depth of water. If passenger traffic
on canals had not been destroyed by the advent of railways, we should,
no doubt, have seen extensive applications of the principle discovered
so curiously by the aid of an alarmed horse, and so skilfully
investigated by a celebrated engineer.
The whole theory of the trail of waves made by a canal-boat is only
comprehensible if it is clearly seen that a water-surface wave has
a certain velocity determined by its wave-length. If the wave-speed
is small, the waves are short. As the speed increases the waves get
longer. Or the matter may be put in another way. We may say that just
as a pendulum has a certain rate of vibration depending on its length,
so a water wave has a certain frequency, and therefore, a certain speed
of propagation dependent upon the wave-length, or shortest distance
from one wave-crest to the next. When a boat moves along a canal the
waves it makes move with it, and the first wave of all moves with the
speed of the boat. Hence the wave-length must accommodate itself to
that speed. As the speed of the boat increases towards that of the
free “long wave,” the wave-length gets greater and greater, and when
the boat-speed is equal to that acquired by a heavy body, say a stone
in falling through half the depth of the canal, then there is only one
wave, and the boat rides up on that one. The next wave is practically
so far behind that it is non-existent, and the boat ceases to be
followed by any trail of waves, or “wash.”