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curvature of the guides and vanes from the lips at which the fluid enters
between them to the lips at which it leaves them shall be gradual, and
nowhere angular or sudden. In the turbine the passages between the fixed
guides gradually diminish from the lips at which the fluid first enters to those
at which it leaves them, until finally the sectional area of the passages is
such that they will just discharge the desired quantity of fluid with the
desired velocity. The lips at which the fluid leaves them must be so formed
as to direct the fluid in a direction inclined at about 20 to the direction of
motion of the vanes (the exact angle being determined by the circumstances
under which the turbine is intended to work). The passages between the
moving vanes have a sectional area just sufficient to receive the fluid as
discharged from the fixed guides, and their lips have a direction parallel to
the direction in which the fluid is moving relative to them. The openings
between the vanes gradually diminish, and the lips at which the fluid leaves
them are inclined in the opposite direction to that in which they are moving,
so that the fluid on issuing from them shall be driven back as fast as the
vanes move forwards, and hence have no motion in the direction in which the
vanes are moving. The length of the passages, and the closeness of the guides
and vanes, are matters of very great importance owing to the loss of work
which is caused by friction between the fluid and the surfaces over which it is
gliding, which loss renders it important that the passages should be formed
so as to expose the minimum of surface to the moving fluid consistent with
the performance of their functions. The rules for forming the passages
depend on the way in which these passages are arranged, or the class to

102



148 IMPROVEMENTS IN TURBINES AND CENTRIFUGAL PUMPS. [20

which the turbines or pumps belong, but in all cases they are the same as
those for forming a single turbine or pump to work with the pressure and
with the same quantity of fluid as the several individuals of the combined
turbines. The best proportions for a vortex turbine are shown in the draw-
ings, Figs. 2 and 3. The size of the turbine depends on the quantity of
fluid which is to pass through it, and is given by the formula



/
V



W



where A is the area of all the openings between the guides where the fluid
emerges from them, W is the weight of one cubic foot of the fluid, p is the
difference in the pressure of the fluid on entering and leaving the turbine in
pounds (Ibs.) per square foot, Q is the quantity of fluid in cubic feet per
second, and the diameter of the wheel is given by D = J2QA, where D is the
diameter in feet. I have now particularly described the nature of my
invention and the mode of carrying the same into effect, and claim as my
invention Firstly, the arrangement and combination of two or more turbines
together so that the pressure necessary to work the second turbine may be
transmitted through the fluid in the first, and the pressure or power of the
fluid will in passing through the combined turbines in succession impart a
portion of its entire pressure or power to each turbine substantially as here-
inbefore described. Secondly, The arrangement and combination of two or
more centrifugal pumps or fans in which the fluid after leaving the moving
passages is received into fixed passages, or passages moving in the opposite
direction, so formed as to deprive it of all velocity of whirl, or give it a
velocity of whirl in the opposite direction as hereinbefore described. Thirdly,
The construction, combination and arrangement of turbine apparatus as
hereinbefore described and illustrated by Fig. 2 of the accompanying drawings.
Fourthly, The combination and arrangement of two or more turbines similar
to that hereinbefore described and illustrated by Fig. 2 of the drawings sub-
stantially as hereinbefore described and illustrated by Fig. 3 of the accom-
panying drawings. Fifthly, The combination and arrangement of two or more
turbines as hereinbefore described and illustrated by Fig. 4 of the accompany-
ing drawings.



21.



ON THE UNEQUAL ONWARD MOTION IN THE UPPER AND
LOWER CURRENTS IN THE WAKE OF A SHIP; AND THE
EFFECTS OF THIS UNEQUAL MOTION ON THE ACTION
OF THE SCREW-PROPELLER.

[From the "Transactions of the Institution of Naval Architects," 1876.]

(Read April 7, 1876.)

THE very important part which the tendency of the water to follow
in the wake of a ship plays in the action of the screw-propeller has often
been the subject of remark. It has been very prominently brought forward
by Mr Froude and others, and is, I believe, now very generally accredited a
place in all considerations of the very complicated phenomena which envelop
the action of the screw. There is one effect of this wake, however, which
I think has not hitherto received the attention which its importance demands,
and this is the subject of my present communication.

Of the various phenomena which have been developed during our
experience of screws, none have given more trouble than their tendency to
cause vibrations; and although certain causes have been suggested for this,
it has never received a satisfactory explanation. This, I think, arises from
the fact, that in the calculations and estimates which have been hitherto
made respecting the screw, it has been uniformly assumed that the blades of
the screw act with equal effect in all positions that the screw acts equally
on all the water through which it sweeps. If this assumption were correct
there could be no tendency in the screw to cause vibrations except by throw-
ing water against parts of the ship. But this equal action can only be
assumed to exist on the supposition either that the water through which the
screw moves is initially at rest, or that it is all moving with the same
velocity. Now, this supposition will, I think, on closer examination, be seen



150 ON THE UNEQUAL ONWARD MOTION IN THE UPPER [21

to be very far from true ; and in recognising what is the actual condition of
the water, I think we can see what are the causes of general phenomena
which have been hitherto only partially explained, besides the above
mentioned tendency to cause vibrations which is the peche habituel of the
screw-propeller.

Last year, while investigating the action of a screw on the steering of a
vessel, my attention was drawn to the tendency which the screw has to turn
the ship out of her direct course. This tendency I found was very generally
recognised, and was attributed, like the tendency to cause vibrations, to the
action of the water thrown by the screw obliquely against the stern-post.

That this explanation was not the true one, I was at once able to convince
myself by removing the stern-post, when I found that the tendency of the
screw to turn the ship out of her course was increased. I was thus led to
conclude that the upper blade, or blades of the screw, experienced greater
lateral resistance than the lower blade or blades ; for the stern of the ship
was always driven in a direction opposite to that in which the upper blades
were moving. On looking for the cause of this resistance it appeared that
it might arise from the water in which the upper blades worked following
the ship faster than that below ; and on comparing the various tendencies
which the ship had to turn when moving at different velocities, with what
might be expected to result from such an unequal motion, I found sufficient
agreement to confirm me in this opinion. Being at that time concerned
with the steering, I only examined this phenomenon so far as it related to
the investigation in hand, the results of which investigation were contained
in a Paper read before Section G at the British Association last year. Sub-
sequently, however, it occurred to me that this difference in the speed of the
following currents must play an important part in the action of the screw-
propeller, particularly as regarded the vibrations.

The Relative Speed of the Upper and Lower Currents in the Wake.

As is well known, a ship imparts an onward motion to the water in its
wake in two ways by the friction of the skin, and by the wave which follows
the ship. From neither of these causes does it appear that the motion
imparted to the water will be equally distributed through the whole area of
the wake ; but, on the other hand, it appears that both causes will act to
give the water near the surface a greater onward velocity than that which is
on a level with the keel of the ship, and that water which is directly behind
the stern-post a greater velocity than that which is more on one side.

When a long narrow plane is dragged through the water in the manner
adopted by Mr Froude in his experiments on surface friction, its only effect,
in the way of setting the water in motion, is that of skin-resistance ; but



21] AND LOWER CURRENTS IN THE WAKE OF A SHIP, ETC. 151

even here the upper water will be made to move faster than the lower. The
motion imparted to the water in the immediate vicinity of the plane is
rapidly communicated to the adjacent water, and so becomes more or less
dissipated. Now at the top of the plane the only direction in which this
dissipation can extend is laterally, whereas towards the bottom of the plane
the dissipation can extend downwards as well as sideways, and is therefore
much more rapid, leaving the water near the bottom of the plane moving
with less velocity than that near the top. So that, looking at a ship as a
long narrow plane, we see that even so there would be not only a difference
between the velocity of the water in the middle of the wake and that
towards the outside, but that there would also be a difference in the velocity
at different elevations. A ship, however, differs considerably from a plane,
and its form tends further to increase the inequality in the motion of the
water.

The water which fills the opening left by the ship in large part rises up
from beneath its bottom, and in rising carries up to the surface that water
which has received the greatest onward motion from rubbing against the
skin, supplying its place below by fresh water without any onward velocity.
This would be the case even if the run of the ship were in the form of a
vertical wedge, and the actual form of the ship, which is more like an
inclined plane than a vertical wedge, tends greatly to increase this action, for
the water moves upwards along what are called the geodetic lines. See
Kankine's Shipbuilding, p. 83.

The fact that the lines of a ship are much fuller near the surface than
those below tends also to give the upper water greater forward motion.

Again, the form of a ship is such as to cause a wave to follow it, the crest
of the wave being not far from the stern-post. This wave also causes a greater
onward motion in the particles of water near the surface than those which are
below.

We see therefore, taking all the causes together, that there is probably a
very considerable difference in the relative onward velocity imparted by the
ship to the water in which the upper and lower blades of the screw work.
There is also a difference in the velocity of the water at different lateral
distances from the middle of the wake, but this latter variation is not of any
direct importance as regards the object of this communication and therefore
will not be considered farther.

The Actual Velocity of the Wake.

Before we can form an estimate of the probable magnitude of the actual
difference in the velocity with which the upper arid lower currents move, it is
necessary to arrive at some conclusion as regards the proportion which the



152 ON THE UNEQUAL ONWARD MOTION IN THE UPPER [21

velocity of the wake bears to that of the ship. The actual motion imparted
by a ship to the water in its wake has never, so far as I am aware, been experi-
mentally investigated ; there are however two ways in which estimates have
been formed ; by observations on the surface, and by calculations based on
the resistance of the ship.

If one may judge from various incidental comments, one finds that the
observation of the motion at the surface of the wake has led to much higher
estimates of its velocity than the calculations from the ship's resistance.

Mr G. B. Rennie remarks, " The current caused by the onward motion of
the ship has a velocity at the stern equal to that of the ship itself*."

Mr Griffith says, " The water in which the screw works is an eddy which
follows the ship at the same speed or nearly so... if a patent log were placed
in the screw opening, it would not even approximately indicate the speed of
the ship t"

I would remark here that I do not make these quotations in order to show
that they are wrong, but simply to show that observation of the surface has
led those who have had the best opportunities of judging, to form a high
estimate of the onward motion imparted to the wake for the purpose of
comparing this estimate with that based on the resistance of the ship.

In his Marine Engineering, Rankine gives a rule for calculating the
velocity of the wake (see p. 249); and, applying this rule to the 'Warrior' (a
very long ship), he finds that the speed of the water near the stern-post is '09
the speed of the ship.

We see, therefore, how widely this estimate differs from the estimates
formed from observations at the surface. The previous argument, however,
regarding the difference between the velocity at the surface and that below
will go a long way to reconcile these estimates.

Rankine's estimate is based on the supposition that all the water following
the ship has the same onward motion imparted to it. A very different result,
however, is arrived at, if instead of the entire mass of water in the wake, it is
only, or principally, the upper layers that are supposed to be set in motion.
The speed imparted to the water must be inversely proportioned to the
volume acted on, so that if the motion only extends to the bottom of the ship,
and gradually dies out, instead of the velocity being 10 per cent, it will be
20 per cent, of that of the ship.

This seems to me to agree with what may be observed on looking over the
stern of a paddle steamer, or a sailing ship. In the case of the steamer, the
inner ends of the lines of foam left by the paddles become curved forwards as

* Modern Screw Propulsion, p. 19. By N. P. Burgh. t Ibid. p. 45.



21] AND LOWER CURRENTS IN THE WAKE OF A SHIP, ETC. 153

they approach the stern, where they join the wake, and are violently dragged
forward with a velocity of certainly more than one- tenth that of the ship.

As a rough estimate, therefore, I should conclude that in a ship with a
fairly fine run the velocity of the wake, at the surface, is not less than '20 that
of the ship, while at the level of the keel the water is practically stationary.
And, in the cases of ships, moving at an abnormal speed, carrying a high
stern wave, or having full sterns, the difference may be increased to almost
any extent.

The Effect on the tierew.

Having now shown that there is a considerable difference in the onward
velocity in different parts of the ship's wake, it only remains to consider what
effect this difference would have on the action of the screw.

Compared with the speed of the ship the difference is after all but small,
and if the thrust of the screw depended on the speed of the ship, this small
difference might well be neglected ; all that would result would be a difference
of some 20 per cent, in the pressure on the upper and lower blades. I cannot
help thinking that it is owing to some such confusion as this between the
action of the screw and the speed of the ship that the unequal motion of the
water in the wake has remained unattended to for so long. When we realize
the fact that the thrust of the screw does not depend on the speed of the ship,
but on the difference between the speed of the ship and the geometrical speed
of the screw the speed at which it would have to move forward were the
water unyielding ; and that this difference, called the slip, is somewhere
between one-tenth and one-fourth the speed of the ship, we see at once what
an important influence an increase in the speed of the water anything like
one-fourth the speed of the ship would have. Hence, although the inequality
in the motion of the water is small as compared with the speed of the ship,
as compared with the slip it is very large, and this is the essential com-
parison.

The slip of a screw would be somewhere between one-tenth and one-
fourth the speed of the ship if it were equally distributed over the entire area
through which the screw acts. But if there is a difference in the rate at
which the water is following the ship at different parts of the section of the
screw race, then the slip, and consequently the pressure on the blades of the
screw, will be greatest at those places where the water is following the ship
fastest.

Taking the mean slip at '2, and supposing the upper blades to be working
in a current which has an onward velocity '2 greater than that in which the
lower blades are working, then the slip at the tops of the upper blades would
be '3, and that at the tops of the lower blades only '1 ; so that the resistance



154 ON THE UNEQUAL ONWARD MOTION IN THE UPPER [21

at the tips of the upper blades would be three times as great as that at the
tips of the lower blades. Or, to put it roundly, the area of the water on
which the screw acts to drive the ship forward would be virtually reduced, it
would be the blades above the shaft that principally drive the ship, the lower
blades merely passing through the water.

The Tendency to cause Vibrations.

Under these circumstances it is clear that the lateral resistances which the
upper and lower blades encountered would no longer balance each other. For
example, ou a two-bladed screw the pressure on the blades would only be
equal when they were both on a level with the shaft. As the one rose
towards the vertical position the resistance would increase, while that on the
lower blade would dimmish. The action of the screw would, therefore, be to
cause an intermittent force, urging the stem in the direction opposite to
that in which the tips of the upper blades were moving.

The magnitude of this intermittent force would be very considerable
under the circumstances assumed above, it would, while it acted, be com-
parable to the entire lateral resistance encountered by the screw. It would,
therefore, afford sufficient explanation of the screw's tendency to cause vibra-
tions, which the shock caused by the water thrown by the screw against the
stern-post does not. It would also fully accord with what experience has
shown respecting the effect of the screw on the steering of the ship.

Effect on the Efficiency.

Such an inequality in the action of the screw as that described above,
would not necessarily reduce its efficiency as a propeller. So long as there
was some small slip left to the bottom blades there could be no actual
retardation of the ship. But if the inequality in the motion of the water
should at any time bear such proportion to the mean slip that the lower
blades could not, as it were, screw themselves through the water fast enough
to keep up with the ship, then they would have to be dragged through the
water, and would retard the ship. Such a result would only be experienced
when the inequality of motion in the water was more than double the mean
slip of the screw. Such a state of things, it would appear, could only be
brought about by a vessel moving at an abnormal speed and carrying a large
stern wave, or by a vessel having a very full stern, conditions which are
invariably found to result in loss of efficiency and excessive vibration, and
very often in what is called negative slip. The loss of efficiency which
usually attends negative slip, has received what appears to be a satisfactory
explanation as being due to the back suction, or reduction of pressure which
the action of the screw causes on the stern of the ship. And that it is in some
part at least due to this cause has been proved by Mr Froude by actual



21] AND LOWER CURRENTS IN THE WAKE OF A SHIP, ETC. 155

experiment. But, considering that when this action occurs, all the conditions
which would cause the lower blade to drag back are known actually to exist,
it would seem to be highly probable that at least in part, the loss of efficiency,
as well as the excessive vibration, is due to the unequal motion of the water
on which the upper and lower blades of the screw act.



Disadvantage of Large Screws.

It can be easily seen that the effects which have been attributed to the
unequal motion of the water would be greater with screws, which are large
in proportion to the draught of the ship, than with those which are smaller.

There are two reasons for this. In the first place the larger the screw
the smaller must be the mean slip, and consequently the greater would be
the proportion which the inequality of the motion of the water would bear
to it. On the smaller would be the margin, allowed for the difference in the
slip at the top and bottom of the blades. And, secondly, the larger the
screw the greater would be the difference in the motion of the water in which
the upper and lower blades worked.

Now I believe it has been found, as a matter of experience, that there is
a limit to the size of the screws which give the best results for each ship.
This limit is doubtless in part due to the increased friction which large screws
experience, owing to their increased surface ; but the friction must be much
larger than what we have reason to suppose it is, if this alone can account
for the limit. It seems probable therefore that this limit is another result of
the inequality of the motion of the following waters.

A few years ago a large Atlantic steamer was fitted with a screw, which
could be lowered until its blades extended below the bottom of the ship.
Various advantages would appear as likely to result from such an arrangement.
But it seems to me to be probable that the disadvantages resulting from
the inequality in the motion of the wake would be considerably increased,
for the lower blades of the screw would descend into the water with no
following motion at all, while the upper blades would still be high up in the
wake. I do not know what was the result of the experiment, but I have
heard that the plan had to be abandoned on account of the excessive
vibration.

Conclusion.

It is not my object in this Paper to enter upon the question as to what
modification in the construction or dispositions of screws might be suggested
by the recognition of the unequal motion of the wake and its effects. Any
suggestions I might make would be premature. My endeavour has been



156 ON THE UNEQUAL ONWARD MOTION IN THE CURRENTS, ETC. [21

solely to elucidate further the actual conditions or circumstances of the
problem of screw propulsion, it being my conviction that a complete know-
ledge of the conditions of any problem must be conducive to its eventual
solution. My opportunities of studying the action of screws are limited, and
in venturing to come before you, my inducement has been that my ideas
would be criticised by those who have much better opportunities. If, through
ignorance, I have been occupying time by dilating on what is unimportant or
already known, I can only hope that I may have your indulgence ; a claim
which I feel entitled to make, as it is only the importance which you were
pleased to attach to my former communication which has emboldened me to
come forward again.



22.

ON THE REFRACTION OF SOUND BY THE ATMOSPHERE.

[From the " Philosophical Transactions of the Royal Society of London,"

Vol. CLXVL, pt. 1.]
(Read January 6, 1876.)

IN a paper read before the Royal Society, May 1874, I pointed out that
the upward diminution of temperature in the atmosphere (known to exist
under certain circumstances) must refract and give an upward direction to
the rays of sound which would otherwise proceed horizontally; and it was
suggested that this might be the cause of the observed difference in the
distinctness with which similar sounds are heard on different occasions,
particularly the very marked advantage which night has over day in this
respect. At the time at which that paper was written no direct experiments
or observations had been made to verify the truth of this suggestion, and
therefore its probability rested on its reasonableness. Since that time,
however, I have carried out a series of observations and experiments which,



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