the size being such that it came nearly to the surface. It would be thought
that the larger screw would, when immersed till its centre was at the same
depth as the smaller one, have offered more resistance to the spring, and so
have been less liable to race, but it was not so ; the larger screw would race,
just in the same manner as the smaller one had done, whenever the surface
was broken. This last experiment seems to show conclusively that it is the
admission of air which causes racing.
So far, then, the racing is shown experimentally to be the result of the
admission of air to the screw, and not simply the diminished area of the part
immersed ; and it now remains to explain the precise way in which the air
diminishes the resistance. This is done from theoretical considerations.
It will appear from the following reasoning that there are two different
ways in which the admission of air diminishes the resistance of the screw :
In the first place it interferes with the power of the screw to obtain water ;
and in the second it reduces the resistance which would otherwise be offered
54 CAUSES OF THE RACING OF THE ENGINES OF SCREW STEAMERS. [9
by the water which the screw does get, and causes this water to turn round
with the screw.
The driving power of any propeller will depend on the quantity of water
on which it acts in a given time, and on the backward velocity which it
imparts to this water. Now the quantity of water on which a propeller acts
will depend on the power of the propeller to draw water, not so much when
the boat is moving fast, for then it will necessarily have fresh water to act
upon ; but when from any cause the boat is going slowly, when it is starting,
towing, or meeting a head wind, then the screw has to depend mainly on its
power of drawing a supply of water. If the quantity of water is small, the
speed imparted to it must be great ; and anything which reduces the power
of a propeller to draw water reduces its resistance, and consequently allows
its speed to increase. Hence if the mere fact of the screw breaking the
surface of the water so as to let air down behind its blades diminishes its
power to draw water, it will diminish its resistance, and cause it to race.
Now, although it seems to have been overlooked so far, there can be no
doubt that the admission of air does act in this way. For the power of
a propeller to supply itself with water manifestly depends on the rapidity
with which fresh water will flow into the place of that which is driven
Let us suppose A to be a vertical plate below the surface of the water,
and capable of being driven forward with any velocity; then, if it were
to start from rest, its velocity might be such that the water immediately
behind it would or would not start off as fast; that is, its initial velocity
might be such that the water would not keep up, and a space would be left
between the plate and the following water. So long as its velocity was
not sufficient for this, the quicker the velocity of the plate, the greater would
be the velocity of the following water ; but after this limit had been once
exceeded, the initial speed with which the water would follow would not
depend on the speed of the plate, but would be the same for all speeds.
That is to say, that urge the plate forwards as fast as we might, we could
9] CAUSES OF THE EACING OF THE ENGINES OF SCREW STEAMERS. 55
not get the water to follow at above a certain velocity. This velocity may
be stated in terms of the pressure of the water against the plate before
it begins to move, for it would obviously be that with which water would
flow into the end of an empty pipe, or rather through an opening in the
position of the plate ; therefore the greatest quantity of water which a
propeller could draw, would be equal to that which would flow into a vertical
opening in the same position as the area through which the propeller acts.
Now the velocity, with which water would flow through such an opening,
would be proportional, and generally equal to the velocity which a body
would acquire in falling freely through a vertical distance equal to the
depth of water that would be necessary to produce such a pressure as that
on the plate.
Hence, the limit of the power of a propeller to supply itself with water,
will depend on the pressure of the water over the vertical area through
which the propeller acts. The pressure of the atmosphere will or will not
be included in this, according to circumstances. For if A is entirely below
the surface, and moves too fast for the following water, it will leave a vacuum
behind it, and the water will follow as fast as it could flow through an
opening into a vacuum ; in this case the pressure on A, must not only include
the actual pressure of the water, but also the pressure of the atmosphere.
If, however, A extends to the surface, or communicates with the surface
in any way, then the space will be filled with air, and the water will only
follow as fast as it would flow through an opening on which the pressure of
air acts ; in this case the effective pressure will only be the actual pressure
of the water. If, therefore, air can get behind the plate, the greatest
velocity at which the fluid will follow will be equal to that which would
be acquired in falling through AB. But since the pressure of the atmo-
sphere is equal to that of 30 feet of water, if the air cannot get in, then the
greatest velocity will be due to 30 + AB. Hence the power of a propeller to
draw water will depend on the depth at which its plates act below water ;
and also on whether or not the air is let in, the exclusion of air being as good
as 30 feet additional immersion.
Suppose, then, that a stationary screw-propeller, totally immersed,
were driven so fast that it was getting its maximum quantity of water,
and that driving it faster would only cause a vacuum behind its floats.
Then the quantity of water would be equal to that which would flow
through an opening of the same size as the area through which the
propeller acts, and 30 feet below the actual position of the screw. If, how-
ever, the air were let in, then the actual quantity would only be equal to
what would flow through such an opening in the actual position of the screw.
Thus, if its lowest point were 12 feet below the surface, the mean suction
power over the whole area would be equivalent to a head of 36 feet of water,
5G CAUSES OF THE RACING OF THE ENGINES OF SCREW STEAMERS. [9
30 for the atmosphere, and 6 for the mean pressure of the water. If then
(by means of a wave), air were let in behind the floats, the suction power
would be reduced until it was only equivalent to a head of 6 feet. And
since the velocity of the water would be proportional to the square root
of the head, the quantity of water which the screw would draw would be
reduced from 6 to 2, or by more than half. And if the same driving force
were maintained, the slip would have to be more than doubled to make up
for the diminished quantity of water.
The diminution of power caused by admitting the air, or more correctly,
the increase gained by excluding it will really be constant at all depths,
but when compared with the power arising from the pressure of the water,
it will be much greater for small depths; that is, the ratio of these quantities
will diminish with the depth. This explains the fact that the screws of
small boats are more liable to race than those of larger ones, and it was
doubtless the exaggerated form of racing which existed in the small model
that caught my attention, and led me to connect it with this cause. This
also explains the fact that the racing causes the boat to turn out of its
course. For as long as the air is excluded, the top of the screw will be
as well able to obtain water as the bottom ; but as soon as the pressure of
the atmosphere is taken off, the power of getting water will increase with
the depth, and consequently the bottom of the screw will get more than the
top, and the resistance at the bottom will consequently be greater than it is
at the top, and the boat will be pushed to one side.
The direct effect of the admission of air behind the propeller blades,
to diminish the quantity of water, will be the same for all classes of pro-
pellers, and therefore the same for the paddle as the screw ; but as, in the
former, the air is always admitted, there will be no more racing from this
cause in a storm than in a calm. If, however, this effect were the only one
which the admission of air produced, a screw, even when breaking the
surface, would be a better propeller than paddles for starting or towing;
that is, because of its greater depth of immersion, it would have less
tendency to race. But there is another way in which the existence of air
in the water on which the propeller acts will diminish its power, both to
drive the water away and get more ; and although this effect will not be of
much consequence to a direct acting propeller, like a paddle, yet it is
aggravated to almost any extent in a revolving and oblique acting propeller
like the screw.
Air increases the tendency of the water to whirl round with the screw,
by diminishing the power of the screw to clear itself of the water it has set
in motion. It has often been noticed, when a vessel is starting, that the
screw seems rather to whirl the water round, than to drive it astern. It can
be shown that the admission of air will be conducive to this end to a very
9] CAUSES OF THE RACING OF THE ENGINES OF SCREW STEAMERS. 57
great extent. And the mere fact that the whirling of the water has been
observed, proves that at such times there was air in it. If the blade of a
screw is driving not simply water but air and water, as it passes any
particular portion of the mixture, the pressure will not simply drive it in
front of the blade, as it would if it were a solid mass of water, but will
compress the air bubbles, which as soon as the blade has passed will expand
again, driving some of the water backwards and some of it forwards.
This action of the air in water is analogous to that of an elastic string,
connecting two heavy balls A and B. It will only require about half the
force to impress a certain motion on B in the direction BC, that it would
have required if the string had been inelastic, for then both balls would have
had the same velocity ; and as it is, when the force is removed, the elasticity
will partially stop B and accelerate A. If when connected in this way, a force
is impressed on B, equal to what would be necessary to give the two balls
a certain velocity, then B will start with a greater velocity, which the force
must follow up. So it is with the air and water. If the propeller gets as
great a pressure, when acting on air and water, as when acting on unbroken
water, it must move very much faster through it. This will be the result
both of the compression of the air in front and the extension of that behind
the blade. Thus the air, by virtue of its elasticity, will require an increased
velocity in blades of an oblique propeller ; and this increased velocity will,
by friction, increase the tendency of the water to whirl with the blade.
And each blade will leave a following mass of air and water behind for the
next blade to act upon.
This effect of the air will not exist in the case of direct action, such
as that of the paddles, for the water remains in front of the blade for a
longer period, and the one blade does not come upon the leavings of the
other. Thus we see the admission of air behind the blades of a propeller
will reduce the power of the propeller to supply itself with water ; and in
the case of the screw will aggravate this evil by necessitating (on account of
the elasticity it gives to the water) a higher velocity in the blade to impart
the same velocity to the water ; which is again aggravated by the tendency
which the increased velocity has to whirl the water round. So that the
tendency of the screw to race may be said to be due entirely to the admission
of air below the surface.
It would seem that, if this is the explanation of racing, all that is
necessary, in a calm sea, to render a screw much superior to paddles in
stopping, starting, or towing, is to give it sufficient immersion.
58 CAUSES OF THE RACING OF THE ENGINES OF SCREW STEAMERS. [9
This has been tried and proved to be the case so far as an experiment on
a model is a proof. No matter what might be the power employed, so
long as the surface was unbroken, there was a corresponding towing power ;
and so long as this condition was maintained, the screw started and stopped
the boat quite as well as it was possible for paddles to do.
A larger steam model capable of towing with a force of 1 Ib. was tried
with two different screws the one 3 inches in diameter and the other 4.
The small one was covered by about an inch of water, and it was found that
this screw would not race even when the boat was held still. The larger
one, however, which was only covered by about one quarter of an inch,
did race when the boat was held. It would seem therefore that it is of more
importance to secure a sufficient depth of water over the screw than to
increase the diameter, and it seems probable that some of the advantage of
twin screws is due to the fact that they are generally covered to a greater
depth than a single screw.
ON THE CONDENSATION OF A MIXTURE OF AIR AND
STEAM UPON COLD SURFACES.
[From the " Proceedings of the Royal Society," No. 144, 1873.]
(Head May 1st, 1873.)
1. THE object of this investigation is to ascertain how far the presence
of a small quantity of air affects the power of a cold surface to condense
steam. A priori it seemed probable that it might retard condensation very
much ; for when pure steam comes up to a cold surface and is condensed,
it leaves an empty space which is immediately filled with fresh steam ; so
that the passage of the steam up to the cold surface is unobstructed, and
if the surface could carry off the heat fast enough, then the rate of con-
densation would be unlimited. If, however, the steam is mixed with air,
then, as the mixture comes into contact with the cold surface, the steam
will be condensed and the air will be left between the fresh steam and the
cold surface ; so that, after condensation has commenced, that surface will
be protected by a stratum of air, and fresh steam will have either to displace
this, or pass through it, before it in turn can be condensed.
2. This question, besides its philosophical interest, has important
practical bearings on the steam-engine.
First. If the quantity of air mixed with the steam- affects the rate at
which it condenses, then the ratio which the pressure of air bears to the
pressure of steam in a condenser will materially affect its efficiency : this is
particularly important with reference to the surface-condenser.
Second. If air prevents the condensation of steam, then by sending air
into the boiler of a high-pressure engine, the condensation at the surface
of the cylinder will be prevented, which, if allowed to occur, becomes a
source of great waste ; for when the steam comes into a cold cylinder it
condenses, heating the cylinder and leaving water, which will again be
60 ON THE CONDENSATION OF A MIXTURE OF AIR [10
evaporated as soon as the steam escapes ; and this, in evaporating, will cool
the cylinder. By preventing this, the mixing of air with the steam would
effect the same object as the steam-jacket, only in a more efficient manner ;
for the heat communicated to the steam in the cylinder from the jacket is
not nearly so effective as that which is communicated from the boiler, in
consequence of the steam in the cylinder being at a lower temperature than
that in the boiler.
3. The experiments for this investigation were, by the kind permission
of Dr Roscoe, carried out by Mr Pasley, a student in the Chemical Laboratory
of the Owens College ; and I beg to tender him my best thanks.
4. In making these experiments two objects were particularly kept
First. To ascertain if there is a great difference in the rate of con-
densation of pure steam and a mixture of steam and air to ascertain in fact,
whether pure steam condenses at an unlimited speed.
Second. To ascertain if (and according to what law) the effect of air on
the condensation increases as the proportion of air to steam increases.
5. Of these two undertakings the first is much the most difficult. The
rate of condensation of pure steam is so great that it is practically impossible
to measure it ; and to institute a comparison between this and the condensa-
tion of a mixture of steam and air is like comparing the infinite with the
finite. It is practically impossible to keep any surface cold when an unlimited
supply of pure steam is condensed upon it, so that under such circumstances,
the quantity of pure steam condensed is limited by the power of the surface
to carry off the heat. The best method of obtaining a qualitative result
seems to be by introducing sufficient cold water into a flask of steam to
condense it all, and ascertain whether this condensation is effected suddenly
6. The presence of hot water in the flask with the steam very much
assists in ascertaining the rapidity of condensation. When there is no hot
water in the flask, the condensation by the injected water is only a question
of time ; the gauge will come to the same point whether the condensation
is quick or slow, the only difference being in the speed at which it will rise
a difference not easy to appreciate, especially when the motion is quick.
But if hot water is present, then as the steam in the flask is condensed, it
is replaced by fresh steam from the water, and the interval between the
condensation and the consequent ebullition is the only time allowed for
the creation of a vacuum ; the vacuum which is attained in the interval
will therefore depend on the rapidity of condensation. The interval will be
very short ; arid the better the vacuum the shorter it will be ; so that unless
10] AND STEAM UPON COLD SURFACES. 61
the condensation is very sudden, there will be but a slight reduction of
If, however, the condensation is really instantaneous, a perfect vacuum
may exist for an instant. Hence, when there is water in the flask, the
rapidity of condensation is indicated by the height to which the gauge
rises, instead of the speed with which it rises ; and this is much easier to
7. The apparatus employed in making these experiments consisted of
a glass flask, fitted with a mercurial vacuum-gauge, and pipes for admitting
water and air, or allowing steam to escape.
The flask and all the pipes were freed from air by boiling; and when
all the air had been driven out the pipes were closed, the lamp removed,
and the flask allowed to cool until the gauge showed a slight vacuum ; the
water-pipe was then opened and a few drops of water allowed to enter and
fall through the flask ; as they did so the mercury rushed up the gauge, and,
by its momentum, above the point for a perfect vacuum, showing that the
condensation was instantaneous. Immediately afterwards the gauge fell
nearly to its starting-point. Next, the flask was allowed to cool and a little
air was let in (about equal to half an inch of mercury in the gauge, or about
a sixtieth of the volume of the flask). The lamp was then replaced, and the
operation was repeated as before : this time, however, as the cold water
entered, the mercury did not rush up the gauge, but rose slowly a small
distance and there remained.
8. This experiment shows, therefore, that there is a great difference in
the rates at which pure steam, and steam with air, condense on a cold surface,
so great in fact that the speed with pure steam must be regarded as nearly
9. To compare the various effects of different quantities of air, two
methods have been used, which may be described as follows :
I. A surface-condenser is formed within the boiler or flask, so that the
steam may be condensed as fast as it is generated. Then, when a flame of a
certain size acts on the boiler, the effect of the air is to cause the pressure of
steam in the flask to increase. This method is founded on the assumption
that the rate at which steam will condense at a cold surface is, cceteris
paribus, proportional to its pressure an assumption which is probably not
far from the truth.
II. With the same apparatus as in method I. the rate of condensation
is measured by the quantity of water condensed in a given time, obtained
by counting the drops from the condenser, the pressure within the flask
being kept constant. This method does not involve any assumption ; but
62 ON THE CONDENSATION OF A MIXTURE OF AIR [10
the conditions for its being accurate are such as cannot be obtained; for
not only must the temperature of the condenser and the temperature of
the steam remain constant, but the pressure of the steam must also remain
constant, and if the two former conditions are fulfilled the latter cannot be ;
for the temperature of the steam will be the boiling-point of the water in the
flask ; and if this is to remain constant, the pressure of air and steam must
be constant, and therefore, as the pressure of the air increases, the pressure
of the steam must decrease. This variation of pressure is not very great ;
and its effect may be allowed for on the assumption that the condensation is
proportional to the pressure of steam. This is accomplished by dividing the
drops by the pressure of the steam.
These methods, neither of which, as it appears, is rigorous, seem never-
theless to be the best ; and fortunately the law which the effect of the
additions of air follows, is of such a decided character as to be easily dis-
tinguished ; and the two methods give results which are sufficiently con-
cordant for practical purposes.
10. The apparatus employed in these experiments consisted of a glass
flask, in which a surface condenser was formed of a copper pipe passing in
and out through the cork. This pipe was kept cool by a stream of water,
and was so fixed that all the condensed water dropped from it, and the drops
could be counted. The flask was freed from air by boiling ; the volume of
air passed into the flask could be accurately measured ; and ample time
was allowed for the air in the flask to produce its effect before more was
For the experiments according to method I., the flame under the flask,
and the stream of water through the condenser, were kept constant from first
to last. For those made according to method II., in one case the stream
of water was kept constant, and in the other it was altered, so that the
effluent water was kept at a constant temperature.
11. The results of these experiments are shown in Tables I., II., III.
The letters which head the columns have the following meanings :
f stands for the volume of the flask in cubic centimetres.
a stands for the volume of the air at the pressure of the atmosphere.
h stands for the height of the barometer in millimetres of mercury at the
time of the experiment.
^ stands for the height of mercury in the gauge in millims.
t stands for the temperature Centigrade of the effluent water.
j stands for the temperature of the water in the flask, found from
Regnault's tables of boiling-points.
AND STEAM UPON COLD SURFACES.
PI ho hi stands for the pressure within the flask in millims. of mercury.
CL t + 274
p 2 = -j + h - ^ stands for the pressure of the air within the flask
Jf 1 + 2 7 4s
corrected to the temperature T : .
p s =p 1 p 2 stands for the pressure of the steam.
stands for the ratio of the pressure of the air in the flask to that of the
A = 756, = 9, /=500.