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+ 8-0


11-0


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+ 7'8


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9-8


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10-0


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Mean 10-05


Mean 9*25










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3-5




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5-4


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substituted for oil. The effect of the blacklead seems to have been slightly
to diminish friction, not only when starting from rest, but when rolling back,
which confirms me in the opinion that the contrary result with oil was due to
its obstructive action.

India-rubber was then tried. A plate of this substance, three-eighths of
an inch thick, was glued to a piece of wood to prevent it working forward.
The results are shown in Table III. The friction was very much greater
than in the previous experiments, and the advantage lies with the clean
surface.

These results leave no doubt that rolling-friction does not depend



18]



ON ROLLING-FRICTION.



127



greatly on the coefficient of sliding- friction between the roller and the surface.
They are, however, completely in accordance with the explanation previously

TABLE III.
Cast-iron Roller on India-rubber.



Clean.


Blackleaded.




Readings.




Readings.
















To.


From.




To.


From.






-22-0


+ 14-0


36


-24


+ 18


42


IB


-28-0


+ 15


43


-19


+ 15


34


2


-12-0


+ 18


30


-18


+ 19


37


S


-19-0


+ 15


34


-23


+ 17


40


1


-16-0


+ 16


32


-22


+ 17


39




-18-0


+ 15


33


-23


+ 14


37


I


-25-0


+ 12


37


-25


+ 17


42


1


-23-0


+ 15


38


-24


+ 15


39




Mean 35'4


Mean 3875










-2


+ 28


30





+ 26


26


"- 1


-5


+ 26


31


- 2


+ 22


24


m


-6


+ 27


33


- 1


+ 25


26


a


-4


+ 28


32


- 2


+ 22


24


J.d


-3


+ 30


33


-10


+ 22


32




-4


+ 30


34


-14


+ 19


33


y O

c? ?3


-6


+ 24


30


- 6


+ 24


30


1


-7


+ 25


32


- 6


+ 23


29




M


Me


in 31-9


Me


an 28







given of the manner in which sliding-friction acts to prevent the deformation
of the surfaces at the point of contact.

The Tendency to Oscillate.

Another circumstance which was observed while making these experiments
also offers strong evidence of this deformation, namely the tendency which the
roller has to oscillate. This was always exhibited whenever the roller was
slightly disturbed from rest on the level plane, and it was certainly not due to
the fact of its having settled into a hollow ; for when on india-rubber it would
make several considerable oscillations in whatever position it was placed. By



128



ON ROLLING-FRICTION.



[18



blackleading the surface this tendency was considerably reduced, although not
altogether destroyed. These oscillations could not have been caused by the
mere resistance which the one surface offered to the sliding of the other over
it, unless also this resistance threw the surfaces into constraint from which
they are constantly endeavouring to free themselves.

The Effect of the Softness of the Materials.

Having found that oil did not reduce the resistance, the experiments were
continued with a view to ascertain how far the softness of the material had
anything to do with it. As materials of several degrees of softness had already
been tried, the only question was to settle how far the difference in the results

TABLE IV.
Cast-iron Roller on Brass.



Glean.


Oiled.




Readings.




Readings.
















To.


From.




To.


Prom.






-13-2


-5-5


7-7


-2-0


+ 3-8


5-8


-^


- 5-5


+ 2-0


7-5


-4-5


+ 1-2


5-7


2


- 3-2


+ 5-0


8-2


-2-8


+ 3-8


6-6





- 3-5


+ 4-5


8-0


-2-9


+ 5-2


8-1


1


- 3-5


+ 3-8


7-3


-1-7


+ 5'8


7-5


a


- 7-0


+ 1-5


8-5


-5-0


+ 1-0


6-0


i


- 5-0


+ 2'2


7-2


-3-0


+ 3-5


6-5


i

02


- 4-6


+ 3-0


7'6


-3-0


+ 2-9


5-9




Mean 7'75


Mean 6*5








fl


-2-4


-0-8


1-6


-1-5


+ 1-0


2-5




-2-4


-0-4


2-0


o-o


+ 1-8


1-8


i


-1-8


+0-7


2-5


-1-2


+ 1-6


2-8


C5


-2-0


-0-4


1-6


-2-0


+ 0-6


2-6


|g


-2-8


-1-0


1-8


-2-3


+0-5


2-8


*{


-2-5


+ 0-2


2-7


-2-0


+ 1-0


3-0


* 2

O fl


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2-2


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+ 1-5


2-7


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2-2


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2-5


m














1








Me


an 2'07


Me


an 2'58







observed was due to their softness and how far it might be due to some other
difference in their nature. To show this cast-iron and brass were tried, which



18]



ON ROLLING-FRICTION.



129



are of much the same hardness as glass, and yet of an altogether different
nature in other respects, the surface of the glass being highly polished, while
that of the metal was dull as it had been left by the grinding. The results of
these experiments are contained in Tables IV. and V.



TABLE V.
Cast-iron Roller on Cast-iron.



Clean.


Oiled.




Readings.




Readings.
















To.


From.




To.


From.






-6-5


4-0-3


6-8


-1-3


4-4-0


5-3


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4-2-4


5-2


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4-2-5


5-3


2


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4-3-5


6-1


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+ 2-5


6-0


3


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4-2-3


4-8


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4-3-8


6-3


2


-0-6


4-4-5


5-1


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+3-2


5-4




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4-3-9


4-8


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4-3-0


5-3


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5-5


-5-0


4-0-8


5-8


!;


-2-8


4-4.2


7-0


4-1-0


4-6-5


5-5




Mean 5*66


Mean 5'61










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4-6-9


2-5


o-o


4-2-3


2-3


"- 1


-0-7


4-1-6


2-3


-1-8


4-0-8


2-6


ID




-3-5


-0-8


2-7


-1-0


4-1-3


2-3


d


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-1-0


2-8


4-0-2


4-2-3


2-1


8 S3


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4-1-8


2-3


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4-2-2


2-2


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4-0-1


2-1


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4-2-0


2-6


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4-2-2


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4-1-8


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03














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an 2-57


Me


an 2-36







The means of the results for all the materials are contained in Table VI.
Comparing these we see at once the effect of softness : the cast-iron, brass, and
glass are very nearly the same, and the slight difference is not greater than may
be accounted for by a slight difference in the smoothness of the surfaces. Of the
three, according to hardness cast-iron should have given the least results;
and so it does, as far as starting from rest is concerned, although when rolling
back the result is the other way. Box-wood appears to offer about double the
resistance of cast-iron ; and india-rubber about ten times as much in the case
of rolling back, and six times as much in starting from rest.

o. E. 9



130



ON ROLLING-FRICTION.



[18



TABLE VI.

Showing the Mean of the Results for the various conditions of the
Surface and manner of Starting.



The nature of the Surface.


Starts from rest.


Started in the opposite
direction.


Mean.


Clean.


Oiled or
blackleaded.


Clean.


Oiled or
blackleaded.


Cast-iron


5-66
6-32
7-75
10-05
35-37


5-61
5-96
6-53
9-25
38-75


2-57
T93
2-07
5-71
31-87


2-36
2-57
2-587
2-34
28-00


4-05
4-19
4-73
7-09
33-24


Glass


Brass


Box-wood


India-rubber





Experiments on Actual Slipping.

My object in the second series of experiments was to find by actual
measurement how far the roller rolled short of its geometrical distance.
Since the exceedingly small slipping on a hard surface precluded all chance
of measuring it, these experiments were made on strips of india-rubber glued
to wood : these were in general long enough to allow of two complete revolu-
tions of the roller. The strips were of different thicknesses. This difference
of thickness has an effect to vary the degree of indentation and the intensity
of the pressure, as well as the lateral extension. On the thick india-rubber
the indentation was considerable ; and, owing to the large bearing-surface
thus obtained, the intensity of the pressure beneath the roller must have
been comparatively small, as must also the lateral extension ; whereas with the
thin strips the indentation was small, but the pressure and consequent lateral
extension must have been correspondingly great. These considerations serve
to explain the differences in the results of the experiments, which are given
in Tables VII. and VIII.

TABLE VII.

Showing the Actual Slipping of a Cast-iron Roller.



The nature of the Surface.


The distance travelled.


The amount
of
the slipping.


In one
revolution.


In two

revolutions.


A steel bar (polished)


17-82


35-64
35-2
34-8
35-15


00
44
84
49


India-rubber, 01)15 inch thick, glued to wood...
0-08 inch thick


0-36 inch thick









18]



ON ROLLING-FRICTION.



131



TABLE VIII.

Showing the Actual Slipping with an India-rubber Tire 0'75 inch thick

glued on to the Roller.



The nature of the Surface.


Distance tra-
velled in one
revolution.


Circumference
of the
ring.


The amount
of
the slipping.


A steel bar


22-55


22-5


0-05


India-rubber 0'156 inch thick (clean)


22-55




-0-05


(blackleaded) ...
0'08 inch thick (clean)


22-55
22-5




-0-05
O'O


H (blackleaded)


22-52




-0'02


0-36 inch thick (clean)


22-39




+0-11


(blackleaded)


22-42




+ 0-08


0*75 inch thick (clean)


22-4




+ 0-1


(blackleaded) . ...


22-4




+0-1











These experiments show that a hard roller on a soft surface rolls short of
its geometrical distance, whereas a soft roller on a hard plane rolls more than
its geometrical distance, but to a smaller degree, and that when the roller and
the plane are of equal hardness the roller rolls through less than its geometrical
distance, which results are in exact accordance with what has previously been
explained.

The Effect of Heat and Viscosity to cause Friction.

While making the experiments which have been described, two other
causes of resistance to rolling besides friction suggested themselves to me,
and were to a certain extent verified. The first of these is the transference
of heat which takes place within both the plate and the roller in the neighbour-
hood of the point of contact. As the roller moves forward it is continually
compressing the material in front of the point of greatest pressure, and
this material expands again so soon as the roller is past. During com-
pression there will be a change in the temperature of the material com-
pressed, which change will be readjusted again as the material expands,
supposing that in the interval between compression and expansion there
has been no heat communicated to or taken from the portion of material
affected. But since the change of temperature caused by compression will
place the part compressed out of accord with that immediately surrounding
it, a transference of heat will necessarily take place. The quantity of heat
thus transferred will depend on the length of the interval, i.e. the speed of
the roller, and on the conducting-power of the material.

This transference will cause resistance to the roller, for the material will

92



132 ON ROLLING-FRICTION. [18

not expand to the same temperature, and hence to the same volume, as that
from which it was compressed, and hence it will take more work to compress
it than it will give out in expanding.

It does not, however, follow that the greater the transference of heat the
greater the resistance ; for if a sufficient time be allowed the transference of
heat will readjust the temperature as fast as expansion takes place. There
is some speed, therefore, for which the resistance arising from this cause will
be a maximum. If, therefore, the material be a good conductor and the
motion slow, the transference of heat will prevent any variation of temperature
during either compression or expansion. When such was the case the resist-
ance would increase with the speed, a fact which was very evident when the
rolling took place on india-rubber ; for it was possible to give the plane such
an inclination that the motion of the roller was scarcely perceptible, and any
increase in the inclination was followed by a corresponding increase in the
speed of the roller.

As already stated, there is another cause of resistance ; and this may partly
explain the result : this is viscosity.

If we stretch a piece of india-rubber, or any material, when released it
does not immediately come back to its original length, but at once comes back
a certain distance and then recovers the rest more or less slowly. Hence as
the roller moves forward the compressed material will require time for its
complete expansion, and hence will offer less resistance to the roller when the
motion is slow than when it is rapid.

Conclusion.

The foregoing remarks must be regarded as relating only to the nature of
rolling-friction. I have not attempted to ascertain the laws which connect its
magnitude with the various circumstances which affect it. As far as they go
I can see no reason to doubt the two laws propounded by Coulomb, viz. that
for the same material the resistance to rolling is proportional to the weight
of the roller, and inversely proportional to its diameter. In addition to these
laws, however, it appears clear to me that there must be another law connect-
ing rolling-friction in some way with the softness of the tires of the wheels
and the road. In addition to the instance of india-rubber tires already
mentioned, there are several other phenomena connected with wheels which
point to such a law, and can be explained by the recognition of the slipping
under the roller.

Steel and Iron Rails.

The very great advantage in point of durability of steel rails over iron has
been a matter of much surprise, it not being sufficiently accounted for by the



18] ON ROLLING-FRICTION. 133

greater hardness of the steel, supposing it to be subjected to the same wear-
ing action as the iron. This is at once explained, however, by the recognition
of the fact that hardness tends to reduce the slipping and hence the wearing
action, as well as to enable the rail the better to withstand the wear to which
it is subjected.

That rails should wear at all in places where they are straight and where
brakes are not applied is a matter which calls for an explanation, and this, so
far as I am aware, has not hitherto been given ; mere crushing, however much
it might deform the rail, would not cause such a reduction of weight as
actually takes place. The explanation of this phenomenon also at once follows
the recognition of the slipping which attends rolling.

A little consideration also serves to show that the scaling of wrought-iron
rails is the result of the repeated lateral extension of the surface in the rail
under the action of the wheel. The systematic way in which this takes place
shows that it is due to something more than the mere imperfection in the
iron. There is no doubt that the grain of the iron has a great deal to do with
it ; but considering the multitudinous ways in which iron is used and that
this is the only one in which scaling takes place, it is clear that it must be
due to some cause directly connected with the action to which the rail is
subjected. Now every time a wheel passes over a point in a rail it tends to
slide the upper strata of the rail over those beneath them, and thus causes
tangential stress. If the rail were homogeneous this would hardly cause it to
scale ; but owing to the grain in the iron some strata are stronger than others,
and the weaker strata are called upon to do more than their share of the yield-
ing, and so become still weaker and eventually give way.

There are other phenomena which, having been hitherto unnoticed or
unexplained, might be shown to arise from the slipping which takes place
during rolling; but perhaps those I have mentioned are sufficient to show
that the effects of the action are not altogether without practical importance.



19.

ON THE STEERING OF SCREW-STEAMERS.

From the "Report of the British Association," 1875.

THERE does not appear, as far as my observation goes, to be any par-
ticular difficulty in steering screw-steamers so long as they are going ahead
under steam, but rather the other way ; they then seem to be better to
steer than almost any other class of ships. Great difficulty often occurs,
however, when they are stopping, starting, or otherwise manoeuvring. Their
vagaries are then so numerous as to give the idea that there is a certain
degree of capriciousness and uncertainty about their behaviour. This is,
of course, mere fancy ; and did we but know them, it is certain that there
are laws which these steamers follow under all circumstances. In the
hope of arriving at these laws, I have been investigating this subject
now for twelve years as opportunity offered ; and I had come, as I thought,
to some leading facts, when the failure of the 'Bessemer' to enter Calais
Harbour on the 8th of May last seemed to establish them.

It will be remembered that the ship entered between the piers at
a speed of 12 or 13 knots, the tide running strong right across the mouth
of the harbour, that on her entering between the piers the engines were
reversed, and that the ship turned, under the influence of the current,
in spite of her rudder ; so that Capt. Pittoch, in his letter to the Times,
attributed the accident entirely to her failing to steer at the time.

On reading of the accident I thought it would be a good opportunity to
call attention to the subject of steering steamers; and I wrote a paper,
which was published in the Engineer of June 4th, 1875, in which I
explained why the act of stopping a ship must necessarily affect her power
of steering pointing out that when a ship is stopping the water will be
following her stern relatively faster than when she is moving uniformly,
and consequently that the effect of the rudder will be diminished ; that the



19] ON THE STEERING OF SCREW-STEAMERS. 135

longer the ship the greater will be the difference ; also that this effect is
greatly increased when a ship is stopping herself with her propellers, as
was the ' Bessemer' ; for then not only is the retardation of the vessel much
more rapid, but the water has a forward motion imparted to it by the
propellers, which motion, if the propellers are near the rudder, may be
greater than that of the ship, under which circumstance the effect of the
rudder's action will be reversed. Since publishing this paper in the
Engineer I have carried the investigation further ; and the object of the
present paper is to give an account of some experiments on model boats
driven by screws, and the conclusions to which these experiments have
led me.

Two models were used in making these experiments ; the one 2' 6" long,
driven by a spring, and the other 5' 6", driven by steam. In both models
the rudders were broad in proportion to the boats. In the clockwork model
the rudder was almost close to the screw, there being no stern-post. In the
steam model there was a wide stern-post, and the rudder was an inch and
a half behind the screw.

Both boats went straight with their screws driving them ahead and with
their rudders straight, and they both answered their rudders easily with
their screws going, turning in circles of from four to six feet radius. When
the screws were stopped and the boats carried on by their own way, they
both answered their rudders, but much more slowly than when their screws
were going, the smallest circle being now, as near as I could estimate, from
twelve to fifteen feet radius.

In order to try the effect of the screw, when reversed, on the steering of
the spring-model, the model was towed by a cord attached (as shown in the




accompanying figure) to a point T amidship about one-third of her length
from her bow, so that the towing had little or 110 tendency either to keep
her straight or turn her. The rudder was then set at an angle of 45 or
thereabouts, so as to turn her head to the right, towing was commenced, the
boat turning in a circle to the right. The screw was then started in the
reverse direction ; whereupon the boat ceased to turn to the right, and
commenced turning to the left to an extent depending on the slowness with
which she was being towed. When towed very quickly, at from two to
three miles an hour, she came nearly straight forward, but at the fastest
speed showed no tendency to turn to the right.



136 ON THE STEERING OF SCREW-STEAMERS. [19

The rudder was then set so as to turn the boat to the left, and the
operation was repeated with very nearly corresponding results so long as
the screw did not race ; but the action of the reversed screw on the rudder
when set to the left was not so great as when set to the right. This
difference led me to suppose that the screw itself might exert an influence
to turn the boat to the left when it was reversed, although it had been found
to exert no such influence when going ahead. This was at once shown to be
the case by setting the rudder straight and starting the screw reversed ; the
boat immediately turned to the left, but not fast unless the screw raced, then
she turned very rapidly.

These direct effects of the screw to turn the ship appear to me to account
for several of the anomalies which have hitherto beset the subject; and
further on in the paper I shall discuss them at length.

The steam model was provided with paddles as well as screw, and the
screw could be reversed without reversing the paddles, in which case the
paddles overpowered the screw, and the boat moved forward somewhat
slowly. In this boat the screw was so deeply immersed that it would not
race, and it had no direct effect to turn the boat when reversed like that of
the spring model.

When the screw was reversed and the boat drawn slowly forward by the
paddles, the effect on the rudder was almost to destroy its action, it having
only a slight power to turn the boat in the opposite direction to that in
which it would have turned the boat had the screw been going ahead.
Practically the boat had lost all power of steering. Coupled in this way
with the paddles the screw turned but slowly, the engine being held up by
the opposing actions. On releasing the paddles and allowing them to turn
freely, arid applying the whole power of the engine to the screw, the model
behaved almost exactly as the spring model had done, showing when towed
against the screw a strong tendency to turn in the opposite direction to that
in which the rudder was set.

The screw was then set full speed ahead ; and when the boat had acquired
way the rudder was set, so that she began to turn rapidly to the right ; the
screw was then reversed, and by the time the boat had lost all forward way
she had turned to the left through an angle of 30, so great was the effect of
the screw on the rudder when stopping the boat.

This completed the list of the experiments, which, however, were n )>< -nird
over and over again with exactly the same results.

Conclusions to be drawn from the experiments. The general conclusion is
that in screw-steamers the effect of the rudder depends on the direction of



19] ON THE STEERING OF SCHEW-STEAMERS. 137

motion of the screw rather than on the direction of motion of the boat. Or
we have the three following laws :

1. That when the screw is going ahead the steamer will turn as if she
were going ahead, whether she have stern-way on or not.

2. That when the screw is reversed the rudder will act as if the vessel
were going astern although she may be moving ahead.

3. That the more rapidly the boat is moving in the opposite direction to
that in which the screw is acting to drive it, the more nearly will the two
effects on the rudder neutralize each other, and the less powerful will be its
action. It would appear reasonable to suppose that a boat may move fast



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