at the suggestion of some of the proprietors of the Great Western
Railway Company, with a view to determine various points connected
with the structure and the working of railways. A part of these
experiments were intended to determine the mean amount of the
resisting force opposed to the moving power, and this part was
conducted by me. After having tried various expedients for
determining the mean amount of resistance to the moving power, I
found that no method gave satisfactory results except one founded on
observing the motion of trains by gravity down steep inclined
planes. When a train of waggons or coaches is placed upon an
inclined plane so steep that it shall descend by its gravity without
any moving power, its motion, when it proceeds from a state of rest,
will be gradually accelerated, and if the resistance to that motion
was, as it has been commonly supposed to be, uniform and independent
of the speed, the descent would be uniformly accelerated: in other
words, the increase of speed would be proportional to the time of
the motion. Whatever velocity the train would gain in the first
minute, it would acquire twice that velocity at the end of the
second minute, three times that velocity at the end of the third
minute, and so on; and this increase of velocity would continue to
follow the same law, however extended the plane might be. That such
would be the law which the descending motion of a train would follow
had always been supposed, up to the time of the experiments now
referred to; and it was even maintained by some that [Pg409] such a
law was in strict conformity with experiments made upon railways and
duly reported. The first experiments instituted by me at the time
just referred to afforded a complete refutation of this doctrine. It
was found that the acceleration was not uniform, but that with every
increase of speed the acceleration was lessened. Thus if a certain
speed were gained by a train in one second when moving at five miles
an hour, a much less speed was gained in one second when moving ten
miles an hour, and a comparatively small speed was gained in the
same time when moving at fifteen miles an hour, and so on. In fact,
the augmentation of the rate of acceleration appeared to diminish in
a very rapid proportion as the speed increased: this suggested to me
the probability that a sufficiently great increase of speed would
destroy all acceleration, and that the train would at length move at
a uniform velocity. In effect, since the moving power which impels a
train down an inclined plane of uniform inclination is that fraction
of the gross weight of the train which acts in the direction of the
plane, this moving power must be necessarily invariable; and as any
acceleration which is produced must arise from the excess of this
moving power over the resistance opposed to the motion of the train,
from whatever causes that resistance may arise, whenever
acceleration ceases, the moving force must necessarily be equal to
the resistance; and therefore, when a train descends an inclined
plane with a uniform velocity, the gross resistance to the motion of
the train must be equal to the gross weight of the train resolved in
the direction of the plane; or, in other words, it must be equal to
that fraction of the whole weight of the train which is expressed by
the inclination of the plane. Thus if it be supposed that the plane
falls at the rate of one foot in one hundred, then the force
impelling the train downwards will be equal to the hundredth part of
the weight of the train. So long as the resistance to the motion of
the train continues to be less than the hundredth part of its
weight, so long will the motion of the train be accelerated; and the
more the hundredth part of the weight exceeds the resistance, the
more rapid will the acceleration be; and the less the hundredth part
of the weight [Pg410] exceeds the resistance, the less rapid will
the acceleration be. If it be true that the amount of resistance
increases with the increase of speed, then a speed may at length be
attained so great that the amount of resistance to the motion of the
train will be equal to the hundredth part of the weight. When that
happens, the moving power of a hundredth part of the weight of the
train being exactly equal to the resistance to the motion, there is
no excess of power to produce acceleration, and therefore the motion
of the train will be uniform.
Founded on these principles, a vast number of experiments were
made on planes of different inclinations, and with loads of
various magnitudes; and it was found, in general, that when a
train descended an inclined plane, the rate of acceleration
gradually diminished, and at length became uniform; that the
uniform speed thus attained depended on the weight, form, and
magnitude of the train and the inclination of the plane; that the
same train on different inclined planes attained different uniform
speeds—on the steeper planes a greater speed being attained. From
such experiments it followed, contrary to all that had been
previously supposed, that the amount of resistance to railway
trains had a dependence on the speed; that this dependence was of
great practical importance, the resistance being subject to very
considerable variation at different speeds, and that this source
of resistance arises from the atmosphere which the train
encounters. This was rendered obvious by the different amount of
resistance to the motion of a train of coaches and to that of a
train of low waggons of equal weight.
The former editions of this work having been published before the
discovery which has resulted from these experiments, the average
amount of resistance to railway trains, there stated, and the
conclusions deduced therefrom, were in conformity with what was
then known. It was stated that the resistance to the moving power
was practically independent of the speed, and on level rails was
at the average rate of about seven pounds and a half per ton. This
amount would be equivalent to the gravitation of a load down an
inclined plane falling 1/300, and consequently in ascending such a
plane the moving power would have to encounter twice [Pg411] the
resistance opposed to it on a level. As it was generally assumed
that a locomotive-engine could not advantageously vary its
tractive power beyond this limit, it was therefore inferred that
gradients (as inclinations are called) ought not to be constructed
of greater steepness than 1/300. It was supposed that in
descending gradients more steep than this the train would be
accelerated and would require the use of the brake to check its
motion, while in ascending such planes the engine would be
required to exert more than twice the ordinary tractive power
required on level rails. As the resistance produced by the air was
not taken into consideration, no distinction was made between
heavy trains of goods presenting a frontage and magnitude bearing
a small proportion to their gross weight and lighter trains of
passenger-coaches presenting great frontage and great magnitude in
proportion to their weight. The result of the experiments above
explained leads to inferences altogether at variance with those
which have been given in former editions of the present work, and
which were then universally admitted by railway engineers. The
tendency of the results of these experiments show that low
gradients on railways are not attended with the advantageous
effects which have been hitherto ascribed to them; that, on the
contrary, the resistance produced by steeper gradients can be
compensated by slackening the speed, so that the power shall be
relieved from as much atmospheric resistance by the diminution of
velocity as is equal to the increased resistance produced by the
gravity of the plane which is ascended. And, on the other hand, in
descending the plane the speed may be increased until the
resistance produced by the atmosphere is increased to the same
amount as that by which the train is relieved of resistance by the
declivity down which it moves. Thus, on gradients, the inclination
of which is confined within practical limits, the resistance to
the moving-power may be preserved uniform, or nearly so, by
varying the velocity.
(201.) The series of experiments which have established these
general conclusions have not yet been sufficiently extended
and varied to supply a correct practical estimate of the limit
which it would be most advantageous to impose upon the [Pg412]
gradients of railways; but it is certain that railways may be laid
down, without practical disadvantage, with gradients considerably
steeper than those to which it has been hitherto the practice to
recommend as a limit.
The principle of compensation by varied speed being admitted, it
will follow that the time of transit between terminus and terminus
of a line of railway laid down with gradients, varying from twenty
to thirty feet a mile, will be practically the same as it would be
on a line of the same length constructed upon a dead level; and
not only will the time of transport be equal, but the quantity of
moving power expended will not be materially different. The
difference between the circumstances of the transport in the two
cases will be merely that, on the undulating line, a varying
velocity will be imparted to the train and a varying resistance
opposed to the moving power; while on the level line the train
would be moved at a uniform speed, and the engine worked against a
uniform resistance. These conclusions have been abundantly
confirmed by the experiments made in last July with the Hecla
engine above referred to. The line of railway between Liverpool
and Birmingham on which the experiment was made extended over a
distance of ninety-five miles, and the gradients on which the
effects were observed varied from a level to thirty feet per mile,
a great portion of the line being a dead level. The following
table shows the uniform speed with which the train ascended and
descended the several gradients, and also the mean of the ascent
and descent in each case, as well as the speed upon the level
parts of the line:—
——————————————————————————————————————————————————
| Speed. |
|———————————————-————————————————————————
Gradient.| Ascending. | Descending. | Mean.
——————————————————————————————————————————————————
One in |Miles per hour.|Miles per hour.|
177 | 22·25 | 41·32 | 31·78
265 | 24·87 | 39·13 | 32·00
330 | 25·26 | 37·07 | 31·16
400 | 26·87 | 36·75 | 31·81
532 | 27·35 | 34·30 | 30·82
590 | 27·37 | 33·16 | 30·21
650 | 29·03 | 32·58 | 30·80
| | |————————
Level | | | 30·93
——————————————————————————————————————————————————
[Pg413] From this table it is apparent that the gradients do
possess the compensating power with respect to speed already
mentioned. The discrepancies existing among the mean values of the
speed are only what may be fairly ascribed to casual variations in
the moving power. The experiment was made under favourable
circumstances: little disturbance was produced from the
atmosphere; the day was quite calm. In the same experiment it was
found that the water evaporated varied very nearly in proportion
to the varying resistance, and the amount of that evaporation may
be taken as affording an approximation to the mean amount of
resistance. Taking the trip to and from Birmingham over the
distance of 190 miles, the mean evaporation per mile was 3·36
cubic feet of water. The volume of steam produced by this quantity
of water will be determined approximately by calculating the
number of revolutions of the driving wheels necessary to move the
engine one mile. The driving wheels being 5 feet in diameter,
their circumference was 15·7 feet, and consequently in passing
over a mile they would have revolved 336·3 times. Since each
revolution consumes four cylinders full of steam, the quantity of
steam supplied by the boiler to the cylinders per mile will be
found by multiplying the contents of the cylinder by four times
336·3, or 1345·2.
The cylinders of the Hecla were 12-1/2 inches diameter, and 18
inches in length, and consequently their contents were 1·28 cubic
feet for each cylinder: this being multiplied by 1345·2 gives
1721·86 or 1722 cubic feet of steam per mile. It appears,
therefore, that supposing the priming either nothing or
insignificant, which was considered to be the case in these
experiments, 3·36 cubic feet of water produced 1722 cubic feet of
steam, of the density worked in the cylinders. The ratio,
therefore, of the volume of this steam to that of the water
producing it, was 1722 to 3·36, or 512·5 to 1. The pressure of
steam of this density would be 54·5 pounds per square inch.[34]
Such, therefore, was the limit of the average total pressure of
the steam in the cylinders. In this experiment the safety-valve of
the boiler was screwed down to 60 pounds per square [Pg414] inch
above the atmospheric pressure, which was therefore the major
limit of the pressure of steam in the boiler; but as the actual
pressure in the boiler must have been less than this amount, the
difference between the pressure in the cylinder and boiler could
not be ascertained. This difference, however, would produce no
effect on the moving power of the steam, since the pressure of
steam in the cylinders obtained by the above calculation is quite
independent of the pressure in the boiler, or of any source of
error except what might arise from priming. The pressure of 54·5
pounds per square inch, calculated above, being the total pressure
of the steam on the pistons, let 14·5 pounds be deducted from it,
to represent the atmospheric pressure against which the piston
must act, and the remaining 40 pounds per square inch will
represent the whole available force drawing the train and
overcoming all the resistances arising from the machinery of the
engine, including that of the blast-pipe. The magnitude of a
12-1/2 inch piston being 122·7 square inches, the total area of
the two pistons would be 245·2 square inches, and the pressure
upon each of 40 pounds per inch would give a total force of 9816
on the two pistons. Since this force must act through a space of
three feet, while the train is impelled through a space of 15·7
feet, it must be reduced in the proportion of 3 to 15·7, to obtain
its effect at the point of contact of the wheels upon the rails:
this will give 1875 pounds as the total force exerted in the
direction of the motion of the train. The gross weight of the
train being 80 tons, including the engine and tender, this would
give a gross moving force along the road of about 23·4 pounds per
ton of the gross load, this force being understood to include all
the resistances due to the engine. This resistance corresponds to
the gravitation of a plane rising at the rate of 1/95, and
therefore it appears that such would be the inclination of the
plane by the gravitation of which the gross resistance would be
doubled, instead of such inclination being about 1/300, as has
been hitherto supposed.
Since the remarkable and unexpected results of this series of
experiments became known various circumstances were brought to
light, which were before unnoticed, and which [Pg415] abundantly
confirm them. Among these may be mentioned the fact, that in
descending the Madeley plane, on the Grand Junction Railway, which
falls for above three miles at the rate of twenty-nine feet a
mile, the steam can never be entirely cut off. But, on the other
hand, to maintain the necessary speed in descending, the power of
the engine is always necessary. As this plane greatly exceeds that
which would be sufficient to cause the free motion of the train
down it, the power of the engine expended in descending it,
besides all that part of the gravitating power of the plane which
exceeds the resistance due to friction and other mechanical causes
must be worked against the atmosphere.
This estimate of the resistance is also in conformity with the
results of a variety of experiments made by me with trains of
different magnitudes down inclined planes of various inclinations.
(202.) In laying out a line of railway the disposition of the
gradients should be such as to preserve among them as uniform a
character as is practicable, for the weight and power of the
engine must necessarily be regulated by the general steepness of
the gradients. Thus if upon a railway which is generally level,
like that between Liverpool and Manchester, one or two inclined
planes of a very steep character occur, as happens upon that line,
then the engine which is constructed to work upon the general
gradients of the road is unfit to draw the same load up those
inclinations which form an exception to the general character of
the gradients. In such cases some extraordinary means must
generally be provided for surmounting those exceptionable
inclinations. Several expedients have been proposed for this
purpose, among which the following may be mentioned:—
1. Upon arriving at the foot of the plane the load is divided, and
the engine carries it up in several successive trips, descending
the plane unloaded after each trip. The objection to this method
is the delay which it occasions—a circumstance which is
incompatible with a large transport of passengers. From what has
been stated, it would be necessary, when the engine is fully
loaded on a level, to divide its load into two or more parts, to
be successively [Pg416] carried up when the incline rises 52 feet
per mile. This method has been practised in the transport of
merchandise occasionally, when heavy loads were carried on the
Liverpool and Manchester line, upon the Rainhill incline.
2. A subsidiary or assistant locomotive engine may be kept in
constant readiness at the foot of each incline, for the purpose of
aiding the different trains, as they arrive, in ascending. The
objection to this method is the cost of keeping such an engine
with its boiler continually prepared, and its steam up. It is
necessary to keep its fire continually lighted, whether employed
or not; otherwise, when the train would arrive at the foot of the
incline, it should wait until the subsidiary engine was prepared
for work. In cases where trains would start and arrive at stated
times, this objection, however, would have less force. This method
is at present generally adopted on the Liverpool and Manchester
line.
3. A fixed steam-engine may be erected on the crest of the
incline, so as to communicate by ropes with the train at the foot.
Such an engine would be capable of drawing up one or two trains
together, with their locomotives, according as they would arrive,
and no delay need be occasioned. This method requires that the
fixed engine should be kept constantly prepared for work, and the
steam continually up in the boiler.
4. In working on the level, the communication between the boiler
and the cylinder in the locomotives may be so restrained by
partially closing the throttle-valve, as to cause the pressure
upon the piston to be less in a considerable degree than the
pressure of steam in the boiler. If under such circumstances a
sufficient pressure upon the piston can be obtained to draw the
load on the level, the throttle-valve may be opened on approaching
the inclined plane, so as to throw on the piston a pressure
increased in the same proportion as the previous pressure in the
boiler was greater than that upon the piston. If the fire be
sufficiently active to keep up the supply of steam in this manner
during the ascent, and if the rise be not greater in proportion
than the power thus obtained, the locomotive will draw the load up
the incline without further assistance. It is, however, to be
observed, that in this case [Pg417] the load upon the engine must
be less than the amount which the adhesion of its working wheels
with the railroad is capable of drawing; for this adhesion must be
adequate to the traction of the same load up the incline,
otherwise, whatever increase of power might be obtained by opening
the throttle-valve, the drawing wheels would revolve without
causing the load to advance. This method has been generally
practised upon the Liverpool and Manchester line in the transport
of passengers; and, indeed, it is the only method yet discovered
which is consistent with the expedition necessary for that species
of traffic.
In the practice of this method considerable aid may be derived
also by suspending the supply of feeding water to the boiler
during the ascent. It will be recollected that a reservoir of cold
water is placed in the tender which follows the engine, and that
the water is driven from this reservoir into the boiler by a
forcing pump, which is worked by the engine itself. This pump is
so constructed that it will supply as much cold water as is equal
to the evaporation, so as to maintain constantly the same quantity
of water in the boiler. But it is evident, on the other hand, that
the supply of this water has a tendency to check the rate of
evaporation, since in being raised to the temperature of the water
with which it mixes it must absorb a considerable portion of the
heat supplied by the fire. With a view to accelerate the
production of steam, therefore, in ascending the inclines, the
engine man may suspend the action of the forcing pump, and thereby
stop the supply of cold water to the boiler; the evaporation will
go on with increased rapidity, and the exhaustion of water
produced by it will be repaid by the forcing pump on the next
level, or still more effectually on the next descending incline.
Indeed the feeding pump may be made to act in descending an
incline, if necessary, when the action of the engine itself is
suspended, and when the train descends by its own gravity, in
which case it will perform the part of a brake upon the descending
train.
5. The mechanical connexion between the piston of the cylinder and
the points of contact of the working wheels with the road may be
so altered, upon arriving at the incline, as to [Pg418] give the
piston a greater power over the working wheels. This may be done
in an infinite variety of ways, but hitherto no method has been
suggested sufficiently simple to be applicable in practice; and
even were any means suggested which would accomplish this, unless
the intensity of the impelling power were at the same time
increased, it would necessarily follow that the speed of the
motion would be diminished in exactly the same proportion as the
power of the piston over the working wheels would be increased.
Thus, on the inclined plane, which rises fifty-five feet per mile,
upon the Liverpool line, the speed would be diminished to nearly
one fourth of its amount upon the level.
[Illustration]
FOOTNOTES:
[30] Some of the preceding observations on inland transport,
as well as other parts of the present chapter, appeared in
articles written by me in the _Edinburgh Review_ for October,
1832, and October, 1834.
[31] Wood on Railroads, 2d edit.
[32] The cost of coke has risen considerably since the date of
this report.
[33] I am indebted to the enlarged edition of Tredgold on the
Steam Engine, published by Mr. Weale, for the drawings of this
engine. The details of the machine are very fully given in
that work, the description of them being supplied by Mr.
Stephenson himself.
[34] See Table of Pressures, Temperatures, and Volumes, in
appendix.
[Pg419]
[Illustration]
CHAP. XII.
LOCOMOTIVE ENGINES ON TURNPIKE ROADS.
RAILWAYS AND STONE ROADS COMPARED. — MR. GURNEY'S STEAM
ENGINE. — CONVENIENCE AND SAFETY OF STEAM CARRIAGES. —
HANCOCK'S STEAM ENGINE. — OGLE'S STEAM ENGINE. — TREVETHICK'S
INVENTION. — DR. CHURCH'S STEAM ENGINE.
(203.) We have hitherto confined our observations on steam-power,
as a means of transport by land, to its application on railways.
But modern speculation has not stopped there; various attempts
have been made, and attended with more or less success, to work
steam-carriages on common roads. The mere practicability of this
project had long been regarded as very questionable; but enough
has been done to show that the only doubt which can attend it, is
as to whether it can be profitably resorted to, as a means of
transport, and this question [Pg420] has been materially affected
by the recent extension of railways. In comparing the effect of a
stone road with an iron railway, there are two circumstances which
give great superiority and advantage to the latter: first, the
resistance opposed by a railway to the moving power, no matter
what that moving power may be, is considerably less in proportion
to the load than on a stone road. The average resistance on a good
level stone road, to the motion of carriages drawn at the speed
usually attained by the application of horse-power, may be taken
at about a thirty-sixth part of the load, while the resistance to
a load drawn upon a railway _at the same speed_ probably does not
amount to a tenth part of this resistance. Thus the moving power,
whatever it may be, would produce on a railway ten times the
useful effect which it would produce on a stone road; secondly,
the resistance which is opposed to the moving power on a level
railway is much more uniform than on a stone road, and,
consequently, the moving power is less subjected to jerks and
inequalities. This renders the application of inanimate power more
easy on the railway. Those inequalities of surface which increase
the amount of resistance on stone roads as compared with railways
also produce a jolting motion in the carriage, to counteract
which, the use of springs become necessary. These springs render
the motion of that part of the carriage which rests upon them
different from that part of the carriage which supports them; and
in the application of steam-machinery it becomes necessary so to
connect the moving power with the wheels that the machinery may
have one motion, and the wheels which are put in mechanical
connexion with that machinery, and driven by it, shall have
another motion. This, it is true, is the case with locomotive
engines on railways; but owing to the greater smoothness and
equality of the railway surface the difference between the motion
of the carriage body suspended on springs and that of the wheels
is much less than it would be on a stone road.