J. Foster Plagg
PRACTICAL RAILWAY ENGINEER.
MECHANICAL AND ENGINEERING OPERATIONS
COMBINED IN THE MAKING OF A RAILWAY.
I. CURVES, GRADIENTS, GAUGE, AND
II. EARTH-WORKS, CUTTINGS, EMBANK-
MENTS, AND DRAINS.
III. RETAINING WALLS, BRIDGES, TUN-
IV. PERMANENT WAT AND CONSTRUC-
V. STATIONS AND THEIR FITTINGS, LO-
COMOTIVE POWER AND ALL AR-
RANGEMENTS BELONGING THERETO,
WITH FIFTY ENGRAVINGS.
BY G. DRYSDALE I5EMPSEY, C.E.
JOHN WEALE, 59, HIGH HOLBORN.
PRINTED BY W. HUGHES,
KING'S HEAD COURT, GOUGH SQUARE.
T r J. f.
IN the series of Papers of which this is the first, it is proposed to offer a
condensed account of the engineering and mechanical operations and structures
which are combined in the making and equipment of a railway.
To do this as efficiently as the limits of the allotted space will allow, it is
proposed to select examples from works already executed, presenting a useful
collection of materials and facts, arranged so as to be adapted for ready appli-
cation by Royal Engineers and others on whom may devolve the conduct of
similar works at home and abroad.
Without any pretensions to a complete history of any individual railway, the
work will aspire to the character of such a record as will assist an engineer in
applying his professional knowledge, with readiness and certainty, in the design
and execution of the works required for any line committed to him.
It will be evident that the subject comprises two main and consecutive
divisions, viz. : first, the formation of the railway as a road or track ; and
secondly, the furnishing of this road with all the fittings and appurtenances by
which it is adapted to the purposes of traffic.
Thus, the one division includes the levelling of the original surface of
ground, the raising or lowering it as may be necessary, including tunnelling,
the construction of bridges and viaducts to sustain the line over valleys, roads,
or rivers, or to carry roads, &c., over the railway; and also the arrangement of
rails and their supports, constituting technically the permanent way, by
which the road is specially adapted for the rapid and uniform passage of
engines and carriages.
The second division comprehends stations and their fittings, locomotive
power and all arrangements belonging thereto, with carriages, &c.
Before commencing the construction, or indeed deciding the course of a
railway, there are some preliminary considerations respecting its lateral and
vertical deviations from a right line, and also the width of surface that will be
required for the railway, which need the careful attention of the engineer.
These deviations constitute the curves and gradients, and the width of surface
is determined by the intended gauge of the line and slopes of its cuttings and
Although involving considerations of a somewhat theoretical character, these
subjects claim a portion of our space, in order to exhibit briefly what has been
advanced in the way of theory, and what has been adopted by engineers in
CURVES, GRADIENTS, GAUGE, AND SLOPES.
The theory of a perfect railway requires that it shall follow a right line on
plan, and be uniformly level from end to end.
These two conditions are made impracticable by the interposition of hills,
rivers, towns, depots, &c., between the intended termini of the line, which
must be avoided, or crossed, or passed within certain limits ; by the difference
of levels of the intended termini ; the undulations of the surface of country
through which the route will pass, &c.
But all such deviations from the theoretical line are ruled in their nature
and extent by circumstances peculiar to the railway system as hitherto carried
out by means of steam locomotive power. 1
CURVES. The principles regulating all lateral deviations are, first, that they
can be made only in curves, angles being incompatible equally with the speed
to be attained on railways, and with the constantly parallel axes of the four or
six-wheeled machines impelled upon them ; secondly, that as the perfect condi-
tion is a right line, so does comparative perfection consist in the minimum
amount of deviation from it, that is, in the largest possible radius of curvature;
and thirdly, that in order to impose the least diminution of speed, small curves
1 It is necessary to remark that the peculiarities of curves, gradients, &c., which distinguish the
Dalkey branch of the Dublin and Kingstown Railway, which is now worked upon the atmospheric
system, will be disregarded in this series of Papers, which will be devoted to the details connected
with the steam locomotive system. The little experience yet had of pneumatic propulsion would
exclude it from these Papers, while the great importance deservedly attached to it entitles it to a
should always be near to stations or stopping-places, and that the more distant
curves are from these, the larger should be their radius.
To estimate the effects of curves, let us conceive a railway to consist only of
one horizontal rail, traversed by a vertical wheel of infinitely small breadth,
impelled by a force exactly sufficient to move it at a given velocity. Even with
this arrangement we know that the wheel could not be made to deviate from a
rectilineal course, without an additional power, equal to its centrifugal force, be
applied to it, or without reducing the velocity of its motion.
If the rail, being curved, present a level surface, and the periphery of the
wheel be made of some appreciable breadth, say two inches, it is evident that a
rubbing action must take place, tending to wear away the one edge of the
wheel and the other edge of the rail, until the former shall assume the figure of
the frustum of a right cone having its apex at the intersection of the centre of
curvature of the rail with a horizontal line produced from the axis of the wheel;
and the rail, in like manner, will become worn to an inclined surface to suit
the conical surface given to the periphery of the wheel.
Beyond the power lost in overcoming the centrifugal force of the wheel, there
will, therefore, be a further loss incurred by this friction between the wheel
But if the railway consists of two parallel rails, at some distance, say 5 feet,
apart, and is traversed by carriages having two or three pairs of wheels, each
pair fixed to one axle, and the two or three axles made, by their connexions
with the carriage frame, to revolve always parallel with each other, several such
carriages being linked together in one train, and impelled by one engine, it will
be seen that not only will this friction be much increased, but that the
resistance arising from the centrifugal force will be so likewise.
The wheels on the inner rail will be attempting to describe a smaller curve
than the wheels on the outer rail, and will be made to rub backwards upon
the rail, while the outer wheels are getting over the excessive space ; thus pro-
ducing a severe torsion of the axles and straining of the frame and the parts
connecting it with the axles. The centrifugal force of each pair of wheels may,
moreover, be regarded as acting in a direction different from that of each other
pair of wheels, and an engine drawing several carriages thus situated will have
to overcome the sum of these forces. In reference to this latter effect, it must
be also noticed that on entering and leaving the curve, whether in a right line
or a curve of contrary flexure, the engine and each of the carriages in succes-
sion will be taking a still more different course than over the curve of equal
radius, thus augmenting the effect alluded to.
To mitigate the evils consequent upon the adoption of curves, two expedients
have been introduced, viz., giving a conical form to the wheel-tires, and raising
the outer rail.
By making the tires of the wheels conical, the bases of the cones being
towards each other, it is assumed that when the centrifugal force drives the
flange of the outer wheel towards the edge of the rail, and, at the same time,
withdraws the flange of the inner wheel from its rail, the diameters of the
wheels are rendered practically unequal, in exactly the manner required in
order to get rid of the dragging which takes place when equal and cylindrical
wheels are made to describe curved lines.
The extent to which this inequality should amount depends, 1st, upon the
radius of the curve ; 2nd, the sizes of the wheels ; 3rd, the distance at which
they are placed apart, in other words, upon the gauge of the railway ; 4th, the
velocity at which they are impelled ; and 5th, the extent of play allowed be-
tween the gauge of the rails and the width across the outside of the wheel-flanges.
Of these five elements there are two, viz., the radius of curvature, and the
velocity, which are, of course, various over different parts of the line, and for
which, therefore, the same carriages and engines cannot be equally well adapted.
One of these, however, may be made somewhat to counteract the other ; that
is, the velocity may be modified according to the curve traversed, reduced
speed producing less centrifugal force, thus forcing the wheels less from their
central position, and creating less difference of diameters. It follows, that in
order to render the conical wheels available, the speed must be reduced in
proportion as the radius of curvature is reduced.
The other expedient, viz., raising the outer rail over curves, was recom-
mended, with other suggestions, by Tredgold, in his ' Practical Treatise on
Railroads and Carriages,' first published in 1825. 2 The following is quoted
from the second edition of the Treatise, published in 1835.
" When a considerable degree of curvature is given to a railroad, the rails of
the outer curve should have a slight rise to the middle of the curve, and the
rails should be stronger in a lateral direction in both lines. The object of
making a slight ascent to the middle of the curve of the outer rail, is, to
2 According to Weale's ' Scientific Advertiser,' in the third number of which publication, dated
February 20th, 1838, appeared an interesting memoir of this justly celebrated man.
counteract the tendency of the carriage to proceed in a straight direction,
without its rubbing so forcibly against the guides, as we have observed in cases
where roads have had a considerable curvature. Straight lines ought to be
obtained, if possible ; but when it is determined to accomplish any object by
means of a curved line, the rails should be cast or formed of the proper figure,
as no combination of straight rails can be rendered free from angles, which
both cause an irregular motion, and a great increase of lateral stress on the
rails." (Pages 135-6.)
The object being to counteract the tendency of the flanges of the wheels to
rub against the outer rails, (as impelled by the centrifugal force,) it will be seen
that this expedient does, to some extent, destroy the purpose sought by making
the wheel-tires conical.
Hence it will be readily conceived, that a very delicate and exact adjustment
of these contrivances is needed, in order that they shall produce their desired
De Pambour was, it is believed, the first to treat these matters analytically;
and as the result of his reasoning, (the general correctness of which is commonly
conceded), we may quote his statement, 3 that with an average velocity of 20
miles an hour, a radius of curve of 500 feet, wheels 3 feet diameter, gauge of
railway equal to 4*7 feet, and 2 inches play of the wheels between the rails,
the least inclination that should be given to the tires of the wheels is rath, that
is, the tire should belong to a cone, the radius of whose base is to its axis as
one is to twelve. He goes on to state, 4 that
" It is customary to give an inclination of yth. The motive for making it so
considerable, is to prevent all possibility of the flange rubbing against the rail,
either in case of a strong side-wind, or in case of some fortuitous defect in the
level of the rails, by which the waggons would be thrown on the lower rail.
Having seen above that, with an inclination of j^th, there would be no danger
of the flange rubbing in the curves, that danger will be still more impossible
with an inclination of yth."
Pambour also determines that with this radius of curvature, velocity, inclina-
tion of tire, gauge of line, and size of wheels, the outward rail should have a
surplus elevation of 2'83 inches. 5
3 ' A Practical Treatise on Locomotive Engines upon Railways,' pages 286, &c. (Weale, 1836.)
The first edition appeared in French early in the year 1835.
4 Ibid, page 289. 5 Ibid, page 287.
Solving his formulae for some usual cases, he produces 6 the following
Table of the Surplus Elevation to be given to the outward Rail in the Curves.
Surplus of elevation to be given to
the rail in inches, the velocity of
the motion in miles, per hour,
Designation of the Waggons and the Way.
Waggons with wheel, 3 feet . . . . <
Way 4 - 7 feet
Play of the waggon on the way, 1 inch . <
Inclination of the tire of the wheel, |th . <
Considering, however, the extreme difficulty, if not impossibility, of realizing
in practice the exact conditions and proportions determined by these inquiries,
it may reasonably be doubted whether by far the larger part of the friction,
straining, and loss of power belonging to curves, without these expedients, does
not still remain, with their inevitably imperfect execution.
Morever, there is another effect arising from the conical tires, which was
thus referred to by the editor of the 'Railway Magazine : ' 7
" It is plain, from the conical structure of the wheels, that if the upper
surface of the rail be horizontal, the whole of the pressure must lie on the inner
edge of the rails, and be constantly tending to thrust them outwards. This
must not only twist the rails out of their vertical position, and thrust them out,
but the whole wear and tear being on one edge, and, as it were, on a line, the
wheels themselves must wear in grooves, and the rails rub away on the inner
edge alone, both of which have already happened on the Liverpool line."
This is usually sought to be corrected, either by inclining the surface of the
sleeper or support for the chairs so as to throw the top surface of the rails
downwards to suit the wheels, or by forming the chairs so as to hold the rails
in this inclined position, or by inclining the top surface of the rail itself.
This method, however well adapted for straight lines, evidently tends, upon
curves, to destroy the proper condition of the wheel upon the outer rail, the top
6 ' A Practical Treatise on Locomotive Engines upon Railways,' page 290.
7 No. x. December, 1836. Page 405.
surface of which should incline downwards from the other rail, rather than
towards it, in such manner that the surfaces of both rails should coincide with
a line directed to the point wherein the produced axis of the wheels would meet
the centre of curvature of the railway.
In like manner, it will be understood, that the raising of the outer rail is
directly destructive of this desirable relation between wheels and rails ; and we
are thus obliged to recognize some imperfections even in the theory of the
expedients referred to, although it may be difficult to conceive how the defects
resulting from curves can be practically and completely surmounted.
Without careful experiments (which it is believed have never been made)
upon the relative power requisite to move a given load over a straight and a
curved line, respectively, both with and without the expedients described, and
also with wheels and rails formed to the true conical line, tending to the centre
of curve and wheel-axle produced, neither the exact defects of curves, nor the
value either of present remedies, or of others that may be proposed, can be
As might be predicated from our present state of uncertainty on this subject,
we find that the practice of engineers, in the adoption of curves, differs most
widely; some securing curves of large radius, at great sacrifices of cost; and
others, again, choosing very small ones, on considerations of minor economy.
Thus, on the Great Western Railway, " the curves are in general very slight,
chiefly of 4, 5, or 6 miles radius. Mr. Brunei considered, that even a mile
radius is not desirable, except at the entrance to a depot, where the speed of the
engines is always greatly slackened. And, except in these instances, the only
deviation from his rule, which he has admitted, is in the curve, about Jth of a
mile below one of the inclines, where the radius is f ths of a mile."'
In his evidence on the projected Brighton Railway, in 1836, Mr. R. Stephen-
son stated, that the line he proposed had no curve of smaller radius than
IJ mile, which he considered a very convenient radius for passenger traffic.
From a quotation which will presently be made, under the head " Gradients,"
it will be seen, however, that Mr. Stephenson would not limit the minimum of
curvatures even to f ths of a mile, if other circumstances of a sufficiently
important character dictate the choice of smaller curves.
On the Birmingham and Gloucester line, (which is curved nearly throughout
8 ' Railway Magazine,' vol. i. page 418.
its whole length,) on the Edinburgh and Glasgow, and on other railways, the
general radius of the curves is 80 chains or 1 mile ; 9 while on the Chester and
Birkenhead, Birmingham and Derby, Arbroath and Forfar, and others, this is
the minimum radius adopted for the curves.
The Taff Vale Railway (a single line) was reported in April, 184 1, 10 by Sir F.
Smith, then Inspector-General of Railways, as having curves of the following
radii and length.
These curves appear to have been adopted to avoid repeated crossings of the
river Taff by viaducts, and also to save the formation of some lofty embank-
ments; but Sir F. Smith thought it necessary to propose "that a suggestion
should be offered to the Directors of the Taff Vale Railway, recommending them
to call upon the engineer to fix the maximum rate of speed to be used round
such of the several curves as have a shorter radius than ^ a mile," although it
did not appear that any difficulty had been experienced in working the engines
round these curves "at a velocity of upwards of 20 miles an hour."
The Manchester and Leeds Railway has curves generally of 60 chains radius,
and some which are still less. 11
The Northern and Eastern Railway joins the Eastern Counties line in a sharp
curve, but it is mainly very straight, occasionally extending for several miles in
a perfectly straight direction. The gradients are also good.
9 Whishaw's ' Railways of Great Britain and Ireland.' 4to. 1842. (Weale.)
10 Report of the Officers of the Railway Department, page 132. 1842.
11 Whishaw's ' Railways of Great Britain and Ireland.'
The London and Birmingham has been constructed through a difficult
country, but with a special view to good curves and gradients. The result is
the judicious adoption of moderate curves and gradients.
Each of the lines here referred to has gradients corresponding mainly with
the character of its curves, sharp curves and steep gradients being usually
allied, and vice versa. Nevertheless, we cannot escape the inference that some,
if not much, of the startling difference of the average velocities attained on
these five railways, as exhibited in the following tabular statement, compiled
from the 'Third Report of the Officers of the Railway Department,' 1843, is
due to the difference of their curves only.
Northern and Eastern ... 36 miles per hour.
Great Western 33
London and Birmingham . . 27
Manchester and Leeds ... 24
Birmingham and Gloucester . 23 ,,
The last line is distinguished by its very steep gradients and planes, as will
be noticed presently.
At or near termini and junctions, which are always arrived at, and departed
from, at a very diminished speed, a small radius may be safely used : thus the
Chester and Crewe line leaves the latter terminus in a curve of 18 chains
radius; and the Grand Junction joins the Liverpool and Manchester in two
curves of 10 chains radius each: but throughout the line the greatest possible
curvature should be aimed at. Even in approaching first and second-class
stations this rule must be kept in view, for the latter ought to be passed by
mail and some other trains at full speed, and it may be sometimes essential
that the former should also.
GRADIENTS. The deviations from a horizontal level, constituting the inclina-
tions or gradients of a railway, have to be considered with a careful reference to
economy in the construction of the line, involving the quantity of earth-work,
of tunnelling, of bridge-work, &c., &c. ; and also with a reference to the attain-
ment of the desired velocity from station to station, and to the constant expenses
incurred in engine power, and in wear and tear of engines, carriages, and brakes,
in working the trains over these inclinations.
Widely differing opinions as to the proper limits of inclination are held and
have been acted upon by the several eminent engineers, under whose manage-
ment British railways have been constructed. By quoting briefly from these
opinions, we shall be possessed of the reasons on which they are built ; and an
after reference to the practical features of construction and of results obtained
upon some existing lines, may assist us to judge of the value of these opinions.
The attempt to deduce positive rules from these would be about as difficult as
it would be supererogatory, for the actual circumstances of each case present
peculiarities which the judgment of the engineer must estimate, and his dis-
cretion can alone provide for.
In a Paper on the ' Economy of Railways in respect of Gradients,' by Mr.
Vignoles, read at the tenth meeting of the British Association for the Advance-
ment of Science, held in September, 1840, the author " disclaimed asserting
that sharp curves or steep gradients were preferable to straight and level lines;
but he would endeavour to show that good practicable lines might be and had
been constructed, on which trains sufficient for the traffic and public accom-
modation could and did move at the same, or nearly the same velocities, and
with little, if any, additional expense. On an average, the hitherto ascertained
cost of the principal lines might be divided thus :
Land 10 per cent.
Stations and carrying establishment .20 ,,
Works of construction proper i . 50
though of course these items differed considerably in various railways ; but
in general it might be said that the works of construction constituted one-
half of the whole first cost." Mr. Vignoles stated " that he had analysed
railway expenses of working, and had reduced them to a mileage, that is,
the average expense per mile per train, as deduced from several years' ex-
perience and observations of various railways under different circumstances,
and with greatly different gradients, some of which lines were enumerated.
The result on passenger and light traffic lines was, that the total deductions
for expenditure from gross receipts was 3s. per mile per train ; 2s. 6d. being
the least, and 3s. 4d. the highest ; and that this average seemed to hold good,
irrespective of gradients or curves."