48 hours, 70 lbs.
72 hours, 75 lbs.
15 days, 150 lbs.
50 days, 390 lbs.
SAND.
267. Sand is the product of the decomposition of granitic and schistose
rocks, and weighs, per unit of bulk, somewhat less than one half of the
rock producing it; owing to the spaces between the grains. The amount of
lime necessary to fill these spaces must be known before we can form a
solid mass with the least lime. The amount of void may be found by
filling a measure with sand, and then pouring in water: the volume of
water is that of the spaces. In pebbles of one half inch in diameter the
void amounts to about one half, in gravel about five twelfths, in common
sand two fifths, and in very fine sand, one third. Clean sharp sand
obtained from the beds of rivers is the best for mortars.
268. In mixing the ingredients for mortar, the lime is first spread on a
platform and wet by sprinkling with water, which causes it to give off a
great deal of heat and vapor, and fall into a powder. The sand is then
applied, and the whole brought with water to a consistent paste.
The proportions for common mortar for dry work are
Sand, 1½ to 2
Lime, 1
It is well always to use a small quantity of cement; the parts which
have in practice been found perfectly satisfactory are
Cement, 1
Lime, 3
Sand, 6
For hydraulic mortar the following proportions have been used with
success:—
Cement, 2
Sand, 3
269. Concrete is made by mixing broken stone, brick, or shells, with
cement mortar; it is used for foundations, backing of arches, and for
making artificial stone. The common proportions are
Cement, 1 or 2
Sand, 1½ or 3
Broken stone, 5 or 10
The cement and sand are first mixed as for cement mortar; the broken
stone is added and the whole well mixed and immediately applied before
it has time to set. Both concrete and cement mortar should be made as
required for use, and in no case applied after standing over three
hours.
FLASHING MORTAR.
270. Flashing consists of a thin coat of cement mortar made with a very
large part of cement. It is used to protect the face of walls exposed to
the wet; such as the top of arches. Stone liable to disintegration may
be protected by flashing.
POINTING MORTAR.
271. Pointing is used to protect the joints of masonry, and is made by
mixing cement and sand with a minimum of water. The joint is first cut
out to the depth of from one half to one inch, carefully brushed clean,
moistened with water, and filled with the mortar, which is well rubbed
with a steel tool. To give architectural effect, plaster of Paris
(Gypsum) is sometimes used in pointing.
GROUT.
272. Grout is thin-tempered mortar, composed almost entirely of cement
and water. It is run into the joints, and is useful in filling crevices
in masonry which cannot be filled with mortar.
CONSTRUCTION OF ARCHES.
273. The foundations being secured, and the piers and abutments being
carried up to the springing line of the arch, the centres are carefully
adjusted to their places and the arch is commenced. When the voussoirs
begin to bear upon the centre (which is when the angle of the joint with
the horizontal is greater than the angle of repose of one stone upon
another), the frame is liable to change of form, (particularly when the
arch is flat,) which must be provided for by counter loading the centre
in various points as the work proceeds. Great care should be taken to
make each stone point in the direction of the radius of the arch. To do
this effectually, their thickness should be marked upon the outer rib of
the centre. The line of the joint may then be fixed by a straight-edge
placed both on the centre and the rib mark, or by a template so cut that
when one side is level the other shall stand at the proper angle. Excess
of weight upon one side of the centre causes a depression at that point,
and a corresponding rise at the opposite side of the arch. Both sides
being loaded, the haunches settle, and the crown rises. The point where
the centre is first loaded will determine the point where the frame is
to be temporarily weighted. Such precautions, however, need only to be
taken in arches of over fifty feet span, unless the curve is quite flat.
The keystone should be put into the proper place, but not driven until
the rest is finished. The back joints are then closely wedged and
cemented with thin tempered mortar, and the whole is left to set. The
masonry of the spandrels is brought up to about one fourth the height of
the arch, or enough to prevent by their weight any change of form of the
curve. The centres are then struck and the soffit and voussoir joints
cleaned and pointed. The facing and road-way may next be carried up; the
parapet coping and drains finished off; and the whole pointed. Parapets
are shown in figs. 127 and 128. The spandrels, fig. 129, may be carried
up solid or hollow; their weight must be enough to stiffen sufficiently
the arch. It should, at least, be carried up solid to the line _c c c_;
the shaded mass being of well-cemented rubble. Above this the filling
may be of masonry, solid or arched, or even of well-rammed layers of
earth. The road-way should, in all cases, be well drained, that the
water may not sink through to the masonry.
[Illustration: Fig. 127. Fig. 128.]
[Illustration: Fig. 129.]
The apparatus for handling stone (cranes, lewises, and derricks) is much
better understood by inspection than by description.
Wherever walls support masses of earth, the thrust may be somewhat
lessened by ramming the earth behind the wall in layers inclining
backward. In laying up the courses each should be well cleaned and
moistened before the mortar is laid upon it. When a stone has been once
placed upon the mortar bed, it should not be moved at all _laterally_,
but may be gently mauled on top.
CULVERTS AND DRAINS.
274. Small culverts are made by covering two side walls with large flat
stones; the bottom being paved with stone at least nine inches deep,
laid dry. The general dimensions of such structures depend somewhat upon
the class of masonry, but as this is generally the _third_ or _fourth_,
will not vary much.
Opening. Side walls. Cover. Heads.
2 × 2 3 × 2 12 2 × 10
2 × 3 3 × 3 12 3 × 10
3 × 3 3 × 3 12 3 × 11
3 × 4 3½ × 4 15 4 × 12
4 × 4 3½ × 4 15 4 × 13
4 × 5 3½ × 5 18 5 × 15
5 × 5 4 × 5 18 5 × 16
5 × 6 4 × 6 18 6 × 18
Figs. 130, 131, and 132, show plans for culverts of from 5 to 25 feet
span.
[Illustration: Fig. 130.]
[Illustration: Fig. 131. Fig. 132.]
RETAINING WALLS.
275. A wall made to sustain a mass of earth or water, to resist
overthrow, requires a certain thickness. A body of earth assumes what is
termed the natural slope, the inclination of which depends upon the
adhesion of the soil, but may be taken as one and one half horizontal,
to one vertical, (1½ to 1), as an average.
The problem is, knowing the height of the wall and the form of the mass
of earth to be supported, to find the thickness of the wall.
Let A B 6 F, represent the thickness of the wall. Its centre of gravity
is at O, and is horizontally projected at _m_. The centre of gravity of
the thrusting triangle of earth, B 4 6, is C, (found by the cutting of
lines joining any two angles to the centre of the opposite sides,) is
horizontally projected at C^{_a_}, and the horizontal component of the
thrust is exerted at 2, tending to overthrow the wall with a leverage, 6
2.
[Illustration: Fig. 133.]
The overthrowing power is, then, the area of the triangle B46 × the
weight of the unit of area × the leverage 6 2. And the resisting power,
the area AB × B6 × the weight of a unit of area by one half breadth, or
_m_ 6; or, calling _w_ the weight of the wall, and _w′_ that of the
triangle, B 4 6, and _L_ and _L′_ the leverage respectively of the wall
to resist and of the earth to overthrow; we must have at least
_wL_ = _w′L′_,
and to insure stability,
_wL_ > _w′L′_
or,
_L_ = (_w′L′_)/_w_,
and as _L_ = half base finally, the thickness, or
2_L_ = (2_w′L′_)/_w_
276. _Example._—Let the height of wall be twenty feet, slope one and one
half to one; if a cubic foot of earth weighs one hundred lbs., and of
masonry, one hundred and sixty lbs., we have the overthrowing force,
20 × 15 × 1 × 100 × 2 × 20/3,
and the resisting force, (assuming the thickness as eight feet, in order
to get the area),
20 × 8 × 1 × 160 × 8/2.
Or performing the operations,
For overthrowing, 100,000 lbs.
For resisting, 102,400 lbs.
If the wall in place of retaining only the mass B 4 6, retains the bank
B E F^{_a_}, the pressure will evidently be increased. The centre of
gravity of the trapezoid B E F^{_a_} 6, is at C′, which is horizontally
projected at C′^{_a_}, and the horizontal component of the thrust acts
at 3 with the leverage 63.
Any superincumbent load, as a train of cars at E F^{_a_}, will again
increase the pressure, not only by reason of weight, but from shocks and
vibration.
For resisting lateral pressure, the beds of masonry are best when rough
dressed. For vertical loads, hammer dressed beds are the best.
The leverage of resistance is very much increased by battering the wall
in front, as at A D. The centre of gravity is then horizontally
projected at _m′_, but the distance D _m′_ is much greater than F _m_.
[Illustration: Fig. 134.]
The amount of masonry remaining the same, by decreasing the top, and
increasing the base, the strength is very much increased.
When retaining walls are exposed to shocks or pressures special
directions, they may be very much aided by buttresses opposing directly
such forces, as in fig. 134.
The increase of strength thus made by a small bulk of masonry is very
great.
All abutments, wing-walls, and side walls of culverts, come under the
head of retaining walls.
When the face of the wall does not by its position admit of buttresses,
as in fig. 134, it may be dovetailed into the earth; the latter being
firmly rammed around the masonry, as in fig. 135.
[Illustration: Fig. 135.]
277. The weight of the different earths and stones are shown in the
following table.
Name of material. Weight per cubic foot.
Brick, common 97 to 125
Brick, stock 115 to 135
Brickwork, (average,) 90 to 95
Chalk, 144 to 166
Granite, 164 to 187
Marble, 111 to 117
Mortar, (hair,) dry 80 to 86
Puzzolano, 160 to 178
Slate, 157 to 180
Stone, (average,) 140 to 150
Clay, (common,) 110 to 125
Clay and gravel, 150 to 170
Earth, common, 95 to 126
Gravel, 100 to 110
Quick-lime, 50 to 55
Quartz sand, 170 to 175
Common sand, 88 to 93
Shingle, 88 to 92
Earth, loose 90 to 95
Stone work, (hewn,) in wall, 160 to 175
Stone work, (unhewn,) in wall, 125 to 140
CHAPTER XII.
FOUNDATIONS.
278. Foundations may be divided into four classes.
Those on _firm_, dry land.
Those on _unfirm_ dry land.
Those on _solid_ bottom, under water.
Those on _unfirm_ bottom, under water.
Foundations upon firm dry land require only to be placed at a sufficient
depth to be out of the way of frost; varying from one foot in the
Southern, to two and three feet in the Middle, and four and five feet in
the Northern States. The first course should consist of small, flat
stones placed dry, but well packed by hand, upon the bottom; upon the
top of this layer, the mortared or cement masonry should be commenced.
The object of the first course of small stones is to apply the weight of
the superincumbent masonry as equally as possible to the ground. All
boulders and rounded stones should be carefully kept out of the
foundation.
Unfirm soils are prepared by driving piles, upon which a platform
holding the masonry is placed; or by placing the lower courses directly
upon the heads of the piles. Sand piles are made either by driving and
withdrawing a wooden pile and filling the hole thus made with sand; or
by digging trenches and filling such with sand. The applied weight is
thus spread over the entire surface of the sides and bottom, instead of
being placed upon the bottom only. When the weight of a heavy structure
is thrown upon a few small points of support, they may be made the piers
and abutments of a series of inverted arches, by which the whole surface
beneath the structure is made to assist in bearing the load. Foundations
upon yielding or sandy and wet soils may be secured by piling around the
whole structure; by which the earth is kept from spreading. Foundations
upon dry land do not generally give much trouble to the engineer; but
operations carried on under water require all the science and patience
that he is master of.
279. Three methods of founding under water may be noticed,
By driving piles.
By coffer-dam.
By caisson.
In very shallow water, where no danger arises from contracting the
water-way, we may throw in loose stones until the surface is reached;
and commence thereon the lower courses of the masonry. This is termed
“Enrockment.”
PILE DRIVING.
This operation has for its object the consolidation of naturally weak
bottoms; for piles driven close together tend to prevent that
compression that might take place under a heavy structure. Piles may
resist either by friction against the soils through which they are
driven, or by bearing upon a firm substratum at too great a depth to be
reached by uncovering. Piles driven in clay have sometimes acted as a
conductor to water, which, insinuating itself along the side of the
wood, produced settling which would not otherwise have taken place.
Experience has shown that four feet apart from centre to centre, when
there is a good substratum, is near enough to bear the heaviest loads.
The fact that a pile refuses to enter further, does not show that it has
reached a bed strong enough to bear the required load; for though it may
bear upon a solid bottom, or resist penetration by side friction, when
the load has been for some time upon the pile, it may be found too weak
to stand. Piles have in some cases refused to enter the ground from the
blow of a 1,500 lbs. ram, falling twenty feet, when first driven, and
have afterwards gone down three feet from a ram of 1,000 lbs.
The following formula, showing the resistance which a pile should offer,
is given by _Weisbach_ in Mechanics of Engineering, Vol. I. p. 285.
First, when the ram remains upon the pile after the blow,
_P_ _s_ = (_G′^2_ × _H_)/(_G_ + _G′_).
And, second, when the ram does not remain upon the pile,
_P_ _s_ =(_G′_/(_G_ + _G′_))^2 × _GH_
_Example._—A pile weighing five hundred lbs. is driven two feet, by
forty blows of a 1,000 lbs. ram falling six feet. Required the weight
which may be safely supported by the pile without further penetration.
The notation in the formula above is thus,
_G_ = the weight of the pile.
_G′_ = the weight of the ram.
_H_ = the fall of the ram.
_s_ = penetration per blow.
_P_ = the weight in lbs.
The penetration per blow will be 2/40 or .05 feet; and the formula for
the second case
(1000/(1000 + 500))^2 × (500 × 6)/.05 = 48,000 lbs.
Of which _one tenth_ or _one twelfth_ only is the maximum load which
should be placed upon the pile permanently. The surest test of the power
of a pile is to load it temporarily, when the time and place admit.
Perronet considered fifty tons, or 112,000 lbs. as not too great for a
twelve inch pile; and allowed twenty-five tons for a pile of nine inches
in diameter.
That the point of the pile may not be shattered by contact with the hard
earth, an iron shoe is sometimes fitted to the lower end; and that the
head may not split, an iron ring is driven on to the top.
The force of the blow given by a ram depends upon the weight of the ram
or monkey, and upon the velocity at which it strikes the pile; the
velocity depends upon the height from which it falls. The velocities of
bodies falling freely being as the times, and the spaces fallen through
as the squares of the times, we have the following rules; and from them
the table succeeding.
Given the _velocity_ of a body to find the _space_ through which it must
fall,
((Velocity in feet per second)/8)^2 = space in feet.
Thus a weight to acquire a velocity of two hundred feet per second, must
fall through a height of
(200/8)^2 = 625 feet.
Given the _space_ fallen through, to find the _velocity_.
√(height in feet × 64.3) = velocity in feet per second.
Thus the velocity of a body falling twenty feet will be
√(20 × 64.3) = 36 feet per second.
_Momentum_ is the product of weight by velocity; therefore, to find the
force of the blow given by a ram of given weight, falling a given
height, we find, first, the velocity by rule two. Also, given the weight
of ram, the necessary velocity to produce any required effect being
found, it is easy to find the height, and the reverse.
_Examples._—Suppose we have a ram weighing 2,000 lbs. and wish to strike
a blow of 25,000 lbs.; the velocity must be
25000/2000 = 12½ feet per second;
and to acquire that velocity, the height fallen must be (rule one)
(12½/8)^2 = 2.43 feet.
Again, if we have a pile-engine which admits of a fall of fifteen feet,
and we wish to strike a blow of 18,000 lbs., we first find the velocity
(rule two) thus:—
√(15 × 64.3) = 31 feet per second nearly,
whence the weight
18000/31 = 581 lbs.
The form of the common pile-engine is too well known to need
description.
Mr. Nasmyth’s system of pile-driving consists in forcing the pile into
the ground by a great number of blows following each other in rapid
succession. Piles were driven by his engine at the United States Dry
Dock, at Brooklyn, (N. Y.,) as follows: A pile was sunk fifty-seven feet
by a hammer of 4,500 lbs.; it was driven forty-two feet in seven minutes
by three hundred and seventy-three blows.
MITCHELL’S SCREW PILE.
Mitchell’s screw pile is a cast-iron column, around the lower part of
which is a spiral flange. It is screwed into the ground, and offers
great resistance to vertical pressure, on account of the large bearing
surface obtained.
DR. POTTS’S ATMOSPHERIC SYSTEM.
280. All methods of placing foundations in difficult positions must
yield to the above plan, which consists in exhausting the air from a
hollow cast-iron cylinder; when the pressure upon the surface of the
ground, outside of the cylinder, forces the earth immediately under the
pile to its interior; at the same time the pile sinks into the opening
thus made, both by its weight and by the atmospheric pressure from the
outside. The earth is moved from the interior of the pile; and when sunk
to the necessary depth, the interior is filled with concrete.
A very successful application of the above system was made at the
Goodwin Sands, at the mouth of the Thames River, (England). These sands
change their position with every violent storm, and are yet so compact
that a steel bar could be driven only eight feet with a sledge hammer;
and a pointed rod three inches in diameter, when sunk thirteen feet
deep, required forty-six blows from a one hundred lbs. ram falling ten
feet to drive it one inch. But a hollow pile two and a half feet in
diameter was sunk seventy-eight feet, at the rate of ten feet per hour
for a part of the time. In case of meeting with rock, the pile may be
converted into a diving-bell, and the obstruction moved.
The pile is cast in lengths of ten or twelve feet, and flanged together
with cemented joints.
In founding a bridge at Rochester, (England,) a pile of this nature was
loaded with thirty tons of iron rails, which caused a settlement of
three fourths of an inch. The rails being removed and the air exhausted,
by a single effort the pile descended six and a half feet. One hundred
tons of rails were then placed upon the pile, when the settlement was
again three fourths of an inch. (This small depression was owing to the
compression of the soil.)
The piles supporting the Shannon bridge, on the Midland Great Western
Railroad, (England,) were sunk by this system; and are ten feet in
diameter, and filled with concrete.
After wooden piles have been driven, they are cut off at the proper
level to receive the lower courses of the masonry. In some cases square
timber caps are placed upon the pile heads, and thereon a plank floor.
In others, the spaces between the piles are filled with cement and
concrete.
COFFER-DAM.
281. In founding in water from five to twenty-five feet deep, a
contrivance called a “coffer-dam,” is sometimes used. It is formed by
driving a double or triple row of piles around the foundation; which
rows are made water tight, either by tongued and grooved square piles,
or by round piles, to which is fastened a sheathing of plank. The space
between the courses of piling is emptied of water and packed closely
with clay or other material impervious to water. The interior of the dam
is then pumped dry and the masonry laid as on dry land. The thickness of
the dam depends upon the depth of water; the pressure upon the lower
part being of course much greater than that at the upper. If it was
considered as a mass resisting by its weight, overthrow from the
pressure of the water, the thickness would be easily calculated. Thus,
if the water is twenty feet deep the whole hydrostatic pressure upon
each lineal foot of the dam is 20 × 1 × 10 × 62½ = 12,500 lbs.; and as
the weight of water increases in the order of the terms of an
arithmetical progression, as also the pressure, it may be expressed by
the elements of a triangle, of which the height is the depth; and as the
centre of gravity of a triangle is at two thirds of the height from the
vertex, the pressure may be regarded as concentrated at one third of the
depth from the bottom; and the leverage of the above 12,500 lbs. is
20/3 = 6.67 feet;
and the overthrowing force is 83,375 lbs. The resisting force of a clay
dam twenty feet high and ten feet thick, would be
20 × 10 × 110 × 10/2 = 110,000 lbs.
Determining the thickness thus, would make the dam, when in deep water,
very thick; and it is generally best to brace the inside against the
ground, and when the masonry will admit, against that.
Dams of the following thickness have proved perfectly secure:—
Depth of water. Thickness.
6 feet. 3 feet.
10 feet. 5 feet.
15 feet. 8 feet.
20 feet. 12 feet.
25 feet. 14 feet.
The best form for a large coffer-dam is circular, or elliptical; as the
pressure is thus resisted more equally in all places than when there are
flat sides and angles in the plan.
To keep the dam dry while the work is going on, pumps are rigged along
one side of the dam the lower ends of which are placed in a trench or
well which drains the bottom.
The piers of the Victoria bridge at Montreal, (Canada,) are put down by
coffer-dams. Some of the piers being in but few feet of water, and upon
a rocky bottom, which did not admit of the driving of piles; the dams
for such were built in sections, floated to the site and anchored.
FOUNDATION BY CAISSON.
282. In deep water the coffer-dam becomes very expensive, on account of
the size and length of the piling, and the quantity of bracing required.
In such cases recourse is had to the caisson; which is simply a box in
which the masonry is built, and afterwards sunk to the proposed site.
The manner of putting down a piece of masonry by caisson will best be
shown by an example.
Suppose we wish to sink a pier thirty feet long, twenty feet high, and
six feet wide, in twenty feet of water.
Let the caisson bottom be of two courses of square 12 × 12 timbers,
fastened strongly at right angles to each other. Let the courses of
masonry be two feet thick. Assume the weight of a cubic foot of stone as
one hundred and sixty lbs., a cubic foot of wood at thirty, and of water
sixty-two lbs. per foot.
Every floating body will sink until it has displaced a quantity of water
equal to its own weight.
If the bottom is ten feet wide and thirty-five feet long, it will weigh
35 × 10 × 2 × 30 = 21,000 lbs.
one course of masonry weighs
30 × 6 × 2 × 100 = 57,600 lbs.
one course of side timbers, 12 × 12, which are laid upon the sides of
the raft,
(2 × 35 + 2 × 8) × 30 = 2,580 lbs.
Now load the bottom with one course of masonry and three courses of side
timbers, and we have
Stone 57,600 lbs.
Bottom of caisson 21,000 lbs.
Three side courses 7,740 lbs.
——————
In all: 86,340 lbs.
which divided by 62, gives 1,392; which divided by the area of the
caisson bottom, gives
1392/350 = 3.98
or nearly four feet, for the depth at which the caisson will float. This
leaves the sides one foot above the water surface.
Putting on a second course of masonry and three more side courses of
timber, we have
Floor 21,000 lbs.
Two courses masonry 115,200 lbs.
Six side courses 15,480 lbs.
———————
In all 151,680 lbs.
which divided by 62, and by 350, gives seven feet very nearly; leaving
the top one foot above the surface.
In the same manner we proceed until the caisson grounds upon the bed,
which has been previously prepared, either by pile-driving or by
dredging. The bottom being reached, the sides are taken off, and the
masonry remains upon the floor. The caisson may at any time be grounded
by filling with water, and may be raised again by pumping out. The
masonry may be laid either from barges or rafts at the site, or at the
shore. Guide piles are necessary to insure the descent in the proper
manner, and to prevent overturns.
In laying stone under water, it is to be remembered that masonry
submerged loses 62/100 nearly of its weight, and is consequently more
liable to be injured by shocks than when above the surface.
CHAPTER XIII.
SUPERSTRUCTURE.
283. Nothing aids more the proper accomplishment of any object than a
correct idea of what is wanted. The following definition is given by Mr.
W. B. Adams, of what good superstructure should be:—
“The principal requirements of permanent way are: That it shall be well
drained, especially in contiguity to the substructure; that the weight
and damaging power of the locomotives and rolling stock should be
considered the data for calculation; that the strength, hardness, and
tenacity of rails, and the immobility of the substructure should be
adapted to the hardest work to which the railway is to be subjected;
that the substructure should have an amount of bearing surface
proportioned to the load to be borne, and the nature of the rail and
ballast; and a sufficiently fair hold in the ground to prevent looseness
or lateral motion, from the side lurches of the engines and trains; that
the rails should possess so much vertical and lateral stiffness, either
in themselves or in their fastenings, as to prevent all deflection; and
have sufficient hardness of surface not to laminate or to disintegrate
beneath the rolling loads; also, to have sufficient breadth or tread
surface to diminish the crushing effect of the wheels.
“They should be as smooth as possible, to prevent concussion, and be
laid at the proper angle, and the curves regularly bent, so as to insure
the accurate tread of the wheels. The joints should be so made that the
rails may practically become continuous bars, yet with freedom to
contract and expand without being too loose. And with all this there
should be interposed between the rails and the solid ground, some medium
sufficiently elastic to absorb the effect of the blows of the wheels,
without being crushed or forced down into the ballast, and yet stiff
enough to keep the upper surface of the rails in a uniform plane.”
TIMBERWORK.
284. The timber-work supporting the rails consists either of cross ties
of wood, hewn flat on top and bottom, of dimensions from 6 × 7 to 7 × 9,
and 2½ or 3 feet longer than gauge; or of longitudinal sawed timbers
rectangular in section, placed directly beneath the rail, and giving it
a bearing throughout the whole length.
Longitudinal bearings seem to possess no advantage over cross ties, but
are subject to some decided disadvantages. In case of removal, two rails
at least must be taken up to admit of the replacing a timber; while with
cross ties any one may be taken out and replaced without even affecting
the immediate passing of a train. A continued bearing is no better than
a broken one, as the strength of the timber itself offers very little
resistance to the weight of a locomotive. Strength is not to be expected
in the timber-work; it is only the elastic medium between the rail and
the ground serving to maintain the rail in a proper position. The
strength is in the rail. The distance at which to place cross ties
depends upon the weight of engines traversing the road, the nature of
the ballast, and the strength of the rail; somewhere between two and
four feet from centre to centre.
The amount of superficial bearing which the timber-work ought to give
per lineal foot of rail, is differently estimated by different
engineers.
Upon the 4′ 8½″ gauged roads of America, 1¾ square feet per lineal foot
of rail has been allowed.
Several of the English roads give the following:—
Name of road. Gauge. Square feet per lineal foot of rail.
London and N. W. Railway, 4′ 8½″ 3
Great Western, 7′ 0″ 2½
S. and W. of Ireland, 5′ 3″ 3⅔
Midland G. W. of Ireland, 5′ 3″ 27/12
If ties are made eight inches wide, and eight feet long; we have the
following amounts of bearing surface per lineal foot of the rail with
different distances of the ties.
Distance C to C of tie. Superficial feet per lin. foot.
2 2.66
2½ 2.13
3 1.78
3½ 1.53
Of course the longer the tie is made the greater may be the distance
between, provided the rail will bear it. Mr. Peter Barlow, in his report
of August, 1835, to the directors of the Liverpool and Manchester
Railway, fixes the following dimensions for superstructure.
Distance between insides of ties being
3′ 3′ 9″ 4′ 5′ 6′
Weight in lbs. per yard. 50 59 61 67 79
Depth of rail in inches. 4½ 4⅝ 4¾ 5 55/16
At the time these dimensions were given, however, much less weight was
applied to the rails than at the present day. As the bearing is
increased, the rail must become heavier and more expensive; but the
number and cost of the ties is lessened. The report above referred to,
concludes that five feet bearings, involving heavier rails, would cost
no more, after the road bed is consolidated, than shorter ones; but that
on embankments and soft subsoils, it would be at first somewhat more
expensive.
285. The object of the ballast is, first, to transfer the applied load
over a large surface; second, to hold the timber-work in place,
horizontally; and third, to carry away the rain water from the
superstructure; it also furnishes the means of adjusting the timber-work
to the proper position. It should be at least one half way up the depth
of the tie, and deep enough below the under surface to prevent the
timber being forced down by the passing weight. From various
observations it appears that there should be one and a half times the
depth of the tie of ballast, beneath the under surface; or the whole
depth of ballast should be from two to two and one half times the depth
of tie.
For ballast, broken stone, gravel, or other dry, durable, and porous
material, is suitable.
A perfectly inelastic road bed is not to be desired. Something is
necessary to absorb the shocks given by the wheels, and prevent their
reaction against the machinery. To supply this amount of elasticity, and
to transmit the weight evenly to the ground, is the duty of the ballast
and timber-work.
Of late years there has been applied, in England, cast-iron
hemispherical bowls, designed to take the place of both tie and chair.
Such answers very well when there is no lack of ballast, and where
wooden ties are worth from seventy-five cents to one dollar each.
SECTION OF THE RAIL.
286. A good rail must be able to act as a girder, or supporter, between
the ties, as a lateral guide upon curves; and must possess a top surface
of sufficient hardness and size to resist the rolling wear of the
wheels.
Lbs. per yard. Tons per mile.
(2,240 lbs.).
One square inch of rail section weighs, 9.9 15.72
Two inches of rail section weighs, 19.8 31.42
Three inches of rail section weighs, 29.7 47.14
Four inches of rail section weighs, 39.6 62.84
Five inches of rail section weighs, 49.5 78.56
Six inches of rail section weighs, 59.4 94.28
Seven inches of rail section weighs, 69.3 110.00
Eight inches of rail section weighs, 79.2 124.50
Nine inches of rail section weighs, 89.1 140.01
Ten inches of rail section weighs, 99.0 155.57
Single line of Double line of
rails. rails.
Thus, at sixty dollars per ton, each square inch of section costs
$943.20 per mile, or $94,320 per one hundred miles, whence the necessity
of rolling the rail to the form which shall give the greatest strength
with the least weight.
The sections most in use in America are shown in fig. 136, and 137.
[Illustration: Fig. 136.]
Fig. 136 gives the most direct bearing, is compact, and brings the
fibres at top and bottom more directly in opposition with the
compressive and extensive strains. The top of the rail being curved to a
radius of ten or twelve inches, the load is applied nearly to a single
point; whence the whole resistance in fig. 137, depends upon the lateral
resistance of the piece _a b c d_ to being pushed down.
An objection is sometimes made to fig. 136, on the ground that it splits
off on the line _n n_: this will not be the case when the head is joined
to the web by a proper curve, as in fig. 136. This splitting off happens
full as often in fig. 137 as may be seen where it is in use; and it
might be supposed to act in that manner; because if the weight is
transferred at all from the point of application to the web, it must be
in the direction _e f_.
[Illustration: Fig. 137.]
The rails in present use upon our roads, weigh from fifty to
seventy-five lbs. per lineal yard; and are laid upon cross ties placed
at a distance of from two and one half to four feet from centre to
centre.
OF THE ACTUAL DIMENSIONS OF RAILS.
Digesting carefully the results of the experiments of Barlow, Fairbairn,
and Hodgekinson, and the experience of Mr. W. B. Adams, and other
English engineers; also the conclusions arrived at by the Berlin
Convention of 1850, appointed to determine the best form of section, we
come to the following limiting dimensions.
THE HEAD.
Mr. Barlow limits the width of head at two and one half inches as the
maximum; the Berlin Convention, at two and one fourth inches; W. B.
Adams, at two and one half; and all of the above recommend supporting
the edges of the head well from the rib.
THE VERTICAL RIB.
The experiments of the Prussian engineers fix the thickness for a rail
four inches high, at one half of an inch, and a rail four and one half
inches high, at 0.6 or 6/10 inch. Mr. Barlow makes it six tenths of an
inch for a four and one half inch rail, and 0.75, or three fourths inch
for a rail four and five eighths inches high, and for four and three
fourths inches high, 0.8, eight tenths inch.
THE BOTTOM FLANGE.
The use of this is more for bearing and fastening, than for supporting
strength. The Prussian engineers make three and one half inches an ample
base for a rail five inches high. The edge for one half or three fourths
of an inch, should be nearly horizontal, or parallel with the base, to
allow the spike to have a good bearing.
OF THE INCLINATION.
As the tread of the wheel is conical, the top of the rail must be
inclined to fit this cone, otherwise the wear will come upon the inner
edge of the rail only. This may be done in two ways; by placing the rail
base level, and inclining the vertical axis of the cross section of the
rail, and making the tread square with that axis; or by making the rail
section true, and inclining the base, either by cutting the tie, or by a
wedge placed between the rail and the tie.
OF THE HEAD CURVATURE.
If the top surface of the rail were perfectly flat, and the wheel tire
does not happen to fit it exactly, (from want of the proper position of
the rail, by settling, or other cause,) the wheel will bear entirely
upon one edge, and would soon destroy the rail. To remedy this, a slight
convexity is given to the top. Mr. Clark (in R. R. Mach.), recommends
the top to be curved to a radius of _ten_ or _twelve_ inches.
OF THE VERTICAL DEPTH (HEIGHT) OF THE RAIL.
Mr. Barlow’s general results are as follow:—
Distance from inside to inside of tie. Height of rail.
3′ 0″ 4½″
3′ 9″ 4⅝″
4′ 0″ 4¾″
5′ 0″ 5″
6′ 0″ 51/16″
In the London edition (1836) of Barlow’s Strength of Materials, page
402, in a report to the London and Birmingham Railway Co., upon the best
form and upon the strength of rails; after a carefully conducted set of
experiments, and an elaborate theoretical deduction of results, the
writer comes to the following five sections of rails possessing the
maximum strength, with the least weight.
Dimensions. No. 1. No. 2. No. 3. No. 4. No. 5.
Height, 4½ 4⅝ 4¾ 5 55/16
Breadth at top, 2¼ 2¼ 2¼ 2¼ 2¼
Depth of top, 1 1 1 1 1
Thickness of rib, 0.6 0.75 0.8 0.85 1.0
Width of lower flange, 1¼ 1½ 1½ 1⅔ 1⅔
Depth of lower flange, 1 1 1 1⅛ 1½
Weight per yard, 51.4 58.8 61.2 67.4 79
Distance C. to C. of ties, 3′ 3′9″ 4′ 5′ 6′
This table shows the ratio of material which should be placed in the top
and bottom.
With the above dimensions, and joining the curve of the head to the rib
at two and one fourth inches from the top of the head, we obtain a
strong and well-shaped rail, with the least material possible. See fig.
136.
As an example of the application of the above, the table below has been
formed, showing four standard forms, which will be found to unite all of
the requirements of good rails; the general form being that of fig. 136.
Dimensions. The weight of the rail being, in lbs.,
60 65 70 75
Width of head, 2½ 2½ 2½ 2½
Rad. of top, 12 12 12 12
Height of rail, 4 4¼ 4½ 4¾
Thickness of rib, 0.6 0.6 0.65 0.7
Breadth of base, 3½ 3½ 3¾ 4
Depth of head at point A B, 2¼ 2¼ 2½ 2½
Thickness at edge of lower web, ½ ½ ½ ½
and the following figures show the weights which should be applied to
differently spaced sleepers.
Distance centre to centre of tie. Distance clear. Weight of rail.
1½ feet, 1 feet, 60 lbs. per yard.
2 feet, 1½ feet, 60 lbs. per yard.
2¼ feet, 1¾ feet, 60 lbs. per yard.
2½ feet, 2 feet, 60 lbs. per yard.
2¾ feet, 2¼ feet, 65 lbs. per yard.
3 feet, 2½ feet, 65 lbs. per yard.
3¼ feet, 2¾ feet, 70 lbs. per yard.
3½ feet, 3 feet, 75 lbs. per yard.
The amount of inclination or bevel to be given to the cross section of
the rail, depends _directly_ upon the cone of the wheel, and
_indirectly_ upon the gauge of the track. (See Chapter XIV. part 2.) The
radius of curvature being averaged at 2°, or 2,865 feet,
Feet or Inches.
For the 4′ 8½″ gauge it should be .0017 .020
For the 5′ gauge, .0017 .020
For the 5½′ gauge, .0019 .022
For the 6′ gauge, .0021 .025
in the width of the rail, or two and one half inches.
The above dimensions embrace all of the best results of experiment and
experience, and at the same time satisfy the conditions demanded by the
mechanical and physical nature of the material—iron.
CHAIRS AND JOINTS.
287. The chairs most common at present are made of a wrought iron plate,
with two lips, either cut and punched up, or forged up, to hold the
lower web of the rail. Such chairs weigh from six to ten pounds each,
and are less liable to break than the common form of cast-iron chairs.
It is probable that a cast-iron chair may be made, however, with
properly shaped lips, and so hollowed out as to be at once strong and
light. (See Clarke’s R. R. Machinery, “Permanent Way.”)
Of late the chair of Mr. David L. Davis, of Dedham, Mass., has attracted
considerable attention, and bids fair to be the means of obtaining a
better rail surface than has heretofore been possible. This gentleman
has been for twenty years Road-master of the Boston and Providence
Railroad, and has had ample opportunity for considering the subject of
track laying in every respect. The rail bears upon a cap of wrought
iron, which rests upon a piece of rubber, lying in the chair. The
testimony of the leading managers of the New England Railroads bears
witness of the excellence of the arrangement.
The practice of notching _each end_ of the rail causes the expansion to
be exerted directly _against_ the fastenings, which should not be the
case. Some point should be _fixed longitudinally_, to resist the end
shocks from the wheel. This point should be either the _centre_ or _one
end_ of the rail. End chairs may hold the rail laterally, and
vertically, but not longitudinally.
The weakest part of the track is that, where, to resist the concussions
of the wheels it should be strongest, namely, at the joint: here we lose
the strength of the rail and depend entirely upon the tie. The flattened
ends of rails which have been laid for a few years show the bad effect
of the common joint. The complete remedy for this is, so splicing the
rail that it is as strong at the joint as elsewhere. The method termed
“fishing,” is not much more expensive than the ordinary method of
jointing, it is perfectly effectual, and has had the test of long and
successful use. It consists in bolting a plate two and one half feet
long, two and one half or three inches wide, and from one third to one
half inch thick, to the ends of both rails making the joint; one plate
being placed on each side. The plates are convexed a little from the
rail as in fig. 138, so that being sprung by screwing on the nuts, the
latter shall not work loose by the vibration of the rail.
[Illustration: Fig. 138.]
In the above arrangement there is no tie below the joint, but the latter
lies midway between two sleepers.
Another method of “fishing” is, to place a piece of ¶ᕼ¶ or ¶⊤¶ iron
beneath the rail, bolting it firmly to the lower flanges.
In bolting rails together at the ends, the bolt holes must be cut a
little larger than the bolt, to allow for the expansion of the iron.
The effect of the joint upon the passing carriage, is the jumping
motion; the middle of each rail being a summit, and the end a
depression, (the strength at the joint being taken away); and if the
joints are not opposite to each other, there is generated a very
injurious and dangerous side rocking. Figs. 138, 138 A, and 138 B, show
the methods of fishing.
[Illustration:
Fig. 138 A.
Fig. 138 B.
]
[Illustration: Fig. 139.]
To avoid the wear caused by frequent joints, various forms of compound
rails have been proposed; consisting of two or more parts breaking
joint. One form has been contrived in which the section is vertically
halved; another of three parts, a head placed on top of a double
vertical web. Fig. 139 shows what would seem to answer any purpose (if
compound rails are at all allowable). The joint is here divided into
four parts, so that the strength of the bar at any point is reduced only
one fourth. In bolting the parts together the joints should be left open
enough (see in advance) to allow for contraction; and the bolt-holes, as
before noticed, should be longer than the bolts. (This enlargement,
extending only in the direction of contraction, and not in the line of
the force.) The upper part of such a rail should be hardened to resist
the rolling of the wheels, while the webs must possess the strength to
act as a girder.
It is questionable whether, by dividing the rail, particularly when it
is done horizontally, we do not prevent the mutual extensile and
compressive actions which ought to have place in the top and bottom; for
we cannot make the bolts perfectly tight because of expansion.
Some of the compound rails which have been laid in America have given
good results, others have not.
Mr. W. B. Adams observes, that a compressed rail to be as strong as a
sixty pound whole rail, must weigh ninety lbs. per yard.
Some engineers have proposed such a rail that when one side becomes worn
it may be turned over so that the lower may become the upper table. This
is quite wrong in principle; as when the lower fibres have been
subjected for some time to extension, they are entirely unfitted to
oppose compression.
OF THE LIFE OF RAILS.
288. The time which a rail will last, depends upon the form and weight,
and _on the quality of the iron_; and upon the number, weight, and speed
of engines and cars passing over it.
NOTE.—The effect of _quality_ is altogether too little regarded in
America. How worthy of attention it is may be seen by the following.
Upon the same road were used two kinds of seventy-two pound rails,
each five inches deep, and having a bearing surface of 2.7 inches in
width. The one was worn out with a tonnage of 41,000,000 tons, the
other of 22,000,000 tons; the difference being entirely in the
_quality_ of the iron.
Upon the Philadelphia and Reading Railroad there have been used
forty-five pound rails of reheated and refined iron, which have
lasted for eighteen years; and that with a very heavy traffic upon
them. While upon other American roads, English sixty pound rails
have required renewing in one, two, three, and four years.
The durability of rails is practically independent of time, and depends
entirely upon the amount of work done. The repairs of iron, depending
upon flaws and other physical defects, will be greater at the
commencement of operations than afterwards. After the first one or two
years the regular depreciation begins. The first Liverpool and
Manchester rail weighed thirty-five lbs. per yard, and the locomotive
seven and a half tons. As the traffic increased, so did the necessary
weight of engines, and a corresponding increase in the strength and
weight of rails was also rendered necessary. In 1831, the average weight
of engines with tenders was eighteen tons. In 1855, the maximum engine
with tender, fuel, and water weighed sixty tons; and in like manner the
rails increased from thirty-five to eighty-five lbs. per yard.
Messrs. Stephenson and Locke, in a report to the London and
North-western Railroad Company, in 1849, recommend the adoption in
future of an eighty-five lb. rail.
Upon the roads of Belgium are used rails of fifty-five and sixty-four
lbs. per yard; but it is asserted that an eighty lb. rail would allow of
ten times more traffic.
For the average of American roads, when the iron is good, (_in
quality_,) fifty-five, sixty, and at most sixty-five lbs., will probably
be found ample for the heaviest traffic: the rail being of the form
already given, and supported on ties not more than two and a half feet
from centre to centre.
Mr. Belpaire, (of the Belgium engineers,) concludes, from many
experiments, that in sixty miles, each engine abrades 2.2 lbs.; each
empty car 4½ oz.; and each ton of load 1.4 oz.; the amounts being in
direct ratio to the several weights.
Captain Huish, of the London and North-western Railroad, (England,)
estimates (Report of April, 1849) that fifty trains per day, or 18,250
trains per annum, for twenty years, would wear out a seventy lb. rail.
The Belgian engineers have concluded that 3,000 trains per annum, for
one hundred and twenty years, would wear out a fifty-five lb. rail.
Now 120 × 3,000 = 360,000 Belgian, and 20 × 18,250 = 365,000 English, a
very satisfactory coincidence, as the different observers did not know
of each other’s proceedings. The difference, 5,000 trains, being
accounted for by the use of heavier engines upon the roads of England.
From the above results the following table is formed, showing the life
of rails under from two to one hundred trains per day. American roads
being less nicely finished, as regards the road-bed, will of course wear
out rails faster than the roads of Europe. The table will serve as a
base for estimates.
Trains per day. Trains per year. No. of years’ life of rails.
2 600 604
4 1,200 302
6 1,800 201
8 2,400 151
10 3,000 121
12 3,600 100
14 4,200 86
16 4,800 75
18 5,400 67
20 6,000 60
30 9,000 40
40 12,000 30
60 18,000 20
80 24,000 15
100 30,000 12
Probably one half of the above numbers of years would show the full life
of rails upon American roads.
As those rails which are most used wear out the soonest, they should be
made accordingly heavier. Such are those at depot grounds and at
sidings.
NOTE.—From the reports of the Reading (Penn.) Railroad it appears
that in 1846 153/209 of the damaged rails were split; and that in
1845 285/295 were split.
As regards the _quality_ of railroad iron, it is generally
notoriously bad, and its makers know it as well as those who buy it.
Railroad companies are not willing to pay for good iron. Comparisons
between American and English iron amount to little. First rate iron
can be made in England or in America, and so can that which will
last about two years. Time will convince companies that the most
expensive iron is the cheapest.
TABLE OF THE WEIGHT PER MILE OF DIFFERENT RAILS.
Weight in lbs. Tons per mile. Tons per mile.
per yard. (2,000 lbs.) (2,240 lbs.)
50 44.00 39.29
55 48.00 43.21
60 52.80 47.19
62 54.56 48.71
64 56.32 50.28
66 58.05 51.86
68 59.84 53.43
70 61.60 55.00
72 63.36 56.57
74 65.12 58.14
76 66.88 59.71
78 68.64 61.28
80 70.40 62.86
TRACK-LAYING.
289. As wrought iron expands 0.0000068 of its length per degree
(Fahrenheit) of heat, a change of 130° will cause the following
expansions:—
In a 15 feet rail .0135 ft.
In a 18 feet rail .0162 ft.
In a 20 feet rail .0176 ft.
and that the track may be kept in the right vertical and horizontal
line, rails laid in cold weather must not be placed in contact; but
separated by space enough to allow expansion to take place. In hot
weather they may be placed close together. Calling 100° the maximum and
-30° the minimum, we form the following table for the average lengths of
rail, (20 feet).
At 100° place the rails in contact.
90° at a distance of .00136 feet .016 inches.
80° at a distance of .00272 feet .032 inches.
70° at a distance of .00408 feet .049 inches.
60° at a distance of .00544 feet .065 inches.
50° at a distance of .00680 feet .082 inches.
40° at a distance of .00816 feet .092 inches.
30° at a distance of .00952 feet .114 inches.
20° at a distance of .01088 feet .131 inches.
10° at a distance of .01224 feet .147 inches.
0° at a distance of .01360 feet .163 inches.
-10° at a distance of .01496 feet .179 inches.
-20° at a distance of .01632 feet .196 inches.
-30° at a distance of .01768 feet .212 inches.
[Illustration: Fig. 140.]
The proper distance of rails may be fixed by the use of the steel plates
shown in figs. 140 and 140 A, which are marked with the temperature,
according to their thickness, as in the above table.
To incline the rail base may be used, when the rail is not bevelled,
wedges one foot long and six inches wide, spiked with the rail to the
tie. When the chairs are of cast-iron, they may be cast to the required
slope.
[Illustration: Fig. 140 A.]
FROGS.
290. When one line of rail crosses another, a contrivance called a frog
is used; see figs. 141 and 142.
[Illustration: Fig. 141.]
That the wheel may run smoothly from _a_ to _c_, fig. 141, the rail _b
f_ must be cut at D, and the rail _a c_ must be cut at the same point.
Cutting the two gives the form shown in the figure, and further
developed in fig. 142.
In order that the flange of the wheel shall not leave the line _a c_,
when at the break D, the guard rail _m m_ is used to confine the
opposite wheel. It should be placed at a distance of two inches from,
and parallel with, the main rail _g g_, from opposite six inches below
the frog point at _s_, to six inches above the shoulder at _s′_. From
the ends of the parallel line _n n_ the guard rail should gently curve
away at both ends. Thus the wheel will be gradually brought into the
right line, kept so until the break in the rail is passed, and finally
easily released. To place and maintain the guard rail in the right
position, it is well to put both it and the main rail into a double
chair, which is spiked to the sleeper.
[Illustration: Fig. 142.]
The form and dimensions of the cast-iron frog depends upon the angle at
which the cutting rails cross, and upon the size of the wheel tire.
To draw the frog, proceed as follows:—
[Illustration: Fig. 142 A.]
Let _a c b_ be the angle. Parallel with and two inches from _b c_ draw
_d e_, _e_ being in _a c_ produced. In the same manner fix the point
_g_. At the width of the rail head (from 2¼ to 2½ inches) draw, parallel
to _a c_, L 8. The point 8 is the limit to the solid steel. At double
the rail width, or 4½ inches, draw, also, parallel to _a c_, 16. 6; 5. 6
is the limit of the flat steel, generally about half an inch in
thickness. This is the least amount of steel allowable; it is best to
steel the whole tongue, and all of that part of the wings acted upon by
the wheels. The geometric point is generally very thin, and is omitted
to a distance far enough back to make the point a third or half an inch
wide, which is rounded off; _e L_ and _d k_ are made two and a half
inches; as also _f m_ and _g n_; _k_ 10 and _m_ 11 are made six or seven
inches, and joined to _d_ and _f_ by a curve, abrupt at first, but
afterwards more gentle. The distances, 5 _a_ and 6 _b_ must be such that
_a_ 9 is three and one eighth inches, (depending upon the breadth of
rail base,) _o m″_ is from three to four inches. At the other end of the
frog _e h_ must be enough to make _s t_ at least an inch, when _e h_ and
_i g_ are from three to four inches; _i m′_ being, as at the other end,
three or four inches. The steel plates N N are one half inch in
thickness. The surface, N, is two inches above the bottom, M. The lower
plate, M, is two inches thick. A B, C D, and E F are six or seven inches
wide, and one inch thick. The spike holes 11/16 square, the spike being
one half inch. The sharp edges, _i g_, _e h_, _a c_, _b c_, should be
rounded off to fit the wheel at A, fig. 142 A. The surface of the tongue
N 9 should be formed to a double incline to fit the wheel cone.
NOTE.—Fig. 142 A gives the shape and dimensions of the largest
tires.
Another method of making a frog is to cut and weld the rails _a_ and _b_
of the track, as in fig. 143. The continuations of these rails are bent
as shown in the figure.
[Illustration: Fig. 143.]
The whole angle is placed upon a firm wooden bearing.
There is no weaker part of the track than the frog. To make up the
strength at such places a heavy longitudinal timber twelve feet long
will answer a good end.
SWITCHES.
291. The object of the switch is to adjust a single line of rails to two
or more pairs, so that any two lines may be made continuous. The form in
general use consists of two rails, as at _a b_, _a b_, fig. 144, moving
upon _a_ and _a_ as centres. Here the tangent point of the turnout curve
is at _c_. The data given for the switch are the length of switch rail
and the motion at the toe (_c_) (which determine the direction of the
starting tangent) and the radius of curvature of the turnout curve. The
required elements are, the angle of frog at _b_ and the distance from
_a_ to the point of the frog.
[Illustration: Fig. 144.]
The following formula and table are by Josiah Hunt, Esq., (at present
chief engineer of the Hannibal and St. Joseph Railroad, Mo.). The
formula was first published in Appleton’s Mechanics’ Magazine, vol. 1,
p. 575.
_D_ = 2(_g_ – _s_) × (cot. _S_ × cot. _F_)/(cot. _S_ + cot. _F_).
Where _S_ = angle of switch.
_F_ = angle of frog.
_s_ = the movement.
_g_ = the gauge.
_Example._—How far from the toe of the switch is the point of the frog,
the gauge being 4′ 8½″, the rail twenty feet long, and moving five
inches; the frog being six feet long, six inches wide across the head,
and three inches at the mouth?
We have
_D_ = 2(4.708 – .417) × (240/5 + 72/(6 + 3))/(240/5 + 72/(6 + 3))
or, _D_ = 8.582 × (48 × 8)/(48 + 8) = 58.85 feet.
In laying the rails, the distance from the point to the end of the frog
(towards the switch) is to be taken from the above.
Table showing the distance between the frog and switch, gauge 4′ 8½″,
movement of switch-rail five inches. Frog six inches across head, and
three inches at mouth. Main track being straight.
┌───────────────┬─────────────────────────────┐
│Length of frog.│ LENGTH OF SWITCH RAIL. │
├───────────────┼────┬────┬────┬────┬────┬────┤
│ │ 12 │ 14 │ 16 │ 18 │ 20 │ 22 │
├───────────────┼────┼────┼────┼────┼────┼────┤
│ 3 │29.1│29.7│30.1│30.4│30.7│30.9│
│ 3½ │33.3│34.0│34.5│35.0│35.3│35.6│
│ 4 │37.3│38.2│38.8│39.4│39.8│40.2│
│ 4½ │41.1│42.2│43.0│43.7│44.3│44.7│
│ 5 │44.8│46.1│47.1│47.9│48.5│49.1│
│ 5½ │48.3│49.8│51.0│51.9│52.7│53.2│
│ 6 │51.7│53.4│54.8│55.9│56.8│57.6│
│ 6½ │55.0│56.9│58.5│59.8│60.8│61.7│
│ 7 │58.1│60.3│62.1│63.4│64.7│65.7│
│ 7½ │61.2│63.6│65.6│67.2│68.5│69.6│
└───────────────┴────┴────┴────┴────┴────┴────┘
292. When the switch rail is short, the angle between the main line and
the switch rail, when switched, is considerable; and causes quite a
shock to the passing engine. The switch shown in fig. 145 remedies the
evil, makes the machinery compact, and the calculation simple. The
tangent point of the turnout curve is at _n n_ (the usual heel). In
place of adjusting the single to the double line of rails, the double is
adjusted to the single line. The data given are the gauge and radius of
curve; and as before, the elements required the frog angle and distance
from switch to frog point.
[Illustration: Fig. 145.]
Now
Rad.^2 – (Rad. _less_ gauge)^2 = distance^2,
or _R^2_ – (_R_ – _g_)^2 = _D^2_,
and _D_ = √(_R^2_ – (_R_ – _g_)^2).
The angle of frog is also
Sin angle of frog = (Sin 90 log _D_)/(log _R_).
The length of this switch rail depends upon the radius of curvature. The
distance between the two rails at S must be enough to admit the wheel
flange, that is, at least two inches.
Let A B, fig. 146, be the straight rail; E D the curved one. Draw G H
parallel with and two inches distant from the inner edge of A B. No
point of the curved rail must fall within G H; whence E is the
turning-point, and E D the length, found as follows.
Let _R_ equal the radius of curve to outside of outer rail; _d_ equal
two inches plus width of rail, or _i e_, and _D_ equal _D E_.
Then
_D_ = √(_R^2_ – (_R_ – _d_)^2).
[Illustration: Fig. 146.]
_Example._—Let the radius of outer rail be five hundred feet, and the
gauge five feet. We have, then, the distance
(A.) _D_ = √(500^2 – 495^2) = 72 feet, very nearly.
Also, Sin _E C D_ = (Sin 90 log _D_)/(log _R_),
(B.) or (Sin 90 log 72)/(log 500) = 8° 17′,
and the length of switch
(C.) √(500^2 – 499.65^2) = 18¾ feet nearly.
Five hundred feet is, therefore, about the longest radius for which such
switches should be used.
SIDINGS AND CROSSINGS.
Crossings occur where two tracks cross, and consist of four frogs, with
the corresponding guard rails, as in fig. 147.
[Illustration: Fig. 147.]
ELEVATION OF THE EXTERIOR RAIL.
293. The motion of a train of cars around a curve is accompanied by a
tangential force, depending in amount upon the velocity of the train and
the radius of curvature. This force tends to throw the cars from the
track; and is counteracted by elevating the exterior rail.
The centrifugal force of any body in motion in a curved line is shown by
the formula
(_WV^2_)/(32_R_).
Where _W_ is the weight in lbs.
_V_ the velocity in feet per second.
_R_ the radius of curvature,
and 32 the accelerating force of gravity.
The force tending to throw the car from the rail is not _centrifugal_
but _tangential_, but it matters not whether the body is kept in
position by _tension_ upon the _inside_ or by _compression_ on the
_outside_; the amount of the force is the same.
[Illustration: Fig. 148.]
The horizontal projection of the centre of gravity of the car, when at
rest, is at _c_, fig. 148, and when in motion the direction of the
weight should be _a b_; and the inclination, _c′ a′ b′_, must be such
that _a b_ will be perpendicular to _c′ a′_; to effect which, _c′ b′_
should be to _a′ b′_ as the weight to the tangential force; or _E_ being
the elevation of the rail, _g_ the gauge, _W_ the weight, and _c_ the
tangential force; we have
_E_ : _g_ :: _c_ : _W_,
or _E_ = (_cg_)/_W_, and _c_ being = (_WV^2_)/(32_R_);
finally _E_ = ((_WV^2_)/(32_R_))_g_/_W_ or (_V^2__g_)/(32_R_) = _E_.
Where _W_ = weight of a car.
_V_ = speed of train in feet per second.
_g_ = gauge of road.
_R_ = radius of curve.
_E_ = elevation of outer rail in feet and decimals.
_g_ and _R_ are the only fixed quantities in the formula; and the
average weight and speed of a car must be assumed.
Examination of the formula shows how important it is that all trains
should run at such a velocity as to demand the same elevation of rail.
The absolute elevation must be arranged to meet the requirement of the
fastest trains; and other trains must conform, even at a disadvantage.
NOTE.—The subject of the mechanics of traversing railroad curves, is
yet quite in the dark. The action of the train, as caused by its own
momentum, is _tangential_; while the action of the engine tends to
pull the cars against the _inner_ rail, being _opposed_ to the first
motion. This might require a reduction of the elevation given by the
formula when the engine is exerting a strong tractive power, but
when running without steam the full elevation is needed, (see
chapter III.)
[Illustration: Fig. 149.]
In laying and maintaining the rails to the proper elevation, a
clinometer attached to a rail gauge, as in fig. 149, answers a good end:
the small arc being graduated according to the different elevations
required by curves of different radii. Thus the index of the level being
placed at 2°, when the rails are fitted to A and B, the elevation is
correct for a 2° curve; or for a curve of 2,865 feet radius.
The difference in gauge of one foot makes a difference in the elevation
of but 0.009 feet, or about ⅒ of an inch.
The following table is calculated for the average of the different
gauges in use, thus,—
4.7
5.0
5.5
6.0
——————
4)21.2
——————
Average gauge, 5.3 feet.
TABLE OF ELEVATION OF OUTER RAIL.
┌───────────────┬─────────────────────────────────────────────────────┐
│Radius of curve│ ELEVATION OF OUTER RAIL IN FEET AND DECIMALS, THE │
│in feet, being │ VELOCITY IN MILES PER HOUR BEING │
├───────────────┼────────┬────────┬────────┬────────┬────────┬────────┤
│ │ 10. │ 15. │ 20. │ 25. │ 30. │ 40. │
├───────────────┼────────┼────────┼────────┼────────┼────────┼────────┤
│ 250│ .130 │ │ │ │ │ │
│ 500│ .070 │ │ │ │ │ │
│ 1,000│ .037 │ .079 │ │ │ │ │
│ 2,000│ .018 │ .040 │ .074 │ .111 │ │ │
│ 3,000│ .013 │ .026 │ .048 │ .074 │ .106 │ │
│ 4,000│ .009 │ .020 │ .037 │ .058 │ .079 │ .154 │
│ 5,000│ .007 │ .016 │ .031 │ .045 │ .065 │ .119 │
│ 6,000│ .006 │ .013 │ .024 │ .037 │ .053 │ .095 │
│ 7,000│ .005 │ .011 │ .021 │ .033 │ .046 │ .086 │
│ 8,000│ .004 │ .010 │ .018 │ .029 │ .039 │ .077 │
│ 10,000│ .003 │ .008 │ .010 │ .022 │ .032 │ .059 │
└───────────────┴────────┴────────┴────────┴────────┴────────┴────────┘
CHAPTER XIV.
EQUIPMENT.
PART I.
LOCOMOTIVES.
As the locomotive engine is the power by which railroads are worked, and
as its proportions and dimensions are so intimately connected with the
physical character of the road, it is thought proper to take space
enough at this point to examine the general principles of its
construction, and of its adaptation to the work required of it upon
railroads.
Under the general principles, we recognize the production and
consumption of steam, the disposition of weight upon the several pairs
of wheels which shall secure the necessary adhesion, the application of
the power generated in the boiler to the moving of the wheels, and that
general arrangement of parts which shall render the use of power
economical.
BIRTH AND GROWTH OF THE LOCOMOTIVE.
294. The first idea of the application of steam to locomotion, is due to
the unfortunate Solomon de Caus, of Normandy (France), who was confined
in a madhouse for insisting that steam could be made to move wheeled
carriages.
295. In the year 1784, William Murdoch, the friend and assistant of
James Watt, built a non-condensing steam locomotive engine, on a scale
of about one inch per foot, having
Cylinders, ¾ × 2 inches,
Wheels, 9½ inches,
and Weight, 10 lbs.
This little engine, however, accomplished the speed of ten miles per
hour.
296. In 1802, Richard Trevethick patented the application of the
non-condensing steam-engine to the propelling of carriages on railroads;
his engine was fitted with one horizontal cylinder, which applied its
power to the wheels by means of spur gear.
297. In 1825, the truck was first applied, to relieve the driving wheels
of a part of the weight, and to enable the engine to pass freely around
curves.
298. In 1827, Timothy Hackworth applied the blast pipe, for the purpose
of draft. He applied, also, spring balances to the safety-valves, and
used the waste steam to heat the feed water. This engine drew one
hundred tons, at five miles per hour, and forty-five tons on a fifty
feet grade.
299. In 1828, M. Seguin (France) introduced the multitubular boiler.
300. In 1829, the directors of the Liverpool and Manchester Railroad
offered a premium for the best locomotive, which should draw three times
its own weight, at ten miles miles per hour. The “Rocket,” by Robert
Stephenson, of Newcastle on Tyne, was the successful competitor, and
drew the load required, seventy miles, at an average speed of 13.8 miles
per hour; its maximum velocity was twenty-nine miles per hour; it
evaporated 5.4 lbs. of water per pound of coke, and 18.24 cubic feet per
hour of water.
301. From 1830 to 1840, the changes that were made were rather those of
dimension, proportion, and arrangement, than of essential elements of
steam producing.
302. In 1840, several truck frame engines were sent to England from the
Norris Works of Philadelphia. These locomotives would draw a load of one
hundred and twenty tons over a sixteen feet grade, at the rate of twenty
miles per hour.
303. In 1845, the Great Western Railroad, of England, was supplied with
an engine of twenty-two tons weight, having cylinders 15¾ × 18, wheels 7
feet, heating surface 829 square feet. This locomotive carried
seventy-six and one half tons at a velocity of fifty-nine miles per
hour. The consumption of coke was 35.3 lbs. per mile, and of water,
201.5 cubic feet per hour.
THE ENGLISH LOCOMOTIVE OF 1850.
304. The “_ne plus ultra_” for the seven feet gauge (Great Western
Railway) by Gooch, has inside cylinders 18 × 24 inches, one pair of
eight feet driving wheels, grate area twenty-one square feet. Fire-box
surface, one hundred and fifty-three feet. Three hundred and five two
inch tubes, giving 1,799 feet of surface. Total heating surface, 1,952
square feet. Weight of engine, empty, thirty-one tons; of tender, eight
and one half tons; whole weight with wood and water, fifty tons.
Evaporating power, three hundred cubic feet of water per hour. This
engine can draw two hundred and thirty-six tons, at forty miles per
hour.
The maximum for the London and North-western Railroad, four feet, eight
and one half inches gauge (Crampton’s patent), has cylinders 18 × 24
inches; wheels, eight feet; two hundred two and three sixteenths inch
(outside diameter) tubes; grate, twenty-one and one half square feet;
fire surface, one hundred and fifty-four feet; tube surface, 2,136 feet;
whole heating surface, 2,290 square feet; weight, loaded, thirty-five
tons; twelve tons upon driving wheels; tender, twenty-one tons, loaded;
whole weight, fifty-six tons.
THE AMERICAN LOCOMOTIVE OF 1855.
305. The engine “Charles Ellet, Jr.,” drew on the 9th of August, 1854,
forty tons, over a grade of two hundred and seventy-five feet per mile,
and over grades of two hundred and thirty-eight feet, upon curves of
three hundred feet radius. This engine has wheels four and one half feet
in diameter coupled seven feet apart; cylinders 14 × 26 inches; and
weighs, including wood and water, 53,058 lbs. This is a tank locomotive,
the tender is dispensed with, and in its room a tank containing one
hundred cubic feet of water, and one cord of wood is used. This engine
was built by Richard Norris and Son.
An engine built by the Cuyahoga Steam Furnace Co. of Cleveland, Ohio,
performed the following feat.
An ordinary passenger train was carried one hundred and one miles, over
a total ascent of 1,255 feet of grades, making twenty stops, at an
average speed of twenty-five miles per hour, with a consumption of only
ninety cubic feet of wood.
The same engine drew an average load of three and one third cars four
hundred and thirty miles, making seventy-five stops, surmounting a total
ascent of 5,439 feet, averaging twenty-five miles per hour, with one
tender full of wood only.
In the months of July and August, 1856, two engines upon the Pacific
Railroad (Missouri), one by R. K. and G., and one by Palm & Robertson,
ran each one hundred and twenty-five miles, with three passenger and one
baggage cars, using only one cord of wood.
NOTE.—For an interesting example of what can be done by the American
locomotive, and an illustration of engineering peculiarly American,
the reader is referred to a description of the “Mountain top track”
at the Rock-fish Gap crossing of the Blue Ridge (Va.), by the
Virginia Central Railroad, given by the engineer under whose
direction the work was proposed and executed (Charles Ellet, Esq.),
from which is extracted the following:—
“The eastern slope is 12,500 feet long, and rises 610 feet; the
average grade being 2574/10 feet, and the maximum 29568/100 feet per
mile. The least radius of curvature 234 feet; upon which curve the
grade is 2376/10 feet per mile. The western slope is 10,650 feet
long, and falls 450 feet; the average grade being 223⅒, and the
range 27984/100 feet per mile.
“The engines, which have taken loads ranging from twenty-five to
fifty tons up one slope at seven and one half miles per hour, and
down the opposite one at six miles per hour, making four trips of
eight miles per day for three years, were designed and built by M.
W. Baldwin & Co., Philadelphia, and have three pair of forty-two
inch wheels all coupled, the flange base being 9′ 4″, cylinders 16½
× 20 inches, weigh, with wood and water, 55,000 lbs., or
twenty-seven and one half tons. They run without a tender, the
engine carrying its own feed; thus gaining the double advantage of
increasing the adhesion of the engine, and avoiding the resistance
of a tender.”
GENERAL DESCRIPTION.
306. The locomotive is a non-condensing, high pressure engine, working
at a greater or less degree of expansion, according to the labor to be
performed, and placed upon wheels which are so connected with the
piston, that any motion of the latter is communicated to the former, by
which the whole is moved.
The power exerted in the cylinder and referred to the circumference of
the driving wheel, is called _traction_; its amount depends upon the
cylinder diameter and steam pressure, upon the diameter of wheel and
stroke, this latter being the distance between the wheel centre and
point of application of power.
The means by which the “traction” is rendered available for moving the
engine and its load, is the resistance which the wheel offers to
slipping on the rail, or its bite, and is called adhesion; it is
directly as the weight applied to the wheels, but depends also upon the
state of the rails. It varies from nothing, when there is ice on the
rail, to one fifth of the weight upon the driving wheels when the rail
is clean and dry, and in some cases has reached as high as nearly one
third. It should be enough to resist the maximum force of traction, that
is, the wheel should not slip when the engine is doing its greatest
work.
_Steam producing_, _Traction_, and _Adhesion_, are the three elements
which determine the ability of an engine to perform work. The
proportions and dimensions of the machine depend upon the duty required
of it; sufficient adhesion for a required effect should be obtained
rather by a proper _distribution_, than by _increase_ of weight.
Fig. 150 shows the relative position of parts in the locomotive engine
as at present constructed in America.
1 2, Grate upon which the fuel is placed.
1 2 3 4, Interior fire-box.
5 6, Exterior fire-box.
7 7 8 8, Shell of the boiler.
9 9, Boiler flues.
10 11 12 13, Exhaust chamber, or smoke box.
14, Steam dome, entrance to steam pipe.
15, Steam pipe.
16, Piston.
18, Piston rod.
19, Connecting rod.
20, Crank.
21, Driving wheel.
22, Blast pipe.
23, Chimney.
27 28, Leading wheels, supporting the front end of the engine,
turning on a swivel, 29.
30, “Blow off” safety-valve.
[Illustration: Fig. 150.]
307. The operation of generating and applying steam for the production
of motion is as follows:—
The boiler and the space between the two fire-boxes being filled with
water, (high enough at least to cover the flues and the top of the inner
box,) fire is applied to the fuel placed upon the grate; the heat which
fills the fire-box and tubes, is communicated to the water and converts
the same to steam; which entering the mouth of the pipe, 15, flows to
the cylinder, where it forces the piston to the end of the stroke. This
motion is transferred through the connecting rods and cranks to the
wheels, which revolving, move the engine upon the rails. At the same
time the eccentrics, placed upon the driving axle, give a motion to the
valve gear, and thence to the valves, by which the admission of steam is
stopped at the first end of the cylinder, and commenced at the other.
The volume of steam which entered during the first half stroke is forced
out of the cylinder by the returning piston, up the blast pipe, and out
at the chimney, where a vacuum is produced, which can be supplied with
air only from the chamber 10 11 12 13; after a few strokes the air is
exhausted from the _chamber_, which can be refilled only by the external
air _drawn through the fuel, furnace, and tubes_. The more complete this
vacuum, the stronger the current of air drawn through the fire, which
(current) is the draft. The admission of fresh air is regulated by a
damper placed at 2. The fuel is placed upon the grate by means of a door
in the rear of the fire-box. The necessary height of water is maintained
in the boiler by pumps worked by the engine, in such a manner as to
secure at all times the proper supply. The proportions and dimensions of
the boiler, the engine, and the carriage, with the rules for obtaining
the same will be considered shortly.
DUTIES EXPECTED OF LOCOMOTIVE ENGINES.
308. The work required of any engine depends upon the nature and amount
of traffic, and upon the physical character of the road.
The nature of the traffic, whether bulky or compact, and whether
requiring quick or slow transport, determines somewhat the number and
size of the trains, and consequently the number and power of the
engines.
A road with steep grades and sharp curves, with the same amount of
traffic, will need stronger engines than a road with easy grades and
large curves.
The amount of motive power and cost of working it, depends in a great
degree upon the disposition of grades as regards the direction of the
traffic movement. The most economically worked road will be either a
level one, or one where the bulk of the traffic is moved _down_ hill.
The mineral, commercial, or agricultural nature of the country,
determines the direction of the traffic, and the physical nature, the
arrangement of the grades.
The different kinds of labor required of locomotives, necessitate the
employment of engines of different proportions; and the different
classes of railways, require engines possessing different amounts of
power.
309. The classification of locomotives should be determined according to
the following relations.
_Department_ depends upon commercial duty.
_Division_ depends upon character of road.
_Order_ depends upon weight of trains.
_Class_ depends upon speed of trains.
NOTE.—The general classification is given at the end of this
chapter.
High rates of speed are generally combined with light loads, and heavy
trains are required to move at the lower velocities.
Great speeds require the rapid production and consumption of a large
bulk of steam of but little density; large wheels and short stroke, that
the ratio of velocities of piston and wheel may be as great as possible.
Heavy trains consume less steam by bulk, per mile, but of a much greater
density, and combine a long stroke with a small wheel, by which great
leverage is obtained.
In general, engines for winter use should be heavier than those for
summer, upon the same ground, as natural causes are more liable to
resist adhesion in the winter.
The locomotive engine may be so proportioned as to run at any speed from
ten to sixty miles per hour, over grades from ten to two hundred feet
per mile, and to carry loads from two hundred to two thousand tons.
The rules by which the necessary dimensions to perform any required duty
are fixed, depend upon the very simplest mechanical laws.
NOTE.—The formulæ expressing the most proper relations to exist
between the several steam-producing and steam-consuming parts are
more reliable than the assertions of any machinist in America, and
though taken from books, are the result of the experience of the
most able and practical men for twenty years. Operatives are too apt
to despise book knowledge, forgetting that the very knowledge so
despised is the result of more practice than a lifetime can afford
them. Railroad managers are too apt to receive as indisputable, the
opinions of men who are _practical_, simply because they understand
nothing of _principle_.
Since the work of D. K. Clark (England) has appeared, any dimension
from the beginning to the end of a locomotive may be fixed, to the
eighth of an inch, with absolute correctness, and there is no excuse
for departing from the proper proportions. It does not follow that
because a locomotive does actually start off and draw the train,
that it is properly made. A race-horse can draw a plough, and a yoke
of oxen a “trotting buggy,” but this is by no means the correct
adaptation of power.
310. The elements which govern the requirements of power are
The maximum grades.
The weight of the train.
The required speed.
And the elements which govern our ability to produce the power needed,
The grate area.
The heating surface.
The cylinder diameter.
The steam pressure.
The stroke.
The diameter of wheels.
The weight upon driving wheels.
MECHANICAL AND PHYSICAL PRINCIPLES GOVERNING THE CONSTRUCTION OF THE
LOCOMOTIVE ENGINE.
RESISTANCE TO THE MOTION OF RAILROAD TRAINS.
311. The exact resistance to the motion of a railroad train cannot be
determined, as some of the elements are so variable; for example, the
state of the weather. An approximate estimate, near enough for practice,
is easily obtained. To arrive at correct data the observations must be
made upon trains working under the same conditions that they are subject
to in practice.
The whole resistance is made up of several partial resistances, some of
which are constant at all speeds, and some of which increase with the
velocity.
The engine and tender resistance is composed of the friction of pistons,
cross heads, slide valves, cranks, eccentrics, pumps, the back pressure
of the blast, and various erratic movements, rolling, twisting, and
pitching together with both wheel and axle friction, which is common to
the engine and tender.
The atmospheric resistance is not due to the direct action of the air
upon the front and sides of the train entirely, but chiefly to the
exhausting action in the rear. The train has, as it were, to pull along
a large column of air like the water in the wake of a ship; form or
amount of frontage has little or no effect. The resistance depends upon
the bulk of the train and its velocity. A train with the same frontage
offers more resistance as its bulk increases.
Oscillatory resistance is caused by irregularities in the surface of the
rails, and increases with the velocity, and also with increase of height
of the centre of gravity of the car or engine.
Frictional resistance may be divided into wheel and axle friction. That
of the axle is composed of two parts, the direct vertical friction on
the journal, and the side friction on the collar, consequent upon
lateral motion. The vertical friction is independent of the surface
pressed or of velocity, but is directly proportional to the pressure,
and the same remark applies to that of the collars. As the diameter of
wheel increases, the oscillation is increased, the centre of gravity
being raised. The direct cause of the vertical friction is the weight of
the car or engine, and of the lateral irregularities in the surface of
the rails, which cause the car to sway from side to side. Wheel friction
which acts between the periphery of the wheel and the surface of the
rail increases with the load, and decreases as the wheel diameter
augments.
For the total resistance to the motion of a railroad train, D. K. Clark
gives the following formula:—
(_V^2_)/171 + 8 = _R_,
Where _R_ is the resistance in lbs. per ton,
and _V_ the velocity in miles per hour.
From this expression we form the following table:—
Velocity in miles per hour. Resistance in lbs. per ton.
10 8.585
12 8.842
15 9.315
20 10.339
25 11.655
30 13.263
40 17.356
50 22.620
60 29.052
100 66.480
From a great number of experiments made by Mr. Clark, the relative
resistance to the motion of inside and outside connected engines is as
follows:—
Inside connections 17
Outside connections 14
The effect of curves, bad state of the road, and adverse winds, amounts
(according to the same author) to the following percentages:—
Bad state of the road 40
Curves 20
Strong head and side winds 20
—
In all 80
The resistance due to grades depends entirely upon the rate of incline,
and is quite independent of all other considerations. The _relative_
effect of grades decreases with the absolute increase of resistance on a
level. Thus common roads admit of steeper grades than do railroads,
because the level resistance is much more upon the former than on the
latter.
The exact determination of the resistance due to any grade depends upon
the very simple mechanical principle, regulating motion upon the
inclined plane. For each foot rise of grade per mile, the resistance per
ton is
2240 × 1/5280.
Thus the resistance to one ton upon a forty feet grade is
2240 × 40/5280 or 17 lbs.
And if we are moving at thirty miles per hour the sum of all other
resistances is, by the formula, or the table at the end of Chapter XIV.,
part I., 13.3 lbs. per ton; whence the whole resistance to the motion of
one ton, at thirty miles per hour, upon a forty feet grade, is
17 + 13.3 or 30.3 lbs.
and one hundred tons would be one hundred times as much. Table 1, at the
end of Chapter XIV., part I., gives the whole resistance to the motion
of trains of from fifty to one thousand tons, moving at speeds varying
from ten to one hundred miles per hour, and table 2 gives the resistance
upon grades from ten to one hundred feet per mile.
TRACTION AND ADHESION.
312. The whole steam pressure upon both pistons, referred by means of
the crank, connecting, and piston rods, and wheel, to the rail, is
called “traction.” It is the _drawing_ power of the engine. Its amount
depends upon the diameter of cylinder, steam pressure, stroke, and
diameter of wheel.
By increasing the steam pressure, we increase the power. By increasing
the cylinder diameter, we increase the power. By increasing the stroke,
we increase the power. By decreasing the wheel diameter, we increase the
power. And by adjusting the dimensions of the above parts, we may give
any desired amount of power to the engine.
The formula expressing the tractive power of an engine, of any
dimensions, is
((2_A_) _P_ × 2_S_)/_C_.
Where _A_ = the area of one piston.
_P_ = the steam pressure in cylinder per square inch,
_S_ = the stroke in inches.
_C_ = the circumference of the wheel in inches.
The formula is expressed verbally as follows: Double the stroke and
multiply it by the total steam pressure on both pistons; divide the
product by the circumference of the driving-wheel in inches.
ADHESION.
313. As observed on page 307, the adhesion or the bite of the wheels
upon the rail is, as an average, from one fifth to one sixth of the
weight; one fifth when the rail is in a good state, and less when wet or
greasy; we cannot depend upon more than one sixth in practice.
Therefore, if the tractive power of an engine is 3,000 lbs. we must, to
make it available, place 3,000 × 6 or 18,000 lbs. upon those wheels
which are connected with the machinery, (driving wheels).
FUEL.
314. The fuels employed in the locomotive engine for the evaporation of
water are wood, coal, and coke. In England the latter is used
exclusively. In America the first has, on account of its cheapness, been
quite generally adopted; but of late railroad companies have been
turning their attention to coal and coke.
The immense beds of coal distributed throughout the United States will
furnish fuel to railroad companies almost without limit. Its position as
well as its amount will render its adoption practicable in nearly all of
the States. Ohio alone contains more coal than all of Great Britain. The
following table is from the iron manufacture of Frederick Overman.
Name of State. Area of Coal-fields.
Georgia 150 square miles.
Maryland 550 square miles.
Alabama 3,400 square miles.
Tennessee 4,300 square miles.
Michigan 5,000 square miles.
Missouri 6,000 square miles.
Indiana 7,700 square miles.
Ohio 11,900 square miles.
Kentucky 13,500 square miles.
Pennsylvania 15,437 square miles.
Virginia 21,195 square miles.
Illinois 44,000 square miles.
———————
In all 133,132 square miles.
315. The following table (also from the works of Overman) gives the
nature and evaporative power of the different American coals.
┌────────────────────┬──────┬──────────┬──────────┬────────┬──────────┐
│ │State │ │ Steam of │Quantity│Percentage│
│ Name of Coal. │where │Percentage│ 212° │of heat │of coke by│
│ │found.│of carbon.│evaporated│ by │ weight. │
│ │ │ │ per lb. │volume. │ │
├────────────────────┼──────┼──────────┼──────────┼────────┼──────────┤
│ │ │ │ │ │ │
│ _Anthracite._ │ │ │ │ │ │
│Beaver Meadow, │ Pa. │ 88.9 │ 10.4│ 94 │ │
│Forest Improvement, │ Pa. │ 90.7 │ 10.8│ 94 │ │
│Lehigh, │ Pa. │ 89.1 │ 9.6│ 94 │ │
│Lackawanna, │ Pa. │ 87.7 │ 10.7│ 94 │ │
│ │ │ │ │ │ │
│ _Coke._ │ │ │ │ │ │
│Midlothian, │ Va. │ │ 10.3│ 92 │ .66 │
│Cumberland, │ Md. │ │ 10.3│ 92 │ .75 │
│ │ │ │ │ │ │
│ _Bituminous._ │ │ │ │ │ │
│Maryland, │ Md. │ 73.5 │ 11.2│ 85 │ │
│Cumberland, │ Md. │ 74.3 │ 11.0│ 85 │ │
│Blossburg, │ Pa. │ 73.4 │ 10.9│ 85 │ .83 │
│Karthans, │ Pa. │ 73.8 │ 9.8│ 85 │ .88 │
│Cambria County, │ Pa. │ 69.4 │ 10.2│ 85 │ │
│Clover Hill, │ Va. │ 56.8 │ 8.5│ 85 │ .68 │
│Tippecanoe, │ Va. │ 64.6 │ 8.5│ 85 │ │
│Pittsburgh, │ Pa. │ 55.0 │ 8.9│ 85 │ .68 │
│Missouri, │ Mo. │ │ │ │ .57 │
└────────────────────┴──────┴──────────┴──────────┴────────┴──────────┘
316. The employment of the several varieties of wood depends more upon
the commercial than the chemical character. The following table shows
the specific gravity, the nature and the evaporative value of the
different species.
┌────────────┬────────┬────────┬────────┬──────────┬────────────┐
│ Species. │Specific│Specific│Specific│Degrees of│ Species. │
│ │gravity │gravity │gravity │heat which│ │
│ │ green. │ air │ kiln │ may be │ │
│ │ │ dried. │ dried. │generated.│ │
│ │ │ │ │ │ │
├────────────┼────────┼────────┼────────┼──────────┼────────────┤
│Hickory, │ │ │ │ 3000 │Hickory. │
│White Oak, │ 1.07 │ 0.71 │ 0.66 │ 3000 │White Oak. │
│Black Oak, │ │ │ │ 3000 │Black Oak. │
│Red Oak, │ 1.05 │ 0.68 │ 0.66 │ 3000 │Red Oak. │
│Beech, │ 0.98 │ 0.59 │ 0.58 │ 3000 │Beech. │
│Birch, │ 0.90 │ 0.63 │ 0.57 │ 3000 │Birch. │
│Maple, │ 0.90 │ 0.64 │ 0.61 │ 3000 │Maple. │
│Yellow Pine,│ │ │ │ 2800 │Yellow Pine.│
│Chestnut, │ │ │ │ 3000 │Chestnut. │
│Pitch Pine, │ │ │ │ 2800 │Pitch Pine. │
│White Pine, │ 0.87 │ 0.47 │ 0.38 │ 2800 │White Pine. │
├────────────┼────────┼────────┼────────┼──────────┼────────────┤
│ Species. │Specific│Specific│Specific│Degrees of│ Species. │
│ │gravity │gravity │gravity │heat which│ │
│ │ green. │ air │ kiln │ may be │ │
│ │ │ dried. │ dried. │generated.│ │
│ │ │ │ │ │ │
└────────────┴────────┴────────┴────────┴──────────┴────────────┘
┌────────────┬──────────┬────────┬──────┬────────┬────────────┐
│ Species. │Percentage│Quantity│Weight│Relative│ Species. │
│ │ of │of heat │of one│value as│ │
│ │Charcoal. │ as to │ cord │ fuel. │ │
│ │ │volume. │ in │ │ │
│ │ │ │ lbs. │ │ │
├────────────┼──────────┼────────┼──────┼────────┼────────────┤
│Hickory, │ 44.69 │ 25 │ 4469 │ 1.00 │Hickory. │
│White Oak, │ 21.62 │ 25 │ 3821 │ 0.81 │White Oak. │
│Black Oak, │ 23.80 │ 25 │ 3254 │ 0.71 │Black Oak. │
│Red Oak, │ 22.43 │ 25 │ 3254 │ 0.69 │Red Oak. │
│Beech, │ 32.36 │ 25 │ 3236 │ 0.65 │Beech. │
│Birch, │ │ 25 │ │ │Birch. │
│Maple, │ 27.00 │ 25 │ 2700 │ 0.57 │Maple. │
│Yellow Pine,│ 24.63 │ 23 │ 2463 │ 0.54 │Yellow Pine.│
│Chestnut, │ 25.25 │ 25 │ 2333 │ 0.52 │Chestnut. │
│Pitch Pine, │ 19.04 │ 23 │ 1904 │ 0.43 │Pitch Pine. │
│White Pine, │ 18.68 │ 23 │ 1868 │ 0.42 │White Pine. │
├────────────┼──────────┼────────┼──────┼────────┼────────────┤
│ Species. │Percentage│Quantity│Weight│Relative│ Species. │
│ │ of │of heat │of one│value as│ │
│ │Charcoal. │ as to │ cord │ fuel. │ │
│ │ │volume. │ in │ │ │
│ │ │ │ lbs. │ │ │
└────────────┴──────────┴────────┴──────┴────────┴────────────┘
Of the relative value of wood and coal, we have the following results of
experience.
In the engines of the Baltimore and Ohio Railway 2.55 lbs. of pine wood
were found equal to one pound of Cumberland coal.
On the Reading Railroad (Pennsylvania), three pounds of pine wood equal
to one pound of Anthracite coal.
Mr. Haswell estimates the best varieties of wood fuel to contain twenty
per cent. of carbon.
Walter R. Johnson found that one pound of wood, upon an average,
evaporated two and one half pounds of water.
The average percentage of coke from American bituminous coal from the
above table is seventy-three per cent., and the average percentage of
carbon, sixty-seven and one half per cent.
317. The following table shows the relative properties of good coke,
coal, and wood.
┌───────────────────────────────────────────────────┬─────┬─────┬─────┐
│ Name of fuel. │Coke.│Coal.│Wood.│
├───────────────────────────────────────────────────┼─────┼─────┼─────┤
│Weight per cubic foot, in lbs. │ 63 │ 80 │ 30 │
│Degrees of heat generated. │4300 │4000 │2800 │
│Percentage of carbon, in the fuel. │ 95 │ 88 │ 20 │
│Economic bulk, or cubic feet required to stow one │ 80 │ 44 │ 107 │
│ ton. │ │ │ │
│Economic, or stowage weight per cubic foot. │ 28 │ 51 │ 21 │
│Cubic feet of air to evaporate one lb. of water. │22.4 │ 32 │ 16 │
│Equivalent economic bulk, to evaporate the same │ 13 │ 10 │ 60 │
│ weight of water. │ │ │ │
│Weight of water evaporated per lb.of fuel in │ 8½ │ 6 │ 2½ │
│ ordinary practice. │ │ │ │
│Relative value as fuel, disregarding the actual │ 100 │ 71 │ 29 │
│ cost. │ │ │ │
└───────────────────────────────────────────────────┴─────┴─────┴─────┘
The power of fuel depends upon the amount of carbon in it.
Pure coke is solid carbon.
Hence its superior value as a heat generator.
OF THE PROCESS OF COKING.
318. Anthracite coal is used for locomotive fuel in its natural state.
It is employed chiefly upon those roads on the eastern slope of the
Alleghanies. The bituminous coal lies in the Mississippi valley, and may
be found anywhere between the summits of the Alleghanies and the Rocky
Mountains. This, in its natural state, contains so much pitchy matter as
to render it unfit for locomotive purposes. Upon being heated, it melts,
runs into a mass, and clogs the grate; requiring frequent poking and a
strong draft. But when the bitumen is burnt off by slow and careful
baking, (as described below,) no fuel equals it.
Just as carbonized wood is charcoal, so carbonized coal is coke. Coke is
bituminous coal deprived of its bitumen, the raw coal being baked in
ovens having vents so regulated as to admit air enough to char, without
consuming the coal. The ovens being closed at the proper time, the fire
is gradually extinguished, and the coke, compacted into large masses,
requiring to be broken up before taken out. Coal may be coked by piling
loosely in heaps, covering with earth, and firing through openings,
which, after forty or fifty hours, are closed. In preparing coke,
however, in the large quantities required for railroads, and that it may
be of the very best quality, a good deal of care must be taken.
Probably in no place more or better coke is made, or the operation more
skilfully carried on, than at the Camden-town station of the London and
North-western Railroad, (England).
The company have built eighteen ovens, in two rows, all discharging
their volatile gases into a horizontal flue terminating in a chimney one
hundred and fifteen feet high; having an internal diameter of eleven
feet, and being three feet thick, (making the external diameter
seventeen feet). The ovens are elliptical, 11 × 12 feet inside, with
walls three feet thick. The height is ten feet, the first three feet
from the ground being solid, and furnished with a fire brick floor, on
which the coal is placed. Each oven communicates with the flue by an
opening in the top two and one half feet by twenty-one inches; which
opening is closed by an iron damper, to regulate the draft. The openings
for the doors are three and one half feet square outside, and two and
three fourths inside, being closed with iron doors four and one half by
five feet, lined with fire brick, and balanced in opening by
counterweights. (The object of the chimney and horizontal flue is to
carry the smoke and unburned gases so far up that they shall not be a
nuisance. In America we might allow the smoke of each oven to escape
through a low chimney of its own, (ten or twelve feet high,) and save
the cost of a large stack; like the coking ovens in our foundries).
The operation of coking is carried on as follows:—Each alternate oven is
charged between eight and ten A. M. every day, with three and one half
tons of good coals. A whisp of straw is then thrown in, which takes fire
from radiation from the top, and inflames the smoke then arising from
the surface, by the reaction of the hot sides and bottom upon the body
of the fuel. In this way the smoke is consumed at the very point of the
process, where it would otherwise be the most abundant. The coking
process is a complete combustion of the volatile principles of the coal.
The mass of coal being first kindled at the surface, where it is
supplied with an abundance of oxygen, because the doors in front and
vents in the rear are open, no more smoke goes from the chimney than
from that of a common kitchen fire. The gas generated from the slightly
heated coal cannot escape destruction in passing up to the bright flame
of the oven. Any deficiency in oxygen for consuming the smoke is
supplied by the air entering the grooves of the dampers.
As the coking process advances most slowly from the top to the bottom,
only one layer is consumed at a time; while the surface is covered with
red-hot cinders, ready to consume any particles of carburetted or
sulphuretted hydrogen gases which may escape from below. The greatest
mass cannot emit more gases than the smallest heap.
The coke being perfectly freed from all smoky and volatile matters, by a
calcination of forty hours, is cooled down to a moderate ignition by
sliding in the dampers and opening the doors, which had been partly
closed during the latter part of the operation.
The coal is now converted into a clean, crystalline, porous, columnar
mass, of a steel-gray color, and so hard as to cut glass. This is broken
up and taken out—coke. It is sometimes extinguished by a watering-pot.
This is wrong, it ought not to be wet, and even more, ought to be
immediately shut up in fire-proof boxes and bins. Even left to itself in
the air, it absorbs moisture rapidly, which must be burned off in the
boiler; it should by all means be kept in a dry place. Mr. Woods
(England) observes, that coke may absorb as much as eight per cent. of
water in going from the oven to the storehouse. The amount of absorption
depends upon the nature of the coke. D. K. Clark records the following,
the coke being immersed in water.
No. 1. Close-grained and good, absorbed 14.5 per cent. of water.
No. 2. Porous and ordinary, absorbed 21 per cent.
No. 3. Very close-grained and good, 9 per cent.
The time of coking may be stated generally as fifty hours, though it is
somewhat improved by being allowed forty hours more; this gives time for
a better consolidation, and gives a firmer, brighter, and more
crystalline mass.
Mr. Gooch, of the Great Western (England) Railroad, experimented upon
the time of coking with the following results.
In oven. Yield per ton of Water evaporated Result.
coal. per lb. of coke.
48 hours 12.71 cwt. 7.1 lbs. 902.
72 hours 12.00 cwt. 7.7 lbs. 924.
Thus, though the yield per ton is decreased by a greater time, the value
of the coke per pound is augmented, and the increase overbalances the
decrease.
Firstrate coal gives from seventy-five to eighty per cent. by weight, of
compact glistening coke, weighing about 14 cwt. per chaldron,
(thirty-six bushels). The bulk is increased from ten to fifty per cent.
In breaking out the coke from the ovens, a great deal is unavoidably
reduced too fine for use in the locomotive furnace under a strong draft;
such may, however, be used in firing up, in standing still, and at the
stations.
In taking the coke from the ovens it should be separated into the three
following classes.
Large coke. Cubes of 9 inches to the side.
Medium coke. Cubes of 6 inches to the side.
Small coke. Cubes of 3 inches to the side.
Pittsburgh coal carefully coked for forty-eight hours, gives
seventy-five per cent., by weight, and one hundred twenty-five per cent.
by bulk, of firstrate, firm, bright, clean coke.
The best test for coke is to place it in water. Water, weighing
sixty-two and one half pounds per cubic foot, should not float good
coke, which ought to weigh sixty-three pounds per cubic foot, therefore
if the coke floats it is too light.
Much of the bituminous coal in the Mississippi valley does not coke, but
burns up. A large part cokes moderately well, but not so well as the
Pittsburgh coal. In estimating for a comparison of fuels, the particular
coal of any location must be tested.
OF THE COMPARATIVE VALUE OF WOOD, COAL, AND COKE.
This question divides itself into two parts,
The relative cost of the different fuels,
and The relative power to produce heat.
319. It does not follow that because coke in England, anthracite in
Pennsylvania, or wood in New England, is the most economical fuel, that
either of the above will be so in Ohio, Indiana, or Illinois, or because
wood is the cheapest in some parts of a State, that it is so throughout,
or even that one fuel should be applied to the whole length of a single
road.
The heat used to evaporate water in the locomotive boiler is developed
by combustion; combustion is produced by chemically combining the oxygen
of the air with the carbon of the fuel; whence, that material containing
in a given cost the largest amount of carbon will produce heat the most
economically.
From the table on page 320, we see that, by bulk, thirteen of coke are
equal to sixty of wood; that one pound of coke evaporates eight and one
half pounds of water; that one pound of wood will evaporate two and one
half pounds of water. Tables of specific gravity give as an average
weight per cubic foot of hard wood, thirty pounds. A cord of wood, by
very careful measurement, contains one hundred cubic feet _solid_, or
one hundred twenty-eight feet _as piled_, taking the average size of
wood; whence a cord will weigh three thousand pounds. And we have as the
relative evaporative efficiency of a cord of wood and a ton of coke,
2240 × 8½ = 19040,
3000 × 2½ = 7500.
Now if the cost of a cord of wood is to the price of a ton of coke as
7,500 to 19,040, it is immaterial which we use.
As an example of the use of the above proportion, when the absolute cost
of wood, coal, coke, and labor are known, take the following.
If wood, cut and ready for burning, costs $3.00 per cord, how much may
be given for a ton of coke?
As 7,500 is to 19,040, so is 300 to 762, or $7.62.
From the same proportion we form the following table.
Cost per cord of wood Price that may be paid
ready for burning. per ton for coke.
(Cents.) (Cents.)
200 508
225 571
250 635
275 698
300 762
325 825
350 877
375 952
400 1016
425 1079
450 1143
475 1206
500 1270
In the comparison above, the maximum evaporative power of wood has been
used, 2½ lbs., and the ordinary power of coke, 8½ lbs. of water per
pound of fuel.
320. In making coke in large quantities, the ovens should be at the
mines, as we thus save transporting the extra weight of coal over coke.
The cost of making coke, exclusive of the cost of the coal, is
approximately as follows:—
10 ovens capable of making annually 5,000 tons of coke, $5,000
Sheds, and apparatus to correspond, 3,000
——————
In all, 8,000
Annual interest at 6 per cent., 480
Annual cost of attendance, 2 men, 1,000
——————
The sum of which is, $1,480
And the cost per ton, 0.296/10
or in round numbers, thirty cents per ton; and if coal is $1.50 per ton,
adding twenty-five per cent. we have $1.87 as the cost of coal that will
make one ton of coke, to which add the cost of making per ton, thirty
cents, and we have as the whole cost of one ton of coke $2.17; and from
the rule on page 327 we see that wood must not cost over $0.85 per cord
to be as economical as coke at $2.17; of course inferior qualities of
coal will give less good coke and change the comparison.
COMBUSTION.
321. The combustible element in all fuels is carbon; the heat necessary
for steam producing, is obtained by combining the carbon of the fuel
with the oxygen of the air, forming carbonic acid gas.
Carbonic acid gas consists of
Oxygen 16} Parts by
Carbon 6} weight.
Atmospheric air consists of
Oxygen 8} Parts by
Nitrogen 28} weight.
Whence, for the combustion of one pound of carbon, we require
Carbon 1.00
Oxygen 2.66
But to obtain 2.66 of oxygen from the atmospheric air, we also use
nitrogen in the proportion of 28 nitrogen to 8 oxygen; whence, for
converting one pound of carbon to carbonic acid, we require
Oxygen 2.66
Nitrogen 9.31
—————
Or 11.97 lbs. of atmospheric air.
From careful observations on the gases passing through the chimneys of
well-constructed boilers, oxygen is found free, varying in amount from
one quarter to one half of the quantity necessary for combustion; this
is owing to the mechanical obstructions to the perfect conversion of the
air arising from leakage through the fuel.
More than the above 11.97 lbs. of air should, therefore, be applied to
the fire for each pound of carbon consumed. Twenty-five per cent. is
found by experience to be a sufficient surplus allowance to convert the
carbon.
Whence, to 11.97
add 3.03
—————
and we have 15.00 lbs. of atmospheric air per lb. of carbon.
Air weighs .075 lbs. per cubic foot, whence 15/.075 or 200 cubic feet of
air are necessary for the proper combustion of one lb. of pure carbon.
Knowing the necessary amount of air for one lb. of carbon, and also the
percentage of carbon in the different kinds of fuel, it becomes a simple
arithmetical operation to fix the bulk of air required for any species
of coal, coke, or wood. The result of such a calculation is shown in the
seventh column of the table on page 320.
“There are two causes why all the heat which fuel may furnish is not
obtained. First, that the inflammable gases evolved by the heat are not
all consumed from want of a sufficient supply of oxygen, the air drawn
through the fire being only sufficient to decompose more fuel than when
decomposed it could burn, or supply with oxygen. The thick smoke that
escapes from a chimney when fresh fuel is thrown on a hot fire, is
unconsumed gas; decomposed from the fuel, but without oxygen enough to
burn—although there may have been a sufficient supply of heat. From this
cause it is, perhaps, that flame is seen coming from the top of a
steamboat chimney which appears to be continuous from the furnace; but
which, in fact, is ignited by contact with the air, having retained
sufficient heat for that purpose.
“All smoke-consuming furnaces are simply means of admitting fresh air to
the unconsumed gases above the fire, which, in a common chimney, will
effect the object, as so large a mass of smoke retains the necessary
amount of heat. This only prevents the nuisance of smoke. To render the
gases thus reheated useful in evaporating water, this supply of oxygen
must be added while the gases are yet in the flues.” This might seem
difficult. Mr. McConnell (England) divides the flues of his locomotives
into two parts, connecting the front ends of the first part and the back
ends of the second part by a space of twelve or fifteen inches, (called
by him a ‘combustion chamber,’) into which he admits any required amount
of fresh air. (See appendix E.)
“A second cause why the full value of the fuel produced is not obtained
is, that so much is abstracted from the gases in passing through long
tubes, that there is not enough left to continue combustion, although
the inflammable gas is still there. That a tube or any substance in the
way of the hot gases does absorb the heat enough to prevent the burning
of the gas, is proved by the action of Davy’s Safety Lamp; this is a
common light surrounded by a wire gauze, which so absorbs the heat from
the flame as to extinguish the latter at the wire; by applying fire
above the gauze, the gas is again kindled, showing plainly that want of
heat above had quenched the flame.” See Stöckhardt’s Chemistry;
translation by C. H. Peirce, M. D., Cambridge, Mass., 1852, page 105.
We require, then, in every boiler, first, to have a sufficient supply of
oxygen to decompose the fuel; next, a quantity above the fire to consume
the produced gases; third, such an arrangement of communicating surface
that so much heat shall not be abstracted from the gases as to deaden
their combustion, until just as they are discharged, at which period
they ought to be consumed. (See appendix E.)
GENERATION OF STEAM.
322. The means of producing the power is of course of the first
importance.
The heat generated in the fire-box is conducted through the tubes to the
exhaust chamber; during which passage it is imparted to the metal, and
from thence absorbed by the adjacent water, which being thereby made
lighter, rises to the surface and gives place to a new supply. The duty
of the furnace is to _generate_, and of the tubes to _communicate_,
heat.
The power of a plain surface to generate steam, depends upon its
position and on the ability of the material to transmit heat An
experiment recorded in Clark’s Railway Machinery, gave the following
results: A cubic metallic box submerged in water and heated from within,
generated steam from its upper surface more than twice as fast as from
the sides when vertical, while the bottom yielded none at all. By
slightly inclining the box the elevated side produced steam much faster,
while the depressed one parted so badly with it as to cause overheating
of the metal.
Acting upon this result, most builders of engines of the present day
give an inclination of from one inch to one quarter of an inch per foot
to the sides of the inner fire-box. That the heat should be applied in
the most effectual manner to the water, the latter should _circulate_
freely around the hot metal, carrying off the heat as soon as it reaches
the surface. As the heat is applied to the _inside_ of the furnace and
tubes, it must, therefore, be the _inside_ dimensions which determine
the amount of heating surface.
NOTE.—If we multiply the interior surface of a tube by the intensity
of heat applied, and divide the product by the exterior surface, we
shall have the intensity at the outside. We also _apply more heat_
to the _outside_ of a tube, which, passing to the inner surface,
augments in intensity per unit of area.
The area of the inner fire-box is not all available for heating, but
requires to be reduced as follows:—
For the fire-door.
For the ferrule area.
For the top stays.
For the side stay bolts.
The area is, therefore,
Sides, twice length by height, less stay bolts.
Back, height by width, less fire-door.
Front, height by width, less ferrule area.
Top, length by width, less top stays.
TUBES.
323. The tubes or flues, varying in number from one hundred to three
hundred, in diameter from one and a half to three inches, and in length
from eight to sixteen feet, furnish the real communicating surface. The
amount of heating surface thus obtained for any length, number, and
diameter, is given in table 10, Chapter XIV., Part I. The surface of a
single tube is found by the formula
(_Ld_3.1416)/144.
Where _L_ = the length,
and _d_ = the diameter, both in inches.
The efficiency of circular tubes is a matter not yet fully understood.
They certainly give a large amount of surface in a small boiler. Pambour
considered the value of tube area per unit of surface, in terms of the
furnace area, as one third only; that is, three square feet of tube
surface as equal to one foot of furnace area, in power of generating
steam. D. K. Clark makes no distinction between the two surfaces, but
observes “there is reason to believe that in the upper semicircular part
of each tube the efficiency principally resides. The winding progressive
motion, observable in tubes of considerable diameter, confirms this
conclusion, as it is with much probability due to the cooling of the
upper portion of the gases of combustion, which, as they cool also,
become heavier and descend laterally, to make room for the hotter smoke
next the bottom of the flue; the general result of which is the spiral
motion of the current in its progress onwards.” Certainly the upper half
of the tube would part much easier with the steam than the under one,
even supposing the applied heat to be the same.
At page 340 of “Overman’s Mechanics,” is the following: “The application
of heat to a _concave_ surface is wrong in principle. The heat in gases
is conducted to other bodies, and among themselves by _convection_ only.
This quality of gases causes the convex form of a vessel to be the most
profitable in absorbing the heat of ascending gases, because the motion
of the gas causes a constant change of particles on the convex body. On
a _concave_ surface exposed to the influence of moving gases, but little
effect is produced; because the particles of gas in the concavity are at
rest. A plane surface is for the same reason an imperfect form for
absorbing heat; it must be exposed at an angle of 45° to obtain the best
effect of the heating gases. In all cases if we wish to obtain the best
effect from the fuel, we should expose a convex surface to the current
of hot air. The direction of the motion of the hot gases decides the
position of the metal which is to absorb the heat; if the current is
horizontal the pipes must be vertical. Gases do not convey heat by
radiation. Tubes and other vessels containing water must be so placed
that the hot gases play around the outside.
“If we lead a current of hot air around a cylinder we shall observe that
a particle of air plays but a short time upon its surface, when it gives
way to another; the particles play almost around the cylinder, and a
concentration or increase of density behind the pipe is the result. The
relative position of pipes in the range is not indifferent, and the
distance of one from the other must be related to their diameter.”
The conducting power of the metal composing the fire-box and tubes, is
one condition which limits the rate of evaporation, when the heat is
abundant on the one side and circulation free on the other, as the water
certainly carries off the heat as fast as it arrives at the outer
surface.
All the heat should be extracted if possible from the gases before they
enter the smoke box. We should so arrange the flues, that without so
much contracting the passage for the exit of the gases as to need too
strong a blast, yet to confine the gases until their full value is
extracted.
Several attempts have been made to apply the ideas of Clark and Overman,
but as yet they have been very indirect and have met with only moderate
success. (See Appendix, E.)
EVAPORATION, PRESSURE, TEMPERATURE, AND DENSITY.
324. The character of work to be done determines the nature of the steam
to be used.
The quantity of work to be done shows the amount of steam to be
produced.
The amount and character of the steam required, fixes the dimensions and
proportions of the boiler.
A cubic foot of water, at a temperature of 62°, weighs 62.321 lbs.
A cubic foot of steam, generated at 212° Fahrenheit, under the
atmospheric pressure (14.7 lbs. per square inch) weighs .03666 lbs.
Whence one cubic foot of water boiled at 212°, makes 1,700 cubic feet of
steam.
The total heat of saturated steam (steam produced in contact with the
water), consists of two parts at all temperatures; the _latent_ and the
_sensible_. The sensible heat is that shown by the thermometer, and
varies with the pressure. The latent heat absorbed during the generation
of steam, amounts to three fourths of the whole. As the temperature at
which the steam is produced increases, the bulk produced from a given
unit of water _decreases_, but the pressure and the total heat increase.
(See C. R. M. p. 59, 61, Regnault’s experiments.)
Table 8, Chapter XIV., Part I., gives the properties of saturated steam,
produced under pressures varying from fifty to one hundred and fifty
pounds per square inch.
The steam produced over water is called saturated, and an application of
heat to an isolated volume of this steam, raises both the temperature
and pressure, the volume and density remaining the same. The saturation
is then no more, and the steam is surcharged. If the heat be withdrawn,
pressure and density fall, and a precipitation of water takes place. The
priming of steam in a cylinder is an illustration of this. D. K. Clark,
in Railway Machinery, urges the necessity of thoroughly drying the steam
before applying it to the pistons in this manner, he says, ten per cent.
may be gained at low velocities, and in some cases forty per cent. at
high speeds.
MOTION OF STEAM IN PIPES.
325. Steam may flow from any vessel into a vacuum, into the open air, or
into steam of a less density. The velocity of efflux of steam is the
same as that of a stream of water flowing under a pressure equal to that
of the steam. Steam flowing into the atmosphere of course has 14.7 lbs.
per inch resistance to meet, which is equivalent to a reduction of 14.7
lbs. of its pressure. The following numbers show the velocity of efflux
of steam into the open air under different pressures.
Pressure. Velocity, in feet per second.
50 1791
60 1838
70 1877
80 1919
90 1936
100 1957
110 1972
120 1990
130 2004
LOSS OF PRESSURE CAUSED BY THE MOTION OF STEAM.
326. The loss of power suffered by the steam during its motion from the
boiler to the cylinder is caused by condensation in passing through cold
pipes, and by friction and sharp bends. The total fall that may be
caused by a combination of circumstances is from ten to fifteen per
cent. at low velocities, and from fifty to sixty per cent. at high
speeds. The fall of pressure decreases as the square of the velocity of
motion, that is, the fall at a velocity of 1,600 feet per second is four
times as great as the fall at a velocity of eight hundred feet. By well
protecting the steam pipes and cylinders, and by drying, it may be
worked at nearly its initial pressure.
APPLICATION OF STEAM.
327. The steam being generated in the boiler, and conveyed to the
cylinders, is admitted alternately to the opposite sides of the piston,
by which its reciprocations are produced. The first valve applied to
regulating the admission of steam to the cylinder was so arranged that
the steam was admitted during the whole stroke; at the end of which,
ingress stopped and egress commenced at the first end, and ingress
commenced at the second end simultaneously; this caused an unnecessary
resistance to the return movement, by preventing the quick escape of the
first cylinder-full, which had to be _pushed_ out, instead of _flowing_
out. The continuance of the full pressure upon the piston also, until
the end of the stroke, caused a dangerous momentum to be given to the
reciprocating machinery.
These evils are obviated by causing the exhaust passage to open, and the
entering port to close a little _before_ the end of the stroke. This is
effected by moving the valve bodily forward.
Now it is well ascertained, that with very free steam entrances, if we
allow the cylinder to be only partially filled, and then cause the steam
to expand itself, more work is accomplished with a given bulk than when
the cylinder is completely filled. That the steam may have time thus to
expand itself, the return of the piston must not take place until after
the suppression (the stopping of admission).
328. There are four positions of the valve during each half stroke, and
three distinct actions of steam in the same period, which are as
follows:—
Position of valve. Action of steam.
Admission (A).
Entrance.
Suppression.
Expansion.
Release.
Compression.
Admission (B).
The longer the time between suppression and release, of course the more
complete will be the expansion. The entire force of the steam should not
(even if possible) be extracted, as a certain force is necessary to
produce a blast.
The time of expansion is regulated by the proportions of the valve
cover; which may be so adjusted as to fix suppression or release at any
desired part of the stroke.
By the above means any rate of expansion may be established, but when
once fixed will remain the same, the valve being invariably connected
with the eccentric, and thus partaking of its motion.
329. The great step which has been taken in locomotive construction
since 1840 is the invention of the “link motion,” by Williams, which,
perfected by Howe, admits of varying the travel of the valve, and thus
using the steam under any desired rate of expansion. By this
arrangement, the power of regulating the force applied to the piston,
according to the work to be done, is placed in the engineer’s hands, to
be used at any time under whatever conditions the engine may be working.
By this arrangement, two eccentrics to each cylinder are required, (and
in some dispositions of the link, only one). Fig. 150 shows the general
plan of varying the expansion. A fixed relation evidently exists between
the points A and B, two distinct motions are communicated by the
eccentrics C and D through the rods E and F, to the two ends G H, of the
curved link L; the eccentrics are so adjusted upon the driving axle as
to cause the two ends of the link to move in opposite directions, whence
at some point midway there is no motion; the link is movable
(vertically) upon the suspended point L, so that by bringing L to one
end or the other, the motion given to the rod _m_ partakes of the motion
of that eccentric which is nearest to it. Thus the movement of the valve
may be checked, or even reversed in a second, while the engine is in
motion, and that without sudden shocks.
The link is moved by the levers _n n′ n″_ terminating in the bar O,
placed at the foot board of the engine in reach of the engineer. Applied
to this is an iron sector _h h′ h″_ made fast to the frame of the
engine. Now when the point L is in such a part of the link as to place
the valve in a position admitting steam for any fraction of the stroke,
let the point at which the bar O stands upon the sector be marked for
that admission; and so also for any number of different degrees of
expansion. It is plain that the engineer may thus, by fixing the lever
O, use any percentage of admission that is required; and may always know
just what duty the engine is doing. Five minutes’ examination of the
reversing gear upon an engine will render the operation plain.
330. If we cut the steam off at half stroke and then allow it to expand,
of course the mean pressure during the whole stroke is less than that at
entering. The effective mean pressure obtained by any degree of
expansion is shown by the following formula, deduced from a mean of
forty-nine experiments with the Great Britain locomotive, (Great Western
Railroad, England,) having cylinders 18 × 24.
13.5(√(_a_) – 28) = mean pressure
where _a_ is the percentage of admission.
From this formula, table 11 is made.