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thus a=b=

R
R+s

; (3) for either axle in

THE author draws attention first to the case of a simple wagon with rigid wheel-base, and on each of whose axles outer contact, and the other on the midtwo wheels with coned tires are immov- dle of the line; (4) for a diagonal posiably fixed. He gives the most general form of equation between work and tion, thus a= resistance on a curve, and thence derives the form it takes in practical cases, viz.,

L

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or=

R+8

1 R or for b R+s' R the wagon set fairly on the middle of the line, thus a=b=1; (5) for inner contact R+s R

K=Gƒ( 1/1/ + R-116) (1) of both axles, thus a=b=

R Ꭱ

b

...

where K is the resistance, G whole load For investigation of actual resistances on one axle, f coefficient of friction, L and wear, the position assumed by the wheel base, R radius of a curve, s the wagon under the conditions that generwidth of gauge from center to center of ally hold in practice must be ascertained. rails, a ratio of running radius of inner Experience proved that the front axle of to that of outer wheel on front axle, and a wagon with rigid wheel-base always b the same ratio for hind axle. The part ran in outer contact. Theory shows L that it could only be otherwise if the Gf is due to transverse sliding, the R wheel-base were the gauge. Less rest to the rotation of one wheel about was known of the behavior of the hind the other on each axle. This expression axle; to solve the question trials were shows that the resistance is small for made on a line with curves of radii down light load, smooth rails, narrow gauge, short wheel-base, large radius of curvature, and values of a and b near the limit R

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to 8 chains, with wagons of 16.4 and 8.2 feet wheel-bases, in which an arrangement of mirrors showed the play between flange and rail to occupants of the wagon. It was found that the tendency of the hind axle to run in inner contact was much greater for the long than for the short wheel-base; for the (2) latter indeed it ran in outer contact when the curvature was small. Reasons (3) are then given for assuming the law, that the hind axle of a four-wheeled wagon with rigid wheel-base always takes a radial position if sufficient play be provided on the line. Its accuracy (5) was confirmed by experiments with a model. Hence the distance between

(4)

(2) holds for both axles in outer contact, outer rail and outer flange of hind axle

being the height of a chord equal to f,=, and the second member may, in twice the wheel-base is

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most cases, be neglected. K, and K, have not, to the author's knowledge, (6) been taken into account hitherto. K arising from horizontal shifting causes wear of the rail tops, and affects the inner rail most; K, causes wear of the axle seats and holders only; K, resem

then:

(7)

and corresponding to these values of obles the action of a blunt cutter, the we have for the sine of the angle of con

tact of outer front wheel

or

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sin ẞ= +
2R L

flange of the outer front wheel being the cutter, and the inside of outer rail the object cut. For carriages in a train the (8) value of Pais altered by forces in the couplings, and the author investigates this effect minutely.

(9)

Dealing next with six-wheeled carThe constraint necessary to alter the riages, if to the middle axle no more position of a wagon turning a curve than the necessary play be given by arises partly through the axle seats, but thin flanges, cylindrical are better than chiefly from the lateral pressure between conical tires; but with the usual spread the rail and the outer flange of the front of gauge at curves no lateral play is axle. For the former the maximum value required for the middle axle. If there be no spread of gauge, safety requires is K=Gff, where f, is coeffi- a lateral play of 0.2 inch only for a

R

d

cient of friction between axle and axle

wheel-base suited to the curve; but a seat, d diameter of an axle-arm, and "inch on a curve of 8.5 chains radius. wheel-base of 19.7 feet would require 0.8 radius of a wheel; this is a consequence Supposing the loads G on the end axles of the geometrical connection of the axles and wagon. The expression for equal, and that on the middle axle a the lateral pressure is

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fraction n of each of these; so that, Q being the weight of the carriage,

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nQ
n+2'

the whole re

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for inner contact of middle axle:

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where V is the velocity, g the accelera-
tion for gravity, h the cant of outer rail,
and a the angle of conicity of the tires:
here no allowance is made for friction K'''
between flange and rail, but iff, be the
coefficient, and the actual place of con- for outer contact of middle axle:
tact be considered, we have for lateral
pressure, K,=
Pa × fr
three members of Pa are due to the force
to make the front axle take its altered

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adapted to neutralize centrifugal force, comotive, a bogie be used in front, with

is obtained from the equation

V2 gR

h=s =(-o tana).

a rigid axle behind, the resistance, though less than for a rigid four wheeler, (13) is large compared with the value just given. Since bogies with more than one

tion, and for locomotives of reducing the load on the front outer wheel, numerous systems of flexible single axles have been devised. Of these the Adams

After treating generally of the ques- axle have the disadvantage of complication of spread of gauge, the author sums up with the conclusions:-1. Fourwheeled wagons with rigid wheel-base pass curves with greater safety when there is no spread of gauge, and the flanges are unworn, since the angle of contact is then diminished by half: 2. Such wagons run on curves of the minimum radii for their wheel-bases, and

with the usual spread of gauge, with the

hind axle in inner contact, and with less

constraint than if there were no spread of gauge: 3. With the usual spread of gauge the curve resistance is less for worn-out than for unworn tires.

Security is dependent on the relations existing for the outer front wheel, and is greater the greater the vertical, the less the lateral pressure, the smaller the angle of contact, and the more sharply rounded and vertical the places of contact between flange and rail.

The curve resistance and wear are less-the less the vertical and lateral pressure, the less the angle of contact, and the nearer the places of contact between flange and rail lie to the crown of the rail, and for the least possible rounding of these places.

A table is given with corresponding values of R, L, V, h, 6, þ, lateral pressure, and total curve resistance of fourwheeled wagons and locomotives with rigid wheel base.

Arrangements for facilitating the use of longer carriages on curves are next considered. When a carriage constructed on the American bogie system runs on a curve, each car will clearly follow a tangential direction till it runs against the outer rail, and then assume the position natural to a rigid-axled wagon. Owing to the smallness of the distance

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2 R

( being the bogie wheel base) of the hind axle of each car from the outer rail equation (2) holds approximately for each; hence the whole curve resistance to produce the altered direction of the carriage is 2 G1ƒ· G, being the load

L

R'

on a single car axle. If, again, for a lo

guided axle, and the Bissel front axle for locomotives, have been laid aside on account of their dependency for steady motion on the presence of two rigid axles of long wheel-base.

Mr. John Clark devised a three-axled the axle boxes were so connected by wagon, used on Mount Cenis, in which mechanism that the yielding of the middle axle through the height of a chord equal to the wheel-base caused the end yielding of the middle axle, the angu axles to run radially. If λ denote the lar turning of the end axles, since Ø

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L and sin = 2 R'

the condition to

L2 8 R' be fulfilled by the mechanism is sin λ ΦΞ4 -41, which shows that it will suit

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the Cleminson system on the same princurves of any radius. With this, and ciple, the curve resistance and lateral pressure can be almost totally removed. For a locomotive with the Nowotny front axle, which differs from the Bissel axle in having the pivot above the middle of the line joining the wheel centers, instead of being somewhat behind this duration of the front tires, and proporposition, experience has shown that the tionally of the rails, is four times for a rigid axled locomotive of the same wheel-base.

In the search for a simple system of flexible axles for wagons, the central pivot being laid aside, an arrangment allowing the journals with their covers to slide in the long direction of the wagon against single or double incline seats in the boxes, with a central holder to neutralize shocks, was adopted with success. A simpler method lay in providing suitable play between axle box and holder, with the necessary turning power be tween bearing spring and axle box. Several forms of couplings for flexible axles are shown by drawings.

ON THE CONSTRUCTION, PERFORMANCE, AND WORKING OF LIGHT RAILWAY LOCOMOTIVES.

By Hr. VON BORRIES, of Hanover.

Foreign Abstracts of the Institution of Civil Engineers.

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THIS is an essay towards settling the luggage or passengers as part of their conditions, leading dimensions, &c., of load.* A four-coupled engine is to be engines for working "secondary or preferred, unless the traffic is heavy, or light railways, based on the general prin- the conditions unfavorable. The train ciples laid down in Germany for the con- officials should be reduced in number as struction of locomotives, and the building far as possible, since each may be taken and working of light railways. Three to absorb in wages from 6 to 15 per cent. different gauges are considered through- of the working cost. On light railways out, viz.: standard gauge (4 feet 8 the full services of both driver and fireinches), meter gauge (3 feet 33 inches), man are not needed for the engine, and and meter gauge (2 feet 5 inches). therefore the latter may also act as a brakesman, working not only the engine brakes, but also those in the front van, which should be placed in communication with the engine. The guard would also act as a brakesman for his own van, which should always be at the rear of the train, and no other brakesman would be necessary. Continuous brakes are not worth their expense, especially looking to the probability of goods wagons being

Load per Axle.-This is the first element to be fixed in all rolling stock. In light railways the rails are proportioned to the heaviest goods wagon which will run on the line, and the weight per axle of the locomotive must conform to this. With standard gauge, where main line wagons may come over the line, the load per axle should be taken at 9 tons; with meter gauge at 71⁄2 tons (taking 10 tons as load of wagon, and 5 tons as its mixed in the train; but, as a provision weight); with meter gauge at 33 tons (5 tons for load, 2 tons for weight of wagon). These figures agree with the rules of the German Railway Union, except that they give 5 tons for meter gauge, which seems excessive.

for emergency, such goods wagons may be fitted with lever brakes on the Exter system, which may be worked from the engine by means of a cord. The engines should have a gangway at each side, and provision at each end for stepping on to an adjoining vehicle.

General Principles. The leading principles should be simplicity of con- Provisions against Fire and against struction and facility of maintenance. the frightening of Horses.-The danger The blast pipe should be retained, as the of fire must be completely obviated by most economical and automatic method proper spark catchers or extinguishers, of forcing the fire, and the condensation and by closing in the ash pan, so that no of the steam, sometimes insisted on in pop- cinders can escape. Horses are found ulous districts, should be avoided as much to be frightened mainly by the sight of as possible, on account of the expense. a carriage, apparently running of itself, The engines should be tank engines, by violent puffs of smoke or steam (not four-coupled or six-coupled, according the mere escape of steam at the chimto the work to be done. They should ney), and by rapidly moving gear. These be no heavier than is required to produce causes can be removed to a great extent, the requisite tractive force by adhesion, if not entirely, by boxing up the gear, and the speed on steep gradients should by placing an air vessel in the exhaust be lowered so that a boiler suited to this pipe, and by turning the escape from the weight may generate the needful amount cylinders and safety valves into the conof steam. For very steep gradients, the requisite weight may be obtained by using special engines, designed to carry 369: "Van Locomotive."

* Vide Minutes of Proceedings Inst. C.E., Vol. lxi., p.

denser, and that from the injector into as 3 feet 3 inches, the same as for the carthe tank.

riages, which, at 18 miles an hour, the
maximum speed, gives 2.8 revolutions per
second. For the narrow gauges the
speed should not exceed 12 to 15 miles
an hour, and the diameter of the wheels
may be from 2 feet to 2 feet 8 inches.
The length of stroke should be about
half the wheel diameter. The cylinder
diameter may be calculated (for metric
measures) from the following equation:
Tractive force
where 0.011
3.4

Leading Dimensions.-The engines are taken to weigh about 90 lbs. per square foot of heating surface; it being assumed that they are built on the Krauss system, and that the grate surface and tank capacity will be varied according to the gauge. The useful steam generated is taken at 5 lbs. per square foot of heating surface per hour, with a pressure of 150 lbs. The latest cut-off, on the steepest gradient, should not exceed 0.4 of d=0.011x the stroke, which gives mean pressure = 97 lbs., and work done per pound of is Koch's value for the co-efficient of steam = 102,000 foot-lbs. The adhesion machine friction in locomotives. The co-efficient, with sanded rails, may be taken at 0.15; whence, assuming that the engine may lose 11 per cent. of its full weight, through consumption of fuel and water, the tractive force may be taken as 0.133 of the full weight. The wheel diameter for standard gauge may be taken

grate surface should be as large as possible, say heating surface for standard gauge, for meter gauge. The tank may hold 3 cubic feet, and the bunkers 1.1 cubic feet, per ton of engine weight. The above and other leading particulars are combined in the following table:

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Performance of the Engines on va- dients below the steepest at a proper rious Gradients.-The various figures limit; the principle being that the genassumed above give an effective power eration of steam should never be faster for the engine of about 6.3 HP. per ton than it is on the steepest gradient. If weight. The tractive force per ton this gradient is greater than 1 in 100, weight, including friction, will be about the evaporation, with lighter gradients 321 lbs., whence it is calculated that the and higher speed, will remain about the speed required to develop the maximum tractive force is 7 miles an hour; and this should therefore be taken as the speed on the steepest gradient of the

On this assumption the maximum haulage load on various gradients, exclusive of the engine, is given by the table on next page.

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same. If it is less than 1 in 100, the evaporation diminishes rapidly on lighter gradients, and the speed must therefore be regulated by some positive limit, which in Germany is 18 miles an hour.

The gross consumption of water per hour may be taken at 6.5 lbs. per square foot of heating surface, or 0.075 of the weight of the engine. The total weight of water in the tank may be taken at 01 of the engine weight; and, assuming

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