EXPRESS TRAINS.

413. Express trains are a source of vast expense, directly and indirectly, which can never be repaid by any practicable tariff to be levied upon them. Dr. Lardner, (1850):—

Resolved, That this meeting recommend the adoption of a higher rate of fare upon express passenger trains, corresponding in some degree to the increased cost of such trains.—American Railroad Convention of 1854.

INCREASED COST OF WORKING.

This is due to the extra wear and tear of engines, cars, and road, from increased speed, and also to the delays occasioned to other trains in motion at the same time.

The influence of express trains is felt not only by themselves, but by nearly all the trains upon the road.

Note.—To determine the most economical speed, regard need only be had to the variable elements of cost, namely: cost of power, and maintenance of superstructure, and rolling stock; assuming the power expended as the resistance, and the cost of repairs of machinery and superstructure as the velocity, we form the following table:—

Velocity in miles per hour.	Resistance in pounds per ton.	Hours con. in going 300 miles.	Product of column 2 × 3.	Cost of repairs.	Result.
10	8.6	30	258	100	358
15	9.3	20	186	150	336
20	10.3	15	154	200	354
25	11.6	12	139	250	389
30	13.3	10	133	300	433
35	15.2	8.60	131	350	481
40	17.3	7.50	130	400	530
45	19.8	6.67	132
50	22.6	6	136
60	29.1	5	145
100	66.5	3	200

The result is found by adding the product of columns 2 and 3, or column 4 to column 5, from which the minimum cost is seen to be produced by a very little more than fifteen miles per hour. The variable (and above assumed) element is the rate of increase of cost of maintenance.

All trains in motion at the same time within a certain distance of the express, must be kept waiting with steam up, or be driven with extra velocities in order to keep out of the way.

Where the time table is so arranged as to call for speed nearly equal to the full capacity of the engine, it is very obvious that the risks of failure in “making time” must be much greater than at reduced rates; and when they do occur, the efforts made to gain time must be correspondingly greater and uncertain. A single example will be sufficient to show this:—

A train whose prescribed rate of speed is thirty miles an hour, having lost five minutes of time, and being required to gain it, in order to meet and pass an opposing train at a station ten miles distant, must necessarily increase its speed to forty miles an hour; and a train whose prescribed rate of speed is forty miles an hour, under similar circumstances, must increase its speed to sixty miles an hour; in the former case it would probably be accomplished, whilst in the latter it would more probably result in failure; or, if successful, it would be so at a fearful risk of accident.

But a failure in either case would have the effect of retarding the movement of the opposing train, deranging the time of those of the same and of an inferior class in both directions, involving, perhaps, on the part of the latter, the necessity of similar struggles for time, and thus may prove the primary cause of accident to all trains whose movements may have been affected thereby.

The first cost of locomotives, (assuming the cost to increase with the weight,) is thirty per cent. greater for express trains, than for those of the second or third class.

The cost of repairs being assumed as the product of the weight by distance run, and this distance being the same, is as the weight, or increased thirty per cent. (This assumes the power to be equally well adapted.)

The cost of cars does not (though it ought), differ much for express or slow trains; the cost of repairs will certainly be increased.

The interest of construction capital to be charged to expresses, will be, their mileage proportion plus any expense which may have been incurred in reducing curves and grades; the proportion of repairs of superstructure, charged to expresses, will depend on their weight. The locomotive causes 25
29 of the wear of rails, and as the weight of the engines is increased thirty per cent., the increased wear will be of 15
58.

The use of stations and of employees costs no more for express than for accommodation trains.

The repairs of locomotives will be nearly, if not quite, as the product of their weight by the distance run; and this, from the above, will be thirty per cent. greater on an express than on an ordinary train, the distance being the same.

The carriages for express trains ought to be at once stronger and more convenient than those for the slower work, the shocks arising from irregularities in the rails being very much greater as velocity increases; and the runs being very long, passengers require easier seats, even, in some cases, accommodation for sleeping. The cost for repairs, therefore, of express cars, would be somewhat greater than for any others.

COST AND MAINTENANCE OF WAY AND WORKS.

As the speed is increased, the relative effect of grade and curves is lessened, but the absolute danger of passing curves is increased. Express trains require larger radius of curvature, or greater elevation of exterior rail than others, which extra elevation causes an unnecessary resistance to all other trains. The rails to resist large and heavy wheels must be heavier and more firmly fastened. All bridges and viaducts (particularly if on grades or curves), will require more strength to resist the increased shocks to which they will be subject. The wear of rails is nearly as the weight passing over them; the wear of rails consequent upon stopping and starting the trains depends upon the momentum of the train which is to be imparted to them.

The proportion, in which the working expenses are distributed under the several heads on the larger railways of Great Britain, is as follows:—

Direction and management,	7
Way and works,	16
Locomotive department,	35
Cars,	38
Sundries,	4

	100

And the percentage of increase due to fast travelling, to be applied to the several items of expense, with the resulting increase in total expense, is shown below.

Direction and management,	7	0	=	0.0
Way and works,	16	27	=	4.3
Locomotive department,	35	30	=	10.5
Cars,	38	10	=	3.8
Sundries,	4	0	=	0.0

		100		18.6

or 18 per cent. increase, nearly.

Express trains, as worked on many roads, run at an unnecessary speed, to make up for frequent stops. Overcoming a long distance in a short time, depends as much on decrease in the number of stops, as increase in the speed.

The following figures show the effect of decreasing the number of stops.

A train running 400 miles, and stopping once in fifty miles, each stop being five minutes, (including coming to rest and starting,) to pass over the whole distance in eight hours, must run fifty-five miles per hour.

Stopping once in twenty miles, sixty-three miles per hour.

Stopping once in ten miles, eighty-six miles per hour.

The following table shows the velocities of the different classes of trains in England, France, and Belgium, including and excluding stops.

	Express.	1st class.	2d class.	3d class.

EXCLUDING STOPS.

England,	43.9	32.8	32.8	25.2 miles per hour.
France,		27.5	24.3	28.1 miles per hour.
Belgium,		26.2	25.7	27.6 miles per hour.

	Express.	1st class.	2d class.	3d class.

INCLUDING STOPS.

England,	36.5	24.8	24.8	17.5 miles per hour.
France,		22.1	17.9	19.9 miles per hour.
Belgium,		20.7	19.3	18.1 miles per hour.

The distances at which the different classes of trains stop in the several countries, are as follows:—

	1st class.	2d class.	3d class.	Express.

TRAINS STOP ONCE IN

England,	8 miles,	8 miles,	5 miles,	24 miles.
France,	10 miles,	6 miles,	6 miles,	—— miles.
Belgium,	6.8 miles,	5.6 miles,	5 miles,	—— miles.

OF THE INCREASED DANGER OF FAST TRAVELLING.

The causes of accident, beyond the control of passengers, are

Collision by opposition.

Collision by overtaking.

Derailment by misplaced switches and draws.

Derailment by obstacles upon the rails.

Breakage of machinery.

Failure of track or bridges.

Fire.

Boiler explosions.

Those causes which are aggravated by fast travelling are the first, second, fifth, and sixth; the effects of all are worse at high speeds than at low.

The proportion of accidents due to each of these causes, taken at random from one hundred cases on English railways, are as follows:—

Collision,	56
Breaking of machinery,	18
Failure of the road,	14
Misplaced switches,	5
Obstacles on rails,	6
Boiler explosion,	1

	100

In collision by opposition, the engines, tenders, and baggage cars must be demolished before the shock reaches the passengers; in collision by overtaking, the engine of the rear train plunges at once into the last passenger car of the leading train; the force in the last case is the difference of the speeds, in the former the sum. The increase of danger from this cause, attendant upon express trains, is due, first, to the longer time required in stopping, and second, in the greater shock if collision occurs.

Breakage of machinery is more liable to take place while wheels are revolving 25,000 times per hour, than when the speed is less.

Failure of the superstructure of bridges, (particularly when on curves or grades,) is more liable to take place at high than at low velocities.

Accidents from obstacles upon the track, from fire, boiler explosions, and misplaced switches, are no more attendant upon express than upon other trains, but the consequences are worse with the high speeds.

From the analysis above, of one hundred accidents, it appears that eighty-eight per cent. of the cases are due to the causes that are aggravated by increase of speed, and if we assume the aggravation of collision, and breakage of machinery, to be (speed being doubled) as two to one, the danger of travelling a fixed distance, by express, is eighty-eight per cent. greater than by a slow train.