At 80 miles an hour (which is twice as fast as locomotives can go) the power required to overcome the friction of the air in the tunnel, would (on the calculation that it increases according to the square of the velocity) be equal to that of 29,196 horses; which is nearly 130 times as much as the locomotive engines would require: though, owing to this power operating only 22½ minutes, instead of an hour and a half, and to fuel in large stationary engines doing sixteen times as much work as in locomotives, the expense would be only twice as great as in the locomotives, exclusive of the whole of the most enormous expense now incurred, by the repairs of the locomotives being saved (which would, alone, more than make up the difference) and also exclusive of the tunnel costing only one quarter of what the railway has cost, and of the rate of conveyance being four times as fast.
But it is not with respect to a tunnel only, that the resistance of the air opposes an impediment: this resistance being found so serious an obstacle to the progress of the locomotive engines and their loads, that in all trials of, or experiments with them, the state and direction of the wind is noted and allowed for. In the “Account of the Liverpool and Manchester Railway,” published by the Treasurer of that Company (H. Booth, Esq.), he says: “Moreover, at great velocities, the resistance of the air must not be left out of the calculation. At ten miles per hour, it has been found by experiment, that the resistance of the atmosphere is about half a pound weight on a square foot of flat surface; at fifteen miles, the resistance is 1lb. per square foot; and at twenty miles, about 2lbs. per square foot: the increased resistance being, nearly, as the squares of the velocities.” [40]
The surface opposed to the air by a steam-coach, the engines of which its proprietor told me were equal to ten horses power, I found to be 30 square feet. That, opposed by another, the engines of which were said to be equal to twenty horses power, I found to be above 50 square feet: while, when carrying four outsides on the front of the roof, this coach exposed nearly 70 square feet to the action of the air. The surface opposed to the air by the large locomotive engines now used on the Liverpool and Manchester Railway, I understand (when chimney, axle-tree, wheels, and every thing that cuts the air, is taken into account) to be about 40 feet square. Supposing it to be so, at 20 miles an hour, the air will oppose resistance equal to 80lbs. to the progress of the engine; which resistance having to be overcome at the rate of 1760 feet per minute, is equal to 4¼ horses power. At 40 miles an hour, this resistance would be 320lbs.; which resistance having to be overcome at the rate of 3526 feet per minute, would be equal to 34 horses power. At 80 miles an hour, the resistance of the air would be 1280lbs.; which resistance, having to be overcome at the rate of 7,040 feet per minute, would be equal to 270 horses power; while at 100, and 120 miles an hour, the power required would be, respectively, that of 528 and 912 horses.
Now, as the force required at 80 miles an hour, is a few times more than the whole power of those engines, and as Dr. Hutton found that giving the moving body the form of a cone, the height of which equalled the diameter of its base, diminished the resistance of the air only half, it may serve to shew that the statements of those who have given currency to the opinion that we may be conveyed at any velocity on railways, are promulgated by persons who pronounce upon questions without examining them: since, in addition to this resistance of the air to the locomotive engines themselves, would be its resistance to the tenders, and coaches or waggons they drew; and that, too, independent of, and additional to, the resistance opposed by the railway friction of the engines, tenders, and loads, behind them.
That something of this kind prevents very high velocities from being attained on railways, is evident. At the locomotive engine competition on the Liverpool and Manchester Railway four years ago, velocities of from 35 to 40 miles an hour, were attained by engines which were not one-tenth the power of some of those now used; while, at the opening of that railway, three years ago, the engine by which the surgeon was brought to Mr. Huskisson, after his deplorable accident, went 15 miles in 25 minutes, which is at the rate of 36 miles an hour. Yet do not the so much more powerful locomotives now used on that road, go faster than this: a circumstance which may prove that the limit to the velocity of railway conveyance, will arise from a source not calculated on.
“But,” it may be observed, “this objection to the possibility of very high velocities on railways, is counterbalanced by the dilemma in which you place yourself, by supposing it to be possible that any such power as that of 29,196 horses, can, at one time, be made to operate on a tunnel; since, as relates to practical application, it would prove ‘an impossible quantity.’”
The inference I deny; and, when necessary, will disprove. [41] But the term I accept; and will avail myself of, to shew that it is equally “an impossible quantity” that even if a tunnel were ten times as long as one between Manchester and Liverpool, the friction of air which is caused to move in it, in consequence of exhaustion taking place at the opposite end, can ever oppose an impediment such as is here adverted to.
According to the opinion that the friction of the air would increase as the square of the velocity, the friction of the column of air, which, when moved by exhaustion at the rate of 20 miles an hour, in a tunnel eight feet diameter and a mile long, was 288lbs., would, when moved at the rate of 80 miles an hour, be 4608lbs.; which, on the whole area of the tunnel, would be equal to 1.3 inches of mercury. Therefore, supposing that at every mile of a tunnel extending from Liverpool to Manchester, barometer tubes were to be inserted, the bottoms (or basin ends) of which should be open to the atmosphere, and the tops open to the inside of the tunnel, the mercury in each successive tube would (reckoning towards the end at which the exhaustion took place) rise 1.3 inches higher than that in the preceding.
Now as 1.3×23 gives 30, while 1.3×30 gives 39, it appears that at 23 miles from that end of the tunnel at which the atmosphere was admitted, and seven from that where the exhaustion took place, there would be such a vacuum as would raise mercury the whole height of the barometric column; while, at the end of the 30 miles there would be—or rather ought to be, according to this calculation—39 inches of mercury; or a vacuum and a third; which, in addition to its being “an impossible quantity,” places those who contend that the resistance of the friction of air which is caused to move through a tunnel by the pressure of the atmosphere in consequence of exhaustion taking place at the opposite end, increases according to the square of the velocity, in the dilemma of assuming that there is a certain place in a tunnel 30 miles long, where, notwithstanding that a man, a horse, or even an elephant, might walk as freely and unobstructedly along, as a mouse could through a rat-hole, that subtle, permeating, and all-pervading element which we breathe, would, like the stream of the Jordan when under the influence of the miracle by which the Israelites passed over that river, stop, stick fast, and be unable to move farther; a position, which necessarily throws us for an escape from this dilemma, on the conclusion that, though it is certain that the friction of air against the inside of the tunnel will be an impediment, and though it is probable that this impediment will be of some importance, yet must it be equally certain that it will not be the serious impediment which it is supposed it will prove: and it may therefore, safely be assumed, that the objection which presents an insuperable obstacle in the minds of the many who have condemned the method of operation by exhaustion which I propose (because they deemed it analogous to operating per plenum) becomes removed, and is found to be what all the other “insuperable objections” which have been arrayed against the proposition are found to be when grappled with; i.e. baseless and unreal: it being necessary only to put a valve at every half, or quarter of a mile, which should be opened by the carriages as they passed, to render the length of the column of air of the natural density, which must be behind the carriages to drive them along, only a few hundred yards, and its friction consequently unimportant; said valves being (as can easily be done) so arranged, as to close themselves again the moment the carriage had arrived at, opened, and passed by, the next succeeding one.
But though I freely admit that the friction of the air against the inside of the tunnel may waste power to a degree which shall prove not unimportant, yet may it be doubted whether it will be more important than the waste of power occasioned by the present method of railway transmission by locomotive engines.