A Letter to the Kensington Canal Company on the Substitution of the Pneumatic Railway for the Common Railway by Which They Contemplate Extending Their Line of Conveyance

by John Vallance

In the instructions given to Mr. Walker by the Directors of the Liverpool and Manchester Railway (and which called from him the Report criticised by Messrs. R. Stephenson and Locke), it is stated that “the quantity of traffic for which it will be expedient to provide the power of conveyance” is about 4000 tons, from each to the other of those places, daily.

In his publication on the Liverpool and Manchester Railway, Dr. Lardner says, “In the experiments which I have detailed, it appears that a steam engine is capable of drawing 90 tons at the rate of about 20 miles an hour; and that it could transport that weight twice between Liverpool and Manchester in about three hours.” [38a] The weight of this engine alone being 8.1 tons, the whole weight of itself, and its tender, with the necessary supplies of fuel and water, will not be less than twelve tons. Therefore, the friction of the engines (and their tenders) requisite to carry these 4000 tons at the rate of 20 miles an hour, would be 4267 lbs.

The friction of one mile of air in a tunnel eight feet in diameter, when moved at the rate of 20 miles an hour by exhaustion being 288lbs., the friction of it in a tunnel extending from Liverpool to Manchester, will be 8640lbs.: which, though double the friction of these locomotive engines, might be far cheaper for the following reason; and independent of the circumstance, that I could lay down a tunnel capable of carrying all these 4000 tons at one and the same time, from Liverpool to Manchester, for one-fourth of what that railway has cost; [38b] and also independent of the circumstance that the enormous expense now incurred for the repairs of the locomotives (as stated on page [11]) would also be saved.

It is well known that the smaller a steam-engine is, the larger is the proportionate quantity of fuel it requires, and the greater the proportionate expense of working it; while it is equally well known that, owing to the imperative importance of lightness and efficiency over economy in locomotive engines, this disadvantage increases in a most rapid ratio with respect to them. In consequence of this, a quantity of fuel, which, in large stationary engines, such as I should use for exhausting air from the tunnel, would do a given quantity of work, would, in the best of the locomotives on the Liverpool and Manchester Railway, do only one-sixteenth as much work.

Therefore it results, that, notwithstanding the friction of the air in a tunnel 30 miles long would, at the rate of 20 miles an hour, be twice as much as the friction of the locomotive engines, yet, owing to the fuel consumed by the latter, to move themselves and their tenders, being sixteen times as great as large stationary engines, such as I should use, would require to do the same work, the tunnel would, supposing the whole quantity of goods were to be carried at once, be eight times the cheapest mean of conveyance, in point of current expenses only, and without reference to its first cost being only one-fourth that of the railway; and also without reference to the whole of the enormous expense now occasioned by the repairs of the locomotive engines being saved.

But this is not the only proportion in which a tunnel might be cheaper. The 13th paragraph of the Russian Engineer Officer’s Report, states, that he is “convinced that exhaustion to a degree which should give a pressure of fifteen inches of mercury may be effected in the tunnel.” Now, notwithstanding that much more than this may be done in an iron tunnel, yet will I calculate on this only. Fifteen inches of mercury being 7.3 lbs. that pressure on the area of the tunnel, would move above twice the 4000 tons which the Directors of the Liverpool and Manchester Railway estimated would be carried from one to the other of those places every day; which, supposing that weight to be conveyed at one time, would reduce the expense (per ton of goods carried) of overcoming the friction of air moving in a tunnel from Liverpool to Manchester, at the rate of 20 miles an hour, to one-sixteenth of what the power required to overcome the friction of the locomotive engines required to draw the same weight would cost.

And though, owing to its being a received opinion that the power required to overcome the friction of fluids increases according to the square of the velocity, we are to suppose that at 40 miles an hour, the fuel required to overcome the friction of the air would be one-fourth that of the locomotive engines, while at 80 miles an hour it would be equal to that of the engines, still would a quadruple velocity be attained, by the expenditure of only an equal quantity of fuel.

The amount of the power required to overcome the friction of the locomotive engines (and their tenders) necessary to carry 4000 tons weight from Liverpool to Manchester daily, at the rate of 20 miles an hour, is, when expressed in “horse’ power” equal to the power of 225 horses working for an hour and a half. In other words, these locomotives must exert power to this amount, beyond what is required to draw the 4000 tons weight.

The power required to overcome the friction of air, which was moving (by exhaustion) at the rate of 20 miles an hour, in a tunnel of eight feet diameter, extending from Liverpool to Manchester, would be equal to that of 456 horses: which, though double the preceding, would yet be eight times cheaper, owing to large stationary engines, such as I should use, requiring only one-sixteenth part of the fuel required by locomotives to do equal work.

At 40 miles an hour (supposing locomotives could go so fast) the number of horses’ power required to overcome the friction of the air in the tunnel would (according to the received opinion of that friction increasing to the square of the velocity) be 3650: which, though sixteen times greater than that of the locomotive engines and their tenders, yet, in consequence of this power being exerted only for three-quarters of an hour, instead of an hour and a half, and of fuel doing sixteen times as much work in large stationary engines as in locomotives, would be only half so expensive as the locomotives and their tenders would prove.