A Project for Flying: In Earnest at Last!

by Robert Hardley

[Footnote A: The condition of a Balloon propelled by machinery is very analogous to that of a boat in the water driven by oars or paddles. Suppose such a boat to be rowing or paddling up a river against the stream, if a piece of cork be thrown overboard it appears to be carried away with the current. But this is delusive; it is the boat alone which really moves away from the cork. For if the boat be left to its own course, both it and the cork will float down together; and if the use of the oars or paddles be resumed, the distance between the boat and the cork will proceed to develope itself exactly according to the rate of the boat, without any regard to that of the stream. If the stream be excessively rapid, the boatsmen will appear to be exercising very great force to enable them to stem the torrent and avoid being carried backward. Now the resistance which they experience and all its attendant effects are only those which they create for themselves, and which they would experience in exactly the same degree were they to endeavour to move at the same rate in calm water or with the current in their favour. If the current be at the rate of ten miles an hour and they are just able to maintain their place, they are proceeding at the rate of ten miles an hour, and they experience the opposition due to that rate of motion; precisely the same as they would experience if they sought to accomplish the same rate of motion under any other circumstances. And if the current were 100 miles an hour, they would suffer no more from endeavouring to go against it, with the force just ascribed to them, than if they were to exercise the same force in any other direction, or in a water perfectly tranquil. Apply this reasoning to the case of a Balloon propelled by machinery, and much of the obscurity in which it is involved will disappear.]

With these conditions established, it will now be seen that we have nothing to consider, in discussing the probable success of any scheme of aerial navigation with the aid of the Balloon (so far as its mere movements are concerned)[A] except the actual rate of motion which it is competent to accomplish; whether or not it be sufficient to meet the exigencies of the case as they may happen to be estimated. That its capabilities in that respect, be displayed within a room, or in a calm atmosphere, or under what may be called the most favourable circumstances, has nothing in it to disparage or affect the general question. Whatever it can do there, it can do the same in a hurricane; and the only real question is, "whether, what it can accomplish in respect of rate, is enough to answer the purpose in view."

[Footnote A: I have said "so far as its mere movements are concerned;" because the complete success of the scheme, how far it is an available and satisfactory mode of transport, depends upon other conditions besides the accomplishment of a given rate of motion--as for instance, whether it be safe, or practicable, or consistent with a due preservation of the buoyancy of the Balloon, so as to allow of its being employed in voyages of sufficient distance and duration, or capable of being worked at moderate cost, or whether it leave sufficient allowance for cargo; with many others of less striking importance, which the practical aeronaut will readily suggest for himself.]

The model we have been just describing is capable as we have seen, of accomplishing a rate of about six miles an hour. Now the resistance to the progress of a Balloon varies as the squares of the velocities or rates of motion. Accordingly, for the same Balloon to accomplish twice the speed, or twelve miles an hour, it would be necessary to be provided with four times the power. Thus as the spring power employed in the model is equal to a weight of 45 pounds, upon a barrel of four inches in diameter, it would require one competent to raise 180 pounds on the same sized barrel, to enable it to propel the same Balloon at double the present rate.

But with regard to Balloons of different sizes and of the same shape, the power required to produce the same rate of motion, would be as the squares of their respective diameters: for the power is as the resistance, the resistance as the surface, and the surface follows the proportion just assigned. In order, therefore to propel a Balloon of the same form and twice the diameter, at the same rate, it would require a force of four times the amount.

Now to apply this to the consideration of a Balloon of superior magnitude, let us assume one of 100 feet in length, and fifty feet in height. The buoyant power of such a machine, or the weight it would carry, supposing it inflated with gas of the same specific gravity, compared with that of the model, would be as the cubes of their respective diameters; or in, about, the ratio of 420 to one. Such a Balloon, therefore, so inflated, would carry a weight of about 8700 pounds, or above three tons and three quarters. As, however, it would be very expensive to inflate such a vessel with pure hydrogen gas, it would be advisable to found our calculations upon the use of coal gas; under which circumstances the weight it would carry would be limited to about three tons. Deducting from this, one ton for the weight of the Balloon itself and its necessary equipments, there would remain two tons, or about 4500 pounds, to be devoted to the power, whatever it might be, by which the machinery was to be moved, and the living cargo it might have to carry. Nor let the reader be surprised at the magnitude of the figures we are here employing, as if it were something extraordinary or beyond the power of man to accomplish. The dimensions and power we have here assumed is very little greater than those of the great Vauxhall Balloon,[A] and considerably less than some of Montgolfières, or Fire-balloons, which were first employed.

[Footnote A: The height of the Vauxhall Balloon is about eighty feet, its breadth about fifty. It contains 85000 cubic feet of gas, and supports a weight of upwards of two tons.]

Now the resistance which such a Balloon as I have here described would experience in its passage through the air, and consequently the power it would require to establish that resistance compared with those of the model, we have said would be as the squares of their respective diameters, or in, about, the ratio of only fifty-six to one; in other words, whatever force it would take to propel the model at any given rate, it would require just fifty-six times the power to accomplish the same result with the large Balloon we have been describing.

In order to ascertain precisely what this power would be in any given instance, it only remains to find an expression for the spring power with which we have been hitherto dealing, that shall be more generally comprehensible.

This we shall do by a comparison with the power of steam, according to the usual mode of estimating it; that is, reckoning a one-horse power to be equal to the traction or draught of 32,000 lbs. through the space of one foot in a minute. According to this scale, observing the corresponding conditions of the spring--namely, the weight it balances on the barrel, (answering to the force of traction) = 45 lbs., the circumference of the barrel (answering to the space traversed) = one foot, and the time of uncoiling for each turn, (answering to the rate of the operation) say, three seconds and a half--we find the power of the spring employed in the propulsion of the model, to be as nearly as possible the forty-second part of the power of one horse; from whence it is easy to deduce the conditions of flight assignable to the same, and to different sized Balloons of the same shape, at any other degree of speed. Assuming, for instance, a Balloon of 100 feet in length and 50 feet in height, and proposing a rate of motion equal to 20 miles an hour, we have, in the first instance, the power required to propel the model at that rate, compared with that already ascertained for a velocity of six miles an hour, in the ratio of the squares of the two velocities, as nearly ten to one; that is, ten forty-seconds, or about one-fourth of a horse power. To apply this to the larger Balloon, we must take the squares of their respective diameters; which being nearly in the ratio of 56 to 1, gives an amount of 56 times one-fourth or about 14 horses, as the sum of the power required.