A cubical block of wood measuring twelve inches on a side floats on water because it is lighter than water; it weighs, if yellow pine, thirty-eight pounds, whereas the same volume of water weighs about sixty-two pounds. Any substance weighing more than sixty-two pounds to the cubic foot would sink in water.

If our block of wood be drilled, and lead poured in the hole, the total size of wood-and-lead block being kept constantly at one cubic foot, the block will sink as soon as its whole weight exceeds sixty-two pounds. Ignoring the wood removed by boring (as, compared with the lead which replaces it, an insignificant amount), the weight of lead plugged in may reach twenty-four pounds before the block will sink.

This figure, twenty-four pounds, the difference between sixty-two and thirty-eight pounds, then represents the maximum buoyant power of a cubic foot of wood in water. It is the difference between the weight of the wood block and the weight of the water it displaces. If any weight less than this is added to that of the wood, the block will float, projecting above the water’s surface more or less, according to the amount of weight buoyed up. It will not rise entirely from the water, because to do this it would need to be lighter, not only than water, but than air.

Buoyancy in Air

There are gases, if not woods, lighter than air: among them, coal gas and hydrogen. A “bubble” of any of these gases, if isolated from the surrounding atmosphere, cannot sink but must rise. At the same pressure and temperature, hydrogen weighs about one-fifteenth as much as air; coal gas, about one-third as much. If a bubble of either of these gases be isolated in the atmosphere, it must continually rise, just as wood immersed in water will rise when liberated. But the wood will stop when it reaches the surface of the water, while there is no reason to suppose that the hydrogen or coal gas bubbles will ever stop. The hydrogen bubble can be made to remain stationary if it is weighted down with something of about fourteen times its own weight (thirteen and one-half times, accurately). Perhaps it would be better to say that it would still continue to rise slowly because that additional something would itself displace some additional air; but if the added weight is a solid body, its own buoyancy in air is negligible.

Our first principle is, then, that at the same pressure and temperature, any gas lighter than air, if properly confined, will exert a net lifting power of (n-1) times its own weight, where n is the ratio of weights of air and gas per cubic foot.

If the pressures and temperatures are different, this principle is modified. In a balloon, the gas is under a pressure slightly in excess of that of the external atmosphere: this decreases its lifting power, because the weight of a given volume of gas is greater as the pressure to which it is subjected is increased. The weight of a given volume we have called the density: and, as has been stated, if the temperature be unchanged, the density varies directly as the pressure.

The pressure in a balloon is only about 1% greater than that of the atmosphere at sea level, so that this factor has only a slight influence on the lifting power. That it leads to certain difficulties in economy of gas will, however, soon be seen.

The temperature of the gas in a balloon, one might think, would naturally be the same as that of the air outside: but the surface of the balloon envelope has an absorbing capacity for heat, and on a bright sunny day the gas may be considerably warmed thereby. This action increases the lifting power, since increase of temperature (the pressure remaining fixed) decreases the density of a gas. To avoid this possibly objectionable increase in lifting power, balloons are sometimes painted with a non-absorbent color. One of the first Lebaudy balloons received a popular nickname in Paris on account of the yellow hue of its envelope.

Suppose we wish a balloon to carry a total weight, including that of the envelope itself, of a ton. If of hydrogen, it will have to contain one fifteenth of this weight or about 133 pounds of that gas, occupying a space of about 23,000 cubic feet. If coal gas is used, the size of the balloon would have to be much greater. If hot air is used—as has sometimes been the case—let us assume the temperature of the air inside the envelope such that the density is just half that of the outside air. This would require a temperature probably about 500°. The air needed would be just a ton, and the balloon would be of about 52,000 cubic feet. It would soon lose its lifting power as the air cooled; and such a balloon would be useful only for short flights.

The 23,000 cubic foot hydrogen balloon, designed to carry a ton, would just answer to sustain the weight. If anchored at sea level, it would neither fall to the ground nor tug upward on its holding-down ropes. In order to ascend, something more is necessary. This “something more” might be some addition to the size and to the amount of hydrogen. Let us assume that we, instead, drop one hundred pounds of our load. Thus relieved of so much ballast, the balloon starts upward, under the net lifting force of one hundred pounds. It is easy to calculate how far it will go. It will not ascend indefinitely, because, as the altitude increases, the pressure (and consequently the density) of the external atmosphere decreases. At about a 2000-foot elevation, this decrease in density will have been sufficient to decrease the buoyant power of the hydrogen to about 1900 pounds, and the balloon will cease to rise, remaining at this level while it moves before the wind.

There are several factors to complicate any calculations. Any expansion of the gas bag—stretching due to an increase in internal pressure—would be one; but the envelope fabrics do not stretch much; there is indeed a very good reason why they must not be allowed to stretch. The pressure in the gas bag is a factor. If there is no stretching of the bag, this pressure will vary directly with the temperature of the gas, and might easily become excessive when the sun shines on the envelope.

A more serious matter is the increased difference between the internal pressure of the gas and the external pressure of the atmosphere at high altitudes. Atmospheric pressure decreases as we ascend. The difference between gas pressure and air pressure thus increases, and it is this difference of pressure which tends to burst the envelope. Suppose the difference of pressure at sea level to have been two-tenths of a pound. For a balloon of twenty feet diameter, this would give a stress on the fabric, per lineal inch, of twenty-four pounds. At an altitude of 2000 feet, the atmospheric pressure would decrease by one pound, the difference of pressures would become one and two-tenths pounds, and the stress on the fabric would be 144 pounds per lineal inch—an absolutely unpermissible strain. There is only one remedy: to allow some of the gas to escape through the safety valve; and this will decrease our altitude.

Ascending and Descending

To ascend, then, we must discard ballast: and we cannot ascend beyond a certain limit on account of the limit of allowable pressure on the envelope fabric. To again descend, we must discharge some of the gas which gives us lifting power. Every change of altitude thus involves a loss either of gas or of ballast. Our vertical field of control may then be represented by a series of oscillations of gradually decreasing magnitude until finally all power to ascend is gone. And even this situation, serious as it is, is made worse by the gradual but steady leakage of gas through the envelope fabric. Here, in a word, is the whole problem of altitude regulation. Air has no surface of equilibrium like water. Some device supplementary to ballast and the safety valve is absolutely necessary for practicable flight in any balloon not staked to the ground.

A writer of romance has equipped his aeronautic heroes with a complete gas-generating plant so that all losses might be made up; and in addition, heating arrangements were provided so that when the gas supply had been partially expended its lifting power could be augmented by warming it so as to decrease its density below even the normal. There might be something to say in favor of this latter device, if used in connection with a collapsible gas envelope.

Methods of mechanically varying the size of the balloon, so as by compressing the gas to cause descent and by giving it more room to increase its lifting power and produce ascent, have been at least suggested. The idea of a vacuum balloon, in which a rigid hollow shell would be exhausted of its contents by a continually working pump, may appear commendable. Such a balloon would have maximum lifting power for its size; but the weight of any rigid shell would be considerable, and the pressure tending to rupture it would be about 100 times that in ordinary gas balloons.

It has been proposed to carry stored gas at high pressure (perhaps in the liquefied condition) as a supplementary method of prolonging the voyage while facilitating vertical movements: but hydrogen gas at a pressure of a ton to the square inch in steel cylinders would give an ultimate lifting power of only about one-tenth the weight of the cylinders which contain it. These cylinders might be regarded as somewhat better than ordinary ballast: but to throw them away, with their gas charge, as ballast, would seem too tragic. Liquefied gas might possibly appear rather more desirable, but would be altogether too expensive.

If a screw propeller can be used on a steamship, a dirigible balloon, or an aeroplane to produce forward motion, there is no reason why it could not also be used to produce upward motion in any balloon; and the propeller with its operating machinery would be a substitute for twice its equivalent in ballast, since it could produce motion either upward or downward. Weight for weight, however, the propeller and engine give only (in one computed case) about half the lifting power of hydrogen. If we are to use the screw for ascent, we might well use a helicopter, heavier than air, rather than a balloon.

The Ballonet

The present standard method of improving altitude regulation involves the use of the ballonet, or compartment air bag, inside the main envelope. For stability and effective propulsion, it is important that the balloon preserve its shape, no matter how much gas be allowed to escape. Dirigible balloons are divided into two types, according to the method employed for maintaining the shape. In the Zeppelin type, a rigid internal metal framework supports the gas envelope. This forms a series of seventeen compartments, each isolated from the others. No matter what the pressure of gas, the shape of the balloon is unchanged.

In the more common form of balloon, the internal air ballonet is empty, or nearly so, when the main envelope is full. As gas is vented from the latter, air is pumped into the former. This compresses the remaining gas and thus preserves the normal form of the balloon outline.

But the air ballonet does more than this. It provides an opportunity for keeping the balloon on a level keel, for by using a number of compartments the air can be circulated from one to another as the case may require, thus altering the distribution of weights. Besides this, if the pressure in the air ballonet be initially somewhat greater than that of the external atmosphere, a considerable ascent may be produced by merely venting this air ballonet. This involves no loss of gas; and when it is again desired to descend, air may be pumped into the ballonet. If any considerable amount of gas should be vented, to produce quick and rapid descent, the pumping of air into the ballonet maintains the shape of the balloon and also facilitates the descent.

The Equilibrator

Suppose a timber block of one square foot area, ten feet long, weighing 380 pounds, to be suspended from the balloon in the ocean, and let mechanism be provided by which this block may be raised or lowered at pleasure. When completely immersed in water it exerts an upward pressure (lifting force) of 240 pounds, which may be used to supplement the lifting power of the balloon. If wholly withdrawn from the water, it pulls down the balloon with its weight of 380 pounds. It seems to be equivalent, therefore, to about 620 pounds of ballast. When immersed a little over six feet—the upper four feet being out of the water—it exerts neither lifting nor depressing effect. The amount of either may be perfectly adjusted between the limits stated by varying the immersion.

In the Wellman-Vaniman equilibrator attached to the balloon America, which last year carried six men (and a cat) a thousand miles in three days over the Atlantic Ocean, a string of tanks partly filled with fuel was used in place of the timber block. As the tanks were emptied, the degree of control was increased; and this should apparently have given ideal results, equilibration being augmented as the gas supply was lost by leakage: but the unsailorlike disregard of conditions resulting from the strains transferred from a choppy sea to the delicate gas bag led to disaster, and it is doubtful whether this method of control can ever be made practicable. The America’s trip was largely one of a drifting rather than of a dirigible balloon. The equilibrator could be used only in flights over water in any case: and if we are to look to water for our buoyancy, why not look wholly to water and build a ship instead of a balloon?