Flying Machines Today

by William D. Ennis

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.

Buoyant Power of Hydrogen

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.

Lebaudy’s “Jaune”

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.

(Photo by Paul Thompson, N.Y.)

Air Balloon
Built by some Germans in the backwoods of South Africa

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.