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.
[Illustration: 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.
[Illustration: 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.
[Illustration: AIR BALLOON
(Photo by Paul Thompson, N.Y.)
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.