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Fundamentals of Balloon
Flight
By Wasim Quadir
MICDS
Edited by Ray Arvidson
Why does a hot air balloon float?
The common answer to this question for a hot air
balloon is "hot air is lighter than cold air." What does this really
mean?
It means that hot air is less dense than cold air. Remember that density equals
mass divided by volume. The substance with a lower density will float on top of
another with a greater density. When the air inside a hot air balloon is heated,
molecular motion increases, and the volume of the balloon expands. Therefore,
its density decreases. The balloon will float until the density of its gas
equals the density of the surrounding air. The density of the air decreases as
altitude increases; because of gravity; gas molecules are more sparse at higher
elevations. The air is "thinner" at high altitudes. The pilot can
increase his altitude by heating the gas inside the balloon, thus decreasing its
density.
How does Solo Spirit float?
A balloon that depends entirely on hot air to
float would have to carry a tremendous amount of fuel for a long distance trip.
An around-the-world flight would not be possible. Helium is a gas that's less
dense than air (which is 79% nitrogen and 20% oxygen), and therefore rises
without being heated. But a balloon that depends entirely on helium to float
would not work well either; the pilot would have no control over the balloon's
altitude, and at night the helium would cool and the balloon would descend. The
Solo Spirit balloon uses a combination of hot air and helium to maintain
buoyancy and to change altitude, a design known as a de Roziere balloon. An
inner core of helium is surrounded by an envelope of hot air, allowing the pilot
some control over the balloon's ascent and descent, without requiring constant
burning of fuel.
Data: Relating pressure and
temperature to how the balloon floats
The density of a gas is dependent on its
temperature and pressure. Specifically, the density of a gas is inversely
proportional to temperature and directly proportional to pressure. The higher
the temperature, the lower the density, if volume and pressure are held
constant. The greater the pressure, the greater the density, if volume and
temperature are held constant.
If the balloon enters a region of colder air, its lifting
power is increased. The difference between the density of the gas in the balloon
and the surrounding air is much greater when the balloon is in cold air than
when it is in warm surroundings. The relative density of the gas in the balloon
is much less than the surrounding air when the surroundings are cold rather than
warm.
The pressure of the atmosphere also fluctuates. According to the gas laws, if
the balloon travels into an area with a greater atmospheric pressure, it will
tend to rise, and if it travels into an area with a lesser pressure, it will
sink. However, this is not always true in real life. Usually, in high pressure
systems a convection is created which swirls the air downward. This would cause
the balloon to sink. Conversely, in a low pressure system, the convection is
directed upward, causing to balloon to rise.
Activities:
Plot a graph of pressure vs. altitude during the
initial ascent of the Solo balloon during the first 24 hours of the flight,
using at least one point per hour. (You can get the data here.) Are pressure and
altitude directly or inversely related to each other? Enter the data into a
graphing calculator (like a TI-81 or better) and try to find the best regression
function. Is it a linear or exponential trend? Use the equation to determine
what the pressure at 15,000 m would be. Extrapolating from this result, what
would the pressure be at 100 km altitude?
Plot a graph of temperature vs. altitude during the initial
ascension of the Solo balloon during the first 24 hours of the flight, using at
least one point per hour. (You can get the data here.) What changes in
temperature do you notice as the balloon goes higher? Try to explain the trend
that you observe.
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