## How to
Calculate the Weight of Air and Model Hot Air
Balloon Lift - overflite
Hot air balloons fly because
balloon and heated air inside weigh less than
surrounding ambient air displaced by balloon.
Difference in air weights is gross lift.
Difference minus weight of balloon is net lift. Absolute Fahrenheit is used to calculate air
weights at different temperatures. It is the
number of degrees above Absolute Zero. Which
is around minus 460 degrees Fahrenheit. As prime example, 48 Fahrenheit is the same as
508 Absolute Fahrenheit, and 175 degrees
Fahrenheit is the same as 635 Absolute Fahrenheit.
The standard weight of normal average sea level
air is .0765 pounds per cubic foot at 59 F (519
Absolute Fahrenheit). Or 1.224 ounces.
When air temperature goes up, air weight goes
down. By inverse proportion. Do the
math. Multiply 519 by 1.224 to get
635. This means that the heated air will
weigh exactly one ounce per cubic foot at 635
Absolute Fahrenheit. Or 175 F. At 48 F (508 A) a cubic foot of normal pressure
sea level air weighs almost exactly 1 1/4
ounces. Heated by 127 degrees, to 175
F (635 A), it weighs almost exactly an ounce, or
4/5 of its original weight, for a gross lift of a
1/4 ounce per cubic foot. When air temperature goes up, air weight goes
down, by an inverse proportion. From the
ambient of 48 F (508 A) to 175 F (635 A), the
increase is 635/508, or 5/4, since both numbers
are divisible by 127. So the heated air will
weigh 4/5 of its original weight. Or a
reduction of 1/5. From 1 1/4 ounces to an
ounce. For a lift of a 1/4 ounce per cubic
foot.
Mathematically, with two
variables, if one goes down at the same rate
the other one goes up, the variables can be
multiplied times each other, and their product
will be constant. So, at standard normal
pressure sea level, ie. 29.92 inches of mercury
(1013.25 Millibars), the following equations are
true:
## Formulas for
Model Hot Air Balloon Lift:
Gross lift can also be
expressed as a fraction, as follows:
Alternately, the heated air
temperature and the heat rise can be expressed in
terms of gross lift, as follows:
## Effects of
Different Ambient Temperatures on Gross Lift
As example, if the ambient temperature goes up 20
degrees, from 48 F (508 A) to 68 F (528 A), the
increase in temperature and the decrease in air
weight is about 4%, and sea level air weighs
around 1.20 ounces per cubic foot. Heated by
127 degrees, to 207 F (655 A), the temperature
increases by 655/528, or about 24%, and the air
weight decreases proportionately to about .97
ounces per cubic foot. So, the gross lift is
about .23 ounces per cubic foot, or about 8% less
than at an ambient of 48 F. Alternately, if the ambient goes down 20 degrees
to 28 F (488 A), the air weighs around 4% more, or
about 1.30 ounces per cubic foot. Heated 127
degrees to 155 F (615 A) the temperature increases
by 615/488, or about 26% and the air weight
decreases proportionately to about 1.03 ounces per
cubic foot. The result is a gross lift of
about .27 ounces per cubic foot, or about 8% more
than at an ambient of 48 F, and about 16%
more than at an ambient of 68 F ambient. In reality though, the changes in lift are
believed to be slightly less than predicted.
In cold ambients there is "more air to heat," and
at higher ambients there is "less air to
heat." This causes slightly lower heat rises
in cold weather, and slightly higher heat rises in
warm weather, of up to several degrees, for a
given amount of engine power. ## Adjusting
the "635 Factor" to Account for Weather and
Elevation
Elevation reduces air pressure, air weight, and
the temperature where air weighs exactly an ounce
per cubic foot by around 3% per thousand feet,
slightly more for lower elevations, and slightly
less for higher elevations. This reduces the
"635 factor" by around 20 degrees per thousand
feet. Adjustments for altitudes of up to
25,000 feet, that are over 99% accurate, can be
calculated using the following formula:
Note: For altitudes of up to 35,000 feet,
adjustments that are close to 99% accurate can be
calculated by increasing the addition factor to
28; for up to 40,000 feet by increasing the factor
to 29, and for up to 45,000 feet by increasing the
factor to 30, etc.
Accordingly, for a given heat rise, the resulting
lift will be approximately the same as the
percentage of sea level air. In reality
though, higher elevation air is believed to get
somewhat more lift than predicted, since higher
elevation air has "less air to heat," resulting in
a greater heat rise from a given amount of engine
power than at sea level. ## Guidelines
for Balloon Weights at Sea Level:
For unpowered paper balloons the maximum weight
shouldn't be much more than around 1/8th ounces
per cubic foot, since they will tend to cool down
fairly quickly, and you want to have reasonable
flight time. For manned hot air balloons, you can figure that
the gross lift is probably around 1/5th of an
ounce per cubic foot, assuming the air is heated
by around 100 degrees in mild weather, and
slightly more in warm weather. In this
example, 80 cubic feet of volume is required for
each pound of gross lift. So, to lift a
thousand pounds, 80,000 cubic feet of volume would
be required. By Thomas Taylor -- balloons@overflite.com |
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