(1) W : Balloon Volume x Gas Lift
Gross Load ·
[It may be noted from this equation that a balloon can float at
molar volumes less than that compute~ for maximum balloon volume
(i.e., when it is not full). However, under these conditions the
balloon would be in neutral equilibrium, since any vertical force
would cause it to rise or fall until a force in the opposite direc-
tion stopped it. This is also the case with floating extensible
balloons.J
To convert from molar volume to equivalent altitude we must know
the pressure-temperature diatribution of the atmosphere in which
the balloon will float. Since it is difficult to obtain an
accurate distribution for each flight, the atmospheric model as
drawn up by NACA standards has been used. In general the error
obtained in using the NACA standard is not great, but if greater
refinement is desired, date. obtained from averaged radiosonde ob-
servations over a given launching site can be used.
From such knowledge of the distribution of pressure e.nd temperature,
we may plot a curve of molar volume vs. altitude by use of the
following equation:
(2) 1013.3 mb
P1
By use of such a plot we easily find the floeting altitude of a
full non-exter.sible balloon by use of equation {l) to find molar
volume, and then of the plot of equation (2) to find altitude.
The two equations have been combined and graphed in. the form of
an altitude vs. gross load chart with helium &s the lifting gas
for various balloon sizes and verious release sites in the
"Operations" section of this technical report (Part II, page 108).
For the NACA standard atmosphere we may derive an equation for alti-
tude sensitivity by use of the molar volume-altitude relationship.
This is most easily done by plotting molar volume vs. eltitude on
semi-logarithmic paper, since the curve of molar volume vs. altitude
from 40,000 to 105,000 feet (where a constant lapse rate of zero
is assumed) is approximately a straight line on semi-log paper.
The general form of the equation for this portion of the atmosphere
is y =aebz where y is the molar volume and z the altitude.
It is possible to determine empirically the constants a and b.
For example, using the molar volume at 50,000 feet, we find from
*359 rt3 =Molar volume of air at standard conditions {273°K, l atm. pressure)
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