The Roswell Report: Fact vs. Fiction in the New Mexico Desert

$$
\mathrm {(1)} \quad \mathrm {M V} = \frac {\mathrm {B a l l o o n V o l u m e x G a s L i f t}}{\mathrm {G r o s s L o a d}}
$$

[It may be noted from this equation that a balloon can float at molar volumes less than that computed 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 direction stopped it. This is also the case with floating extensible balloons.]

To convert from molar volume to equivalent altitude we must know the pressure-temperature distribution 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, data obtained from averaged radiosonde observations over a given launching site can be used.

From such knowledge of the distribution of pressure and temperature, we may plot a curve of molar volume vs. altitude by use of the following equation:

$$
M V _ {z} = 3 5 9 \frac {f t ^ {3}}{l b m o l} \times \frac {T _ {z}}{2 7 3 ^ {\circ} K} \times \frac {1 0 1 3 . 3 m b}{p _ {z}} \frac {f t ^ {3}}{l b m o l}
$$

By use of such a plot we easily find the floating altitude of a full non-extensible balloon by use of equation (1) 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 as the lifting gas for various balloon sizes and various 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 altitude sensitivity by use of the molar volume-altitude relationship. This is most easily done by plotting molar volume vs. altitude 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=a e^{b z} $ 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 ft $ ^{3} $ = Molar volume of air at standard conditions ( $ 2 7 3^{\circ} \mathrm{K} $ , 1 atm. pressure)