This effect adds to the stability of stratospheric balloon flights. If a system in equilibrium in the stratosphere were to lose lift and descend, the compression of the gas would cause an increase of the lifting gas temperature relative to the air temperature, causing a decrease in unbalance.
Similarly, an initial unbalance causing rise of the system would cause relative cooling of the lifting gas and thus again decrease the unbalance. Hence, the rate of rise or descent in the stratosphere will be limited by the rate of heat exchange due to conduction and radiation, which will counteract this effect of adiabatic heating or cooling.
Empirical evidence indicates that there is a great deal more stability in a stratospheric balloon system than in a similar system floating in the troposphere. This "adiabatic stability" is a principal reason for better performance of stratosphere flights.
E. Diffusion and Leakage of Lifting Gas
The lifting gas of a balloon can be lost by:
- leakage through small holes in the fabric or film;
- solution, migration and evaporation through fabric or film;
- true molecular diffusion through openings, such as the appendix opening.
(1) Leakage
Volumetric flow, $Q$ , of a gas through any given opening in the balloon surface may be evaluated as a function of the area of the opening, $A$ ; the pressure head causing the flow, $h$ , and a coefficient of leakage, $C_d$ .
(1)
$$
Q = C_d A \sqrt{2gh}
$$
where $g$ is the acceleration due to gravity
It would be difficult to evaluate the amount and area of holes in the balloon surface. Let us, then, compare the rate of leakage at any given altitude with leakage at sea level, rather than attempting to evaluate the leakage at a given altitude.
First we shall compare the rate of leakage of a full balloon at any given altitude with leakage of a full balloon at sea level. Let us assume that the area of any opening in the surface of the balloon does not vary with altitude and that the coefficient of leakage is constant. Thus:
(2)
$$
Q \propto \sqrt{h}
$$
where $h$ is pressure head in feet of lifting gas
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