Temperature effects were discussed previously in 'this report.
Those discussions on superheat end adiabatic temperature change
will apply to the general equation. In general, temperature of
the free air and lifting gas can be measured to a fair degree of
accuracy.
Balloon volume at any time is a function of original full balloon
volume plus the summation of all the changes in volume due to pres-
sure and temperature changes and loss of lifting gas. It will
also be affected by loss or gain of: air by the balloon through
diffusion and intake of air through the appendix. The non-
extensible balloon will have a maximum volume and thus any changes
tending to increase the gas volume to a value greater than the
balloon volume will result in a valving of the excess lifting gas
into the air, or {in "the ease of a balloon which will carry in-
ternal pressure) a pressure increase of the lifting gas.
It is for this reason that a non-extensible balloon is said to be
in a state of stable equilibrium in a direction of greater e.l ti-
tude When it is full. Eowever, in a direction of lesser altitude,
and with the case of a p:lrtially full floating balloon, the syste!!_l
is in a state of neutral equilibrium.
Composition of the lifting gas will change due to contamination of
the lifting gas by the entry·of air into the balloon, either by the
flaw of air through thE> appendix opening or by diffusion of e.ir into
the balloon. We may then modify our term for density of the lifting
gas to include a term for the pure gas and a term for the contaminating
air. Using the method of pertial volumes, we me.y equate the density
of the lifting gas at any time by:
p = Pg ( ~ + :iJL )
where: g VbT g Rp Ra
Pg = pressure of the lifting gas
vb • total lifting gas volume
Vp = volume of pure lifting gas in balloon
Va = volume of air in balloon
Rg = epecific gas constant of pure lifting gas
R0 = specific gas constant of air
Then , calling (here we see that since
we may equate:
....!1(-!JL ... _!g_)Tg Rp R0
-59-