We may use this equation to approximate the rise of a full balloon
system when controlled by overcompensated constant ballast flow:
(8) .dl: ~-A
dt dt
where z is the balloon ceiling, t is time, and W is total weight
of the balloon system.
B. Rate of Rise
The equation of Clarke and Korff 1
(1) ..dl.:
dt
F'lz
2 em
21 '"IT" secGt3
has been used to obtain the relationship between rate of rise and
free lift ~r excess buoyancy) for a balloon system of any given
weight. For practical use, the equation has been modified to:
(2) d! Fl/z
dt = 1486 GVi where F is free lift in pounds
and G is gross lift in pounds.
Although this equation was derived for use with extensible spherical
balloons~ it predicts closely the performance of non-extensible
balloons while they are risin~ to floating level. An average value
for the constant in equation .{2) from actual flights is 1600 ft./min(lb. )1/6
The deviatioh from this relationship, evidenced in several flights,
may be due to several variations from the assumptions upon which
the equation is based. This deviation has in general been an in-
crease of rate of rise of from 0 to 25% at higher altitudes.
To explain this increase, let us first investigate the changes
which may occur in the free lift. If any gas leaves the balloon
because of leakage through the balloon or the appendix, the free
lift will be reduced and the rate of rise will decrease (as it
does after the balloon is full and "levels orr"). Therefore, this
variation may be ruled out whenconsidering rise before the balloon
becomes full.
Free lift will vary with changea of temperature of the lifting gas
with respect to the free-air temperature. A change of this sort can
be caused by acquisition of superheat of the lifting gas, or by
temperature decrease or increase caused by adiabatic expansion or
OOilfre&sion of the lifting gas. (These items will be discussed later
in this report.) Actual temperature measurements during rising
portions of flights indicate that there is·no appreciable tempera-
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