roswell

The equation for the force due to buoyancy will then become:
Fa = V. [ Pa !a.(~ Xa )]
b ~- T9 Tp +ro-lf the balloon is of the type that will carry no internal pressure
P. a p • and we may state that:
a g [ I -'- (~ .!L)]
F, = vb Pa LAo To - Tg Rp + Ro
Discussions of the contamination of the lifting gas are included under
the section on "Diffusion and Leakage of Lifting Gas" of this report.
The force due to the weight of the system Fw =W The weight
of the balloon system at any time is a function of the original
weight of the system plus the change of weight of the system. This
change in the weight of the system is caused by the loss of ballast
and the weight of the system at any time ( t ) :
where:
wt = W0 - I Awb....
+
the original weight of the system
the sum of all the losses of balle. st from
time at which W= W.o until the time t
The value of ·the term I ~Wb depends on the type of ballast control.
With no ballast: +co
.~ ~wb = o
If a constant ballast flow is used:
where:
t
IllWb+•o = Jnt t
dt
and
dW
it' : rate of ballast flow
t ela~sed time from t =0 to t: t
If a practical fixed opening type or oallast control is used:
where:
t =
h =
Pb =
pb =
A =
time
head of ballast above opening
viscosity of·ballast fluid
density of ballast fluid
area of opening
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