in the preceding, section on diffusion end leakage the appendix
opening should be small. It can be seen that as we make one
of our conditions better, we must sacrifice at least one of
the others. Therefore, balloons must be designed compromising
rate of rise, balloon thickness, and appendix opening. Methods
of decreasing the eppendix opening, except during the valving
of lifting. gas, are discussed in other sections of this tech•
r.ical report. In general they consist of means of applying
a delicate relief valve, capable of opening to a lerge area
with af!)lication of only slight intems.l pressure, and also
closing tight upon release of this internal pressure.
G. A Ge.tleral Equa.ttc:m of Motion
If we collect and relate the variables incidental to balloon flight,
we may form a general equation of motion. This is most easily ex-
pressed in terms of forces acting upon the balloon systell'.. We may
equate e.n acceleration term plus a drag or friction term against r
term to include all other forces: ·
(1)
This is a differential equation of a type common in mechanical vi-
bration problems, end solution for the variable Z would not be
difficult if relationships of the many variables included in the
the terms n and IF were simple. However, the cornplexi~ of the
balloon system introduces many terms as pe.rts of n and 2; F •
We shall first state the more complex form of equation (1) above
and then attempt to explain tre variables included in each part of
the equation. As will be shown, it is extremely difficult to find
a complete sol•Jtion of the equation since nany of the variables
are in themselves extremely complex and at this time incapable of
accurate solution. Therefor~, our ~iscussion will be more of a
qualitative rather than a quantitative nature.
The general force equation is:
(2) fo2i!+C ~A(Di!f= Vb(P0 -P9 )-W±Fotm
The force due to acceleration
where: FA : t rfe
W : weight of the balloon system
g : acceleration of gravity
021: = acceleration of the balloon system (ln
acceleration in the direction of greater
altitude is considered positive.)
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