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the pressure distribution of the liftinc gas and the internal
back pressure due to valving gas. To find maximum rates of
ascent for various balloons would necessitate a complicated
series of trial and error solution. In general, it has been
more practical to determine a maximum rate of rise for nor.mal
operating conditions for any given size balloon by findin~ the
maximum allowable rate for the balloon rising to its lowest
normal operating level (i.e., we will find the maximum all0?18ble
rate for the worst normal operating conditions and consider
it a maximum for all normal operating conditions.)
Let us take the case of a 20-foot diameter polyethylene balloon
of .001~ thickness. Lowest normal floating altitude is 20,000 ft.
MSL. Let us assume that the balloon will be full and begin
valvinf gas at 15,000 ft. MSL. Assume the appendix diameter
to be 2 foot. Using equation (1) to find maximum allowable
internal pressure and assuming the critical x-y plane to be that
of maximum diameter A~ = D/2 , we have:
A Pall. = 4 SJt = 4(900/2)· .001 = . 007 5 psi
t2· 20
(Here we have introduced a factor of safety by saying Sf =900/2
instead of 900 psi, the ultimate strength in tension of poly-
ethylene.) Pressure distribution:
A.p 012 = A~ :l (I-B) = l-2°·3.38 ·10-4 • .862 = .00291 psi
Allowable back pressure:
A Pbp =Ap 011 - AP012 = .0046 psi
Maximum rate of rise using equation (13)J
( 2780° C A \ fttsecv d a}
= 100.7 ft/sec
= 6000 ft /min
It is evident from this calculation that the rate of rise of the
20-ft. diameter polyethylene balloon is not a critical factor
in bursting unless the open appendix becomes snarled an~ gas is
not allowed to escape.
Rate of rise and appendix openings are important from the stand-
point of balloon design. For operationel reasons it is important
to have a rapid rate of rise. In order to make most efficient
use .of weight, the balloon film should be thin. As mentioned
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