$\Delta p = \text{bursting pressure (psi)}$
$S_f = \text{maximum allowable tensile stress of fabric or film (psi) (for safety } S_f = 1/2 \, S_{\text{max}} \text{ where } S_{\text{max}} = \text{maximum stress in tension)}$
$t = \text{thickness of fabric or film (in.)}$
$D = \text{balloon diameter (in.)}$
or:
(2) $\Delta p = \frac{4 \, S_s}{D}$ for failure of seams
where:
$S_s = \text{maximum allowable tensile strength of seams (lb./in.)}$
$D = \text{balloon diameter (in.)}$
In general, a balloon should be manufactured so that any failure should occur first in the fabric or film and thus the tensile stress of this fabric or film will be the factor in determining bursting pressure.
Since the non-extensible balloons used in constant-level work by the N.Y.U. group have been of the open-appendix type, bursting due to excessive super-pressure has not been a problem. Strength of the balloon must be considered, however, from the standpoints of back pressure induced during rise of a full balloon and pressure distribution of the lifting gas itself inside of the balloon.
(1) Pressure Distribution of Lifting Gas
It was shown in the previous section that the pressure difference across any portion of the balloon surface may be equated:
(3) $\Delta p_z = \Delta z \, \frac{dp}{dz} \, (1 - B)$
A plot of $\Delta p$ against $\Delta z$ would then be a straight line at any given altitude. Maximum allowable balloon pressure—equation (1)—may be plotted as a function of $\Delta z$ , rather than diameter for any given horizontal plane of the balloon surface, $z$ . Using this relationship, cutting any horizontal plane $z - z$ across the balloon (Figure 25), the diameter of the
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