The Roswell Report: Fact vs. Fiction in the New Mexico Desert

[figure] Figure 24. Comparison of pressure head across partially and fully inflated balloons. Thus, the relationship is: (9) $$ Q \propto A \sqrt{\Delta Z} $$ (10) $$ Q \propto V^{\frac{2}{3}} \sqrt{V^{\frac{1}{3}}} \propto V^{\frac{5}{6}} $$ Since the density of the lifting gas is constant, we may then express mass leakage as: (11) $$ L \propto V^{\frac{5}{6}} $$ And then, to compare leakage of a full balloon with leakage of a balloon $\frac{1}{x}$ full: (12) $$ L_F = L_{\frac{1}{x}} (x)^{\frac{5}{6}} $$ -44-