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

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