A vacuum airship should at least float (Archimedes law) and resist external pressure (strength law, depending on design, like the above R. Zoelli's formula for sphere).
k_{\rm L} = 2.79\cdot \frac{\rho_s}{\rho_{\rm atm}} \cdot \sqrt{\frac{P_{\rm atm}}{E}} \cdot (1-\mu^2)^{0.25}