Equations Used in Calculator

$$\rho_{air}=\frac{p_{0}}{R_{air}\cdot (T_{0} + 273.15)}$$
$$m_{g}=\frac{(m_{fl}+m_{b}+m_{p})\cdot p_{0}}{Rg\cdot (T_{0}+273.15)\cdot \rho_{air}-p_{0}}$$
$$V_{g}=\frac{m_{g}\cdot R_{g}\cdot (T_{0}+273.15)}{p_{0}}$$
$$A_{0}=\Bigl(\sqrt[\leftroot{-1}\uproot{2}\scriptstyle 3]{\frac{3\cdot V_{g}}{4\cdot \pi}}\Bigr)^{2}\cdot \pi$$
$$F_{lift}=V_{g}\cdot \rho_{air}\cdot g$$
$$F_{weight}=(m_{b}+m_{p}+m_{g})\cdot g$$
$$\Delta F=F_{lift}-F_{weight}$$
$$v_{0}=\sqrt{\frac{2\cdot \Delta F}{\rho_{air}\cdot C_{D}\cdot A}}$$
$$T_{g}=T_{air}+T_{st}$$
$$p_{sp}=\frac{m_{g}\cdot R_{g}\cdot (T_{g}+273.15)}{V_{b}}-p_{air}$$