User:AKAF/Equations


 * $$\frac{dm}{m}=-\left(\frac{d\left(\frac{V^2}{2}\right)+gdr}{g_0I_{sp}V\left(1-\frac{D+D_e}{F}\right)}\right)$$


 * $$\frac{dm}{m}=-\left(\frac{d\left(\frac{V^2}{2}\right)+gdr}{\eta_0h_{PR}\left(1-\frac{D+D_e}{F}\right)}\right)$$


 * $$\eta_0=\frac{g_0r_0\left(1-\frac{1}{2}\frac{r_0}{r}\right)}{h_{PR}\left(1-\frac{D+D_e}{F}\right)\ln\left(\frac{1}{\Pi_e+\frac{1}{\Gamma}}\right)}$$


 * $$\eta_0=\frac{g_0r_0\left(1-\frac{1}{2}\frac{r_0}{r}\right)}{h_{PR}\left(1-\frac{D+D_e}{F}\right)\ln\left(\frac{1}{1-\Pi_f}\right)}$$


 * $$I_{sp}=\frac{\sqrt{g_0r_0}}{g_0\left(1-\frac{D+D_e}{F}\right)\ln\left(\frac{1}{1-\Pi_f}\right)}$$


 * $$\eta_0=\frac{g_0V_0}{h_{PR}}\cdot I_{sp}=\frac{\mbox{Thrust Power}}{\mbox{Chemical energy rate}}$$


 * $$\Pi_f=1-exp\left[-\frac{\left(\frac{V_{initial}^2}{2}-\frac{V_i^2}{2}\right)+\int{g}\,dr}{\eta_0h_{PR}\left(1-\frac{D+D_e}{F}\right)}\right]$$


 * $$\Pi_f=1-exp\left[-\frac{g_0r_0\left(1-\frac{1}{2}\frac{r_0}{r}\right)}{\eta_0h_{PR}\left(1-\frac{D+D_e}{F}\right)}\right]$$


 * $$\Pi_f=1-e^{-BR}$$


 * $$B=\frac{g_0}{\eta_0h_{PR}\left(1-\phi_e\right)\frac{C_L}{C_D}}$$

in the form of the Breguet range formula


 * $$\Pi_f=1-exp\left[-\frac{g_0R}{\eta_0h_{PR}\left(1-\phi_e\right)\frac{C_L}{C_D}}\right]$$