Page:Project Longshot - Advanced Design Program Project Report.pdf/69

Rh

"Ideal" Rocket Nozzle: Perfect Gas
 * Steady Flow - no shock, friction or heat losses
 * One Dimensional Flow
 * Frozen Chemical Equilibrium


 * Ve (exit velocity) = L E
 * L = Limiting Gas Velocity
 * E = Pressure Expansion Ratio


 * $$E = \sqrt{ 1 - \frac{P_e}{P_t}^\frac{\gamma-1}{\gamma} } \quad\quad (P_e = 0)$$


 * $$L = \sqrt{ \frac{ 2 \gamma \overline{R} T_t}{(gamma-1)M} }$$


 * $$\gamma_{(monoatomic)} = 1.67$$
 * $$\overline{R} = 8.31441$$
 * $$M_{H_1} = 1.00794$$
 * $$T_{t_{critical\,deuterium\,fusion}} = 3.5x 10^8 \,\,\, K$$
 * $$L_{\mathrm{max}} = 379 \frac{km}{sec}$$
 * $$I_{sp} = \frac{V_e}{g} = 39000 \, \mathrm{sec}$$