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Function of γ, the specific heat ratio, defined as: \[\Gamma=\sqrt{\gamma}(\frac{2}{\gamma+1})^{(\gamma+1)/(2(\gamma-1))}\]

Ratio of specific heat at constant pressure c_p, to specific heat at constant volume c_v: \[\gamma=\frac{c_{p}}{c_{v}}\] (Calculated from Γ using numerical methods) \[\Gamma=\sqrt{\gamma}(\frac{2}{\gamma+1})^{(\gamma+1)/(2(\gamma-1))}\]

Ratio of exit pressure P_e, to chamber pressure P₀.
Coupled to the expansion ratio, A_e/A_t with the following equation: \[\frac{A_{e}}{A_{t}}=\frac{\Gamma}{\sqrt{\frac{2\gamma}{\gamma-1}(\frac{P_{e}}{P_{0}})^{\frac{2}{\gamma}}(1-(\frac{P_{e}}{P_{0}})^{(\gamma-1)/\gamma})}}\] (Calculated from A_e/A_t using numerical methods)

Ratio of nozzle exit area A_e, to nozzle throat area A_t.
Coupled to the exit pressure ratio, P_e/P₀ with the following equation: \[\frac{A_{e}}{A_{t}}=\frac{\Gamma}{\sqrt{\frac{2\gamma}{\gamma-1}(\frac{P_{e}}{P_{0}})^{\frac{2}{\gamma}}(1-(\frac{P_{e}}{P_{0}})^{(\gamma-1)/\gamma})}}\] Above a certain threshold of A_e/A_t, flow seperation will occur at sea level.

Ratio of atmospheric pressure P_a, to chamber pressure P₀.
Values above 1 occur briefly during engine startup and are not sustained. A high P_a/P₀ causes flow seperation from the nozzle and side loads.

Pressure reached in rocket combustion chamber. In reality, chmaber pressure P₀, combustion temperature T₀, and mean molecular mass M are not independent and are all determined by the combustion process. A higher chamber pressure results in a higher chamber temperature.

Nozzle throat area. Throat area A_t, must be smaller than nozzle exit area A_e (converging-diverging nozzle) and flow at the throat must be Mach=1 in order to achieve supersonic flow conditions at nozzle exit.

Nozzle exit area. Exit area A_e, must be larger than nozzle throat area A_t (converging-diverging nozzle) and flow at the throat must be Mach=1 in order to achieve supersonic flow conditions at nozzle exit.

Mean molar mass of combusted propellants. In reality, mean molecular mass M, chamber pressure P₀, and combustion temperature T₀ are not independent and are all determined by the combustion process. Propellant types and O/F ratio directly affect mean molar mass and combustion temperature. A small M results in larger exit velocity. Above a certain threshold, values of M correspond to large elements or molecules which cannot be obtained in real-life combustion processes.

Temperature reached in combustion chamber. In reality, combustion temperature T₀, mean molecular mass M, and chmaber pressure P₀ are not independent and are all determined by the combustion process. Propellant types and O/F ratio directly affect combustion temperature and mean molar mass.

At sea level, P_a is approximately equal to 1.013 bar. Higher values correspond to altitudes below sea level. P_a, in bar, is coupled to altitude with the following formula: \[P_{a}(h)=101.325e^{-0.12h}\] where h is distance above sea level.

Distance above sea level. At sea level, Alt. is equal to 0 and P_a is approximately equal to 1.013 bar. Negative altitude values correspond to altitudes below sea level. Alt., in kilometers, is coupled to P_a with the following formula: \[Alt.=ln(\frac{0.9869P_{a}}{-0.00012})/1000\]

Oxidizing agent that accepts electrons from fuel to create combustion. The oxidizer, fuel, and O/F ratio affect the molar mass M, chamber temperature T₀, and chamber pressure P₀.

Fuel gives up electrons to oxidizer to create combustion. The oxidizer, fuel, and O/F ratio affect the molar mass M, chamber temperature T₀, and chamber pressure P₀.

Mixture ratio by mass of oxidizer to fuel. Rockets can run fuel-rich, oxidizer-rich, or at stoichiometric conditions, depending on desired performance. Peak chamber temperature, T₀ is achieved near stoichiometric conditions, but peak C* is achieved at lower O/F ratio (fuel-rich conditions).

Mass flow of propellant through nozzle per unit time. ṁ is proportional to flow density ρ, throat area A_t, and flow velocity v: \[\dot{m}=\rho A_{t}v=\Gamma\frac{p_{0}A_{t}}{\sqrt{T_{0}R/M}}\] R is the universal gas constant equal to 8314.47 [JK^-1mol^-1]

The thrust coefficient is a measure of the increase in thrust provided by the expansion of propellant throught the nozzle. It is defined as the ratio of actual thrust with expansion through the nozzle F, to reference thrust, the thrust created without nozzle expansion P₀A_t: \[C_{f}=\frac{F}{P_{0}A_{t}} = \Gamma \sqrt{\frac{2 \gamma}{\gamma-1}[1-(\frac{p_{e}}{p_{0}})^{\frac{\gamma-1}{\gamma}}]} +(\frac{p_{e}}{p_{0}}-\frac{p_{a}}{p_{0}})\frac{A_{e}}{A_{t}}\] When C_f is negative, flow is said to be seperated from the nozzle in this calculator. However, in reality, flow seperation occurs at certain combinations of atmospheric pressure ratios p_a/p₀ and expansion ratios A_e/A_t in the positive region of C_f. For any fixed atmospheric pressure ratio p_a/p₀, C_f is maximized at p_e = p_a.

Characteristic velocity is a function of propellant characteristics and combustion chamber design. It is independent of nozzle characteristics. It is defined as: \[c^{\ast}= \frac{P_{0}A_{t}}{\dot{m}}=\frac{1}{\Gamma}\sqrt{\frac{R T_{0}}{M}}\] R is the universal gas constant equal to 8314.47 [JK^-1mol^-1]