Propellant

Nomenclature

• When energy is stored in the propellant, it is called “Fuel”
  • Not all propellants are fuels (noble gases)
  • Not all fuels are propellants (nuclear fuel rods)
• Total Expelled Propellant: $M_{\text{p}}$

Effectiveness

• Called “Effectiveness” not “Efficiency”
  • Effectiveness: Less mathemaatically rigorous
  • Efficiency: Thoroughly defined
• Effectiveness: $\eta$

Chemically

• Start from jet equation:
  • $P_{\text{jet}}=\frac{1}{2}\dot{m}{u}_e^2=\eta \dot{E}$
• Note the specific energy of the fuel itself:
  • Specific Energy: $ϵ$
  • $\dot{E}=ϵ\dot{m}$
• Thus: $\frac{1}{2}{u}_e^2=\eta ϵ$

Density

• Ideal Gas:
  • ${\rho }_P=\frac{P}{RT}=\frac{P\overline{M}}{\overline{R}T}$
• Two-Phase:
  • ${\rho }_P=\mathrm{f}\left(T,\mathrm{X}\right)$, where $\mathrm{X}$ is quality
  • $P=\mathrm{f}\left(T\right)$