Impulse

Total Impulse

• $[\text{Impulse}]=[F][t]$
• Generally:
  • $I_{\text{total}}=\int F(t)dt$
  • $F=\dot{m}{u}_e$
• For constant $F$: $I_{\text{total}}=F\Delta t$
• For constant $u_e$: $I_{\text{total}}=u_e\int \dot{m}\mathrm{d}t=u_e{M}_p$
  • $M_p$ is propellant mass

Specific Impulse

• Total Impulse per unit mass (weight at sea level) of propellant used
• $I_{\text{sp}}$, measured in $\text{[sec]}$
  • Proportional to exit velocity
  • Used as a mathematical tool to work outside of unitary constraints