7.3 Rocket Propulsion Principles

Rocket propulsion harnesses Newton's Third Law, expelling mass to generate thrust. The rocket equation links velocity change to propellant mass and exhaust speed. Key components include the combustion chamber, nozzle, and propellant feed system, working together to create powerful thrust.

Engine performance depends on specific impulse, thrust-to-weight ratio, and propellant properties. Rockets excel in high thrust and vacuum operation but face challenges in propellant efficiency. They're crucial for launches, spacecraft maneuvers, and various applications in space exploration and defense.

Rocket Propulsion Fundamentals

Principles of rocket propulsion

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• Based on Newton's Third Law of Motion: for every action, there is an equal and opposite reaction
• Expelling mass (propellant) at high velocity generates thrust in the opposite direction
• Thrust generated by the acceleration and ejection of propellant
  • $F = \dot{m}v_e + (p_e - p_a)A_e$
    • $F$: thrust
    • $\dot{m}$: mass flow rate of propellant
    • $v_e$: exhaust velocity
    • $p_e$: exhaust pressure
    • $p_a$: ambient pressure
    • $A_e$: nozzle exit area
• Rocket equation describes the motion of a rocket under thrust
  • $\Delta v = v_e \ln(\frac{m_0}{m_f})$
    • $\Delta v$: change in velocity (delta-v)
    • $v_e$: effective exhaust velocity
    • $m_0$: initial total mass (including propellant)
    • $m_f$: final total mass (after propellant is expelled)
  • Relates the change in velocity to the propellant mass fraction and exhaust velocity

Components of rocket engines

• Combustion chamber: location where propellants are injected, atomized, mixed, and burned to generate high-pressure, high-temperature gases; designed to withstand extreme heat and pressure
• Nozzle: accelerates the hot gases produced in the combustion chamber to high velocities; converts thermal energy into kinetic energy, generating thrust; converging-diverging (De Laval) nozzle commonly used for optimal expansion
• Propellant feed system: delivers propellants (fuel and oxidizer) to the combustion chamber
  • Pressure-fed systems use pressurized tanks to force propellants into the engine
  • Pump-fed systems use turbopumps to deliver propellants at high pressure
• Injectors: introduce and atomize propellants into the combustion chamber; ensure proper mixing and efficient combustion
• Cooling system: manages heat transfer to prevent engine components from overheating; can use regenerative cooling, where propellants cool the engine walls before injection

Rocket Engine Performance and Applications

Factors in engine performance

• Specific impulse ($I_{sp}$): measure of engine efficiency, indicating how effectively propellant mass is converted into thrust; expressed in seconds, representing the duration a unit of propellant mass can generate a unit of thrust; higher $I_{sp}$ means better engine performance and propellant utilization
• Thrust-to-weight ratio (T/W): ratio of the engine's thrust to its weight; higher T/W indicates a more powerful engine relative to its size; important for launch vehicles and spacecraft maneuverability
• Propellant properties: chemical composition, energy density, and combustion characteristics affect engine performance; higher energy density propellants lead to increased specific impulse and thrust
  • Cryogenic propellants (liquid hydrogen and liquid oxygen) offer high performance but pose storage challenges
  • Storable propellants (hydrazine and nitrogen tetroxide) are easier to handle but have lower performance
• Nozzle design: nozzle expansion ratio and shape influence thrust and efficiency; higher expansion ratios lead to increased exhaust velocity and specific impulse, but may cause flow separation at low altitudes

Rocket propulsion pros and cons

• Advantages
  • High thrust-to-weight ratio enables launch vehicles to overcome Earth's gravity
  • Ability to operate in a vacuum, making rockets suitable for space missions
  • High specific impulse allows for efficient propellant usage and longer mission durations
  • Thrust vectoring and throttling provide control and maneuverability
• Limitations
  • Require a significant amount of propellant, leading to large vehicle sizes and increased costs
  • Limited operational flexibility compared to air-breathing engines, as rockets must carry both fuel and oxidizer
  • Extreme operating conditions put high demands on materials and engineering
  • Environmental concerns, such as noise pollution and the release of combustion products
• Applications
  • Launch vehicles for placing payloads (satellites, spacecraft) into orbit
  • Spacecraft propulsion for orbital maneuvers, interplanetary missions, and attitude control
  • Missile propulsion for military and defense purposes
  • Sounding rockets for atmospheric and space research