Aerospace Propulsion and Orbital Mechanics Fundamentals

Engine Performance Parameters

Where: $m_{\dot{a}}$ = air mass flow, $m_{\dot{f}}$ = fuel mass flow, $V_{EG}$ = exhaust gas velocity, $V_{Air}$ = aircraft speed, $P_e$ = exhaust pressure, $P_0$ = ambient pressure, $A_e$ = nozzle exit area.

Propulsive Power

Propulsive Power: (Thrust times aircraft velocity). Note: zero at start of takeoff.

Fuel consumed per unit thrust.

Efficiency Metrics

Thermal Efficiency: Ratio of output power to input heat energy.

Propulsive Efficiency: Depends on the ratio of aircraft speed to exhaust jet speed.

Engine Components and Cycles

Subsonic Diffuser: Reduces air velocity, recovers pressure before the compressor.

Supersonic Diffuser: Slows supersonic flow to subsonic using shock waves.

Compressors:

• Radial (Centrifugal): High compression per stage, used in small engines.
• Axial: Low compression per stage, used in large engines.

Combustion Chamber:

• Zones: Primary, intermediate, dilution.
• Designed to slow airflow and ensure complete combustion.

Nozzle: Accelerates exhaust gases to increase thrust.

Engine Cycles:

• Reciprocating Engines (Piston Engines): Otto or Diesel cycle.
• Gas Turbines (Turbojets, Turbofans): Brayton cycle.

Propulsive efficiency is highest when exhaust jet velocity is close to aircraft speed. TSFC relates fuel consumption to thrust; it varies with engine type. For rockets, the Tsiolkovsky equation gives $\Delta V$ based on initial/final mass and specific impulse.

Orbital Mechanics Principles

Kepler’s Laws:

• Orbits are ellipses with the central body at one focus.
• Equal areas are swept in equal times (conservation of angular momentum).
• Orbital period squared is proportional to semi-major axis cubed:

Orbital Elements:

Semi-major axis $a$, eccentricity $e$, inclination $i$, argument of periapsis $\omega$, right ascension of ascending node $\Omega$, true anomaly $\nu$.

Coordinate Systems:

• Geocentric-Equatorial: Earth-centered.
• Heliocentric-Ecliptic: Sun-centered.

Types of Earth Orbits by Altitude

LEO (Low Earth Orbit):

160–2000 km, short orbital period (~90 min).

MEO (Medium Earth Orbit):

~2000–35,786 km, includes GPS satellites.

GEO (Geostationary Orbit):

~35,786 km, satellites appear fixed over a point on Earth.

Special Orbits:

• Geosynchronous Orbit (GSO): Same orbital period as Earth’s rotation.
• Sun-synchronous Orbit: Crosses the equator at the same local solar time, useful for Earth observation.

Rocket Propulsion Characteristics

Thrust Equation: Relates thrust to mass flow rate and exhaust velocity.

Specific Impulse ($I_{sp}$): Measure of engine efficiency, in seconds or velocity units.

Thrust-to-Weight Ratio: High for launch vehicles, lower for in-space propulsion.

Types of Rocket Engines:

• Liquid-propellant engines (bipropellant, monopropellant).
• Solid-propellant motors.
• Electric propulsion (ion thrusters, Hall effect thrusters).

Fluid Propellants: Different combinations with trade-offs in performance and complexity.

LAUNCH ROCKETS

Examples included: Ariane 5, Vega, Falcon 9.

Staging: Launch vehicles use multiple stages to increase $\Delta V$ and efficiency.

Mass Budget: Balancing propellant, structural mass, payload, and engines.

Delta-V Budget and Transfer Maneuvers

Typical $\Delta V$ requirements for different mission types (LEO insertion, GTO transfer, interplanetary missions). Importance of correction maneuvers to maintain or change orbit.