Propulsion Systems

Propulsion systems are devices that generate thrust to move vehicles through air or space. Understanding propulsion is essential for aerospace engineering, as it determines mission performance, range, and feasibility.

Newton's Third Law and Thrust

The fundamental principle behind all propulsion systems is Newton's third law: for every action, there is an equal and opposite reaction. Thrust is generated by accelerating mass in one direction, which creates a force in the opposite direction.

Thrust Equation

The general thrust equation is:

Where:

• $T$ = thrust
• $\dot{m}$ = mass flow rate of exhaust
• $v_e$ = exhaust velocity
• $v_0$ = vehicle velocity
• $P_e$ = exhaust pressure
• $P_0$ = ambient pressure
• $A_e$ = exhaust area

The first term is momentum thrust, and the second term is pressure thrust.

Specific Impulse

Specific impulse ($I_{sp}$) is a measure of how efficiently a propulsion system uses propellant:

Where $g_0$ is standard gravity (9.80665 m/s²).

Specific impulse effectively measures the "miles per gallon" of rocket engines.

Aircraft Propulsion Systems

Piston Engines

• Use internal combustion to drive a propeller
• Efficiency: 80-85% (propulsive)
• Specific impulse: ~600-800 seconds
• Applications: Small aircraft, training aircraft

Turbojet Engines

• Compress air, burn fuel, expand through turbine
• Efficiency increases with speed
• Applications: High-speed aircraft

Turbofan Engines

• Uses fan to bypass air around the core
• Better fuel efficiency than turbojets
• Two types: high-bypass (commercial) and low-bypass (military)

The thrust-specific fuel consumption relationship for turbofans:

Where $TSFC$ is thrust-specific fuel consumption, $\eta_{th}$ is thermal efficiency, $\eta_p$ is propulsive efficiency, and $Q_R$ is heating value of fuel.

Turboprop Engines

• Uses turbine power to drive a propeller
• Excellent efficiency at low speeds
• Specific fuel consumption: ~0.4-0.6 lb/lbf·h

Rocket Propulsion

Rockets are the only propulsion system that works in space because they carry their own oxidizer.

Rocket Equation

The fundamental equation for rocket motion is the Tsiolkovsky rocket equation:

Where:

• $\Delta v$ = change in velocity
• $m_0$ = initial mass (with propellant)
• $m_f$ = final mass (without propellant)
• $m_0/m_f$ = mass ratio

Classification of Rocket Propulsion

Chemical Rockets

1. Solid Propellant

   • Fuel and oxidizer mixed and solidified
   • Simple, reliable, cannot be throttled
   • Examples: Space Shuttle boosters, military missiles

2. Liquid Propellant

   • Fuel and oxidizer stored separately
   • Throttleable, restartable
   • Examples: SpaceX Merlin engine, RS-25

3. Hybrid Propellant

   • Solid fuel, liquid oxidizer (or vice versa)
   • Combines benefits of both
   • Examples: SpaceShipOne, P&W hybrid engines

Non-Chemical Rockets

1. Electric Propulsion

   • Ion drives, Hall effect thrusters
   • Very high specific impulse, low thrust
   • Applications: satellite station-keeping, deep space missions

2. Nuclear Propulsion

   • Nuclear thermal rockets (NTR)
   • Nuclear electric propulsion (NEP)
   • Higher specific impulse than chemical rockets

Typical Specific Impulse Values

• Solid rocket: 250-300 seconds
• Liquid oxygen/kerosene: 350-370 seconds
• Liquid oxygen/liquid hydrogen: 450-465 seconds
• Ion thrusters: 2,000-10,000 seconds

Engine Performance Parameters

Propulsive Efficiency

Thermal Efficiency

Overall Efficiency

Nozzle Performance

Rocket nozzles accelerate hot gases to high velocities:

Where:

• $\gamma$ = specific heat ratio
• $R'$ = universal gas constant
• $M$ = average molecular mass
• $T_0$ = chamber temperature

Real-World Application: Stage-and-a-Half Design

Many launch vehicles use a "stage-and-a-half" design where boosters are dropped before the core stage is complete.

Example: Saturn V

The Saturn V first stage used 5 F-1 engines + 5 strap-on boosters:

• Stage 1: 5 F-1 engines (2.5 million lbf total at sea level)
• Stage 2: 5 J-2 engines (1 million lbf total)
• Stage 3: 1 J-2 engine (230,000 lbf)

Mass Ratio Calculations

For a typical rocket stage:

import math

# Mission parameters
delta_v_required = 9500  # m/s (typical for LEO)

# Engine performance
isp_vacuum = 300  # seconds
g0 = 9.80665      # m/s²

# Structure and propellant masses
mass_empty = 10000    # kg
mass_propellant = 40000  # kg
mass_payload = 10000 # kg (total vehicle mass = 50000 kg)

# Calculate achieved delta-v
mass_ratio = (mass_empty + mass_propellant) / mass_empty
delta_v_achieved = isp_vacuum * g0 * math.log(mass_ratio)

print(f"Mass ratio: {mass_ratio:.3f}")
print(f"Achieved delta-v: {delta_v_achieved:.2f} m/s")
print(f"Payload fraction: {mass_payload/(mass_empty + mass_propellant + mass_payload):.3f}")

Your Challenge: Propulsion Trade Study

Compare different propulsion options for a reusable launch vehicle concept.

Goal: Calculate the payload capacity for different engine options and fuel combinations.

Vehicle Parameters

# Base vehicle data
gross_takeoff_weight = 500000  # kg
empty_weight = 100000         # kg (dry mass)
required_delta_v = 9300       # m/s (to LEO)

# Engine options to compare
engine_options = {
    "Option A": {"isp": 311},  # Methane/LOX
    "Option B": {"isp": 363},  # Hydrogen/LOX
    "Option C": {"isp": 285}   # Kerosene/LOX
}

Use the rocket equation to calculate how much payload each option can deliver to orbit.

Hint:

• Use the rearranged rocket equation to solve for payload mass
• Consider that $m_0 = m_{payload} + m_{propellant} + m_{empty}$
• The constraint is that total initial mass is fixed

# TODO: Calculate payload capacity for each engine option
payload_A = 0  # Payload for Option A
payload_B = 0  # Payload for Option B  
payload_C = 0  # Payload for Option C

# Print results
print(f"Option A (Methane/LOX) payload: {payload_A:.0f} kg")
print(f"Option B (Hydrogen/LOX) payload: {payload_B:.0f} kg")
print(f"Option C (Kerosene/LOX) payload: {payload_C:.0f} kg")

# Which option provides the best payload capacity?
best_option = "A"  # Determine which option is best
print(f"Best option: {best_option}")

What trade-offs would influence the final selection beyond just payload capacity?