Aerospace Engineering: Rocket Science and Engineering

Explain what a rocket is, how a rocket engine and propellant produce thrust by action and reaction, and how rockets deploy payloads to low earth, medium earth, and geostationary orbits.

Explore rocket components from the airframe and propulsion system to guidance, navigation, control, payload, and recovery systems, illustrated by the V2 rocket and SpaceX reusable landings.

Examine the main rocket types, from liquid fuel engines and Merlinda engines on Falcon 9 to solid, hybrid, electric ion thrusters, nuclear, and photon-based propulsion, with historic examples.

Explain rocket thrust via Newton's third law, mass flow, exhaust velocity, exit pressure, and ambient pressure, deriving the thrust equation F = Ṁ V + (P_exit − P_ambient) A_exit.

Define impulse as force integrated over time, equal to the change in momentum. Describe specific impulse as impulse per propellant mass divided by gravity, linking exhaust velocity and mass flow.

Relate thrust and weight flow rate to specific impulse, showing ISP as thrust divided by the weight flow rate and its link to weight change over time from propellant use.

Derive the rocket equation: delta v equals the exhaust velocity times the natural log of the initial mass over the final mass, i.e., the mass ratio.

Explore rocket staging, including serial and parallel configurations, and learn how stage masses and propellant drive mass ratios and total delta-v via the rocket equation.

Analyze how drag resists motion and lift lifts rockets, driven by dynamic pressure and the coefficient of drag and lift, with throttle adjustments around max dynamic pressure to optimize performance.

Explore altitude control systems in rocketry—movable fins, gimble thrust, vernier rockets, and thrust veins—and how center of gravity, center of pressure, and PID feedback govern orientation.

Explore rocket engine design by analyzing the combustion chamber, nozzle, and propellant ignition, and apply an ideal cycle using the p–v diagram to relate heat, work, and jet exhaust.

Explore how mass flow rate equals rho A V remains constant in isentropic flow, derive the continuity relation, and analyze subsonic and supersonic behavior in converging-diverging nozzles near the throat.

Deriving the flow equation shows that in isotropic flow, velocity behavior depends on the Mach number: subsonic flow accelerates as area decreases, while supersonic flow accelerates as area increases.

Derive isentropic relations by combining the first and second laws for an ideal gas, showing entropy remains constant in reversible adiabatic processes and yielding PV^gamma and T2/T1 relationships.

Explore how exhaust velocity determines thrust, linking heat transfer to kinetic energy, with factors like combustion chamber temperature, exit temperature, pressure ratio, gamma, and molecular mass shaping engine efficiency.

Compute the ideal thrust and ideal specific impulse for a near sea-level rocket, using chamber pressure, temperature, gamma, and mass flow, and discuss ideal versus optimum and nozzle mach behavior.

Derives the mass flow rate for the entire nozzle using density and velocity throughout the nozzle. Explains how flow density peaks at the throat, guiding converging then diverging nozzle design.

Derive how the maximum flow density occurs at the throat and relate exit and throat areas through the expansion ratio, linking pressure, area, and gamma in a rocket nozzle.

Explore stagnation conditions, entropy changes, and temperature relationships in the combustion chamber, linking Bernoulli’s principle to nozzle expansion and Mach number in rocket propulsion.

Compute the chamber pressure and nozzle area ratio for an ideal rocket at sea level with gamma 1.3, exit pressure 0.1013 mpa, yielding about 1.84 mpa and expansion ratio 3.02.

Analyze how nozzle design and ambient pressure affect thrust, mass flow rate, and exhaust velocity, explaining overexpanded, underexpanded, and ideal expansion, and why exit pressure matching ambient optimizes efficiency.

Compute an ideal rocket nozzle at 25 km altitude to deliver 5000 N thrust, deriving exit velocity, throat area, and exit area from chamber conditions, gamma, and specific gas constant.

Compare the diverging nozzle and the bell shaped nozzle. The parabola guides gas flow and minimizes shock waves by shaping the nozzle from a perfect cone.

Design the combustion chamber and converging nozzle with a contraction ratio of at least four and the length formula for the nozzle, using a 60-degree half angle and wall-stress constraints.

Explore thrust coefficient and c star, showing how exit pressure equal to ambient maximizes thrust and how chamber temperature and mass flow govern c star.

Calculate thrust variance from sea level to 10 km by comparing thrust coefficients for a nozzle with area ratio 6 and gamma 1.2 at 20 atm, yielding about 17.6%.

Compare turbo pump and pressurized feeding systems for liquid-propellant rockets, detailing tanks, plumbing, gas generators, turbines, injectors, and thrust chamber operation with examples from Space Shuttle and Raptor engines.

Explore turbopumps, where hot gas drives a turbine powering a pump moving propellants from tanks to thrust chamber, and see how cavitation at high rpm is prevented by pressurizing tanks.

Explore pogo instability in rocket engines, where pressure fluctuations at the pump inlet affect mass flow and thrust, and see how a small propellant tank stabilizes it via propulsion feedback.

Explains conduction, convection, and radiation as the three heat transfer methods, with examples like a hot pot and radiators, and introduces heat-transfer rate formulas including conduction and the Stefan-Boltzmann law.

Examine rocket engine cooling techniques—regenerative cooling with fuel passages, cooling jackets, and channels, and radiative cooling of the nozzle extension—and compare steady and unsteady heat transfer with convection and radiation.

Explore injector designs that deliver propellants as a fine spray at high pressure for rapid mixing, using axial, parallel, and impinging jet configurations for cryogenic lox/lh2 and vapor-phase hyperbolic propellants.

Show how propellant choice and oxidizer-to-fuel ratio—stoichiometric and about three to three point five—shape characteristic velocity, exhaust velocity, chamber temperature, and rocket performance with LH2/LOX and kerosene-LOX.

Explore solid propellant rocket engines, where propellant grain burns inside a casing with ignition, a burning surface, and insulation to withstand about 3500 kelvin temperatures.

Analyze solid propellant rocket engines by linking mass flow rate, burning area, and burning rate to chamber pressure, density, and propellant-specific burn rate coefficient and combustion index.

Electric propulsion delivers higher specific impulse and exhaust velocity than chemical rockets, enabling faster deep-space missions; it includes electrothermal, electrostatic, and electromagnetic systems like ion and Hall thrusters.

Explore electric thermal thrusters, heating propellants to create high-velocity exhaust. Compare resistive jet and arc jet designs, noting hydrazine use, power ranges, and heat-limited lifetimes.

Explain how xenon ionizes in an ionization chamber under a radial electric field in electrostatic thrusters, producing exhaust velocity and thrust, with electrons guided by a magnetic field.

Examine an electrostatic xenon ion engine used in NASA's deep space probe, calculating exhaust velocity 38,327 m/s, thrust 0.086 N, mass flow 2.26e-6 kg/s, and specific impulse 3,900 s.

Explore how a power supply charges a capacitor, discharges through a switch, and drives current between rails via a metal bar or plasma arc to generate field and Lorentz force.

Explore how a 1 μF capacitor charged to 2000 V powers a thruster with exhaust velocity 13,700 m/s and thrust 860 μN, and determine RC resistors for 0.25 s pulses.