Cycle & propellants—why LOX/CH₄ and a gas-generator.
I chose LOX/CH₄ for clean combustion, good performance, and practical handling. To keep the scope realistic for a class project, I went with an open gas-generator (GG) cycle instead of staged combustion: far fewer integration headaches, no hot-oxygen preburner, and still plenty of shaft power for the pumps. 

Thermal management—regenerative cooling choice.
For regen I ran methane through the cooling channels (not oxygen) to avoid GOX formation and reactivity in hot passages. That choice pushes the fuel pump head higher, but it’s a good trade for materials safety.

Nozzle shape—how I generated the contour.
I first wrote a 2D method-of-characteristics (MOC) contour tool to learn the workflow, then switched to a validated axisymmetric MOC solver to get physically sized hardware. The axisymmetric solution resulted in an exit area that matched with my hand-calculations within a few centimeters, and I used that contour for the final engine CAD.

Turbomachinery—how I sized the pumps and turbine.
I targeted Pc ≈ 60 bar and carried empirical losses (≈20% injector, ≈15% cooling) to set pump discharge pressures. With a 3 bar inlet assumption, the results were about 88.24 bar (CH₄) and 70.59 bar (LOX) at the pump exits. I then computed pump heads, speeds, diameters, and MW-level powers from the course correlations; those powers set the turbine power. With a very fuel-rich GG (ϕ≈10), the turbine inlet temperature sits around 1039 K and the required turbine mass flow comes out near 2.44 kg/s.

CAD linkage—turning numbers into hardware.
Once I had the pump/turbine numbers, I generated blade profiles in ADT and integrated them into the power-pack CAD with the MOC nozzle.

Combustion properties—how I used Cantera.
I used Cantera in Python to compute chamber-gas properties at cryogenic inlet temperatures (∼110 K CH₄, 90 K O₂). From the chosen mass-flow split I got equivalence ratio, T₀, cp, R, and γ, which fed the throat sizing and nozzle performance calculations. For simplicity, I held these properties constant through the nozzle.

Aerodynamics & reference area—drag and planform model.
For drag I used the standard D = ½ ρ v² Cᴅ A with a Mach-bucket Cᴅ approximation (0.2 subsonic, 0.5 transonic, 0.3 supersonic, 0.6 hypersonic). The rocket cross-sectional area ties directly to the engine count and exit areas (tight-packed layout for multi-engine options), so propulsion and aerodynamics stay consistent.

Mass & T/W bookkeeping—tying it to the ascent target.
At liftoff I compute thrust from the sea-level equivalent exhaust velocity and total mass flow, then back out wet mass from T/W = 5. The ascent loop runs until the 8,000 m/s target is reached (or prop is essentially exhausted)