A full worked rocket propulsion sizing case study — the Tsiolkovsky rocket equation applied to a real mission delta-v, a worked proof of why single-stage is infeasible at this delta-v, a two-stage sizing that closes the same mission, and liftoff thrust-to-weight sizing.
The project brief: a small-satellite launch provider needs a first-order propulsion sizing study for a two-stage LOX/RP-1 launch vehicle carrying a 50 kg payload to a 500 km circular LEO, against a 9,400 m/s mission delta-v budget that includes gravity, drag, and steering losses on top of orbital velocity. Deliberately framed as this program's clearest demonstration of the rocket equation's exponential tyranny, it shows — with real numbers, not just an assertion — why staging is a physical necessity at this delta-v rather than an optional efficiency refinement.
This module walks the whole sizing study the way a real launch vehicle systems engineer would: a worked single-stage propellant mass fraction calculation, a numeric proof that no positive-payload single-stage solution exists at an achievable structural fraction, a two-stage sizing that closes the identical mission, and a liftoff thrust-to-weight calculation converting the sized vehicle mass into a concrete stage-1 thrust requirement. The full worked numbers, complete mass budget, and finished design reasoning are part of the unlocked module below.