Every rocket fights the same tragedy: to go faster you carry more fuel, but more fuel is more weight to carry. The arithmetic of that fight is the Tsiolkovsky rocket equation, and it’s brutal — your speed gain rises only with the logarithm of how much of the rocket is propellant. Reaching orbit takes about 9,400 m/s of velocity change. A single stage almost never gets there.
The way out is staging: burn a tank, then throw it away so you stop hauling dead metal. Pick a propellant, a mass ratio, your stages, and your liftoff thrust — then light it and find out if you made orbit or just made a very expensive noise.
🐧 NULL watched the single stage strain and fall back, then watched the second stage drop its empty tank and slip into orbit. NULL marked it: you go up by letting go.
Orbit isn’t about altitude — it’s about speed. To stay up, you have to go sideways fast enough that you keep missing the ground: roughly 7,800 m/s orbital velocity, and about 9,400 m/s of total Δv once you add the losses to gravity and air drag on the way up.
The rocket equation is the villain. Your Δv grows with the natural log of your mass ratio — so doubling your propellant doesn’t double your speed, it adds a sliver. A single stage carrying enough fuel to reach orbit would have to be ~95% propellant by mass, with paper-thin tanks. Almost nothing can be built that light.
Staging is the escape hatch. Burn a tank, drop it, and the log term resets for the next stage — you stop spending thrust to accelerate empty metal. That’s why every orbital rocket in history has stages. In the lab: a single stage at a realistic mass ratio falls short; the same propellant split into two or three stages makes orbit.
And TWR is the gatekeeper. If your thrust doesn’t exceed your weight at liftoff, you don’t go anywhere — you sit on the pad burning fuel. Above 1.0 you climb; real rockets lift at about 1.2–1.4.
The Tsiolkovsky rocket equation:
where Isp is specific impulse (s), g₀ = 9.80665 m/s², and m₀/m_f is the wet-to-dry mass ratio. This lab models identical stages: total Δv = stages × Isp · g₀ · ln(R) — a clean teaching approximation that captures staging and propellant choice exactly, while smoothing over per-stage payload bookkeeping.
Real specific impulses used here: solid booster ~265 s, kerolox (RP-1/LOX) ~330 s, methalox ~360 s, hydrolox (LH2/LOX) ~450 s.
Orbit target: ~7.8 km/s orbital velocity, ~9.4 km/s Δv including gravity and drag losses to low Earth orbit. Liftoff: thrust-to-weight ratio must exceed 1; real first stages lift around 1.2–1.4.
Falcon 9 reference: over 90% propellant by mass at launch; a single-stage-to-orbit rocket would need a mass ratio near 20 (~95% propellant). Stylized: the ascent animation and stage drops are illustrative, not a trajectory solver. Built to teach, not to scare.
Sister lab: What Comes Down (what your satellite leaves when it returns). Flying-Car rockets (eVTOL hover physics + four-environment certification) land in v0.2.