Presets
Playback
Vehicle and flight programme
Change the stage data and the pitch kick, then watch whether the burn reaches orbit.
Layers
Model checks
The science
Rocket equation
With exhaust speed ve = Isp g0 the velocity gained by burning propellant from mass m0 down to mf is Δv = ve ln(m0/mf) (Tsiolkovsky). Staging throws away dry mass so the second burn starts light. A real ascent to low orbit needs about 9.3-9.5 km/s of Δv: 7.8 km/s of orbital speed plus gravity, drag and steering losses.
Equations of motion
The vehicle moves in an Earth-centred inertial plane: r'' = -μ r/|r|3 - (½ ρ(h) Cd A v) v/m + (T/m) ̂u, with ρ(h) = 1.225 e-h/8500 m. The pitch programme is the standard gravity turn: fly straight up, tip over by a kick of several degrees, then thrust along the velocity vector so the angle of attack stays near zero (little side loading). Stage 2 points its thrust a chosen fraction of the way from the velocity direction toward the local horizontal to build orbital speed. Maximum dynamic pressure q = ½ρv2 marks the most stressful moment.
Orbit from the state
The osculating orbit follows from the specific energy ε = v2/2 - μ/r (a = -μ/2ε) and angular momentum h (e2 = 1 + 2εh2/μ2). Perigee above about 100 km (and above the atmosphere) means a stable orbit.
Honest simplifications: generic launcher (no real vehicle is modelled), constant thrust and Isp (real thrust rises with altitude), no Earth rotation or oblateness, no wind, flat-plate-like constant Cd (real Cd changes with Mach number), no throttling or guidance feedback, vertical plane only.
What to try
- Reference preset then "Skip to engine cut-off": the orbit readout should show a perigee above 100 km (an elliptical orbit of roughly 170 by 670 km).
- Gentle kick (6 deg): the path stays steep, the vehicle climbs high but ends with too little horizontal speed for an orbit.
- Underpowered preset: thrust-to-weight near 1.3 wastes propellant fighting gravity.
- Find the max q marker in the second graph.