Liftoff to landing, on one trajectory.
A reusable booster flown end to end: a gravity-turn ascent, main-engine cutoff and staging, then the hard part — a propulsive 'suicide-burn' landing that has to arrive at the pad with zero velocity and zero altitude at once. A thrust-vector attitude loop holds the vehicle steady, and a 500-trial Monte-Carlo bounds where it actually touches down.
Every phase of flight, modelled.
Ascent, staging, descent and landing — each a runnable notebook, built up to a full dispersion analysis and a verification gate.
Ascent
The rocket equation in 1-DoF then a 3-DoF gravity turn: main-engine cutoff at 38.5 km and Mach-scale speed, 13.5 km downrange at a 65° flight-path angle, max-Q held to 42.6 kPa.
Staging
Main-engine cutoff at 72 s leaves a ballistic apex of 130.6 km and reserves 1474 kg — about 7% of propellant — for the recovery burns.
Suicide burn
The hoverslam: a drag-free estimate says ignite at 939 m, but accounting for descent drag a bisection finds the true ignition altitude at 132 m, arriving at 1.49 m/s with 86% margin.
TVC attitude
A thrust-vector control loop gimbals the engine to reject an 8° disturbance and settle to 0.49°, trimming −2.95° against the steady aerodynamic torque.
Landing dispersion
A 500-trial Monte-Carlo over winds and initial-condition scatter gives a 34.0 m circular error probable and a 67.9 m R95 — the landing-pad sizing number.
Globe trajectory
The full ascent, boostback and descent rendered as a phase-coloured 3D arc over Cape Canaveral, with a 2D altitude-versus-ground-track companion.
An attitude loop that holds through the burn.
The descent isn't just a velocity profile — the vehicle has to stay pointed. A thrust-vector control loop gimbals the engine against an 8° disturbance and a steady aerodynamic torque, settling the attitude to 0.49° while the landing burn runs. The same model carries the staging energy budget, so the recovery propellant reserved during ascent is the propellant the landing actually spends — the two phases share one set of numbers instead of being signed off in separate tools.
Every flight number, re-derived and gated.
The sign-off notebook re-derives all seven requirements from the same trajectory the design notebooks fly.
| Result | Target | |
|---|---|---|
| Apogee / MECO altitude | 38.5 km | ≥ 35 km |
| Max dynamic pressure | 42.6 kPa | ≤ 45 kPa |
| Touchdown speed | 1.49 m/s | ≤ 2 m/s |
| Landing CEP (500 trials) | 34.0 m | — |
| Requirements verified | 7 / 7 | PASS |
Trajectory-grade GNC fidelity.
The vehicle is a 3-DoF point mass with a single-channel thrust-vector loop and an exponential-atmosphere drag model — not a full 6-DoF model with a Mach-dependent aerodynamic database, Earth rotation, J2, or a flexible-body structural model, and the boostback leg is illustrative. That is the right fidelity for the questions reusability poses first: how much propellant the landing costs, when to ignite the suicide burn, how tight the touchdown dispersion is, and whether the attitude loop holds — answered on your own vehicle numbers, long before a high-fidelity flight simulator is in the loop.
Fly your own vehicle home.
Book a walkthrough and we'll drop in your stage masses, engine and aero numbers and run the ascent, landing and dispersion studies live.