Launch vehiclesAerospace & marine

Reusable rocket

A reusable launch vehicle from liftoff to landing — gravity-turn ascent, staging, a propulsive suicide-burn touchdown, a thrust-vector attitude loop, and a 500-trial landing-dispersion analysis, the descent flown over a 3D globe.

DjiniousLabModelling & simulation

A DjiniousLab notebook plot of a rocket's gravity-turn ascent trajectory — downrange against altitude — with the main-engine cutoff point marked

ideal ascent Δv: 5068 m/sideal ascent Δv
max dynamic pressure: 42.6 kPamax dynamic pressure
suicide-burn touchdown: 1.49 m/ssuicide-burn touchdown
landing CEP (500 trials): 34.0 mlanding CEP (500 trials)
design notebooks: 9design notebooks
requirements verified: 7 / 7requirements verified

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.

A notebook plot of the gravity-turn ascent trajectory — downrange against altitude — with main-engine cutoff marked — The gravity-turn ascent: starting vertical and pitching over under gravity alone, the booster reaches main-engine cutoff at 38.5 km and 13.5 km downrange — no scheduled pitch program, just the turn the trajectory wants to make.

A notebook plot of the suicide-burn descent — altitude and velocity falling to zero together at touchdown — The suicide burn, where reusability is won or lost: a single late ignition has to null altitude and velocity simultaneously. Ignited at 132 m, the booster arrives at the pad at 1.49 m/s — the descent-drag correction moves ignition more than 800 m lower than the drag-free estimate.

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.

A scatter plot of 500 simulated touchdown points around the target with the circular-error-probable ring drawn — Five hundred landings under dispersed winds and initial conditions: the touchdown scatter and its 34.0 m circular error probable. This is the number that sizes the landing pad and sets how much divert authority the guidance has to keep in reserve.

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

Apogee / MECO altitude: 38.5 km
Max dynamic pressure: 42.6 kPa
Touchdown speed: 1.49 m/s
Landing CEP (500 trials): 34.0 m
Requirements verified: 7 / 7

Target

Apogee / MECO altitude: ≥ 35 km
Max dynamic pressure: ≤ 45 kPa
Touchdown speed: ≤ 2 m/s
Landing CEP (500 trials): —
Requirements verified: 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.