100 t first-stage recovery model

한국어 | README

This is a theoretical 2D software model, not a flight-qualified vehicle. Root seed: 378. The mission is launch, cold separation near 37 km and recovery of the first stage at the original pad. The upper assembly’s 500 kg payload and 700 km circular-orbit insertion are assumed; upper-stage flight is not integrated.

Optional angular sensor errors, packet omissions, the attitude estimator and frozen evaluation assumptions are documented in Validation design. The default observation assumptions here continue to describe the existing operating interface and regression inputs.

Vehicle inventory

The first-stage hull is 20 m long and 3 m in diameter. The upper assembly is 8 m long with lumped COM at station 24 m above the first-stage hull base.

Four installed fins have 6 m² total area, represented by two planar equivalent surfaces with 3 m² combined effective area. The 600 kg allocation includes 360 kg surfaces, 160 kg actuators, 60 kg deployment and 20 kg electrical equipment. Four conceptual legs are represented by two feet at a 4 m half-span; the pad half-width is 10 m.

Feed/pressurization, baffles and separation equipment occupy 1,015 kg inside the airframe/systems budget: 65 kg closed helium, 450 kg bottle/regulation, 150 kg collector hardware, 300 kg baffles and 50 kg pushers. The 1,500 kg retained liquid buffer is part of main propellant, not added mass. These are concept allocations, not measured parts or qualified component designs.

Nozzle pressure correction uses local pressure. Thrust and propellant use share the same actual delivered mass flow. RCS depletion removes available RCS torque.

Coordinates and integrated physics

The launch pad is the local origin: +x east/right, +z up. Position is instantaneous total COM, not the hull base or feet. Pitch theta is clockwise from vertical; positive gimbal rotates thrust clockwise. There are two translations and one rotation, not six spatial degrees of freedom.

thrust_x = thrust * sin(theta + gimbal)
thrust_z = thrust * cos(theta + gimbal)
clockwise_torque = arm_z * force_x - arm_x * force_z

Mass, COM and inertia change with propellant consumption, deployment and staging. Thrust, atmosphere-relative aerodynamic forces, altitude-dependent gravity, local Coriolis projection, RCS/fin moments and internal slosh are coupled. Slosh changes body geometry relative to total COM; it is not a fictitious external force. States are not overwritten at touchdown to manufacture success.

The plant integrates all 19 states. Nominal RK4 step is 0.010 s and control period is 0.020 s. Foot contact uses event detection and smaller near-contact steps. Four supplementary cases use 0.005 s integration steps; this is not a convergence proof over the whole continuous envelope.

Supply, slosh and staging

The reduced supply model uses one equivalent liquid at 826 kg/m³, a 1,500 kg retained collector and a 650 kg/s supply limit. Liquid acquisition depends on proper acceleration. Full nominal demand is approximately 543.8 kg/s; the buffer provides approximately 2.76 s at full flow, with a 0.35 s settling time constant.

main_dot = -delivered
buffer_dot = pickup - delivered
bulk_dot = -pickup

Buffer refill does not consume propellant twice; an inactive engine does not drain retained liquid during coast. Supply shortage reduces mass flow and thrust together and remains an explicit failure check.

Closed isothermal helium follows p = m*R*T/V with two conserved inventories. Bottle volume is 1.3 m³ and total helium is 65 kg. Tank regulation targets 350 kPa, not combustion chamber pressure; inlet supply declines toward 220 kPa. Restart requires at least 350 kg buffer and 280 kPa tank pressure, then an assumed 0.2 s ignition delay. Vessel, volume and supply budgets are theoretical checks.

Slosh uses a nonlinear planar pendulum: 3% of remaining main liquid in a 0.8 m mode, damping ratio 0.12. The coupled mass matrix retains body/modal momentum, Coriolis and centrifugal terms. Restoring action uses proper axial acceleration, not gravity artificially imposed during free fall. A 100 kN modal constraint-force requirement and the tank geometry bound model validity; exceeding the domain fails.

Staging applies equal/opposite impulses with 0.5 m/s relative axial speed, 2 mm lateral offset and 0.15 s equivalent pulse duration. Linear/angular momentum and inherited internal motion are retained. The separated booster is rebased to its own COM; velocity and angular rate are not reset to zero. Recorded pulse- average angular acceleration is not a resolved peak shock.

Guidance and observations

Ascent starts its flow-limited pitch program at 15 s, with a 25° pitch cap. It anticipates cutoff and finite attitude slew, aligns with airflow before engine shutdown and checks the actual separation state. Recovery uses a low-pressure RCS flip, finite-burn return prediction, advance entry braking, horizontal alignment and vertical terminal landing. Prediction is reduced-order guidance, not the acceptance simulation.

The controller uses delayed telemetry, delivered-command history, nominal plant parameters and forecast mean wind. A planar navigation estimator tracks position, velocity and acceleration bias. Raw position/velocity errors are bounded 2D uniform-disk errors; a bound on raw noise is not a bound on filtered error. The controller does not read hidden true wind, thrust or inertia deviations.

Attitude, gyro, propellant and actuator channels are ideal delayed telemetry. Staging safety and ignition interlocks use actual modeled state/supply. These ideal instrument assumptions are not a complete sensor implementation. Acceptance uses the independently recorded true simulated state.

Eligible environmental and healthy deviations

The atmosphere is a layered hydrostatic approximation over 0-100 km. Latitude defaults to 37° for local Coriolis projection; this is not a full 3D geodetic Earth or a measured launch-site weather profile.

Wind profiles must span the full altitude domain. Optional temperature/pressure profiles must also span it. Final density is checked against the fixed nominal atmosphere, so incompatible temperature/pressure/density combinations are rejected. Initial mass deviations belong to equivalent dry structure, not additional fuel.

Gusts have finite time and altitude windows; configuring amplitude does not prove that the flight actually encounters it. Forecast guidance uses mean horizontal wind only. The retained forecast-gust amplitude field is validated/recorded but does not create a forecast gust waveform. Actual vertical wind is also withheld.

Known faults, failed weather/health reviews, precipitation and thunderstorm/hail inputs are excluded. Review booleans do not model lightning or authorize a real launch. Eligible inputs can still fail flight acceptance.

Separation and acceptance

Mission completion, pre-contact flight safety and landing are separate groups; overall success requires every applicable criterion.

These are provisional concept requirements, not certified limits derived from 100 t launch mass. Simple strength and hinge estimates do not resolve shell buckling, fatigue, vibration, thermal damage or a calibrated supersonic fin map.

The kinematic_touchdown assessment ends at first foot contact. Foot speed includes body rotation; position refers to COM. No fixed extra residual reserve is required, but exhausting fuel before completing the mission is a failure. Legs are assumed adequate at ≤1.5 m/s. Contact forces, strut stroke, material strength, engine-off settling and stable standing are not evaluated, not passed.

Recovery-only runs preserve the supplied separation state but reset controller memory and mark upstream ascent checks as not evaluated. They do not establish full-flight success. Replay is presentation only: hiding exhaust at contact does not simulate engine shutdown or post-contact dynamics.

For a full-flight record with upper-stage staging states, replay carries the recorded upper COM position, velocity and angular rate into a separate visual departure. Its illustrative engine starts three seconds after separation, ramps to a prescribed 18 m/s² thrust acceleration with a 1.2 s time constant, and uses 4 s angular-rate damping. A closed-form display curve includes constant gravity at separation; it is not a variable-mass upper-stage dynamics or orbit solution. The dashed overview ends at 100 km altitude or the end of the recording. These visual assumptions do not consume simulated fuel or change first-stage states, acceptance or telemetry. Missing staging states and recovery-only records do not fabricate an upper-stage departure. Clip bounds select recorded seconds only; full-flight rendering remains the default.

Local UI contract

The optional ui extra exposes the packaged HTML interface through a loopback-only FastAPI application. Flight calculations run in a separate local process. Only one calculation or video-rendering job runs at a time; the interface polls its status without starting another flight. No external API, analytics or CDN is used. Mutation requests require the application’s per-session token and same-origin checks. Download routes accept only the app’s generated result and media filenames.

The UI keeps the current 100 t design, seed 378, active fins, first-contact landing assessment and 0.01 s integration step fixed. Environment and uncertainty inputs are validated by AprConditions and RecoveryDisturbances, including combined density and altitude-profile constraints. Completed flight failures retain their results and are distinct from execution errors. Missing contact measurements are not reported as zero or as passing landing criteria.

The result view uses recorded values and the calculation’s input snapshot. Graphs may use a bounded sample set for display; the downloadable JSON retains the full record. First-contact speed values use landing-gear contact-point kinematics. Only a successful full mission enables video generation from its existing record. User-selected video intervals and resolutions affect rendering, not acceptance. MP4 generation renders individual frames on the CPU and can take considerably longer than flight calculation. Longer clips and higher resolutions add work; use a short 640 × 360 interval for a quick preview. The UI explains this before generation and while rendering. Keep the application open; recorded graphs and tables remain available. No fixed wait time or GPU-rendering speedup is promised. The Windows launch-dm100.bat launcher locates a working Python 3.12 interpreter, creates an isolated .venv and installs the project with the ui and video extras. It reuses a healthy environment and preserves/rebuilds an unusable or relocated environment instead of trusting the presence of python.exe. First setup and repairs require internet access. --setup-only prepares the environment without opening the app; other arguments are forwarded to the local application. Python itself is a prerequisite, not an automatic download. The local UI remains a source-installed application. Fresh Windows installation and Linux-container checks are recorded in environment reproduction. Korean replay labels on Linux require a Hangul font. Standalone executable distribution is outside the current release.

Evidence and limitations

The original design recorded 205 development, 72 previously observed regression and nine supplementary full-flight checks. The 277 primary and nine supplementary denominators remain separate. Minimum main/RCS remaining were 2,958.185391 / 95.875194 kg; maximum RCS use was 204.124806 kg. Maximum foot vertical speed over all 286 checks, including a half-step case, was 1.2550572 m/s.

The current repeated regression and newly frozen evaluation measurements are in the numerical report. Original records and new evaluation populations have separate denominators.

The tracked configs/apr-regression-v1.json preserves the 286 declared inputs, seed modes and integration steps for portable reruns. They are known regression conditions, not new independent holdout. Results record all failures, fuel ledgers, actual gust exposure, source/input hashes and execution integrity. Finite sampled success does not prove the continuous envelope.

Outside scope: separate cryogenic fuel/oxidizer flow, boiling and pump cavitation, multi-mode fluid impacts, flexible structure, connector/pyroshock transients, combustion/restart reliability, upper-stage ignition/plume and orbital flight, detailed heating/ground damage and leg/pad material strength. Helium inventory transfer conserves mass, but its redistribution does not separately update COM. No measured parameter calibration or real-vehicle safety certification is claimed.