# ORIOLE / WRDE initial design and feasibility study

**Release 0.2.5-martin · 2026-09-10 · preliminary, not qualified hardware.** Trajectory 0.2.4-finch; CAD 0.2.1-swift; reference chemistry 0.2.0-oriole with flight-linked chemistry and 0.2.4-finch conservation audit. Computed on 146 / lessokaji-9v74x2.

Live artifact: https://wrde.artifact.oa.lessokaji.com/  
LAN: http://192.168.0.146:8796/  
New workspace: /root/Desktop/src/wrde/ai-deck/0.2.0-oriole  
Original preserved: /root/wobble-engine on 146; D:\work\projects\wrde on TH155.

## Result and feasibility

The best searched 24 t hybrid reaches **153.58 km apogee**, with **4.640 km/s inertial speed** there. Its perigee is **-4975 km**, inside Earth. This is suborbital, not orbital insertion. More altitude alone does not repair the orbital energy deficit.

An ideal instantaneous transfer from this apogee to a circular 200 km orbit still needs approximately **3.20 km/s**. At assumed 360 s Isp, adding propellant at apogee would require approximately **8.1 t**, before accounting for the penalty of carrying it through ascent. This diagnostic does not close a redesigned vehicle.

At air-mode exit, an ideal impulsive transfer/circularization to 200 km requires about 6.14 km/s. From the then-current 13.77 t mass, the ideal rocket equation leaves only **2.42 t total final mass**, before finite-burn losses. Dry mass alone is assumed to be 5 t. No supported WRDE efficiency credit repairs this difference.

**Deliverables are real concept CAD and reduced-physics computations. Neither a feasible SSTO nor sustained detonation in these engines has been established.** A returned, landed or crew-safe vehicle is not simulated.

## Initial CAD and mechanism

Three assemblies: oriole-mini.step/.stl, wrde-air.step/.stl, wrde-hybrid.step/.stl; component STL files are included. Units are **millimetres**. STEP uses real OCCT boundary-representation solids. All component shapes passed kernel validity checks; this does not prove assembly fit, stress margins or manufacturability. Flow/installation envelopes intentionally overlap. The STL compound is not one printable pressure vessel.

The craft is 14 m long, 9 m span, with a 45 m² assumed aerodynamic reference area. Outer mold line, delta surfaces, cabin, twin engine installations and separate tank volumes are modeled. Aerodynamic coefficients are assumptions, not CAD-derived CFD. Pressure-vessel walls/endcaps, insulation, landing gear and detailed crew systems are absent.

Both engines have 700 mm diameter, 24 mm thick disks, 0.25° tilt, 74.48° relative phase, and 20 Hz mechanical wobble. Disk centers are ±32 mm. The active radial band is 290–348 mm; minimum analytic face gap is 38.162 mm. Hub/carrier/shaft, inlet, manifold, collector and nozzle shapes are design envelopes. The hybrid adds oxygen feed and air isolation envelopes.

Q=Rz(phi) Rx(beta) Rz(-phi) returns material orientation each cycle without continuous full disk turns. **It does not have strictly zero instantaneous axial spin:** -0.001196 rad/s. The HTML material markers make this convention inspectable. Real bearing, anti-rotation and seal mechanisms remain unresolved.

Rim acceleration is 24.12 m/s² versus approximately 145,247 m/s² in the earlier candidate. Lower frequency reduces inertia, but pressure support is still a critical failure gate. A simple 100 mm cantilever strip, 24 mm thick, at illustrative 8 MPa gives **417 MPa** bending stress; reducing effective unsupported span to 50 mm gives 104 MPa. Actual supports, temperature-dependent allowables and transient pressure footprint are required. Oxygen detonation spikes can exceed the illustrative 8 MPa substantially. **This hot-face disk is mechanically unqualified.**

A stationary pressure-supported hot chamber with a separate cold-side wobble flow-control element is a useful next architecture trade. It is not silently substituted for the supplied hot-disk concept.

## Two propulsion variants and power

**A: pure methane–air WRDE.** Ram compression supplies air. External Mach 2.2 start is required; no static thrust or vacuum operation is claimed. The pure-air demonstrator starts at 18 km with 1.5 t fuel, 5 t dry and 0.3 t reserve, totaling 6.8 t. It is a different initial-mass mission from the hybrid. A self-starting version needs a compressor and a closed shaft-power/mass budget.

**H: methane–air plus methane/LOX WRDE.** Rocket mode supplies takeoff/boost and the final burn; the air inlet is isolated for rocket operation. “Hybrid” means combined-cycle operation, not a solid-fuel hybrid rocket. Both propellants are liquid in storage, while the chemistry calculations start with gases. Feed-system power, evaporation and injection performance remain unestablished.

Flight thrust is a **required/assumed performance map**, not measured thrust or coupled WRDE CFD output. Total rocket vacuum ceiling: 480 kN, 360 s Isp, O/F 3.5 and combined effective exit area 0.60 m². Throttle limits thrust acceleration to 3.2 g; total aerodynamic proper load is evaluated separately.

Airflow uses 3.2 m² total capture area, factor 0.8 and map cap 180 kg/s. F=ṁair[(1+f)Ve−V] explicitly deducts ram drag. Recovery is 0.82/0.65/0.42/0.20 at Mach 2.2/3/4/5. Combustor total-pressure multiplier 0.92 gives **no detonation pressure-gain credit**. Assumed CH₄ LHV 50 MJ/kg, equivalence ratio ≤0.9, combustion/nozzle efficiencies 0.96/0.94, product cp 1250 J/kg/K, γ=1.28, and product-temperature cap 3000 K. Ideal ambient expansion assumes an adaptable nozzle. High-temperature variable composition and installed inlet/nozzle losses require higher fidelity. [NASA thrust formulation](https://www.grc.nasa.gov/www/BGH/ramth.html).

Near air exit, computed whole-vehicle net thrust is 54.2 kN, drag 29.4 kN, lift 121.4 kN and airflow 72.2 kg/s. Chemical fuel-input power is 189.3 MW; propulsive power F·V is 75.2 MW. Peak rocket chemical input is 1.51 GW. **Usable disk-shaft power has not been solved**; chemical power cannot be substituted for it.

## Mass and tank volume

| Allocation | Mass / kg |
|---|---:|
| Airframe and landing structure | 1300 |
| Tanks, insulation, feed | 650 |
| Two engines, inlets, nozzles | 1250 |
| Thermal protection | 650 |
| Cabin, life support, pilot | 420 |
| Avionics, actuation, electrical | 330 |
| Dry contingency | 400 |
| **Dry, including 120 kg pilot/suit in cabin allocation** | **5000** |
| Reserved inert mass, not spent in ascent | 300 |
| Optimized CH₄ loading | 5291.1 |
| LOX loading | 13408.9 |
| **Gross** | **24000** |

These are explicit engineering allocations, not weighed or structurally sized hardware. Tank gross volumes are 14.975 m³ CH₄ and 13.399 m³ LOX. At assumed densities 422/1141 kg/m³, the selected loading leaves 16.3%/12.3% volume unfilled, exceeding the 5% minimum ullage screen. Storage thermodynamics, slosh, boiloff and CG migration are not solved. The fuel guard leaves approximately 149.2 kg methane beyond the separate 300 kg reserve.

## Best searched path to space

Equatorial eastward launch includes Earth rotation. Idealized rocket runway roll to nominal 115 m/s consumes propellant and accounts for rolling resistance/lift/drag; distance is 424 m. It does not qualify tires, rotation, abort or a real runway.

| Event | Time / s | Altitude / km | Air speed / km/s | Flight path / deg | Mass / t |
|---|---:|---:|---:|---:|---:|
| Liftoff | 7.0 | 0.02 | 0.120 | 3.00 | 23.048 |
| Air mode start | 110.0 | 17.85 | 0.666 | 25.53 | 15.169 |
| Air mode end | 362.0 | 29.36 | 1.387 | 0.67 | 13.769 |
| LOX depletion | 466.2 | 91.04 | 4.304 | 11.72 | 5.449 |
| Apogee | 609.7 | 153.58 | 4.165 | -0.00 | 5.449 |

Event states are nearest 2 s saved samples; times come from the integrator. Air exit is near Mach 4.60 and 29.36 km. The fuel guard may trigger before requested switch Mach 4.687. Rocket thrust elevation is scheduled from 24.70° toward 4.07° over 230.5 s, subject to atmospheric angle and load limits.

Peak q: **33.66 kPa**. Peak proper load: **3.56 g**. Nose heating estimate: **238.4 kW/m²**, integrated **33.7 MJ/m²**. Heating uses 1.83e−4 sqrt(rho/Rnose) V³ with 0.5 m nose radius. It predicts neither wall temperature nor thermal-protection life. [Sutton–Graves](https://ntrs.nasa.gov/citations/19720003329).

The simulation ends at apogee. **Descent, reentry, crossrange, landing and crew survival are not solved.**

## Gravity-loss hypothesis

| Case | Apogee / km | Final inertial km/s | Gravity / m/s | Drag / m/s | q / kPa | Proper g |
|---|---:|---:|---:|---:|---:|---:|
| 24 t hybrid / best searched | 153.6 | 4.640 | 953 | 1096 | 33.7 | 3.56 |
| Steeper hybrid ascent | 238.7 | 4.408 | 1158 | 1104 | 33.7 | 3.58 |
| Pure air / externally started | 29.6 | 1.884 | 117 | 598 | 30.4 | 3.39 |
| Optimistic engine / same mass | 167.6 | 4.902 | 970 | 771 | 33.9 | 3.60 |
| Conservative engine / same mass | 125.0 | 4.003 | 917 | 1285 | 33.4 | 3.51 |
| Same vehicle / rocket only | 147.1 | 4.259 | 926 | 483 | 55.0 | 3.46 |

Hybrid post-liftoff signed integrals: thrust impulse 6112.0, gravity 952.8, drag 1096.4, steering 18.6 m/s. These close the air-relative speed budget; runway fuel/velocity are separate. Lift reduces along-path gravity demand but does not eliminate gravitational work. Induced drag and longer residence time can offset the benefit.

The rocket-only comparison keeps initial total mass and the engine/airframe dry allocation, but rebalances propellants to O/F=3.5. Its roughly 14.54 t LOX requirement marginally exceeds this tank's nominal 5%-ullage capacity, so it needs a small tank reallocation. Its pitch policy is independently optimized. Different endpoints prevent interpreting the difference as a universal Δv reduction.

The selected hybrid has greater drag loss and similar gravity loss to the rocket-only comparator. Air breathing is not enough to close orbit here. ±20% air thrust, ±15% drag, 340–380 s Isp and 2.5–6 t dry-mass fixed-guidance sensitivities also do not establish orbit. The dry-mass sweep retains loaded propellant, so gross mass changes.

## Detonation chemistry

Cantera 3.2 and Caltech SDToolbox compute CJ speeds and finite-rate planar ZND. ZND uses **1% speed overdrive**, avoiding the exact CJ sonic endpoint. These are ideal gas-phase results, not sustained rotating-engine CFD. [Caltech methods](https://shepherd.caltech.edu/EDL/PublicResources/sdt/), [Cantera](https://cantera.org/3.2/examples/python/index.html).

| Case | T / K | p / bar | CJ / m/s | Induction / mm | Exothermic scale / mm |
|---|---:|---:|---:|---:|---:|
| air-cold | 300.0 | 1.013 | 1803.0 | 12.53677 | 0.236408 |
| air-design | 700.0 | 5.000 | 1771.4 | 1.19727 | 0.102934 |
| air-hot | 1000.0 | 5.000 | 1760.9 | 0.50632 | 0.090319 |
| oxygen-design | 300.0 | 30.000 | 2606.0 | 0.00390 | 0.000540 |
| flight-air-entry | 446.1 | 0.706 | 1751.9 | 16.70291 | 0.354828 |
| flight-air-mid | 840.4 | 1.021 | 1733.8 | 3.52359 | 0.320033 |
| flight-air-exit | 1178.5 | 1.227 | 1719.1 | 1.25515 | 0.287968 |

Flight-linked cases use actual modeled inlet total states and an assumed Mach 0.15 plenum static conversion. This is a coupling assumption; inlet recovery against detonation backpressure is not established.

The 1000 K reference prints an exact-CJ equilibrium-state nonconvergence warning. Its downstream equilibrium T/P is excluded from qualified output. Its separately solved frozen overdriven shock passes the conservation screen and initializes ZND. Raw warnings and residuals are retained. Small conservation error does not erase solver nonconvergence.

GRI30 highT contains 53 species/325 reactions; SHA-256 840f5d412cb8c0a1874ce48efed47ffb53a57225a61daca129e661cc4a4f9c14. Reaction-mechanism uncertainty remains, especially for high-pressure methalox. No cell-width correlation is inferred from induction length. The oxygen reference's frozen shock is approximately 198 MPa at 3 MPa unburnt pressure; that is not an 8 MPa mean chamber state.

The prior approximately 11.7 mm CFD cells do not resolve these micrometre-scale oxygen reaction layers. Finite-rate moving-chamber CFD with real injection, phase change, heat loss, wave/refill interaction and convergence is required before either concept is called sustainably detonating. Laboratory methane-air and methalox rotating detonation evidence supports studying these mixtures, not the current mechanism. [Methane-air experiments](https://doi.org/10.1016/j.energy.2020.118598), [NASA methalox RDRE development](https://ntrs.nasa.gov/api/citations/20250000643/downloads/NASAs%20RDRE%20Dev%20AAS%20Teasley%20Final.pdf).

## Recovered project and open design gates

The September 6 work ran 3,072-cell, 53-species moving reactive CFD for 100 μs of a closed-port startup, with 11 saved states and reported 2.75 ppm mass drift. It did not establish a sustained wave or resolved induction scale.

Its 844.7 Hz structural screen reported 28.45 mm displacement and 11.62 GPa elastic extrapolated stress, outside small-deformation/elastic validity. Pressure-only stress was 367.7 MPa. The earlier candidate was rejected. The new slow wobble is a proposal; old thermal/stress fields are not new validation.

Next gates are a manufacturable pressure-supported/sealed mechanism and a closed pressure/flow/power cycle, followed by resolved reactive CFD and flexible thermal/structural coupling. No new full-engine CFD, wind-tunnel data, experimental performance, six-degree-of-freedom control, TPS design or human-rating evidence is claimed.

## Numerical scope and reproduction

Flight equations use variable gravity and a rotating spherical Earth; orbital elements use inertial velocity. Atmosphere uses standard geopotential layers through 84.852 km, followed by a simple 6.5 km scale-height extension; aero density is zeroed above 150 km. Mach above the continuum atmosphere is only a diagnostic. [U.S. Standard Atmosphere](https://www.ngdc.noaa.gov/stp/space-weather/online-publications/miscellaneous/us-standard-atmosphere-1976/).

Final RK4 uses 0.5 s steps, shortened at depletion. Search uses 2 s steps, seed 41, differential evolution and 1050 evaluations over q target, air exit Mach, pitch endpoints/duration and fuel loading. It is a best searched policy, not a global optimum. Penalty limits: 55 kPa, 4 g, 800 kW/m²; altitude goal 150 km accompanies maximum perigee. Final constraints are evaluated on the finer history.

0.5→0.25 s refinement changes apogee by -24.16 m, perigee by -342.34 m, peak q by -0.93 Pa. This is numerical sensitivity, not physical accuracy.

The source bundle contains Python models, HTML, raw JSON/CSV, CAD, figures, version manifest and SDToolbox license. It excludes operator credentials. Dependencies: NumPy, SciPy, Matplotlib, Cantera 3.2.0, CadQuery 2.8.0/OCCT 7.9.3. The supplied scripts regenerate models, chemistry, CAD and report; server.py serves site/ on 8796. CAD on this host uses its VTK library directory in LD_LIBRARY_PATH. Run long tasks in TerminalMan.

Figures: [trajectory](trajectory-overview.png), [chemistry](chemistry-overview.png). The separate OA completion report records public-browser acceptance and exact live terminal/browser locations. This numerical study is the delivered result; full feasible-engine/SSTO qualification remains open.

Additional primary references: [NASA SSTO design matrix](https://ntrs.nasa.gov/api/citations/19970005131/downloads/19970005131.pdf), [CadQuery exports](https://cadquery.readthedocs.io/en/latest/importexport.html), [HAYNES 230 material data](https://haynesintl.com/en/alloys/alloy-portfolio/high-temperature-alloys/haynes-230/).