{
  "validation": {
    "station_cases_energy_and_thrust_checks_passed": 10,
    "zero-extraction_limiting_cases_passed": 3,
    "dual_temperature_cap_checks_passed": true,
    "burner_cap_mode_positive_extraction_exceeds_accelerator_cap": true,
    "dual_cap_mode_has_no_accelerator_cap_exceedance": true,
    "figure_overlay_is_comparison_only": true
  },
  "title": "Equation-based reconstruction of NASA/TP-2000-210387 Figure 2 reference cycle",
  "source": {
    "record": "https://ntrs.nasa.gov/citations/20000095934",
    "pdf": "https://ntrs.nasa.gov/api/citations/20000095934/downloads/20000095934.pdf",
    "equations": "Printed pp. 5–18 (PDF pp. 11–24); Figure 2 printed p. 21 (PDF p. 27)",
    "copyright": "NASA NTRS record says U.S. Government work; public use permitted."
  },
  "status": "Preliminary conditional reconstruction from the simplified NASA equations; not author code, test data, or a vehicle-performance prediction. Independent reviewers checked its algebra under the stated closures. It is compared with separate approximate visual readings without fitting; the historical readings are under review and do not establish a mismatch with NASA numerical results. This is not a validated reproduction.",
  "figure2_reported_inputs": {
    "freestream_static_temperature_K": 220.0,
    "fuel_heating_value_MJ_per_kg": 45,
    "combustion_efficiency": 1.0,
    "diffuser_total_pressure_ratio": 0.7,
    "burner_total_pressure_ratio": 0.95,
    "nozzle_total_pressure_ratio": 0.98,
    "generator_isentropic_efficiency": 0.9,
    "accelerator_isentropic_efficiency": 0.9,
    "preionizer_power_fraction": 0.05,
    "generator_enthalpy_extraction_ratios": [
      0,
      0.25,
      0.5
    ],
    "burner_exit_stagnation_temperature_limit_K": 3000.0
  },
  "gas_constants_added_for_reconstruction": {
    "gamma": 1.4,
    "R_J_kg_K": 287.05,
    "cp_J_kg_K": 1004.675,
    "reason": "NASA Figure 2 text says it uses air properties but does not tabulate these exact reconstruction constants. They are explicit perfect-air choices here."
  },
  "closures_added_for_this_reconstruction": {
    "preionizer_total_pressure_ratio": 1.0,
    "cooling_expansion_total_pressure_ratio": 1.0,
    "nozzle_exit_pressure": "ambient-matched (pe=pa); the source schematic supports an ambient-pressure exit as a generic cycle boundary, but applying it at every Mach point is an ideal perfectly expanded nozzle choice, not a published fixed-nozzle match. It forces the Eq. 64 pressure-thrust term to zero."
  },
  "two_temperature_limit_modes": {
    "figure2-burner-cap-case": "Sets burner exit T0,4=3000 K as stated for the Figure 2 calculation; independently flags the report's additional 3000 K accelerator-exit limit. By the model equation T0,6=T0,4+positive accelerator heat addition, every successful positive-extraction case exceeds that separate limit. The no-extraction case does not. These are conditional model consequences, not tested operation.",
    "dual-cap-sensitivity": "For sensitivity only, lowers selected burner-exit T0,4 until both report constraints T0,4<=3000 K and T0,6<=3000 K are satisfied. This is not the Figure 2 curve."
  },
  "pointwise_diagnostic_mach6_extraction025": {
    "mach": 6.0,
    "generator_enthalpy_extraction_ratio": 0.25,
    "digitized_source_plot_specific_thrust_kN_s_per_kg": 0.58,
    "estimated_visual_reading_interval_kN_s_per_kg": [
      0.5299999999999999,
      0.63
    ],
    "reconstruction_specific_thrust_kN_s_per_kg": 0.6970971150168468,
    "reconstruction_minus_visual_read_kN_s_per_kg": 0.11709711501684683,
    "reconstruction_pressure_thrust_N_s_per_kg": 0.0,
    "reconstruction_temperature_after_accelerator_K": 3417.5871216361056,
    "reported_general_accelerator_temperature_limit_K": 3000.0,
    "generator_extraction_J_per_kg_air": 458843.9746835442,
    "preionizer_allocation_J_per_kg_air": 22942.19873417721,
    "accelerator_addition_J_per_kg_air": 435901.775949367,
    "energy_split_residual_J_per_kg_air": 0.0,
    "interpretation": "The old 0.58 reading and residual are retained as audit history only; the mismatch inference is withdrawn. Current raster observations are manually read, not NASA-tabulated data. Full uncertainty is incomplete; agreement or disagreement is not validated.",
    "legacy_comparison_status": "withdrawn_as_evidence_of_source_mismatch",
    "current_raster_observation": {
      "mach": 5.996330197831868,
      "ordinate_kN_s_per_kg": 0.7133315378400212,
      "same_column_ink_band_not_total_uncertainty": [
        0.7057904659305141,
        0.7208726097495284
      ],
      "model_at_same_mach_kN_s_per_kg": 0.6978008493094767,
      "model_minus_reading_kN_s_per_kg": -0.015530688530544512,
      "status": "manual raster observation; total calibration and selection uncertainty incomplete; no validated agreement or source error"
    }
  },
  "equation_checks": {
    "freestream": "T0,a=Ta[1+(gamma-1)Ma^2/2]",
    "preionizer_and_diffuser": "T0,1=T0,2=T0,a/(1-zeta*epsilon_g)",
    "generator": "T0,3=T0,2(1-epsilon_g); pi_g=(1-epsilon_g/eta_g)^(gamma/(gamma-1))",
    "burner": "(1+f)cpT0,4=cpT0,3+eta_c*f*q_f",
    "accelerator_power": "epsilon_a(1+f)cpT0,5=(1-zeta)epsilon_g*cpT0,2",
    "accelerator_pressure": "NASA Eq. 53",
    "nozzle_and_thrust": "NASA Eqs. 57, 62, 64 with p_e=p_a closure"
  },
  "digitized_curve_overlay": "nasa-mhd-cycle-overlay-audit.json summarizes unfit model-versus-source-redraw residuals (95 visual readings, RMS 0.0401 and maximum absolute 0.1261 kN s/kg). These are historical differences against old project readings under review; the old allowances are not validated total uncertainty. Do not infer NASA source disagreement from these residuals. The overlay is audit history, not validation.",
  "source_equation_cross_reference_review": {
    "source_locator": "Final NASA/TP-2000-210387: Figure 2 discussion, printed p. 20 / PDF p. 26; Eqs. 36 and 53, PDF pp. 18 and 22. Earlier NASA preprint 20000032786: Eqs. 26 and 30, PDF p. 8; Figure 2 discussion, PDF p. 11.",
    "reported_reference": "The final report's Figure 2 discussion points to Eqs. 25 and 28 for generator/accelerator pressure ratios, but the final report's equation sequence identifies 25 and 28 as diffuser relations.",
    "equation_sequence_observed": "By equation content, final-report Eq. 36 is the generator total-pressure ratio and Eq. 53 is the accelerator total-pressure ratio. The 1999 preprint uses earlier numbering: Eq. 26 is the generator pressure-ratio relation and Eq. 30 is the accelerator pressure-ratio relation; its Figure 2 discussion explicitly points to 26 and 30 for those component ratios.",
    "reconstruction_choice": "Use the final report's component equations by content (Eqs. 36 and 53), with the 1999 preprint used only to document the earlier numbering and cross-reference history.",
    "status": "The numbering comparison supports a likely stale or miscited reference in the final report, but its cause is not proven. This does not validate the Figure 2 curve, the project's digitization or reconstruction, nor flight performance."
  },
  "limitations": [
    "No variable cp/gamma, real-gas chemistry, detailed ionization, mass capture/bleed, heat transfer or vehicle drag.",
    "No flight-proven generator-accelerator loop; HVEPS and MAPX results are separate evidence.",
    "Specific thrust is normalized per inlet-air mass flow and cannot be converted to total vehicle force without a matched captured-air flow and installation boundary."
  ]
}