{
  "title": "Hypersonic inlet energy ledger",
  "type": "analytical teaching model; not flight data or a design calculation",
  "assumptions": {
    "gas": "calorically perfect air",
    "gamma": 1.4,
    "specific_gas_constant_J_kg_K": 287.05,
    "cp_J_kg_K": 1004.675,
    "freestream_static_temperature_K": 220,
    "freestream_static_pressure_kPa": 4.0,
    "steady_one_dimensional_flow": true,
    "adiabatic_inlet_no_shaft_work": true,
    "wall_heat_transfer_in_this_model": false,
    "pressure_recovery": "user-selected illustrative total-pressure ratio; not predicted from inlet geometry or validated test data"
  },
  "equations": [
    "a∞ = sqrt(gamma R T∞)",
    "V∞ = M∞ a∞",
    "h_t = cp T + V²/2 = constant for the ideal adiabatic no-work control volume",
    "T_t = T∞ + V∞²/(2 cp)",
    "T_exit = T_t / (1 + (gamma-1) M_exit²/2)",
    "p_t,∞ = p∞ (T_t/T∞)^(gamma/(gamma-1))",
    "p_t,exit = pressureRecovery × p_t,∞",
    "p_exit = p_t,exit / (T_t/T_exit)^(gamma/(gamma-1))"
  ],
  "limitations": [
    "The chosen outlet Mach number and total-pressure recovery are independent teaching controls; their combination is not guaranteed to correspond to a realizable inlet geometry.",
    "Real hypersonic flows can involve variable specific heats, vibrational excitation, dissociation, shocks, viscous layers, mixing, flow distortion, spillage and heat transfer.",
    "Static pressure rise is not electrical work. This model computes no generator output, coolant performance, fuel saving, net thrust or vehicle performance.",
    "The plots and CSV are deterministic analytical outputs and have no statistical uncertainty or experimental confidence intervals.",
    "The NASA real-gas chart reconstruction uses its simple harmonic-vibrator correction and standard-day atmosphere curve fits; it does not model dissociation, ionization, chemistry, shocks or a specific flight trajectory."
  ],
  "visual_reconstruction": {
    "source_figure": "NASA Glenn, Stagnation Temperature - Real Gas Effects, Tom Benson, last updated 2021-05-07; source plot asset stagtmp.gif.",
    "source_page": "https://www.grc.nasa.gov/WWW/BGH/stagtmp.html",
    "local_source_copy": "sources/web/S-FLOW-001-NASA-TT.html",
    "local_original_image_status": "not present in the local source archive; source image was inspected on the official NASA page",
    "reconstruction_type": "faithful equation-based reconstruction of the chart information; not a pixel trace and not original raw data",
    "atmosphere_equations": "NASA Glenn English-unit standard-day atmosphere model, converted from degrees Fahrenheit/feet to Rankine/kilometres",
    "redraw_outputs": [
      "real-gas-stagnation-contours.svg",
      "real-gas-stagnation-contours.csv"
    ],
    "rights_and_attribution": "NASA's public image guidance permits factual educational use of NASA media with source acknowledgment; this redraw does not reproduce the NASA insignia or imply endorsement. Check item-specific third-party credits before reusing other NASA-hosted media."
  },
  "sources": [
    {
      "citation": "Benson, T. (NASA Glenn), Stagnation Temperature - Real Gas Effects, last updated 7 May 2021.",
      "url": "https://www.grc.nasa.gov/WWW/BGH/stagtmp.html",
      "supports": "Definition and figure relationship: seven stagnation-temperature contours over altitude and Mach; solid calorically perfect gas and dashed calorically imperfect gas with vibrational effects; simple harmonic-oscillator equation and the note that differences grow above about Mach 3."
    },
    {
      "citation": "NASA Glenn, Earth Atmosphere Model - English Units.",
      "url": "https://www.grc.nasa.gov/www/k-12/BGP/atmos.html",
      "supports": "Standard-day temperature-versus-altitude curve fits used to regenerate the source chart's atmosphere input."
    },
    {
      "citation": "Slater, J. W. (2024), SUPIN: A Tool for the Aerodynamic Design and Analysis of Supersonic Inlets, NASA/TM-20240008586, §3.10.",
      "url": "https://ntrs.nasa.gov/citations/20240008586",
      "supports": "Inlet state quantities, pressure recovery, kinetic-energy efficiency and separation of total enthalpy from inlet heat transfer."
    },
    {
      "citation": "NASA Glenn, Inlets.",
      "url": "https://www.grc.nasa.gov/www/k-12/airplane/inlet.html",
      "supports": "Inlet role, shock losses, pressure recovery, integration and supersonic flow through a scramjet inlet."
    },
    {
      "citation": "Riggins et al. (2006), Thermodynamic Analysis of Dual-Mode Scramjet Engine Operation and Performance, AIAA 2006-8059.",
      "url": "https://ntrs.nasa.gov/citations/20070000536",
      "supports": "Heat release, irreversibilities and operating-dependent dual-mode behavior; no universal transition Mach switch."
    },
    {
      "citation": "Riggins, D. W. (2002), Analysis of the Magneto-Hydrodynamic (MHD) Energy Bypass Engine for High-Speed Air-Breathing Propulsion.",
      "url": "https://ntrs.nasa.gov/citations/20020073109",
      "supports": "A cycle analysis reporting substantial total-pressure loss and lower modelled performance than a conventional scramjet for the configurations studied at Mach 8–12.2; not a universal result for every MHD architecture."
    },
    {
      "citation": "Benyo, J. (2011), Flow Matching Results of an MHD Energy Bypass System on a Supersonic Turbojet Engine Using NPSS, NASA/TM-2011-217136.",
      "url": "https://ntrs.nasa.gov/citations/20110015567",
      "supports": "A separate modeled turbojet cycle reporting favorable operating results under its selected assumptions; not an experimental flight demonstration."
    },
    {
      "citation": "Air Force Research Laboratory (2007), “Scramjet MHD System Generates Electrical Power” (official HVEPS program summary).",
      "url": "https://www.wpafb.af.mil/News/Article-Display/Article/401319/scramjet-mhd-system-generates-electrical-power/",
      "supports": "The official summary reports a 2-10-kW public range. The inspected 32-page AFRL preprint ADA471429 Table VI distinguishes load-bank measurement (6.52 kW), post-test derived active-channel output (14.38 kW), and calculated matched-load maximum (14.80 kW) for Test 3; no whole-vehicle power or flight benefit was measured."
    },
    {
      "citation": "Litchford, R. J., Bityurin, V. A. & Lineberry, J. T. (1999), Thermodynamic Cycle Analysis of Magnetohydrodynamic-Bypass Airbreathing Hypersonic Engines, NASA NTRS preprint record 20000032786 (document type: preprint submitted to journal).",
      "url": "https://ntrs.nasa.gov/citations/20000032786",
      "supports": "A theoretical MHD energy-bypass engine concept that extracts flow energy electrically; a separate conceptual analysis, not validation of this simple inlet model or a demonstrated engine.",
      "record_relationship": "This is the 1999 preprint record, not NASA/TM-2000-210387. The related but distinct 2000 final technical report is NASA/TP-2000-210387, NTRS record 20000095934, with a different author list including J. W. Cole. Do not treat the two records as the same document or as independent experimental validations."
    },
    {
      "citation": "NASA Langley, Improved Hypersonic Aircraft Flight Control System, LAR-TOPS-364.",
      "url": "https://technology.nasa.gov/patent/LAR-TOPS-364",
      "supports": "A distinct electrode-and-magnet MHD flow-control concept; NASA describes computational evaluations for selected atmospheric-entry conditions."
    },
    {
      "citation": "Riggins, D. W. (2004), Analysis of the Magnetohydrodynamic Energy Bypass Engine for High-Speed Airbreathing Propulsion, Journal of Propulsion and Power 20(5), 779–792, DOI 10.2514/1.4980.",
      "url": "https://doi.org/10.2514/1.4980",
      "record_url": "https://scholarsmine.mst.edu/mec_aereng_facwork/3080/",
      "supports": "The peer-reviewed journal article abstract reports lower thermally balanced MHD-bypass performance than the conventional scramjet across Mach 8–12.2 and attributes it to MHD irreversibility/cooling plus inverse-cycle pressure reduction. The institutional record exposes citation and abstract, not full text or numeric curves; this supports a bounded evidence statement only, not curve reconstruction. It is a distinct, more detailed analysis than NASA/TP-2000-210387 Figure 2."
    }
  ],
  "hveps_reporting_note": "The full AFRL preprint ADA471429 is now inspected. Test 3 Table VI reports 6.52 kW dissipated in the external load bank, 14.38 kW post-test derived active-channel output excluding end-region losses, and 14.80 kW calculated as the maximum at matched load. The abstract calls 14.8 kW peak output, but the table classifies 14.80 kW as a post-test matched-load estimate, not the measured load-bank value. General Atomics separately reports a preliminary 15-kW active-section peak; exact run and processing equivalence is not established. AFRL’s public 2-10-kW range is compatible in scale with load-bank outputs but its exact boundary is not identified. The figures are not vehicle net power. Retained color-copy source SHA-256 (the copy used for figure crop/reproduction): 58BBB34829C30439F3D6AA1AC27E31430C01657DEF5E1F29F959598B4EE734BB. Official NTIS/NTRL PDF SHA-256: CCBC90C0BC0626328B058023D153D2F268767F85DAFD8BFD2A0DBFFACCFA1521. The files are not byte-identical. A side-by-side visual check now covers the displayed Table VI rows and separately compares Figures 16 and 17 (printed p. 16 / physical PDF p. 18): titles, axes, captions, overall time windows, principal waveform shapes and the prominent approximately 32.2 s current spike correspond. The retained third-party crops have different background/trace colors and image rendering. This is a broad visual cross-check, not a pixel-identity or point-by-point data comparison; the traces have not been digitized from the official file, and reproduction rights remain unresolved.",
  "hveps_test_series_note": "Table VI of the inspected full AFRL preprint ADA471429 lists six analysed output points: tests 1, 2, 3, 5, 6 and 7. Test 4 was not reduced because its pressure distribution was anomalous. For each point, load-bank dissipation is distinct from the active-channel output that neglects end-region losses and from maximum power at matched load calculated by post-test load-line analysis. The Site figure and table show all six points; Test 3 uses the 89% mean combustion-efficiency row, while its 81.5% and 96.5% bounds are identified separately. Values are not aircraft net power. Retained color-copy source SHA-256 (the copy used for figure crop/reproduction): 58BBB34829C30439F3D6AA1AC27E31430C01657DEF5E1F29F959598B4EE734BB. Official NTIS/NTRL PDF SHA-256: CCBC90C0BC0626328B058023D153D2F268767F85DAFD8BFD2A0DBFFACCFA1521. The files are not byte-identical. A side-by-side visual check now covers the displayed Table VI rows and separately compares Figures 16 and 17 (printed p. 16 / physical PDF p. 18): titles, axes, captions, overall time windows, principal waveform shapes and the prominent approximately 32.2 s current spike correspond. The retained third-party crops have different background/trace colors and image rendering. This is a broad visual cross-check, not a pixel-identity or point-by-point data comparison; the traces have not been digitized from the official file, and reproduction rights remain unresolved."
}