{
  "title": "Illustrative exit-pressure boundary sensitivity for a conditional NASA/TP-2000-210387 reconstruction",
  "status": "Mathematical exit-state sensitivity only; not a fixed-geometry nozzle prediction, author-code reproduction, or source-validated performance result.",
  "source": {
    "record": "https://ntrs.nasa.gov/citations/20000095934",
    "pdf": "https://ntrs.nasa.gov/api/citations/20000095934/downloads/20000095934.pdf",
    "nozzle_efficiency_equations": "NASA Eqs. 54–56, PDF p. 22 (printed p. 16)",
    "exit_state_and_thrust_equations": "NASA Eqs. 57–64, PDF pp. 23–24 (printed pp. 17–18)"
  },
  "reference_case": {
    "flight_mach": 6.0,
    "generator_extraction_ratio": 0.25,
    "source_model_case": "Figure 2 burner-cap case, not NASA author code",
    "gamma": 1.4,
    "R_J_per_kg_K": 287.05,
    "source_model_p0_exit_over_ambient": 497.91023185951786,
    "source_model_T0_exit_K": 3417.5871216361056,
    "fuel_air_ratio": 0.03900095391257121,
    "freestream_speed_m_s": 1784.043273017782,
    "source_model_nozzle_total_pressure_ratio": 0.98,
    "source_model_accelerator_exit_temperature_K": 3417.5871216361056,
    "reported_accelerator_temperature_limit_K": 3000.0,
    "accelerator_temperature_cap_exceeded": true
  },
  "sweep": {
    "exit_pressure_ratio_q_values": [
      0.7,
      0.8,
      0.9,
      1.0,
      1.1,
      1.2,
      1.4
    ],
    "selection": "Illustrative analyst-selected pressure boundaries, not transcribed from NASA Figure 2 and not fitted to its curve.",
    "held_fixed": "All upstream conditional cycle outputs, including total exit pressure, total exit temperature, fuel ratio and freestream state.",
    "varying_boundary": "Exit static pressure p_e / ambient static pressure p_a.",
    "geometry_treatment": "Exit area per inlet-air mass flow is derived separately at each q from continuity, assuming all air and fuel cross the exit plane. Therefore points do not share a fixed exit area or a fixed-geometry nozzle."
  },
  "equations": {
    "exit_mach": "M_e = sqrt(2/(gamma-1) * ((p0_e/p_e)^((gamma-1)/gamma) - 1))",
    "exit_temperature": "T_e = T0_e / (1 + (gamma-1)*M_e^2/2)",
    "exit_speed": "u_e = M_e * sqrt(gamma*R*T_e)",
    "continuity_area_per_air_flow": "A_e/mdot_air = (1+f)*R*T_e/(p_e*u_e)",
    "momentum_thrust_per_air_flow": "(1+f)*u_e-u_a",
    "pressure_thrust_per_air_flow": "(A_e/mdot_air)*(p_e-p_a) = (1+f)*R*T_e/u_e*(1-1/q)",
    "total_specific_thrust": "momentum contribution + pressure contribution",
    "unit_check": "Each thrust-per-mass-flow term has units m/s = N*s/kg-air."
  },
  "unavailable_source_inputs": [
    "The Figure 2 discussion gives nozzle total-pressure ratio pi_n=0.98 but not nozzle expansion efficiency eta_s(n), the pointwise station-6/exit static-pressure relation, or a fixed exit area/geometry.",
    "Eqs. 54–56 therefore do not select a unique physical nozzle state from the reported Figure 2 values alone.",
    "This sensitivity cannot determine which q applies to NASA's plotted curve and must not be used to tune the reconstruction to that curve."
  ],
  "limits": [
    "Perfect-gas, quasi-one-dimensional reconstruction and single-stream continuity.",
    "All fuel is assumed to exit in the same plane; bleed, capture, spillage and installation drag are omitted.",
    "The reference model's accelerator-exit temperature is about 3418 K, above the report's separate 3000 K limit; this cap conflict remains.",
    "Near cancellation of momentum and pressure terms is a consequence of these conditional exit-state assumptions, not validation of a nozzle or vehicle."
  ],
  "results": [
    {
      "exit_pressure_over_ambient_q": 0.7,
      "exit_mach": 5.258034411805214,
      "exit_static_temperature_K": 523.4163753496006,
      "exit_velocity_m_s": 2411.514459639583,
      "exit_area_over_inlet_air_mass_flow_m2_s_per_kg": 92.47682117855388,
      "momentum_specific_thrust_N_s_per_kg_air": 721.5225509217037,
      "pressure_specific_thrust_N_s_per_kg_air": -27.743046353566168,
      "total_specific_thrust_N_s_per_kg_air": 693.7795045681376
    },
    {
      "exit_pressure_over_ambient_q": 0.8,
      "exit_mach": 5.140510338024163,
      "exit_static_temperature_K": 543.7714895112468,
      "exit_velocity_m_s": 2403.01923429882,
      "exit_area_over_inlet_air_mass_flow_m2_s_per_kg": 84.36118991566599,
      "momentum_specific_thrust_N_s_per_kg_air": 712.6960036889484,
      "pressure_specific_thrust_N_s_per_kg_air": -16.872237983133193,
      "total_specific_thrust_N_s_per_kg_air": 695.8237657058152
    },
    {
      "exit_pressure_over_ambient_q": 0.9,
      "exit_mach": 5.038345395548306,
      "exit_static_temperature_K": 562.3820360878562,
      "exit_velocity_m_s": 2395.2257385570942,
      "exit_area_over_inlet_air_mass_flow_m2_s_per_kg": 77.80651760046177,
      "momentum_specific_thrust_N_s_per_kg_air": 704.5985541789821,
      "pressure_specific_thrust_N_s_per_kg_air": -7.780651760046176,
      "total_specific_thrust_N_s_per_kg_air": 696.8179024189359
    },
    {
      "exit_pressure_over_ambient_q": 1.0,
      "exit_mach": 4.94811852835075,
      "exit_static_temperature_K": 579.5688140068968,
      "exit_velocity_m_s": 2388.0058807370533,
      "exit_area_over_inlet_air_mass_flow_m2_s_per_kg": 72.38408918807929,
      "momentum_specific_thrust_N_s_per_kg_air": 697.0971150168464,
      "pressure_specific_thrust_N_s_per_kg_air": 0.0,
      "total_specific_thrust_N_s_per_kg_air": 697.0971150168464
    },
    {
      "exit_pressure_over_ambient_q": 1.1,
      "exit_mach": 4.867424446588206,
      "exit_static_temperature_K": 595.5681851317814,
      "exit_velocity_m_s": 2381.2651574457145,
      "exit_area_over_inlet_air_mass_flow_m2_s_per_kg": 67.81168639003886,
      "momentum_specific_thrust_N_s_per_kg_air": 690.0934970870846,
      "pressure_specific_thrust_N_s_per_kg_air": 6.781168639003892,
      "total_specific_thrust_N_s_per_kg_air": 696.8746657260886
    },
    {
      "exit_pressure_over_ambient_q": 1.2,
      "exit_mach": 4.794509787949932,
      "exit_static_temperature_K": 610.5598214035995,
      "exit_velocity_m_s": 2374.931642326193,
      "exit_area_over_inlet_air_mass_flow_m2_s_per_kg": 63.89536557075553,
      "momentum_specific_thrust_N_s_per_kg_air": 683.512968836282,
      "pressure_specific_thrust_N_s_per_kg_air": 12.779073114151103,
      "total_specific_thrust_N_s_per_kg_air": 696.292041950433
    },
    {
      "exit_pressure_over_ambient_q": 1.4,
      "exit_mach": 4.667057698467005,
      "exit_static_temperature_K": 638.0517083853779,
      "exit_velocity_m_s": 2363.2730444481763,
      "exit_area_over_inlet_air_mass_flow_m2_s_per_kg": 57.515835936447914,
      "momentum_specific_thrust_N_s_per_kg_air": 671.3996745197398,
      "pressure_specific_thrust_N_s_per_kg_air": 23.00633437457916,
      "total_specific_thrust_N_s_per_kg_air": 694.406008894319
    }
  ]
}