{
  "boundary": "Illustrative design calculations, not Tesla specifications, measurements or a validated vehicle simulation.",
  "thermal": {
    "heat_J": 300000.0,
    "heat_capacity_J_K": 60000.0,
    "conductance_W_K": 500.0,
    "ambient_C": 25.0,
    "limit_C": 45.0,
    "time_constant_s": 120.0,
    "instantaneous_rise_K": 5.0,
    "drive_electrical_input_W": 1000000.0,
    "pulse_duration_s": 3.0,
    "port_to_wheel_efficiency": 0.9,
    "drive_input_J": 3000000.0,
    "wheel_work_J": 2700000.0,
    "period_definition": "start to start; impulse approximation deposits heat at each 3 s pulse end; consecutive deposits remain one period apart",
    "minimum_period_s": 34.52184869421371,
    "cases": [
      {
        "period_s": 20.0,
        "peak_temperatures_C": [
          30.0,
          34.23240862445307,
          37.81506517732202,
          40.84771847588518,
          43.41480407104814,
          45.58779511358354,
          47.42719231944075,
          48.98420843901374,
          50.302194129592365,
          51.41784493033451
        ],
        "periodic_peak_C": 57.56941231548729
      },
      {
        "period_s": 60.0,
        "peak_temperatures_C": [
          30.0,
          33.03265329856317,
          34.87205050442038,
          35.98770130516253,
          36.664377721345595,
          37.074802714465086,
          37.32373805630441,
          37.474724973415995,
          37.56630316785967,
          37.62184815055088
        ],
        "periodic_peak_C": 37.70747041268399
      }
    ],
    "design_comparisons": [
      {
        "name": "base",
        "capacity_J_K": 60000.0,
        "conductance_W_K": 500.0,
        "period_s": 20.0,
        "peak10_C": 51.41784493033451,
        "periodic_peak_C": 57.56941231548729,
        "minimum_period_s": 34.52184869421371
      },
      {
        "name": "double_C",
        "capacity_J_K": 120000.0,
        "conductance_W_K": 500.0,
        "period_s": 20.0,
        "peak10_C": 42.678620851554655,
        "periodic_peak_C": 56.26735910205544,
        "minimum_period_s": 32.04753422988543
      },
      {
        "name": "double_G",
        "capacity_J_K": 60000.0,
        "conductance_W_K": 1000.0,
        "period_s": 20.0,
        "peak10_C": 42.00939191211398,
        "periodic_peak_C": 42.63863236578565,
        "minimum_period_s": 17.260924347106855
      }
    ]
  },
  "gas": {
    "impulse_N_s": 5000.0,
    "effective_exhaust_velocity_m_s": 500.0,
    "specific_gas_constant_J_kg_K": 287.0,
    "cooled_endpoint_temperature_K": 300.0,
    "low_absolute_pressure_Pa": 10000000.0,
    "high_absolute_pressure_Pa": 30000000.0,
    "inlet_absolute_pressure_Pa": 100000.0,
    "overall_isothermal_efficiency": 0.65,
    "compressor_electrical_power_W": 20000.0,
    "consumed_kg": 10.0,
    "volume_m3": 0.04305,
    "cooled_low_mass_kg": 5.0,
    "cooled_high_mass_kg": 15.0,
    "ideal_adiabatic_residual_temperature_K": 193.31820449317627,
    "ideal_adiabatic_residual_pressure_Pa": 6443940.149772543,
    "conditioning_time_s": null,
    "reversible_work_J": 4522909.30095061,
    "electrical_input_J": 6958322.001462477,
    "electrical_input_kWh": 1.932867222628466,
    "refill_wait_s": 347.91610007312386,
    "start_to_start_gas_period_s": 350.91610007312386
  },
  "equations": {
    "thermal_ODE": "C*dtheta/dt=P_heat-G*theta",
    "pulse_recurrence": "theta_n=exp(-Delta/tau)*theta_(n-1)+Q/C, theta_0=0",
    "periodic_peak": "theta_inf=(Q/C)/(1-exp(-Delta/tau))",
    "minimum_period": "-tau*ln(1-Q/(C*theta_limit)); Q/C < theta_limit",
    "gas_mass": "m=p*V/(R*T)",
    "reversible_refill": "V*[p*ln(p/p_atm)-p] evaluated from p_low to p_high",
    "gas_period": "pulse_duration+conditioning_time+reversible_refill/(efficiency*compressor_power); conditioning_time unknown; plotted reference sets it to zero"
  },
  "assumptions": [
    "Drive-loss heat node only; battery I^2R and compressor heat are outside this node",
    "Constant C,G,ambient; no internal gradients, active chiller, coolant transients, speed dependence or thermal derating",
    "Instantaneous heat approximation ignores cooling during the 3 s pulse; finite-pulse RK4 comparison is reported",
    "Thermal and gas examples use independent temperature assumptions: 25 deg C reservoir and 300 K cooled gas",
    "Ideal gas and fixed effective exhaust velocity; real air at 10-30 MPa needs real-gas properties",
    "Reversible isothermal compression into a tank maintained at 300 K; 65% efficiency refers to this minimum work, including electrical losses",
    "Defined reference path: after 3 s pulse, residual gas must first be conditioned to 300 K before isothermal refill. Conditioning time is unknown and set to zero only in the optimistic plotted reference",
    "Adiabatic ideal-gas discharge of 15 to 5 kg would leave about 193 K and 6.44 MPa, not 300 K and 10 MPa. This separate limiting model is not a real discharge prediction",
    "Maximum of recovery bounds valid only for concurrent independent resources; no vehicle-wide sufficiency claim",
    "Drive input already includes Q; compressor electrical input is not all battery heat and must not be double counted"
  ],
  "checks": {
    "recurrence_cases": 1440,
    "maximum_recurrence_residual_K": 1.1368683772161603e-13,
    "finite_pulse_RK4_max_residual_K": 8.526512829121202e-14,
    "finite_pulse_peak_results": [
      {
        "period_s": 20.0,
        "peak10_C": 51.09035661407306
      },
      {
        "period_s": 60.0,
        "peak10_C": 37.465381648085135
      }
    ],
    "finite_pulse_effective_jump_K": 4.938017594333466,
    "finite_pulse_lower_peak_rise_percent": 1.2396481133306714,
    "finite_pulse_minimum_period_s": 34.02701112033818,
    "refill_work_midpoint_relative_error": 1.0577713916989502e-12,
    "checks": [
      "energy partition",
      "gas mass and impulse conservation",
      "zero heat",
      "zero cooling",
      "isolated pulse limit",
      "thermal feasibility boundary"
    ]
  }
}