ThrustOne User Guide

ThrustOne User Guide

ThrustOne supports Apple silicon Macs running macOS 12 or later, and iPads running iPadOS 16 or later.

This guide is generated from the capability catalog, field catalog, model descriptions, and demonstration cases. Demonstration results help identify controls and workflows; they do not represent a specific engine design, performance certification, or full-envelope prediction.

ThrustOne Engine Performance Calculator

Getting started Choose an engine and analysis task, adjust the conditions, then select Calculate (Command-Return). Return or leaving a field commits its value; Escape restores it. Decimal numbers, scientific notation, and the Unicode minus sign are accepted. Units appear beside fields. Internal calculations and exports use SI values. A curve and its results always belong to one complete input state. A changed input makes earlier results stale; recalculate before exporting.

Requirements ThrustOne supports Apple silicon Macs running macOS 12 or later, and iPads running iPadOS 16 or later.

Opening and saving cases Native ThrustOne documents use the .thrustone extension and contain ordinary JSON. On Mac, Open case opens a separate .thrustone or JSON document; Save case exports the current case as JSON. On iPad, use the document browser to open or create separate .thrustone cases. The Case actions menu offers Save Case As and Import into Current Case; importing accepts .thrustone or JSON, validates it first, and explicitly asks before replacing and saving the current document. Cancel keeps its existing contents. Results and chart exports use the native file picker on both platforms.

Available calculations • Turbojet: ideal and loss-based design points, afterburning, explicit-reference double-choked and dual-spool afterburning off-design points, and five standalone components. Compressor map files use shape-preserving interpolation and are never extrapolated. • Turbofan: separate-flow single-spool design, reference-normalized dual-spool separate-flow off-design, and constant-cp dual-spool mixed-flow or mixed-afterburning analyses. Constant-cp mixing matches inlet static pressure and uses the subsonic conservation root. NASA9 variable-cp design analyses include separate flow, mixed flow, and independent post-mixer afterburning. Specific thrust uses total inlet air; fuel-air ratio uses core air. Ideal modes neglect fuel mass addition and assume fully expanded streams. • Liquid rocket: thrust-chamber and nozzle performance with explicit gas properties; altitude, area-ratio, and chamber-pressure sweeps at fixed reference scale; equivalent cylindrical sizing; cylinder-plus-convergent volume allocation; a standalone finite-contraction static chamber plane; and conical or bell reference geometry. Mixture-ratio sweeps never combine values based on different chemical assumptions. • Ramjet: full-engine design point, normal shock, explicit weak or strong oblique shock, Darcy Fanno friction, same-branch Rayleigh heating, and fixed-cp quasi-one-dimensional flow. Flow segments support area, Darcy friction, heat flow, and injected mass. They stop at sonic events or residual limits and retain valid history. • Solid rocket: equilibrium pressure from a supplied burn-rate law and end-burning or internal-port regression transients. Demonstration parameters do not represent a specific propellant. Models start from an established choked state and exclude ignition, erosion, and tail-off blowdown. • TBCC: independent turbojet and ramjet channels combined with an explicit air split. The shared freestream is defined in turbojet fields. Common-inlet matching, variable geometry, and automatic transition are not solved. • RBCC: an ideal ejector-ramjet submodel with specified primary total state, supersonic primary flow, subsonic secondary flow, and a choked ejector exit. It is not a full multimode RBCC cycle. • ATR: an ideal air-turboramjet submodel with specified primary total state, ideal work balance, low-speed mixing, and simplified heating. It excludes a gas generator, pump, and cooling.

Freestream and model limits Turbojet input supports Mach plus ambient state, altitude plus Mach, Mach plus dynamic pressure, and altitude plus dynamic pressure. Altitude is geometric; the standard atmosphere is valid from 0 to 86 km. Legacy JSON altitude values in km convert to m on import. The dynamic-pressure path uses standard air with γ = 1.4.

Ideal cycles use one gas and neglect fuel mass addition. Other constant-cp cycles use supplied cold- and hot-side heat capacities and component losses. Constant-cp calculation is not chemical equilibrium. Liquid-rocket empirical efficiencies correct characteristic velocity or thrust coefficient; they do not change the ideal reference exit velocity. Exit-plane static pressure is not a validated wall-pressure or side-load prediction.

Cases and files Open and save native JSON cases up to 10 MiB and 64 nesting levels. Version 2 uses engine, mode, and the associated input section. Unsupported modes report an error; they are never silently replaced. Some legacy turbojet cases and rocket cases with explicit reference conditions can import; other thermodynamic-table branches have not been migrated.

Edits in JSON Interchange update the form only after Apply JSON. Restore Form Contents discards unapplied text, which is not written to the saved case. Unknown fields are retained as extension data; known fields in this version determine the calculation. The File menu provides Save, Save As, Close, and multiple windows.

Studies and exports Parameter Study operates on currently exposed independent fields. It accepts linear endpoints or explicit value lists, one- or two-dimensional grids, and at most 1,000 total cases. It shows progress and can be cancelled while retaining completed work. Failed rows retain their error. Liquid-rocket plots do not join across failed points. History tables show the first 100 points; JSON, CSV, and graphic exports retain all data.

Study axes, explicit lists, and the two-dimensional switch are saved with a case. The comparison metric and maximum/minimum choice are view state. Grid extrema cover only successful computed points; they are neither continuous nor global optima. A three-point curve may show an endpoint secant slope; reduce the step to check local stability.

Metric Constraints and Comparison Report apply inclusive SI lower and upper bounds to existing results; every selected constraint must pass. Apply the constraints first. Reapplying the same metric replaces its bound; Remove removes it. Rows with missing metrics or errors cannot qualify. The report records the request, axes, constraints, extrema before and after filtering, and each row’s status. Filtering does not rerun the solver and is not continuous optimization or a complete performance envelope.

One-dimensional studies provide local golden-section search. Inspect objective shape with a grid first, specify an interval, and declare that it can be treated as unimodal there. The search uses 4–100 evaluations and stops on combined absolute and relative interval-width tolerances. An out-of-domain, non-finite, missing-metric, or constraint-violating point stops it; that point is not skipped. The result is only the best evaluated point. Budget exhaustion is not convergence, and interval convergence neither proves a global optimum nor bounds objective error. Settings are view state; full conditions and evaluated points export as a separate JSON record.

A history plot can overlay one same-unit series: blue circles are the primary quantity and orange squares the overlay. The legend and numeric table show both. Each series retains its gaps; failed points are not joined. Different dimensions never share a forced vertical axis. A two-dimensional grid shows a discrete feasible set: passing points are colored by objective, red crosses retain solver failures, and gray diamonds retain rejected or missing-metric points. It does not interpolate or draw a continuous envelope. PNG and PDF export are available; the comparison report contains all raw rows and reasons.

Result JSON contains the case used, model mode, SI values, and histories. CSV uses UTF-8 with BOM and CRLF, with every quantity’s unit and an input snapshot. PNG is 1000 × 600; PDF is vector graphics. Stale results cannot be exported as current results.

Offline and privacy Calculations run locally. ThrustOne does not connect to remote services, upload cases, or use model APIs. Files are saved only where you choose.

Scope ThrustOne provides 49 runnable calculation models across turbojets, turbofans, liquid and solid rockets, ramjets, scramjets, TBCC, RBCC, and ATR. The capability catalog and current mode description state each model’s conditions and limits. Interpret results only within the selected model. Demonstration inputs explain operation; they do not represent a specific engine design, performance certification, or full-envelope prediction.

The form footer can switch display between SI and engineering units (kPa, kN, kJ); primary results convert and the preference is saved with the case. Commit any field being edited before switching. The calculation core, JSON, CSV, station data, curves, and explicit lists always use the labeled SI values. Temperature remains K.

Thermochemistry and variable-property models Scramjet full-engine, combustor, and fixed-cp frozen-nozzle modes use explicit heat and mass sources and stop at sonic events. In seven-state fixed-cp F/G input, F = pA + ṁV in N and G = cpT + V²/2 in J/kg. Do not enter reacting-flow total enthalpy containing species formation enthalpies in that form.

NASA9 properties use archived U.S. government species data (NASA/TP-2002-211556) only in the common 200–6000 K range of selected species. Enthalpy includes formation enthalpy; pressure is Pa and molar mass is kg/kmol. Gas equilibrium uses 13 species with no ions or condensed phases. Displayed cp and γ are local frozen-composition properties.

Variable-cp frozen nozzles solve enthalpy, entropy, and mass continuity. Thermochemical rocket tasks can solve chamber equilibrium at specified chamber temperature and pressure, then expand with frozen composition. Chamber temperature can also close from gaseous inlet enthalpy and equilibrium combustion. Along-path equilibrium and user-selected downstream-area freezing are available. These models exclude liquid-propellant vaporization and condensed phases.

Finite-rate reactor mode is constant-volume and externally isothermal. You supply reactions and Arrhenius coefficients. A uses kmol/m³ concentrations and K; Ea uses J/kmol. Default coefficients demonstrate the algorithm and are not a combustion mechanism. Reverse rates derive from selected thermodynamic data. The supplied hydrogen–oxygen 10-species/29-reaction option includes third-body and Lindemann/Troe corrections. Stiffness or step limits retain an incomplete state, which cannot participate in study extrema.

The ramjet path’s final nozzle uses specified exit pressure and back-calculates area. It shows two stations and is not fixed-geometry back-pressure matching. A bell nozzle is arc–parabola geometry with explicit endpoint angles; it is not a validated wall-pressure, separation, or side-load prediction.

Constant-pressure energy closure uses gaseous inlet composition, common inlet temperature, and heat per unit mixture mass to find equilibrium temperature. Zero heat is adiabatic. Every temperature trial must satisfy elemental conservation and equilibrium residuals; an unbracketed user temperature interval is rejected. There is no liquid vaporization, condensed phase, or ion model.

Thermochemical rocket analysis permits specified chamber temperature or inlet-energy closure. Gaseous mixture-ratio sweeps use H2/CH4/CO with O2; MR is oxidizer-to-fuel mass ratio. Every point keeps geometry and back pressure fixed and uses the same chamber-equilibrium and selected nozzle-chemistry model. Best Isp means the maximum among successful samples; failed rows remain and no continuous optimum is inferred.

Variable-cp turbojet and separate-flow turbofan components use NASA9 frozen composition and h(T), s(T,p) inversion. Inlet uses supplied total-pressure recovery only. Compressor and turbine use separately entered isentropic efficiencies; do not treat a previous polytropic efficiency as the same parameter. Nozzles expand to specified exit static pressure and do not perform fixed-geometry matching. This path has no compressor map or combustion reaction. Fan, booster, and bypass nozzle share these components; the mixer has its selected mixing model.

NASA9 turbojet and separate-flow turbofan design points use dry air at 79 mol% N2 and 21 mol% O2. Gaseous H2/CH4/CO fuel is specified by fuel-to-core-air mass ratio, and fuel inlet temperature is included separately in formation enthalpy. The combustor solves adiabatic gas-phase equilibrium, then freezes composition. The turbine drives core-compressor and all-air fan loads. Net specific thrust uses total air; fuel-air ratio uses core air. These modes use fully expanded variable-area exits, not fixed geometry, maps, or off-design matching. They exclude liquid vaporization, cooling, and condensation.

The calibrated variable-property inlet supports altitude plus Mach, Mach plus dynamic pressure, and altitude plus dynamic pressure with contraction ratio, exit Mach, exit static pressure, exit static temperature, or total-pressure recovery. It uses NASA9 dry air and 0–70 km geometric altitude. A contraction inversion explicitly chooses the higher- or lower-Mach root. It does not extrapolate higher cold-atmosphere properties or promise point-for-point agreement with another mechanism database.

NASA9 frozen quasi-one-dimensional flow updates heat capacity and sound speed at every step and checks total-energy residual. Injection must have main-stream composition; injection total enthalpy includes formation enthalpy and may be physically negative. After changing composition, select Update Mass Flow from Inlet State. Sonic, property-range, and residual events retain a valid prefix, which cannot be used for study extrema. It does not mix different compositions or solve finite-rate chemistry.

NASA9 seven-state input supports T/P/M, T/P/V, T/ρ/M, T/ρ/V, P/ρ/M, P/ρ/V, and F/G/ṁ. Here F = pA + ṁV and G = h + V²/2; G includes formation enthalpy. F/G requires an explicit subsonic or supersonic root.

Finite-rate reacting flow integrates species mass flow, momentum, and total energy, so temperature changes with reaction. Each segment may specify injection composition; absent a value, inlet composition is used. Injection total enthalpy includes formation enthalpy, so external heat must not add fuel reaction heat again. Default dissociation coefficients demonstrate the algorithm only. Supply reliable mechanism parameters for a physical study. The model omits transport, diffusion, and automatic transonic matching.

The calibrated full engine connects a dry-air inlet, combustor, and nozzle in either nonreacting mixing or finite-rate mode. Net thrust subtracts captured-air flight momentum. specific_impulse_injected uses all injected mass; air or oxidizer is not automatically called fuel. Geometry is supplied by the user; ambient back-pressure closure, shock trains, and mode transition are not automatic. If any segment is incomplete, full-engine thrust is not reported.

Equilibrium nozzles follow an isentropic path with the same elemental inventory; critical mass flow is found from the internal maximum of ρV. Selected-area freezing switches to fixed composition at the user’s post-throat area ratio. The local frozen Mach there must exceed 1; equilibrium throat state is not automatically a frozen-sonic throat state. The selected point is not a calculated chemical-freeze location. frozen_mach uses local frozen sound speed, not equilibrium sound speed. Property extrapolation is rejected. Current models contain ideal gas only: no liquid vaporization, condensation, wall pressure, post-separation performance, or side load.

The optional hydrogen–oxygen submechanism has 10 species and 29 reactions, including HO2/H2O2, third-body efficiencies, and Troe reactions. Source cm/mol/s and cal/mol values are converted to m/kmol/s and J/kmol. It is neither a full GRI-Mech nor a point-for-point reproduction of other software. NASA9 and hydrogen–oxygen NASA7 are independent selections. The H2/O2 mechanism common range is 300–3500 K. A standalone flow stops outside it or at the integration budget; calibrated full-engine analysis uses NASA9.

The reaction editor can create elementary, third-body, or pressure-falloff reactions. Unlisted collision efficiencies equal 1. Pressure falloff uses Lindemann with optional three- or four-parameter Troe. Units of A vary with reaction order and temperature exponent; check displayed units after changing type. Load replaces reactions, initial composition, and reactor controls. The included data are adapted from the Cantera hydrogen–oxygen submechanism; its BSD license appears under Third-Party Data Licenses. Presets only enter the workflow and do not replace experimental or textbook validation for a specific engine.

Mixture-ratio sweeps can use chamber-exit freezing, along-path equilibrium, or selected-area freezing. Every point uses the same selected model, geometry, and back pressure; older files default to chamber-exit freezing. Failed samples retain their reason. The highest discrete specific impulse is not a continuous optimum.

Variable-cp turbojet and separate-flow turbofan models offer optional core-stream afterburning. Afterburner fuel-air ratio is per core-air mass and uses the same gaseous fuel as the main combustor. Fuel inlet temperature enters formation enthalpy separately; lower heating value is not added again. The afterburner follows the turbine and does not change shaft loads; separate-flow bypass does not afterburn. Total fuel flow and specific fuel consumption include main combustor and afterburner. This mode excludes mixed flow, liquid vaporization, cooling, and map matching.

The turbofan two-stream mixer can use NASA9 variable-property frozen mixing. Enter both streams’ total states, mass flows, compositions, and core inlet Mach. Bypass static pressure matches the core, and areas are recovered from both mass flows; a constant-area exit uses only the subsonic conservation root. Composition mixes by elemental and species mass flow without chemical reaction. Total-pressure recovery is a separate loss downstream of the mixer and does not alter its momentum conservation. This component is not a mixed-flow full-engine match or FAIR/VSH validation.

Offline theory manual Choose Open Theory Manual in Help to read the bundled English reference. Search for a term, move between matches, follow the PDF contents links, or enter a page number. No internet connection is required. Each chapter states its assumptions, equations and interpretation limits.

Current Mode Reference

Turbojet · Variable-specific-heat gaseous-fuel design point

Mode identifier: turbojet.variable_cp_design.

NASA9 dry air and gaseous fuel with adiabatic gas-phase equilibrium combustion, frozen turbine/nozzle composition, optional core-flow afterburning, and a single-spool variable-area exit.

NASA9 dry air and gaseous fuel with inlet temperatures included separately in enthalpy. Adiabatic gas-phase equilibrium sets combustor temperature, then composition freezes. Single-spool load and net thrust are closed with fully expanded, variable-area exits. Optional post-turbine core-stream afterburning uses the same balance model for fuel mass and formation enthalpy; separate-flow bypass does not afterburn. No liquid vaporization, cooling, or map matching.

(1+f) h4 = h3 + f hf;(1+f)(h4−h5)ηm = wc+(1+α)wf;(1+f+fAB)h7 = (1+f)h5+fAB hfAB;F/ṁcore = (1+f+fAB)V9+αV19−(1+α)V0

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Flight Mach number 1 0
Ambient static temperature K 288.15
ambient static pressure Pa 101325
total air flow kg/s 30
Core compressor total pressure ratio 1 10
Compressor isentropic efficiency 1 0.9
Turbine isentropic efficiency 1 0.9
Shaft mechanical efficiency 1 0.99
Total intake pressure recovery 1 0.98
Combustion chamber total pressure ratio 1 0.95
Nozzle total pressure recovery 1 0.98
Fuel/Core Air Mass Ratio 1 0.02
Gaseous fuel inlet temperature K 300
Combustion temperature root lower limit K 1000
Combustion temperature root upper limit K 4500
Output Unit Demonstration result
Afterburner Energy Residual (afterburner_energy_residual) J/kg 0
Afterburner Equilibrium Residual (afterburner_equilibrium_residual) 1 0
Afterburner Fuel Air Ratio (afterburner_fuel_air_ratio) 1 0
Afterburner Mass Residual (afterburner_mass_residual) 1 2.220446e-16
Afterburner Temperature (afterburner_temperature) K 1964.62
Air Flow (air_flow) kg/s 30
Burner Energy Residual (burner_energy_residual) J/kg 0.0036952906
Bypass Ratio (bypass_ratio) 1 0
Compressor Work (compressor_work) J/kg 299594.08
Core Air Mass Flow (core_air_mass_flow) kg/s 30
Equilibrium Residual (equilibrium_residual) 1 7.1054274e-15
Fan Work (fan_work) J/kg -1.70985e-10
Flight Velocity (flight_velocity) m/s 0
Fuel Air Ratio (fuel_air_ratio) 1 0.02
Fuel Mass Flow (fuel_mass_flow) kg/s 0.6
Mole Fraction H (mole_fraction_H) 1 2.4225028e-05
Mole Fraction H2 (mole_fraction_H2) 1 0.00029379233
Mole Fraction H2O (mole_fraction_H2O) 1 0.24835141
Mole Fraction N (mole_fraction_N) 1 1.9326609e-09
Mole Fraction N2 (mole_fraction_N2) 1 0.68769295
Mole Fraction No (mole_fraction_NO) 1 0.00543715
Mole Fraction O (mole_fraction_O) 1 0.00015382082
Mole Fraction O2 (mole_fraction_O2) 1 0.055065199
Mole Fraction Oh (mole_fraction_OH) 1 0.0029814483
Net Thrust (net_thrust) N 41321.856
Shaft Energy Residual (shaft_energy_residual) J/kg 4.0745363e-10
Specific Thrust (specific_thrust) N·s/kg 1377.3952
Total Fuel Air Ratio (total_fuel_air_ratio) 1 0.02
Thrust-Specific Fuel Consumption (tsfc) kg/(N·s) 1.4520161e-05
Turbine Inlet Temperature (turbine_inlet_temperature) K 2154.5966
Turbine Work (turbine_work) J/kg 296686.55
V19 (v19) m/s 0
V9 (v9) m/s 1350.3875

Model notes for this demonstration: - NASA9 variable specific heat with dry air (79 mol% N2, 21 mol% O2) and gaseous H2/CH4/CO fuel. Fuel-air ratio uses core air mass; net specific thrust uses total inlet air mass. - The adiabatic combustor solves 13-species gas-phase equilibrium. Fuel inlet temperature and formation enthalpy enter the energy balance; no separate heating value is added. Composition is frozen downstream. Excludes condensed phases, liquid vaporization, afterburning, cooling, and finite-rate chemistry. - Single-spool work balance with fully expanded streams and variable exit areas. This separate-flow model does not perform fixed-geometry, component-map, mixed-flow, or off-design matching.

Turbojet · Design point

Mode identifier: turbojet.design_point.

Constant-specific-heat cycle with specified compressor pressure ratio and turbine-inlet total temperature.

Constant-specific-heat cycle with specified compressor pressure ratio and turbine-inlet total temperature. Steady, one-dimensional turbojet cycle. The ideal mode uses one gas and neglects fuel mass addition; the loss mode uses constant specific heats in separate cold and hot sections. Off-design operation is limited to the fixed-area, double-choked model.

τr = 1 + (γc − 1) M₀² / 2
τc = πc^((γc − 1)/(γc ec))
S = f / (F/ṁ₀)

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Flight Mach number 1 2
Ambient static temperature K 216.7
ambient static pressure Pa 19400
Compressor total pressure ratio 1 10
Turbine inlet total temperature K 1800
Ambient/Exit Static Pressure Ratio 1 0.5
Cold-side specific heat cp J/(kg·K) 1004
Cold-side specific heat ratio γ 1 1.4
Hot-side specific heat cp J/(kg·K) 1239
Hot-side specific heat ratio γ 1 1.3
Fuel lower heating value J/kg 42800000
Inlet duct maximum total pressure recovery 1 0.95
Combustion chamber total pressure ratio 1 0.94
Nozzle total pressure ratio 1 0.96
Compressor polytropic efficiency 1 0.9
Turbine polytropic efficiency 1 0.9
combustion efficiency 1 0.98
mechanical efficiency 1 0.99
Output Unit Demonstration result
Compressor Isentropic Efficiency (eta_c) 1 0.86406619
Overall Efficiency (eta_overall) 1 0.31186254
Turbine Isentropic Efficiency (eta_t) 1 0.90988422
Fuel Air Ratio (fuel_air_ratio) 1 0.035674253
Exit Mach Number (mach9) 1 2.2528658
Nozzle Total/Static Pressure Ratio (npr) 1 11.622222
Combustor Total-Pressure Ratio (pi_b) 1 0.94
Compressor Total-Pressure Ratio (pi_c) 1 10
Inlet Total-Pressure Recovery (pi_d) 1 0.87875
Nozzle Total-Pressure Ratio (pi_n) 1 0.96
Freestream Total/Static Pressure Ratio (pi_r) 1 7.8244491
Turbine Total-Pressure Ratio (pi_t) 1 0.37462865
Specific Thrust (specific_thrust) N·s/kg 807.05953
Exit Static Temperature / Ambient Temperature (t9_over_t0) 1 3.8460757
Compressor Total-Temperature Ratio (tau_c) 1 2.0771139
Turbine-Inlet Enthalpy / Ambient Enthalpy (tau_lambda) 1 10.250645
Freestream Total/Static Temperature Ratio (tau_r) 1 1.8
Turbine Total-Temperature Ratio (tau_t) 1 0.81553049
Thrust-Specific Fuel Consumption (tsfc) kg/(N·s) 4.4202753e-05
Exit Velocity / Freestream Sound Speed (v9_over_a0) 1 4.2505357

Model notes for this demonstration: - The outlet is not fully expanded; the current kinetic energy decomposition does not include pressure thrust work, so no thermal or propulsive efficiency is reported. The total efficiency is still calculated based on thrust power/fuel chemical power.

Turbojet · Afterburning design point

Mode identifier: turbojet.design_point_ab.

Applies afterburner heat addition and total-pressure loss downstream of the turbine.

Applies afterburner heat addition and total-pressure loss downstream of the turbine. Steady, one-dimensional turbojet cycle. The ideal mode uses one gas and neglects fuel mass addition; the loss mode uses constant specific heats in separate cold and hot sections. Off-design operation is limited to the fixed-area, double-choked model.

τr = 1 + (γc − 1) M₀² / 2
τc = πc^((γc − 1)/(γc ec))
S = f / (F/ṁ₀)

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Flight Mach number 1 2
Ambient static temperature K 216.7
ambient static pressure Pa 19400
Compressor total pressure ratio 1 10
Turbine inlet total temperature K 1800
Ambient/Exit Static Pressure Ratio 1 0.5
Cold-side specific heat cp J/(kg·K) 1004
Cold-side specific heat ratio γ 1 1.4
Hot-side specific heat cp J/(kg·K) 1239
Hot-side specific heat ratio γ 1 1.3
Fuel lower heating value J/kg 42800000
Inlet duct maximum total pressure recovery 1 0.95
Combustion chamber total pressure ratio 1 0.94
Nozzle total pressure ratio 1 0.96
Compressor polytropic efficiency 1 0.9
Turbine polytropic efficiency 1 0.9
combustion efficiency 1 0.98
mechanical efficiency 1 0.99
Afterburner outlet total temperature K 1950
Afterburning total pressure ratio 1 0.98
Afterburner efficiency 1 0.96
Afterburning section specific heat J/(kg·K) 1235.1
Afterburning section specific heat ratio 1 1.3
Output Unit Demonstration result
Compressor Isentropic Efficiency (eta_c) 1 0.86406619
Overall Efficiency (eta_overall) 1 0.27815112
Turbine Isentropic Efficiency (eta_t) 1 0.90988422
Afterburner Fuel / Core Air (f_ab) 1 0.015788294
Main Fuel / Core Air (f_main) 1 0.035674253
Fuel Air Ratio (fuel_air_ratio) 1 0.051462547
Exit Mach Number (mach9) 1 2.2407116
Nozzle Total/Static Pressure Ratio (npr) 1 11.389778
Pi Ab (pi_ab) 1 0.98
Combustor Total-Pressure Ratio (pi_b) 1 0.94
Compressor Total-Pressure Ratio (pi_c) 1 10
Inlet Total-Pressure Recovery (pi_d) 1 0.87875
Nozzle Total-Pressure Ratio (pi_n) 1 0.96
Freestream Total/Static Pressure Ratio (pi_r) 1 7.8244491
Turbine Total-Pressure Ratio (pi_t) 1 0.37462865
Specific Thrust (specific_thrust) N·s/kg 1038.3877
Exit Static Temperature / Ambient Temperature (t9_over_t0) 1 5.1329199
Compressor Total-Temperature Ratio (tau_c) 1 2.0771139
Turbine-Inlet Enthalpy / Ambient Enthalpy (tau_lambda) 1 10.250645
Freestream Total/Static Temperature Ratio (tau_r) 1 1.8
Turbine Total-Temperature Ratio (tau_t) 1 0.81553049
Thrust-Specific Fuel Consumption (tsfc) kg/(N·s) 4.9560049e-05
Exit Velocity / Freestream Sound Speed (v9_over_a0) 1 4.8762172

Model notes for this demonstration: - The step-by-step constant specific heat is used for afterburning, and the cross-section enthalpy reference may jump; it does not represent variable specific heat or chemical equilibrium results. - The outlet is not fully expanded; the current kinetic energy decomposition does not include pressure thrust work, so no thermal or propulsive efficiency is reported. The total efficiency is still calculated based on thrust power/fuel chemical power.

Turbojet · Component calculation

Mode identifier: turbojet.component.

Independent inlet, compressor, combustor, turbine, nozzle, and compressor-map calculations.

Standalone component calculation using the current component inlet state and loss parameters. It does not represent a complete engine cycle or automatic component matching.

wc = cp (Tt,out − Tt,in)
τc = πc^((γ − 1)/(γ ec)) (without a compressor map)

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Inlet total temperature K 390.06
Inlet total pressure Pa 133365
Compressor total pressure ratio 1 10
Compressor polytropic efficiency 1 0.9
Cold-side specific heat cp J/(kg·K) 1004
Cold-side specific heat ratio γ 1 1.4
Output Unit Demonstration result
Compressor Work (compressor_work) J/kg 421819.61
Delta Tt (delta_tt) K 420.13906
E C (e_c) 1 0.9
Compressor Isentropic Efficiency (eta_c) 1 0.86406619
Compressor Total-Pressure Ratio (pi_c) 1 10
Pressure Ratio (pressure_ratio) 1 10
Pt In (pt_in) Pa 133365
Pt Out (pt_out) Pa 1333650
Compressor Total-Temperature Ratio (tau_c) 1 2.0771139
Temperature Ratio (temperature_ratio) 1 2.0771139
Tt In (tt_in) K 390.06
Tt Out (tt_out) K 810.19906

Turbojet · Off-design point

Mode identifier: turbojet.off_design.

Normalized fixed-area, double-choked reference model; compressor efficiency and turbine temperature and pressure ratios retain their reference values.

Normalized fixed-area, double-choked reference model; compressor efficiency and turbine temperature and pressure ratios retain their reference values. Steady, one-dimensional turbojet cycle. The ideal mode uses one gas and neglects fuel mass addition; the loss mode uses constant specific heats in separate cold and hot sections. Off-design operation is limited to the fixed-area, double-choked model.

τr = 1 + (γc − 1) M₀² / 2
τc = πc^((γc − 1)/(γc ec))
S = f / (F/ṁ₀)

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Flight Mach number 1 2
Ambient static temperature K 216.7
ambient static pressure Pa 19400
Turbine inlet total temperature K 1800
Ambient/Exit Static Pressure Ratio 1 0.5
Cold-side specific heat cp J/(kg·K) 1004
Cold-side specific heat ratio γ 1 1.4
Hot-side specific heat cp J/(kg·K) 1239
Hot-side specific heat ratio γ 1 1.3
Fuel lower heating value J/kg 42800000
Inlet duct maximum total pressure recovery 1 0.95
Combustion chamber total pressure ratio 1 0.94
Nozzle total pressure ratio 1 0.96
Compressor polytropic efficiency 1 0.9
Turbine polytropic efficiency 1 0.9
combustion efficiency 1 0.98
mechanical efficiency 1 0.99
Reference Mach number 1 2
Reference static temperature K 216.7
Reference static pressure Pa 19400
Reference turbine-inlet total temperature K 1800
Reference ram temperature ratio 1 1.8
Reference ram pressure ratio 1 7.8244491
Reference inlet pressure ratio 1 0.8788
Reference compressor temperature ratio 1 2.0771
Reference compressor pressure ratio 1 10
Reference compressor efficiency 1 0.8641
Reference turbine temperature ratio 1 0.8155
Reference turbine pressure ratio 1 0.3746
Reference nozzle total-to-static pressure ratio 1 11.62
Reference air flow kg/s 50
Output Unit Demonstration result
N Nr (N_NR) 1 1.0000131
Air Flow (air_flow) kg/s 49.999365
Exit Area / Reference Exit Area (area_ratio_9) 1 1.0000982
Corrected Flow Ratio (corrected_flow_ratio) 1 1.0000442
Compressor Isentropic Efficiency (eta_c) 1 0.8641
Overall Efficiency (eta_overall) 1 0.31184934
Fuel Air Ratio (fuel_air_ratio) 1 0.03567439
Exit Mach Number (mach9) 1 2.2528464
N Nr (n_nr) 1 1.0000131
Net Thrust (net_thrust) N 40350.91
Nozzle Total/Static Pressure Ratio (npr) 1 11.621847
Combustor Total-Pressure Ratio (pi_b) 1 0.94
Compressor Total-Pressure Ratio (pi_c) 1 10.000442
Inlet Total-Pressure Recovery (pi_d) 1 0.87875
Nozzle Total-Pressure Ratio (pi_n) 1 0.96
Freestream Total/Static Pressure Ratio (pi_r) 1 7.8244491
Turbine Total-Pressure Ratio (pi_t) 1 0.3746
Specific Thrust (specific_thrust) N·s/kg 807.02846
Shaft Speed / Reference Speed (speed_ratio) 1 1.0000131
Exit Static Temperature / Ambient Temperature (t9_over_t0) 1 3.8459606
Compressor Total-Temperature Ratio (tau_c) 1 2.0771
Turbine-Inlet Enthalpy / Ambient Enthalpy (tau_lambda) 1 10.250645
Freestream Total/Static Temperature Ratio (tau_r) 1 1.8
Turbine Total-Temperature Ratio (tau_t) 1 0.8155
Thrust-Specific Fuel Consumption (tsfc) kg/(N·s) 4.4204625e-05
Exit Velocity / Freestream Sound Speed (v9_over_a0) 1 4.2504355

Model notes for this demonstration: - The outlet is not fully expanded; the current kinetic energy decomposition does not include pressure thrust work, so no thermal or propulsive efficiency is reported. The total efficiency is still calculated based on thrust power/fuel chemical power.

Turbojet · Dual-spool afterburning off-design point

Mode identifier: turbojet.dual_spool_afterburning_off_design.

Normalized dual-spool reference point with fixed turbine-ratio and choking assumptions; the afterburner can be disabled.

Normalized dual-spool reference point with fixed turbine-ratio and choking assumptions; the afterburner can be disabled. Steady, one-dimensional turbojet cycle. The ideal mode uses one gas and neglects fuel mass addition; the loss mode uses constant specific heats in separate cold and hot sections. Off-design operation is limited to the fixed-area, double-choked model.

τr = 1 + (γc − 1) M₀² / 2
τc = πc^((γc − 1)/(γc ec))
S = f / (F/ṁ₀)

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Flight Mach number 1 0
Ambient static temperature K 288.16667
ambient static pressure Pa 101325.35
Turbine-inlet total temperature Tt4 K 1777.7778
Environment/nozzle outlet static pressure ratio P0/P9 1 1
Cold-side specific heat cp J/(kg·K) 1004.832
Cold-side specific heat ratio γ 1 1.4
Hot-side specific heat cp J/(kg·K) 1235.106
Hot-side specific heat ratio γ 1 1.3
Fuel lower heating value J/kg 42798400
Inlet total pressure recovery 1 0.98
Combustion chamber total pressure ratio 1 0.96
Nozzle total pressure ratio 1 0.98
combustion efficiency 1 0.995
Low pressure compressor isentropic efficiency 1 0.8755
High pressure compressor isentropic efficiency 1 0.8791
Low pressure turbine total temperature ratio Tt5/Tt4.5 1 0.9033
High pressure turbine total temperature ratio Tt4.5/Tt4 1 0.8821
Low pressure turbine total pressure ratio Pt5/Pt4.5 1 0.6127
High pressure turbine total pressure ratio Pt4.5/Pt4 1 0.5466
Reference Mach number 1 0
Reference ambient static temperature K 288.16667
Reference ambient static pressure Pa 101325.35
Reference turbine-inlet total temperature K 1777.7778
Reference inlet total pressure recovery 1 0.98
Reference low pressure compressor total pressure ratio 1 5
Reference high pressure compressor total pressure ratio 1 4
Reference low pressure compressor total temperature ratio 1 1.6668451
Reference high pressure compressor total temperature ratio 1 1.5528523
Reference air mass flow kg/s 82.358767
Afterburner outlet total temperature Tt7 K 2000
Total pressure ratio of booster 1 0.94
afterburner efficiency 1 0.95
Afterburning hot end constant pressure specific heat J/(kg·K) 1235.106
Afterburning hot end specific heat ratio 1 1.3
Output Unit Demonstration result
Afterburner Fuel Air Ratio (afterburner_fuel_air_ratio) 1 0.019546481
Air Flow (air_flow) kg/s 82.362889
Overall Efficiency (eta_overall) 1 0
Propulsive Efficiency (eta_propulsive) 1 0
Thermal Efficiency (eta_thermal) 1 0.36709351
Fuel Air Ratio (fuel_air_ratio) 1 0.055355034
Hp Speed Ratio (hp_speed_ratio) 1 1.0000187
Lp Speed Ratio (lp_speed_ratio) 1 1.0000028
Exit Mach Number (mach9) 1 1.8268453
Main Fuel Air Ratio (main_fuel_air_ratio) 1 0.035808553
Net Thrust (net_thrust) N 111590.32
Nozzle Total/Static Pressure Ratio (npr) 1 5.805244
Pi Ch (pi_ch) 1 4.0001714
Pi Cl (pi_cl) 1 5.0000361
Specific Thrust (specific_thrust) N·s/kg 1354.8617
Tau Ch (tau_ch) 1 1.5528523
Tau Cl (tau_cl) 1 1.6668451
Thrust-Specific Fuel Consumption (tsfc) kg/(N·s) 4.0856593e-05

Model notes for this demonstration: - Dual-spool reference normalization holds turbine temperature and pressure ratios fixed and assumes choking at stations 4, 4.5, and 8. Variable nozzle area isolates afterburner changes from turbine matching. Compressor maps and unchoked operation are not modeled.

Turbofan · Variable-specific-heat single-spool design point (separate-flow or optional mixed-flow)

Mode identifier: turbofan.variable_cp_design.

NASA9 gaseous fuel; gas-phase equilibrium combustion and frozen chamber exit; single-spool separate-flow cycle with fully expanded streams. Optional core-stream afterburning, or explicit equal-static-pressure, constant-area, subsonic conservation mixing with independent post-mixer afterburning. An incompatible mixing root is rejected; pressure loss is not used to fabricate a match. No map matching, fixed-geometry back-pressure matching, or FAIR/VSH reproduction is claimed.

NASA9 dry air and gaseous fuel with inlet temperatures included separately in enthalpy. Adiabatic gas-phase equilibrium sets combustor temperature, then composition freezes. Single-spool load and net thrust are closed with fully expanded, variable-area exits. Optional post-turbine core-stream afterburning uses the same balance model for fuel mass and formation enthalpy; separate-flow bypass does not afterburn. No liquid vaporization, cooling, or map matching.

(1+f) h4 = h3 + f hf;(1+f)(h4−h5)ηm = wc+(1+α)wf;(1+f+fAB)h7 = (1+f)h5+fAB hfAB;F/ṁcore = (1+f+fAB)V9+αV19−(1+α)V0

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Flight Mach number 1 0
Ambient static temperature K 288.15
ambient static pressure Pa 101325
total air flow kg/s 30
Core compressor total pressure ratio 1 10
Compressor isentropic efficiency 1 0.9
Turbine isentropic efficiency 1 0.9
Shaft mechanical efficiency 1 0.99
Total intake pressure recovery 1 0.98
Combustion chamber total pressure ratio 1 0.95
Nozzle total pressure recovery 1 0.98
Fuel/Core Air Mass Ratio 1 0.02
Gaseous fuel inlet temperature K 300
Combustion temperature root lower limit K 1000
Combustion temperature root upper limit K 4500
bypass ratio 1 5
fan total pressure ratio 1 1.6
Fan isentropic efficiency 1 0.9
Output Unit Demonstration result
Afterburner Energy Residual (afterburner_energy_residual) J/kg 0
Afterburner Equilibrium Residual (afterburner_equilibrium_residual) 1 0
Afterburner Fuel Air Ratio (afterburner_fuel_air_ratio) 1 0
Afterburner Mass Residual (afterburner_mass_residual) 1 0
Afterburner Temperature (afterburner_temperature) K 1811.5537
Air Flow (air_flow) kg/s 30
Burner Energy Residual (burner_energy_residual) J/kg 0.00019769655
Bypass Ratio (bypass_ratio) 1 5
Compressor Work (compressor_work) J/kg 346378.1
Core Air Mass Flow (core_air_mass_flow) kg/s 5
Equilibrium Residual (equilibrium_residual) 1 7.1054274e-15
Fan Work (fan_work) J/kg 46404.752
Flight Velocity (flight_velocity) m/s 0
Fuel Air Ratio (fuel_air_ratio) 1 0.02
Fuel Mass Flow (fuel_mass_flow) kg/s 0.1
Mole Fraction H (mole_fraction_H) 1 2.7804503e-05
Mole Fraction H2 (mole_fraction_H2) 1 0.00032993951
Mole Fraction H2O (mole_fraction_H2O) 1 0.24812546
Mole Fraction N (mole_fraction_N) 1 2.9693429e-09
Mole Fraction N2 (mole_fraction_N2) 1 0.68726318
Mole Fraction No (mole_fraction_NO) 1 0.0061442178
Mole Fraction O (mole_fraction_O) 1 0.00017252019
Mole Fraction O2 (mole_fraction_O2) 1 0.054634631
Mole Fraction Oh (mole_fraction_OH) 1 0.0033022407
Net Thrust (net_thrust) N 13409.166
Shaft Energy Residual (shaft_energy_residual) J/kg 8.1490725e-10
Specific Thrust (specific_thrust) N·s/kg 446.9722
Total Fuel Air Ratio (total_fuel_air_ratio) 1 0.02
Thrust-Specific Fuel Consumption (tsfc) kg/(N·s) 7.4575854e-06
Turbine Inlet Temperature (turbine_inlet_temperature) K 2209.355
Turbine Work (turbine_work) J/kg 618742.93
V19 (v19) m/s 279.01181
V9 (v9) m/s 1261.5433

Model notes for this demonstration: - NASA9 variable specific heat with dry air (79 mol% N2, 21 mol% O2) and gaseous H2/CH4/CO fuel. Fuel-air ratio uses core air mass; net specific thrust uses total inlet air mass. - The adiabatic combustor solves 13-species gas-phase equilibrium. Fuel inlet temperature and formation enthalpy enter the energy balance; no separate heating value is added. Composition is frozen downstream. Excludes condensed phases, liquid vaporization, afterburning, cooling, and finite-rate chemistry. - Single-spool work balance with fully expanded streams and variable exit areas. This separate-flow model does not perform fixed-geometry, component-map, mixed-flow, or off-design matching.

Turbofan · Turbofan component calculation

Mode identifier: turbofan.component.

Standalone fan, booster, bypass-nozzle, and two-stream mixer calculations with constant-cp or NASA9 frozen properties. Total states and downstream additional loss are explicit inputs.

Standalone fan, booster, bypass-nozzle, and two-stream static-pressure-matched mixer calculations. The mixer may use constant-cp or NASA9 frozen species and does not solve chemical reaction. A constant-area outlet uses the subsonic conservation root; additional pressure loss acts separately downstream. The full-engine operating point is not closed automatically.

wc = cp (Tt,out − Tt,in)
τc = πc^((γ − 1)/(γ ec)) (without a compressor map)

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Inlet total temperature K 390.06
Inlet total pressure Pa 133365
Compressor total pressure ratio 1 1.6
Compressor polytropic efficiency 1 0.9
Cold-side specific heat cp J/(kg·K) 1004
Cold-side specific heat ratio γ 1 1.4
Output Unit Demonstration result
Compressor Work (compressor_work) J/kg 63017.123
Delta Tt (delta_tt) K 62.766058
E C (e_c) 1 0.9
Compressor Isentropic Efficiency (eta_c) 1 0.89315327
Compressor Total-Pressure Ratio (pi_c) 1 1.6
Pressure Ratio (pressure_ratio) 1 1.6
Pt In (pt_in) Pa 133365
Pt Out (pt_out) Pa 213384
Compressor Total-Temperature Ratio (tau_c) 1 1.1609139
Temperature Ratio (temperature_ratio) 1 1.1609139
Tt In (tt_in) K 390.06
Tt Out (tt_out) K 452.82606

Model notes for this demonstration: - Independent Fan calculation using the shared compression/nozzle solver; it does not perform full-engine matching.

Turbofan · Single-spool separate-flow design point

Mode identifier: turbofan.separate_design.

Separate core and bypass streams with single-spool load balance.

Separate core and bypass streams with single-spool load balance. Separate-flow, single-spool turbofan design point, with core pressure ratio measured from the inlet exit. Total specific thrust is normalized by total inlet airflow and fuel-air ratio by core airflow. The ideal mode neglects fuel mass addition. Dual-spool separate-flow off-design and constant-specific-heat dual-spool mixed-flow submodels are also available; their assumptions are listed with their inputs and results.

F/ṁtotal = (Fcore/ṁcore + α Fbypass/ṁbypass)/(1+α)
S = ṁfuel/F

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Flight Mach number 1 0.8
Ambient static temperature K 216.66667
ambient static pressure Pa 101325
bypass ratio 1 8
fan total pressure ratio 1 1.7
Core compressor total pressure ratio 1 36
Turbine-inlet total temperature K 1666.6667
Ambient / core-exit static-pressure ratio 1 0.9
Ambient / bypass-exit static-pressure ratio 1 0.9
Cold-side specific heat cp J/(kg·K) 1004.832
Cold-side specific heat ratio γ 1 1.4
Hot-side specific heat cp J/(kg·K) 1155.5568
Hot-side specific heat ratio γ 1 1.33
Fuel lower heating value J/kg 42797000
Inlet total pressure recovery 1 0.99
Combustion chamber total pressure ratio 1 0.96
Core nozzle total pressure ratio 1 0.99
Bypass nozzle total-pressure ratio 1 0.99
Compressor polytropic efficiency 1 0.9
Fan polytropic efficiency 1 0.89
Turbine polytropic efficiency 1 0.89
combustion efficiency 1 0.99
mechanical efficiency 1 0.99
Output Unit Demonstration result
Bypass Npr (bypass_npr) 1 2.2858286
Bypass Ratio (bypass_ratio) 1 8
Core Npr (core_npr) 1 3.065042
Compressor Isentropic Efficiency (eta_c) 1 0.84173261
Fan Isentropic Efficiency (eta_f) 1 0.88147899
Overall Efficiency (eta_overall) 1 0.30597905
Turbine Isentropic Efficiency (eta_t) 1 0.92003128
Fuel Air Ratio (fuel_air_ratio) 1 0.028679174
Mach19 (mach19) 1 1.1542052
Exit Mach Number (mach9) 1 1.3934202
Compressor Total-Pressure Ratio (pi_c) 1 36
Inlet Total-Pressure Recovery (pi_d) 1 0.99
Fan Total-Pressure Ratio (pi_f) 1 1.7
Freestream Total/Static Pressure Ratio (pi_r) 1 1.52434
Turbine Total-Pressure Ratio (pi_t) 1 0.065958072
Specific Thrust (specific_thrust) N·s/kg 176.75284
Specific Thrust Bypass (specific_thrust_bypass) N·s/kg 132.71859
Specific Thrust Core (specific_thrust_core) N·s/kg 529.02684
T19 Over T0 (t19_over_t0) 1 1.0561013
Exit Static Temperature / Ambient Temperature (t9_over_t0) 1 3.196129
Compressor Total-Temperature Ratio (tau_c) 1 3.1193513
Fan Total-Temperature Ratio (tau_f) 1 1.1857152
Turbine-Inlet Enthalpy / Ambient Enthalpy (tau_lambda) 1 8.8461538
Freestream Total/Static Temperature Ratio (tau_r) 1 1.128
Turbine Total-Temperature Ratio (tau_t) 1 0.54860834
Thrust Per Core Flow (thrust_per_core_flow) N·s/kg 1590.7755
Thrust-Specific Fuel Consumption (tsfc) kg/(N·s) 1.8028423e-05
V19 Over A0 (v19_over_a0) 1 1.1861396
Exit Velocity / Freestream Sound Speed (v9_over_a0) 1 2.4264433

Model notes for this demonstration: - At least one outlet is not fully expanded; the current kinetic energy decomposition does not include pressure thrust work, so thermal efficiency or propulsion efficiency is not reported. The total efficiency is still calculated based on thrust power/fuel chemical power.

Turbofan · Dual-spool separate-flow off-design point

Mode identifier: turbofan.separate_off_design.

Independent dual-spool reference-normalized matching with separate convergent nozzles and explicit reference conditions.

Independent dual-spool reference-normalized matching with separate convergent nozzles and explicit reference conditions. Separate-flow, single-spool turbofan design point, with core pressure ratio measured from the inlet exit. Total specific thrust is normalized by total inlet airflow and fuel-air ratio by core airflow. The ideal mode neglects fuel mass addition. Dual-spool separate-flow off-design and constant-specific-heat dual-spool mixed-flow submodels are also available; their assumptions are listed with their inputs and results.

F/ṁtotal = (Fcore/ṁcore + α Fbypass/ṁbypass)/(1+α)
S = ṁfuel/F

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Flight Mach number 1 0
Ambient static temperature K 288.16667
ambient static pressure Pa 101325.35
Combustion chamber outlet total temperature/throttle Tt4 K 1666.6667
Cold-side specific heat cp J/(kg·K) 1004.832
Cold-side specific heat ratio γ 1 1.4
Hot-side specific heat cp J/(kg·K) 1155.5568
Hot-side specific heat ratio γ 1 1.33
Fuel lower heating value J/kg 42798400
Inlet total pressure recovery 1 0.99
Combustion chamber total pressure ratio 1 0.96
Core nozzle total pressure ratio 1 0.99
Bypass nozzle total-pressure ratio 1 0.99
Fan isentropic efficiency 1 0.8815
High pressure compressor isentropic efficiency 1 0.8512
Low pressure turbine isentropic efficiency 1 0.9068
combustion efficiency 1 0.99
High pressure turbine total temperature ratio Tt4.5/Tt4 1 0.758
High pressure turbine total pressure ratio Pt4.5/Pt4 1 0.2851
Reference Mach number 1 0.8
Reference ambient static temperature K 216.66667
Reference ambient static pressure Pa 18822.687
Reference combustion chamber outlet total temperature K 1666.6667
Reference fan total pressure ratio 1 1.7
Reference high pressure compressor total pressure ratio 1 21.176471
Reference fan total temperature ratio 1 1.1857
Reference high pressure compressor total temperature ratio 1 2.636
Reference low pressure turbine total temperature ratio 1 0.7262
Reference low pressure turbine total pressure ratio 1 0.2349
Reference inlet total pressure recovery 1 0.99
Reference bypass ratio α 1 8
Reference core nozzle exit Mach number 1 1
Reference bypass nozzle exit Mach 1 1
Reference total air mass flow kg/s 272.15542
Output Unit Demonstration result
Bypass Exit Pressure Ratio (bypass_exit_pressure_ratio) 1 1
Bypass Npr (bypass_npr) 1 1.467572
Bypass Ratio (bypass_ratio) 1 9.1025821
Core Exit Pressure Ratio (core_exit_pressure_ratio) 1 1
Core Npr (core_npr) 1 1.5933537
Overall Efficiency (eta_overall) 1 0
Propulsive Efficiency (eta_propulsive) 1 0
Thermal Efficiency (eta_thermal) 1 0.36371482
Fan Speed Ratio (fan_speed_ratio) 1 0.93839603
Fuel Air Ratio (fuel_air_ratio) 1 0.027688044
Hp Speed Ratio (hp_speed_ratio) 1 1.0000952
Iterations (iterations) 1 23
Mach19 (mach19) 1 0.76103427
Exit Mach Number (mach9) 1 0.86174417
Matching Residual (matching_residual) 1 4.998818e-10
Net Thrust (net_thrust) N 211567.01
Pi Ch (pi_ch) 1 16.555392
Fan Total-Pressure Ratio (pi_f) 1 1.4973697
Pi Tl (pi_tl) 1 0.23960995
Specific Thrust (specific_thrust) N·s/kg 284.78717
Tau Ch (tau_ch) 1 2.444799
Fan Total-Temperature Ratio (tau_f) 1 1.138697
Tau Tl (tau_tl) 1 0.729342
Total Mass Flow (total_mass_flow) kg/s 742.89515
Thrust-Specific Fuel Consumption (tsfc) kg/(N·s) 9.6236421e-06

Model notes for this demonstration: - Reference-normalized approximation with two choked HP-turbine stations, equal fan and LP-compressor outlet conditions, and fixed-throat convergent nozzles. Excludes mixed-flow matching, component maps, and surge prediction.

Turbofan · Constant-specific-heat dual-spool mixed-flow

Mode identifier: turbofan.mixed_constant_cp.

Constant-cp dual-spool mixed-flow cycle with subsonic conservation mixing and optional afterburning; no FAIR/VSH thermochemistry.

Constant-cp dual-spool mixed-flow cycle with subsonic conservation mixing and optional afterburning; no FAIR/VSH thermochemistry. Separate-flow, single-spool turbofan design point, with core pressure ratio measured from the inlet exit. Total specific thrust is normalized by total inlet airflow and fuel-air ratio by core airflow. The ideal mode neglects fuel mass addition. Dual-spool separate-flow off-design and constant-specific-heat dual-spool mixed-flow submodels are also available; their assumptions are listed with their inputs and results.

F/ṁtotal = (Fcore/ṁcore + α Fbypass/ṁbypass)/(1+α)
S = ṁfuel/F

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Flight Mach number 1 0.8
Ambient static temperature K 216.7
ambient static pressure Pa 19400
total air mass flow kg/s 100
Bypass ratio α 1 0.4
fan total pressure ratio 1 3
High pressure compressor total pressure ratio 1 2
Turbine-inlet total temperature Tt4 K 1800
Environment/nozzle outlet static pressure ratio P0/P9 1 1
Cold-side specific heat cp J/(kg·K) 1004
Cold-side specific heat ratio γ 1 1.4
Hot-side specific heat cp J/(kg·K) 1235.1
Hot-side specific heat ratio γ 1 1.3
Fuel lower heating value J/kg 42800000
Inlet total pressure recovery 1 0.98
Combustion chamber total pressure ratio 1 0.96
Mixer total pressure recovery 1 0.97
Nozzle total pressure ratio 1 0.98
Core Mach at mixer inlet 1 0.6
Fan polytropic efficiency 1 0.9
HP compressor polytropic efficiency 1 0.9
Turbine polytropic efficiency 1 0.9
High pressure shaft mechanical efficiency 1 0.99
Low pressure shaft mechanical efficiency 1 0.99
Main combustion chamber efficiency 1 0.99
Afterburner outlet total temperature Tt7 K 1950
Total pressure ratio of booster 1 0.98
afterburner efficiency 1 0.96
Afterburning hot end constant pressure specific heat J/(kg·K) 1235.1
Afterburning hot end specific heat ratio 1 1.3
Output Unit Demonstration result
Afterburner Fuel Air Ratio (afterburner_fuel_air_ratio) 1 0.032292981
Bypass Mixer Mach (bypass_mixer_mach) 1 0.34160978
Overall Efficiency (eta_overall) 1 0.1029191
Propulsive Efficiency (eta_propulsive) 1 0.3333122
Thermal Efficiency (eta_thermal) 1 0.30877688
Fuel Air Ratio (fuel_air_ratio) 1 0.076870508
Ideal Mixer Exit Mach (ideal_mixer_exit_mach) 1 0.60041514
Exit Mach Number (mach9) 1 1.6765082
Main Fuel Air Ratio (main_fuel_air_ratio) 1 0.044577528
Mixer Energy Residual (mixer_energy_residual) W 4.6566129e-10
Mixer Momentum Residual (mixer_momentum_residual) N 2.2737368e-13
Mixer Total Pressure (mixer_total_pressure) Pa 92765.749
Mixer Total Temperature (mixer_total_temperature) K 1318.2191
Net Thrust (net_thrust) N 102483.79
Nozzle Total/Static Pressure Ratio (npr) 1 4.5923828
Pi Th (pi_th) 1 0.83300148
Pi Tl (pi_tl) 1 0.72436919
Specific Thrust (specific_thrust) N·s/kg 1024.8379
Tau Ch (tau_ch) 1 1.246135
Fan Total-Temperature Ratio (tau_f) 1 1.4173172
Thrust-Specific Fuel Consumption (tsfc) kg/(N·s) 5.3576772e-05

Model notes for this demonstration: - Constant-specific-heat dual-spool mixed-flow approximation with matched inlet static pressures and a subsonic mixer-exit root. It does not solve variable-specific-heat thermochemistry. - The mixing pressure loss is used downstream with the total pressure recovery coefficient; ideal_mixer_exit_mach is a conserved mixing state without additional losses and does not represent the local Mach after additional pressure losses.

Liquid Rocket · Thermochemical chamber and equilibrium nozzle

Mode identifier: liquid_rocket.equilibrium_thrust_chamber.

Gas-phase equilibrium isentropic expansion with the same elemental inventory. Critical mass flux closes the throat state; composition can freeze after a selected downstream area ratio. No liquid or condensed phase.

NASA9 ideal-gas, gas-phase equilibrium isentropic expansion. Critical mass flux is found from the maximum along the path; composition may freeze at a selected location. frozen_mach uses local frozen sound speed and is not equilibrium-sound-speed Mach. No liquid phase, condensed phase, or post-separation performance.

s_eq(T,p,b)=sc; V²/2=hc−h_eq; ṁ=At max(ρV); A=ṁ/(ρV); after freezing xᵢ=constant

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Combustion chamber total temperature K 3000
Combustion chamber total pressure Pa 1000000
throat area m² 0.001
outlet/throat area ratio 1 10
Nozzle length m 1
ambient static pressure Pa 10000
Nozzle temperature search lower limit K 500
Relative molar amount 1 2
Relative molar amount 1 1
Output Unit Demonstration result
Characteristic Velocity (c_star) m/s 1921.9662
Chamber Pressure (chamber_pressure) Pa 1000000
Chamber Temperature (chamber_temperature) K 3000
Completed (1 = Yes, 0 = No) (completed) 1 1
Exit Area (exit_area) m² 0.01
Exit Frozen Mach (exit_frozen_mach) 1 3.0181647
Exit Pressure (exit_pressure) Pa 15076.395
Exit Temperature (exit_temperature) K 1966.8467
Exit Velocity (exit_velocity) m/s 3150.9952
Specific Impulse (isp) s 331.26111
Mass Flow (mass_flow) kg/s 0.5203005
Throat Area (throat_area) m² 0.001
Throat Frozen Mach (throat_frozen_mach) 1 0.97279871
Throat Pressure (throat_pressure) Pa 580250.11
Throat Temperature (throat_temperature) K 2859.028
Thrust (thrust) N 1690.2283
Thrust Coefficient (thrust_coefficient) 1 1.6902283

Model notes for this demonstration: - Ideal-gas chemical equilibrium is solved along the chamber and nozzle with a conserved elemental inventory. - Critical mass flux is the interior maximum of ρV along the equilibrium isentrope. frozen_mach uses the local frozen speed of sound; it is not the equilibrium Mach number. - Linear variation of area along the axis is used for display, without accounting for wall pressure, post-separation properties, liquid vaporization, or condensed phase. - Chamber temperature can be specified or solved from gaseous inlet enthalpy at constant pressure; data version: NASA9-c915968268c707d69776909cadd834f1bcb6e44e4aaf1adfc6d5f42f86f6ace4.

History data: - equilibrium_nozzle_profile: 31 points; charts can select a quantity and JSON/CSV exports retain complete data.

Liquid Rocket · Thermochemical nozzle · Specified freeze area

Mode identifier: liquid_rocket.partial_frozen_thrust_chamber.

Gas-phase equilibrium isentropic expansion with the same elemental inventory. Critical mass flux closes the throat state; composition can freeze after a selected downstream area ratio. No liquid or condensed phase.

NASA9 ideal-gas, gas-phase equilibrium isentropic expansion. Critical mass flux is found from the maximum along the path; composition may freeze at a selected location. frozen_mach uses local frozen sound speed and is not equilibrium-sound-speed Mach. No liquid phase, condensed phase, or post-separation performance.

s_eq(T,p,b)=sc; V²/2=hc−h_eq; ṁ=At max(ρV); A=ṁ/(ρV); after freezing xᵢ=constant

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Combustion chamber total temperature K 3000
Combustion chamber total pressure Pa 1000000
throat area m² 0.001
outlet/throat area ratio 1 10
Nozzle length m 1
ambient static pressure Pa 10000
Nozzle temperature search lower limit K 500
Freezing point/throat area ratio 1 2
Relative molar amount 1 2
Relative molar amount 1 1
Output Unit Demonstration result
Characteristic Velocity (c_star) m/s 1921.9662
Chamber Pressure (chamber_pressure) Pa 1000000
Chamber Temperature (chamber_temperature) K 3000
Completed (1 = Yes, 0 = No) (completed) 1 1
Exit Area (exit_area) m² 0.01
Exit Frozen Mach (exit_frozen_mach) 1 3.1688606
Exit Pressure (exit_pressure) Pa 13489.644
Exit Temperature (exit_temperature) K 1716.2393
Exit Velocity (exit_velocity) m/s 3147.5324
Freeze Area Ratio (freeze_area_ratio) 1 2
Freeze Pressure (freeze_pressure) Pa 133673.3
Freeze Temperature (freeze_temperature) K 2499.294
Specific Impulse (isp) s 327.7982
Mass Flow (mass_flow) kg/s 0.5203005
Throat Area (throat_area) m² 0.001
Throat Frozen Mach (throat_frozen_mach) 1 0.97279871
Throat Pressure (throat_pressure) Pa 580250.11
Throat Temperature (throat_temperature) K 2859.028
Thrust (thrust) N 1672.5591
Thrust Coefficient (thrust_coefficient) 1 1.6725591

Model notes for this demonstration: - Gas-phase equilibrium is maintained in the chamber and up to the specified freeze area; composition is frozen downstream. The chemical freeze location is a user input, not a prediction. - Critical mass flux is the interior maximum of ρV along the equilibrium isentrope. frozen_mach uses the local frozen speed of sound; it is not the equilibrium Mach number. - Linear variation of area along the axis is used for display, without accounting for wall pressure, post-separation properties, liquid vaporization, or condensed phase. - Chamber temperature can be specified or solved from gaseous inlet enthalpy at constant pressure; data version: NASA9-c915968268c707d69776909cadd834f1bcb6e44e4aaf1adfc6d5f42f86f6ace4.

History data: - equilibrium_nozzle_profile: 61 points; charts can select a quantity and JSON/CSV exports retain complete data.

Liquid Rocket · Thermochemical chamber and frozen nozzle

Mode identifier: liquid_rocket.thermochemical_frozen_nozzle.

Chamber temperature may be specified or closed from gaseous inlet enthalpy, followed by a NASA9 frozen nozzle. No liquid vaporization.

Chamber temperature may be specified or closed from inlet gas-phase energy, then expanded with NASA9 chamber equilibrium or supplied frozen composition. The throat closes by enthalpy and sound speed. No liquid vaporization or along-path reaction.

h(T*) + a*²/2 = hc;s* = sc;ṁ = ρ* a* At;c* = pc At/ṁ;Isp = F/(ṁg₀)

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Combustion chamber total temperature K 3000
Combustion chamber total pressure Pa 1000000
throat area m² 0.001
outlet/throat area ratio 1 10
Nozzle length m 1
ambient static pressure Pa 10000
Relative molar amount 1 2
Relative molar amount 1 1
Output Unit Demonstration result
Characteristic Velocity (c_star) m/s 1882.5998
Chamber Pressure (chamber_pressure) Pa 1000000
Chamber Temperature (chamber_temperature) K 3000
Completed (1 = Yes, 0 = No) (completed) 1 1
Energy Relative Residual (energy_relative_residual) 1 -2.1508767e-16
Entropy Residual (entropy_residual) J/(kg·K) 0
Equilibrium Residual (equilibrium_residual) 1 3.5527137e-15
Exit Area (exit_area) m² 0.01
Exit Mach (exit_mach) 1 3.2823958
Exit Pressure (exit_pressure) Pa 12171.111
Exit Temperature (exit_temperature) K 1415.6648
Exit Velocity (exit_velocity) m/s 3046.6784
Gross Thrust (gross_thrust) N 1640.0468
Specific Impulse (isp) s 314.84265
Mass Flow (mass_flow) kg/s 0.53118035
Mole Fraction H (mole_fraction_H) 1 0.013682246
Mole Fraction H2 (mole_fraction_H2) 1 0.074845478
Mole Fraction H2O (mole_fraction_H2O) 1 0.82703753
Mole Fraction O (mole_fraction_O) 1 0.0055948684
Mole Fraction O2 (mole_fraction_O2) 1 0.024447863
Mole Fraction Oh (mole_fraction_OH) 1 0.054392014
Throat Area (throat_area) m² 0.001
Throat Pressure (throat_pressure) Pa 566526.73
Throat Temperature (throat_temperature) K 2742.9085
Thrust (thrust) N 1640.0468
Thrust Coefficient (thrust_coefficient) 1 1.6400468

Model notes for this demonstration: - The chamber solves 13-species gas-phase equilibrium. Nozzle expansion holds the chamber-exit composition frozen; it does not follow an equilibrium expansion path. - Chamber temperature is specified by the user; inlet energy closure is not solved. - Does not include finite rate losses, condensed phase, or post-separation properties. - NASA9 data version: NASA9-c915968268c707d69776909cadd834f1bcb6e44e4aaf1adfc6d5f42f86f6ace4.

History data: - nozzle_profile: 101 points; charts can select a quantity and JSON/CSV exports retain complete data.

Liquid Rocket · Finite contraction · Static chamber plane

Mode identifier: liquid_rocket.finite_contraction.

Standalone static chamber plane, finite-contraction subsonic root, and lossless total-state conversion; no heat-addition pressure loss.

A static chamber plane and finite contraction ratio define the subsonic state, followed by lossless total-state conversion. No heat-addition pressure loss.

Tt = T [1 + (γ − 1) M²/2]
Pt = p (Tt/T)^(γ/(γ − 1))
ṁ = ρ u Ac

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
throat area m² 0.01
Contraction area ratio 1 4
gas constant J/(kg·K) 350
specific heat ratio 1 1.2
Chamber-plane static pressure Pa 5000000
Chamber-plane static temperature K 3000
Output Unit Demonstration result
Area Ratio Residual (area_ratio_residual) 1 -9.1038288e-15
Chamber Area (chamber_area) m² 0.04
Chamber Mach (chamber_mach) 1 0.14984332
Chamber Total Pressure (chamber_total_pressure) Pa 5067738.3
Chamber Total Temperature (chamber_total_temperature) K 3006.7359
Chamber Velocity (chamber_velocity) m/s 168.19872
Mass Flow Residual (mass_flow_residual) kg/s 2.7711167e-13
Static Plane Mass Flow (static_plane_mass_flow) kg/s 32.03785
Throat Mass Flow (throat_mass_flow) kg/s 32.03785

Model notes for this demonstration: - Independent static chamber plane input, the total state is obtained through lossless isentropic relationship; it is not applied to other thrust chamber modes. - Finite-velocity heat-addition losses may be significant for contraction ratios below 2; Rayleigh losses and combustion efficiency are not calculated.

Liquid Rocket · Cylindrical chamber and convergent-section sizing

Mode identifier: liquid_rocket.convergent_chamber_geometry.

L*, contraction ratio, and cone half-angle allocate cylindrical and convergent sections; evaporation and combustion efficiency are not predicted.

Characteristic length sets total chamber volume; contraction ratio and conical half-angle allocate cylindrical and convergent sections. Combustion efficiency is not predicted.

Vc = L* At
Vc = V cylinder + V convergence section

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
combustion chamber pressure Pa 6894757
combustion chamber temperature K 3571
specific heat ratio 1 1.24
molecular weight kg/kmol 21.9
Characteristic velocity efficiency 1 1
thrust coefficient efficiency 1 1
scale value See scale selection 0.01
Nozzle parameters See nozzle selection 8
Environmental parameters See environment options 101325
Characteristic length L* m 1
Contraction area ratio 1 4
Convergent-section half-angle ° 45
Output Unit Demonstration result
Chamber Length (chamber_length) m 0.2735079
Chamber Volume (chamber_volume) m³ 0.01
Convergent Length (convergent_length) m 0.056418958
Convergent Volume (convergent_volume) m³ 0.0013164424
Cylindrical Length (cylindrical_length) m 0.21708894
Cylindrical Volume (cylindrical_volume) m³ 0.0086835576
Cylindrical Volume Fraction (cylindrical_volume_fraction) 1 0.86835576
Volume Residual (volume_residual) m³ -6.505213e-19

Model notes for this demonstration: - The geometric assignment of cylinders plus right cones only does not predict droplet evaporation, combustion completeness, or injector structure.

History data: - chamber_convergent_geometry: 3 points; charts can select a quantity and JSON/CSV exports retain complete data.

Liquid Rocket · Thrust-chamber performance

Mode identifier: liquid_rocket.thrust_chamber.

Explicit gas properties; geometry is an equivalent chamber or conical reference. Sweeps retain a fixed reference scale.

Explicit gas properties; geometry is an equivalent chamber or conical reference. Sweeps retain a fixed reference scale. Given the gas temperature, specific heat ratio and molar mass, quasi-one-dimensional isentropic expansion is used. Empirical efficiency only corrects the coefficient of performance; outlet static pressure cannot be used as a verified prediction of wall pressure or side load.

c* = pc At/ṁ
CF = F/(pc At)
Isp = F/(ṁ g₀)

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
combustion chamber pressure Pa 6894757
combustion chamber temperature K 3571
specific heat ratio 1 1.24
molecular weight kg/kmol 21.9
Characteristic velocity efficiency 1 1
thrust coefficient efficiency 1 1
scale value See scale selection 0.01
Nozzle parameters See nozzle selection 8
Environmental parameters See environment options 101325
Output Unit Demonstration result
Characteristic Velocity (c_star) m/s 1774.4478
C Star Ideal (c_star_ideal) m/s 1774.4478
Cf (cf) 1 1.5758352
Cf Momentum (cf_momentum) 1 1.5714872
Cf Pressure (cf_pressure) 1 0.0043480032
Cf Vacuum (cf_vacuum) 1 1.6934028
Exit Area (exit_area) m² 0.08
Exit Mach (exit_mach) 1 3.2241478
Exit Pressure (exit_pressure) Pa 105072.3
Exit Pressure Ratio (exit_pressure_ratio) 1 0.01523945
Exit Temperature (exit_temperature) K 1588.9363
Exit Velocity (exit_velocity) m/s 2788.5219
Exit Velocity Ideal (exit_velocity_ideal) m/s 2788.5219
Gamma Function (gamma_function) 1 0.65618566
Gas Constant (gas_constant) J/(kg·K) 379.65583
Specific Impulse (isp) s 285.13684
Isp Vacuum (isp_vacuum) s 306.40991
Mass Flow (mass_flow) kg/s 38.85579
Throat Area (throat_area) m² 0.01
Thrust (thrust) N 108650

Liquid Rocket · Standalone nozzle performance

Mode identifier: liquid_rocket.nozzle_performance.

Explicit gas properties; geometry is an equivalent chamber or conical reference. Sweeps retain a fixed reference scale.

Explicit gas properties; geometry is an equivalent chamber or conical reference. Sweeps retain a fixed reference scale. Given the gas temperature, specific heat ratio and molar mass, quasi-one-dimensional isentropic expansion is used. Empirical efficiency only corrects the coefficient of performance; outlet static pressure cannot be used as a verified prediction of wall pressure or side load.

c* = pc At/ṁ
CF = F/(pc At)
Isp = F/(ṁ g₀)

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
combustion chamber pressure Pa 6894757
combustion chamber temperature K 3571
specific heat ratio 1 1.24
molecular weight kg/kmol 21.9
Characteristic velocity efficiency 1 1
thrust coefficient efficiency 1 1
scale value See scale selection 0.01
Nozzle parameters See nozzle selection 8
Environmental parameters See environment options 101325
Output Unit Demonstration result
Characteristic Velocity (c_star) m/s 1774.4478
C Star Ideal (c_star_ideal) m/s 1774.4478
Cf (cf) 1 1.5758352
Cf Momentum (cf_momentum) 1 1.5714872
Cf Pressure (cf_pressure) 1 0.0043480032
Cf Vacuum (cf_vacuum) 1 1.6934028
Exit Area (exit_area) m² 0.08
Exit Mach (exit_mach) 1 3.2241478
Exit Pressure (exit_pressure) Pa 105072.3
Exit Pressure Ratio (exit_pressure_ratio) 1 0.01523945
Exit Temperature (exit_temperature) K 1588.9363
Exit Velocity (exit_velocity) m/s 2788.5219
Exit Velocity Ideal (exit_velocity_ideal) m/s 2788.5219
Gamma Function (gamma_function) 1 0.65618566
Gas Constant (gas_constant) J/(kg·K) 379.65583
Specific Impulse (isp) s 285.13684
Isp Vacuum (isp_vacuum) s 306.40991
Mass Flow (mass_flow) kg/s 38.85579
Throat Area (throat_area) m² 0.01
Thrust (thrust) N 108650

Liquid Rocket · Equivalent chamber sizing

Mode identifier: liquid_rocket.chamber_sizing.

Explicit gas properties; geometry is an equivalent chamber or conical reference. Sweeps retain a fixed reference scale.

Characteristic length and throat area set chamber volume and equivalent cylindrical dimensions. No convergent-section allocation.

Vc = L* At
Ac = CR At
Leq = Vc/Ac

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
combustion chamber pressure Pa 6894757
combustion chamber temperature K 3571
specific heat ratio 1 1.24
molecular weight kg/kmol 21.9
Characteristic velocity efficiency 1 1
thrust coefficient efficiency 1 1
scale value See scale selection 0.01
Nozzle parameters See nozzle selection 8
Environmental parameters See environment options 101325
Characteristic length L* m 1
Contraction area ratio 1 4
Output Unit Demonstration result
Characteristic Velocity (c_star) m/s 1774.4478
C Star Ideal (c_star_ideal) m/s 1774.4478
Cf (cf) 1 1.5758352
Cf Momentum (cf_momentum) 1 1.5714872
Cf Pressure (cf_pressure) 1 0.0043480032
Cf Vacuum (cf_vacuum) 1 1.6934028
Chamber Area (chamber_area) m² 0.04
Chamber Diameter (chamber_diameter) m 0.22567583
Chamber Length (chamber_length) m 0.25
Chamber Volume (chamber_volume) m³ 0.01
Exit Area (exit_area) m² 0.08
Exit Mach (exit_mach) 1 3.2241478
Exit Pressure (exit_pressure) Pa 105072.3
Exit Pressure Ratio (exit_pressure_ratio) 1 0.01523945
Exit Temperature (exit_temperature) K 1588.9363
Exit Velocity (exit_velocity) m/s 2788.5219
Exit Velocity Ideal (exit_velocity_ideal) m/s 2788.5219
Gamma Function (gamma_function) 1 0.65618566
Gas Constant (gas_constant) J/(kg·K) 379.65583
Specific Impulse (isp) s 285.13684
Isp Vacuum (isp_vacuum) s 306.40991
Mass Flow (mass_flow) kg/s 38.85579
Throat Area (throat_area) m² 0.01
Throat Diameter (throat_diameter) m 0.11283792
Thrust (thrust) N 108650

Model notes for this demonstration: - Equivalent cylinder length of length Vc/Ac, excluding convergence section assignment, injector structure and finite contraction total pressure correction.

Liquid Rocket · Nozzle contour · Conical or bell

Mode identifier: liquid_rocket.nozzle_contour_design.

Explicit gas properties; geometry is an equivalent chamber or conical reference. Sweeps retain a fixed reference scale.

Conical-nozzle reference contour defined by throat area, exit area ratio, and half-angle.

rt = √(At/π)
re = rt √ε
L = (re − rt)/tan θ

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
combustion chamber pressure Pa 6894757
combustion chamber temperature K 3571
specific heat ratio 1 1.24
molecular weight kg/kmol 21.9
Characteristic velocity efficiency 1 1
thrust coefficient efficiency 1 1
scale value See scale selection 0.01
Nozzle parameters See nozzle selection 8
Environmental parameters See environment options 101325
Cone half-angle ° 15
Points 1 101
Output Unit Demonstration result
Characteristic Velocity (c_star) m/s 1774.4478
C Star Ideal (c_star_ideal) m/s 1774.4478
Cf (cf) 1 1.5758352
Cf Momentum (cf_momentum) 1 1.5714872
Cf Pressure (cf_pressure) 1 0.0043480032
Cf Vacuum (cf_vacuum) 1 1.6934028
Divergence Factor (divergence_factor) 1 0.98296291
Exit Area (exit_area) m² 0.08
Exit Mach (exit_mach) 1 3.2241478
Exit Pressure (exit_pressure) Pa 105072.3
Exit Pressure Ratio (exit_pressure_ratio) 1 0.01523945
Exit Temperature (exit_temperature) K 1588.9363
Exit Velocity (exit_velocity) m/s 2788.5219
Exit Velocity Ideal (exit_velocity_ideal) m/s 2788.5219
Gamma Function (gamma_function) 1 0.65618566
Gas Constant (gas_constant) J/(kg·K) 379.65583
Specific Impulse (isp) s 285.13684
Isp Vacuum (isp_vacuum) s 306.40991
Mass Flow (mass_flow) kg/s 38.85579
Nozzle Length (nozzle_length) m 0.38499072
Throat Area (throat_area) m² 0.01
Thrust (thrust) N 108650

Model notes for this demonstration: - Geometry reference of right cone expansion section only, does not include throat arc, bell shape, wall pressure, separation position or side load. The divergence factor is reported separately and is not applied again to the prescribed performance efficiency.

History data: - conical_reference_contour: 101 points; charts can select a quantity and JSON/CSV exports retain complete data.

Liquid Rocket · Altitude performance

Mode identifier: liquid_rocket.altitude_characteristic.

Explicit gas properties; geometry is an equivalent chamber or conical reference. Sweeps retain a fixed reference scale.

Explicit gas properties; geometry is an equivalent chamber or conical reference. Sweeps retain a fixed reference scale. Given the gas temperature, specific heat ratio and molar mass, quasi-one-dimensional isentropic expansion is used. Empirical efficiency only corrects the coefficient of performance; outlet static pressure cannot be used as a verified prediction of wall pressure or side load.

c* = pc At/ṁ
CF = F/(pc At)
Isp = F/(ṁ g₀)

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
combustion chamber pressure Pa 6894757
combustion chamber temperature K 3571
specific heat ratio 1 1.24
molecular weight kg/kmol 21.9
Characteristic velocity efficiency 1 1
thrust coefficient efficiency 1 1
scale value See scale selection 0.01
Nozzle parameters See nozzle selection 8
Environmental parameters See environment options 101325
Scan starting point m 0
Scan end point m 30000
Points 1 101
Output Unit Demonstration result
Characteristic Velocity (c_star) m/s 1774.4478
C Star Ideal (c_star_ideal) m/s 1774.4478
Cf (cf) 1 1.5758352
Cf Momentum (cf_momentum) 1 1.5714872
Cf Pressure (cf_pressure) 1 0.0043480032
Cf Vacuum (cf_vacuum) 1 1.6934028
Exit Area (exit_area) m² 0.08
Exit Mach (exit_mach) 1 3.2241478
Exit Pressure (exit_pressure) Pa 105072.3
Exit Pressure Ratio (exit_pressure_ratio) 1 0.01523945
Exit Temperature (exit_temperature) K 1588.9363
Exit Velocity (exit_velocity) m/s 2788.5219
Exit Velocity Ideal (exit_velocity_ideal) m/s 2788.5219
Gamma Function (gamma_function) 1 0.65618566
Gas Constant (gas_constant) J/(kg·K) 379.65583
Specific Impulse (isp) s 285.13684
Isp Vacuum (isp_vacuum) s 306.40991
Mass Flow (mass_flow) kg/s 38.85579
Scan Count (scan_count) 1 101
Scan Success Count (scan_success_count) 1 101
Throat Area (throat_area) m² 0.01
Thrust (thrust) N 108650

Model notes for this demonstration: - The sweep keeps the baseline throat dimensions and explicit gas parameters fixed; it does not automatically reset thrust, look up tables, or change the chemical model. Failure points are retained and curves are not connected across failure points.

History data: - altitude_characteristic: 101 points; charts can select a quantity and JSON/CSV exports retain complete data.

Liquid Rocket · Area-ratio sweep

Mode identifier: liquid_rocket.area_ratio_sweep.

Explicit gas properties; geometry is an equivalent chamber or conical reference. Sweeps retain a fixed reference scale.

Explicit gas properties; geometry is an equivalent chamber or conical reference. Sweeps retain a fixed reference scale. Given the gas temperature, specific heat ratio and molar mass, quasi-one-dimensional isentropic expansion is used. Empirical efficiency only corrects the coefficient of performance; outlet static pressure cannot be used as a verified prediction of wall pressure or side load.

c* = pc At/ṁ
CF = F/(pc At)
Isp = F/(ṁ g₀)

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
combustion chamber pressure Pa 6894757
combustion chamber temperature K 3571
specific heat ratio 1 1.24
molecular weight kg/kmol 21.9
Characteristic velocity efficiency 1 1
thrust coefficient efficiency 1 1
scale value See scale selection 0.01
Nozzle parameters See nozzle selection 8
Environmental parameters See environment options 101325
Scan starting point 1 1
Scan end point 1 40
Points 1 101
Output Unit Demonstration result
Characteristic Velocity (c_star) m/s 1774.4478
C Star Ideal (c_star_ideal) m/s 1774.4478
Cf (cf) 1 1.5758352
Cf Momentum (cf_momentum) 1 1.5714872
Cf Pressure (cf_pressure) 1 0.0043480032
Cf Vacuum (cf_vacuum) 1 1.6934028
Exit Area (exit_area) m² 0.08
Exit Mach (exit_mach) 1 3.2241478
Exit Pressure (exit_pressure) Pa 105072.3
Exit Pressure Ratio (exit_pressure_ratio) 1 0.01523945
Exit Temperature (exit_temperature) K 1588.9363
Exit Velocity (exit_velocity) m/s 2788.5219
Exit Velocity Ideal (exit_velocity_ideal) m/s 2788.5219
Gamma Function (gamma_function) 1 0.65618566
Gas Constant (gas_constant) J/(kg·K) 379.65583
Specific Impulse (isp) s 285.13684
Isp Vacuum (isp_vacuum) s 306.40991
Mass Flow (mass_flow) kg/s 38.85579
Scan Count (scan_count) 1 101
Scan Success Count (scan_success_count) 1 101
Throat Area (throat_area) m² 0.01
Thrust (thrust) N 108650

Model notes for this demonstration: - The sweep keeps the baseline throat dimensions and explicit gas parameters fixed; it does not automatically reset thrust, look up tables, or change the chemical model. Failure points are retained and curves are not connected across failure points.

History data: - area_ratio_sweep: 101 points; charts can select a quantity and JSON/CSV exports retain complete data.

Liquid Rocket · Chamber-pressure sweep

Mode identifier: liquid_rocket.throttle_characteristic.

Explicit gas properties; geometry is an equivalent chamber or conical reference. Sweeps retain a fixed reference scale.

Explicit gas properties; geometry is an equivalent chamber or conical reference. Sweeps retain a fixed reference scale. Given the gas temperature, specific heat ratio and molar mass, quasi-one-dimensional isentropic expansion is used. Empirical efficiency only corrects the coefficient of performance; outlet static pressure cannot be used as a verified prediction of wall pressure or side load.

c* = pc At/ṁ
CF = F/(pc At)
Isp = F/(ṁ g₀)

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
combustion chamber pressure Pa 6894757
combustion chamber temperature K 3571
specific heat ratio 1 1.24
molecular weight kg/kmol 21.9
Characteristic velocity efficiency 1 1
thrust coefficient efficiency 1 1
scale value See scale selection 0.01
Nozzle parameters See nozzle selection 8
Environmental parameters See environment options 101325
Scan starting point Pa 1000000
Scan end point Pa 10000000
Points 1 101
Output Unit Demonstration result
Characteristic Velocity (c_star) m/s 1774.4478
C Star Ideal (c_star_ideal) m/s 1774.4478
Cf (cf) 1 1.5758352
Cf Momentum (cf_momentum) 1 1.5714872
Cf Pressure (cf_pressure) 1 0.0043480032
Cf Vacuum (cf_vacuum) 1 1.6934028
Exit Area (exit_area) m² 0.08
Exit Mach (exit_mach) 1 3.2241478
Exit Pressure (exit_pressure) Pa 105072.3
Exit Pressure Ratio (exit_pressure_ratio) 1 0.01523945
Exit Temperature (exit_temperature) K 1588.9363
Exit Velocity (exit_velocity) m/s 2788.5219
Exit Velocity Ideal (exit_velocity_ideal) m/s 2788.5219
Gamma Function (gamma_function) 1 0.65618566
Gas Constant (gas_constant) J/(kg·K) 379.65583
Specific Impulse (isp) s 285.13684
Isp Vacuum (isp_vacuum) s 306.40991
Mass Flow (mass_flow) kg/s 38.85579
Scan Count (scan_count) 1 101
Scan Success Count (scan_success_count) 1 101
Throat Area (throat_area) m² 0.01
Thrust (thrust) N 108650

Model notes for this demonstration: - The sweep keeps the baseline throat dimensions and explicit gas parameters fixed; it does not automatically reset thrust, look up tables, or change the chemical model. Failure points are retained and curves are not connected across failure points.

History data: - throttle_characteristic: 101 points; charts can select a quantity and JSON/CSV exports retain complete data.

Liquid Rocket · Gaseous-propellant mixture-ratio sweep

Mode identifier: liquid_rocket.mixture_ratio_sweep.

Gaseous H2/CH4/CO–O2 mixture-ratio sweep using one NASA9 chamber-equilibrium model and the explicitly selected frozen, equilibrium, or selected-area-freezing nozzle model. Chamber temperature is fixed or set by gas-phase energy closure.

Gaseous H2/CH4/CO–O2 mixture-ratio sweep using one NASA9 chamber-equilibrium model and the explicitly selected frozen, equilibrium, or selected-area-freezing nozzle model. Chamber temperature is fixed or set by gas-phase energy closure.

MR = m_oxidizer/m_fuel; n_f = 1/M_f; n_ox = MR/M_ox; Each sample uses chamber equilibrium and the selected nozzle chemistry, with At, Ae/At, and pa held fixed

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Combustion chamber total temperature K 3000
Combustion chamber total pressure Pa 1000000
throat area m² 0.001
outlet/throat area ratio 1 10
Nozzle length m 1
ambient static pressure Pa 10000
mass ratio starting point 1 2
mass ratio end point 1 10
Number of sampling points 1 21
Output Unit Demonstration result
Best Sample Isp (best_sample_isp) s 506.83147
Best Sample Mixture Ratio (best_sample_mixture_ratio) 1 2
Scan Count (scan_count) 1 21
Scan Success Count (scan_success_count) 1 21

Model notes for this demonstration: - MR is oxidizer-to-fuel mass ratio. Every sample uses the same species data, chamber equilibrium, and Frozen from chamber exit nozzle, with fixed geometry and back pressure; it is not a lookup table interpolation across chemical assumptions. - Chamber temperature is fixed at the user-specified value for every sample; it is not a predicted adiabatic combustion temperature. - The optimal value is only the highest Isp among successfully sampled points, not a continuous or global optimum. Failure points remain and are not connected; no liquid vaporization, condensed phase, finite rate, or separation models.

History data: - mixture_ratio_sweep: 21 points; charts can select a quantity and JSON/CSV exports retain complete data.

Ramjet · Full flowpath · Subsonic combustion

Mode identifier: ramjet.full_engine.

Specified-recovery inlet, subsonic source-term flowpath, and nozzle at specified exit pressure; nozzle exit area is an output.

A specified-recovery inlet connects a subsonic source-term flow segment and a nozzle at specified exit static pressure. Exit area is recovered from mass continuity. This is not fixed-geometry back-pressure matching.

F = ṁe Ve − ṁair V₀ + (pe − p₀) Ae
S = ṁfuel/F

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
specific heat ratio 1 1.4
gas constant J/(kg·K) 287
ambient static pressure Pa 5000
Mach number 1 4
Ambient static temperature K 220
capture area m² 0.02
Total intake pressure recovery 1 0.25
Inlet and outlet Mach number 1 0.4
length m 0.5
Exit area m² 0.02
Darcy friction factor 1 0
heat flow per unit length W/m 100000
Injection mass flow rate per unit length kg/(s·m) 0
Total enthalpy of injection stream J/kg 0
Injection flow axial velocity m/s 0
Number of integration steps 1 200
Nozzle total pressure recovery 1 0.98
Environment/nozzle outlet static pressure ratio 1 1
Nozzle end point spacing m 0.5
Output Unit Demonstration result
Completed (1 = Yes, 0 = No) (completed) 1 1
Energy Relative Residual (energy_relative_residual) 1 2.6970498e-13
Exit Area (exit_area) m² 0.032992651
Exit Mach (exit_mach) 1 3.0072407
Exit Mass Flow (exit_mass_flow) kg/s 1.8835264
Exit Pressure (exit_pressure) Pa 5000
Exit Temperature (exit_temperature) K 338.38689
Exit Velocity (exit_velocity) m/s 1108.8682
Gross Thrust (gross_thrust) N 2088.5825
Inlet Area (inlet_area) m² 0.0118681
Inlet Mach (inlet_mach) 1 0.4
Inlet Mass Flow (inlet_mass_flow) kg/s 1.8835264
Point Count (point_count) 1 201
Specific Thrust (specific_thrust) N·s/kg -80.390412
Thrust (thrust) N -151.41747

Model notes for this demonstration: - Fixed specific heat, explicit heat flow, and mass sources; no reaction dynamics, shock trains, cooling coupling, or automatic mode switching. - Inlet total-pressure recovery is specified by the user. Capture area does not predict spillage or installation drag. - The subsonic combustor feeds a nozzle with specified exit static pressure. Exit area is calculated from mass continuity; this is not fixed-geometry back-pressure matching. - Only the nozzle inlet and exit states are reported. A line between them does not represent a resolved nozzle flowfield.

History data: - flow_profile: 201 points; charts can select a quantity and JSON/CSV exports retain complete data. - nozzle_stations: 2 points; charts can select a quantity and JSON/CSV exports retain complete data.

Ramjet · Full-engine design point

Mode identifier: ramjet.design_point.

Constant-cp relations. The quasi-one-dimensional flow model checks sonic events and integration residuals; it is not a complete inlet–combustor–nozzle chain.

Constant-cp relations. The quasi-one-dimensional flow model checks sonic events and integration residuals; it is not a complete inlet–combustor–nozzle chain. Subsonic-combustion ramjet design point, with no compressor or turbine shaft work. The combustor exit is closed at the specified total temperature; the ideal mode neglects fuel mass addition and requires complete expansion.

F = ṁe Ve − ṁair V₀ + (pe − p₀) Ae
S = ṁfuel/F

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Flight Mach number 1 2
Ambient static temperature K 216.7
ambient static pressure Pa 19400
Combustion chamber outlet total temperature K 1800
Environment/outlet static pressure ratio P0/P9 1 0.5
Cold-side specific heat cp J/(kg·K) 1004
Cold-side specific heat ratio γ 1 1.4
Hot-side specific heat cp J/(kg·K) 1239
Hot-side specific heat ratio γ 1 1.3
Fuel lower heating value J/kg 42800000
Inlet duct maximum recovery 1 0.95
Combustion chamber total pressure ratio 1 0.94
Nozzle total pressure ratio 1 0.96
combustion efficiency 1 0.98
Output Unit Demonstration result
Overall Efficiency (eta_overall) 1 0.20078579
Fuel Air Ratio (fuel_air_ratio) 1 0.04629574
Exit Mach Number (mach9) 1 1.4108471
Nozzle Total/Static Pressure Ratio (npr) 1 3.1023315
Combustor Total-Pressure Ratio (pi_b) 1 0.94
Inlet Total-Pressure Recovery (pi_d) 1 0.87875
Nozzle Total-Pressure Ratio (pi_n) 1 0.96
Freestream Total/Static Pressure Ratio (pi_r) 1 7.8244491
Specific Thrust (specific_thrust) N·s/kg 674.31292
Exit Static Temperature / Ambient Temperature (t9_over_t0) 1 6.396569
Turbine-Inlet Enthalpy / Ambient Enthalpy (tau_lambda) 1 10.250645
Freestream Total/Static Temperature Ratio (tau_r) 1 1.8
Thrust-Specific Fuel Consumption (tsfc) kg/(N·s) 6.8656167e-05
Exit Velocity / Freestream Sound Speed (v9_over_a0) 1 3.4328348

Model notes for this demonstration: - The outlet is not fully expanded; the current kinetic energy decomposition does not include pressure thrust work, so no thermal or propulsive efficiency is reported. The total efficiency is still calculated based on thrust power/fuel chemical power.

Ramjet · Normal shock

Mode identifier: ramjet.normal_shock.

Constant-cp relations. The quasi-one-dimensional flow model checks sonic events and integration residuals; it is not a complete inlet–combustor–nozzle chain.

Calorically perfect-gas normal shock. Input is the upstream supersonic state; output includes downstream state ratios and total-pressure recovery.

M₂² = [1 + (γ − 1) M₁²/2]/[γ M₁² − (γ − 1)/2]

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Upstream Mach number 1 2
specific heat ratio 1 1.4
Output Unit Demonstration result
Density Ratio (density_ratio) 1 2.6666667
Downstream Mach (downstream_mach) 1 0.57735027
Pressure Ratio (pressure_ratio) 1 4.5
Temperature Ratio (temperature_ratio) 1 1.6875
Total Pressure Recovery (total_pressure_recovery) 1 0.72087386
Upstream Mach (upstream_mach) 1 2

Ramjet · Rayleigh flow · Constant-area heating

Mode identifier: ramjet.rayleigh.

Constant-cp relations. The quasi-one-dimensional flow model checks sonic events and integration residuals; it is not a complete inlet–combustor–nozzle chain.

Constant-area frictionless heat addition specified by total-temperature ratio. It retains the inlet Mach branch and checks the choking limit.

ρ u = constant
p + ρ u² = constant
Tt,2/Tt,1 = given value

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Upstream Mach number 1 2
specific heat ratio 1 1.4
Total outlet/inlet temperature ratio 1 1.05
Output Unit Demonstration result
Density Ratio (density_ratio) 1 1.0326284
Downstream Mach (downstream_mach) 1 1.8141774
Pressure Ratio (pressure_ratio) 1 1.1769456
Temperature Ratio (temperature_ratio) 1 1.1397572
Total Temperature Ratio (total_temperature_ratio) 1 1.05
Upstream Mach (upstream_mach) 1 2

Ramjet · Oblique shock · Explicit weak/strong branch

Mode identifier: ramjet.oblique_shock.

Constant-cp relations. The quasi-one-dimensional flow model checks sonic events and integration residuals; it is not a complete inlet–combustor–nozzle chain.

Attached oblique shock with explicit weak or strong branch. The calculation stops beyond the attachment limit and does not substitute a normal shock.

tan θ = 2 cot β (M₁² sin²β − 1)/[M₁²(γ + cos 2β) + 2]

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Upstream Mach number 1 2
specific heat ratio 1 1.4
flow deflection angle ° 10
Output Unit Demonstration result
Density Ratio (density_ratio) 1 1.4584256
Downstream Mach (downstream_mach) 1 1.6405222
Max Deflection Degrees (max_deflection_degrees) ° 22.973532
Pressure Ratio (pressure_ratio) 1 1.7065786
Shock Angle Degrees (shock_angle_degrees) ° 39.313932
Temperature Ratio (temperature_ratio) 1 1.1701513
Total Pressure Recovery (total_pressure_recovery) 1 0.98464402
Upstream Mach (upstream_mach) 1 2

Model notes for this demonstration: - Selected oblique shock branch: weak. The detachment shock wave is not calculated when the maximum attachment rotation angle is exceeded.

Ramjet · Fanno flow · Constant-area friction

Mode identifier: ramjet.fanno.

Constant-cp relations. The quasi-one-dimensional flow model checks sonic events and integration residuals; it is not a complete inlet–combustor–nozzle chain.

Constant-area adiabatic friction flow using the Darcy friction factor. It retains the inlet Mach branch and stops at the sonic limit.

Tt = constant
ṁ = ρ u A = constant
fD L/D = 4 fF L/D

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Upstream Mach number 1 2
specific heat ratio 1 1.4
Darcy friction factor 1 0.02
length/diameter 1 5
Output Unit Demonstration result
Density Ratio (density_ratio) 1 1.1048577
Downstream Mach (downstream_mach) 1 1.6919535
Friction Length Residual (friction_length_residual) 1 -2.3694935e-13
Pressure Ratio (pressure_ratio) 1 1.2646688
Reached Choke (reached_choke) 1 0
Temperature Ratio (temperature_ratio) 1 1.144644
Total Pressure Ratio (total_pressure_ratio) 1 0.7881888
Upstream Mach (upstream_mach) 1 2

Model notes for this demonstration: - Adiabatic constant cross-section; using Darcy f_D·L/D (equal to 4 f_F·L/D), the total temperature remains constant.

Ramjet · Quasi-one-dimensional flow segment

Mode identifier: ramjet.one_d_flow.

Constant-cp relations. The quasi-one-dimensional flow model checks sonic events and integration residuals; it is not a complete inlet–combustor–nozzle chain.

Fixed-cp quasi-one-dimensional integration with area change, heat addition, mass addition, and friction. It checks sonic events and conservation residuals.

ṁ(x) = ρ(x) u(x) A(x)
M(x) = u(x)/√(γ R T(x))

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
gas constant J/(kg·K) 287
specific heat ratio 1 1.4
Inlet static pressure Pa 100000
Inlet static temperature K 300
Inlet velocity m/s 694.37742
Inlet area m² 1
Inlet mass flow kg/s 806.47784
Stream segment 1 length m 1
Flow section 1 outlet area m² 2
Flow segment 1 Darcy friction factor 1 0
Flow segment 1 heat flow per unit length W/m 0
Flow section 1 Injection mass flow rate per unit length kg/(s·m) 0
Flow section 1 Total enthalpy of injected flow J/kg 0
Flow section 1 injection flow axial velocity m/s 0
Flow section 1 Number of integration steps 1 100
Output Unit Demonstration result
Completed (1 = Yes, 0 = No) (completed) 1 1
Point Count (point_count) 1 101

Model notes for this demonstration: - With the specific heat fixed, the total enthalpy of injection uses the cpT zero point. - Uses a circular hydraulic diameter, Darcy friction, heat per unit length, and mass injection. This is not a complete reacting scramjet or isolator model.

History data: - flow_profile: 101 points; charts can select a quantity and JSON/CSV exports retain complete data.

Solid Rocket · Equilibrium Chamber Pressure

Mode identifier: solid_rocket.equilibrium.

Uses a supplied burn-rate law, burning area, and characteristic velocity. Demonstration parameters do not represent a specific propellant.

Uses a supplied burn-rate law, burning area, and characteristic velocity. Demonstration parameters do not represent a specific propellant. Zero-dimensional, constant-temperature combustion chamber with prescribed burn-rate law, characteristic velocity, and thrust coefficient. The transient calculation integrates grain regression and discharged mass, stopping at burnout or when it leaves the choked-flow domain. It does not model ignition, erosion, or tail-off blowdown.

r = rref (pc/pref)^n
ṁout = pc At/c*
mgas = mgas,0 + ρp Vburned − mout

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Reference burning rate m/s 0.005
Reference pressure Pa 6895000
Burn-rate pressure exponent n 1 0.35
propellant density kg/m³ 1750
Characteristic velocity c* m/s 1500
Thrust coefficient CF 1 1.5
environmental pressure Pa 101325
specific heat ratio 1 1.2
throat area m² 0.0001
Burning surface area m² 0.02
Output Unit Demonstration result
Burn Rate (burn_rate) m/s 0.0029726006
Equilibrium Pressure (equilibrium_pressure) Pa 1560615.3
Mass Flow (mass_flow) kg/s 0.10404102
Thrust (thrust) N 234.0923

Model notes for this demonstration: - burnArea is only used in equilibrium pressure mode; transients are calculated from the geometric burn surface.

History data: - history: 0 points; charts can select a quantity and JSON/CSV exports retain complete data.

Solid Rocket · Grain Regression Transient

Mode identifier: solid_rocket.transient.

Constant-temperature zero-dimensional chamber; end-burning or internal-port grain regression with conservative RK4 mass integration. No ignition, erosion, or tail-off.

Constant-temperature zero-dimensional chamber; end-burning or internal-port grain regression with conservative RK4 mass integration. No ignition, erosion, or tail-off. Zero-dimensional, constant-temperature combustion chamber with prescribed burn-rate law, characteristic velocity, and thrust coefficient. The transient calculation integrates grain regression and discharged mass, stopping at burnout or when it leaves the choked-flow domain. It does not model ignition, erosion, or tail-off blowdown.

r = rref (pc/pref)^n
ṁout = pc At/c*
mgas = mgas,0 + ρp Vburned − mout

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Reference burning rate m/s 0.005
Reference pressure Pa 6895000
Burn-rate pressure exponent n 1 0.35
propellant density kg/m³ 1750
Characteristic velocity c* m/s 1500
Thrust coefficient CF 1 1.5
environmental pressure Pa 101325
specific heat ratio 1 1.2
throat area m² 0.0001
Grain length m 0.2
outer radius m 0.08
inner radius m 0.02
gas temperature K 3000
Gas molar mass kg/kmol 24
initial chamber pressure Pa 300000
initial free volume m³ 0.001
Simulation duration s 2
maximum time step s 0.001
Output Unit Demonstration result
Burn Time (burn_time) s 2
Burnout Reached (burnout_reached) 1 0
Completed (1 = Yes, 0 = No) (completed) 1 1
Discharged Mass (discharged_mass) kg 0.37436737
Final Pressure (final_pressure) Pa 3542647.6
Mass Balance Residual (mass_balance_residual) kg 3.3306691e-16
Peak Pressure (peak_pressure) Pa 3542647.6
Peak Thrust (peak_thrust) N 531.39714
Remaining Propellant Mass (remaining_propellant_mass) kg 6.2191205
Total Impulse (total_impulse) N·s 842.32658

Model notes for this demonstration: - The specified time has been reached. - Fixed temperature lumped chamber pressure, given combustion rate law and thrust coefficient; excluding ignition, erosion combustion and nozzle geometry correction.

History data: - history: 2002 points; charts can select a quantity and JSON/CSV exports retain complete data.

TBCC · Explicit Air Split

Mode identifier: tbcc.explicit_split.

Combines independent turbojet and ramjet channels. Common inlet, back-pressure matching, and transition control are not implemented.

Combines independent turbojet and ramjet channels. Common inlet, back-pressure matching, and transition control are not implemented. Combines thrust and fuel flow from two independent cycles using a prescribed air split. It does not model a common inlet, back-pressure matching, or automatic mode switching.

F = F_turbojet + F_ramjet
ṁfuel = ṁfuel,turbojet + ṁfuel,ramjet

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
total captured air flow kg/s 100
Ramjet air fraction 1 0.5
Flight Mach number 1 2
Ambient static temperature K 216.7
ambient static pressure Pa 19400
Compressor total pressure ratio 1 10
Turbine inlet total temperature K 1800
Ambient/Exit Static Pressure Ratio 1 0.5
Cold-side specific heat cp J/(kg·K) 1004
Cold-side specific heat ratio γ 1 1.4
Hot-side specific heat cp J/(kg·K) 1239
Hot-side specific heat ratio γ 1 1.3
Fuel lower heating value J/kg 42800000
Inlet duct maximum total pressure recovery 1 0.95
Combustion chamber total pressure ratio 1 0.94
Nozzle total pressure ratio 1 0.96
Compressor polytropic efficiency 1 0.9
Turbine polytropic efficiency 1 0.9
combustion efficiency 1 0.98
mechanical efficiency 1 0.99
Combustion chamber outlet total temperature K 1800
Environment/outlet static pressure ratio P0/P9 1 0.5
Cold-side specific heat cp J/(kg·K) 1004
Cold-side specific heat ratio γ 1 1.4
Hot-side specific heat cp J/(kg·K) 1239
Hot-side specific heat ratio γ 1 1.3
Fuel lower heating value J/kg 42800000
Inlet duct maximum recovery 1 0.95
Combustion chamber total pressure ratio 1 0.94
Nozzle total pressure ratio 1 0.96
combustion efficiency 1 0.98
Output Unit Demonstration result
Fuel Mass Flow (fuel_mass_flow) kg/s 4.0984996
Net Thrust (net_thrust) N 74068.622
Ramjet Air Fraction (ramjet_air_fraction) 1 0.5
Ramjet Air Mass Flow (ramjet_air_mass_flow) kg/s 50
Ramjet Fuel Air Ratio (ramjet_fuel_air_ratio) 1 0.04629574
Ramjet Fuel Mass Flow (ramjet_fuel_mass_flow) kg/s 2.314787
Ramjet Specific Thrust (ramjet_specific_thrust) N·s/kg 674.31292
Ramjet Thrust (ramjet_thrust) N 33715.646
Specific Thrust (specific_thrust) N·s/kg 740.68622
Total Air Mass Flow (total_air_mass_flow) kg/s 100
Thrust-Specific Fuel Consumption (tsfc) kg/(N·s) 5.5333818e-05
Turbojet Air Mass Flow (turbojet_air_mass_flow) kg/s 50
Turbojet Fuel Air Ratio (turbojet_fuel_air_ratio) 1 0.035674253
Turbojet Fuel Mass Flow (turbojet_fuel_mass_flow) kg/s 1.7837126
Turbojet Specific Thrust (turbojet_specific_thrust) N·s/kg 807.05953
Turbojet Thrust (turbojet_thrust) N 40352.977

Model notes for this demonstration: - This result combines two independent cycles according to the air split ratio given by the user; the common inlet or back pressure matching is not solved. - This result does not include blending, variable geometry, channel gating, or automatic mode switching.

RBCC · Ideal Ejector-Ramjet Submodel

Mode identifier: rbcc.ideal_ejector.

Specified primary total state, supersonic primary flow, subsonic secondary flow, and choked ejector exit; not a complete RBCC.

Specified primary total state, supersonic primary flow, subsonic secondary flow, and choked ejector exit; not a complete RBCC. Ideal constant-area ejector-ramjet: a common gas constant, supersonic primary flow, subsonic secondary flow, choked ejector exit, and complete expansion. This is an RBCC submodel only.

α = ṁsecondary / ṁprimary
φ = (1+α) Vexit/Vprimary − α V₀/Vprimary

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
ambient static pressure Pa 100000
Ambient static temperature K 300
Mach number 1 0.5
specific heat ratio 1 1.35
Secondary-stream total pressure Pa 118000
Secondary stream total temperature K 313.2
Primary-stream total pressure Pa 1500000
Primary-stream total temperature K 3000
Primary-stream throat area m² 1
ejector area m² 12
Final exhaust static pressure (must be equal to ambient) Pa 100000
Final total exhaust temperature K 3000
Output Unit Demonstration result
Bypass Ratio (bypass_ratio) 1 1.9566256
Ejector Exit Pressure (ejector_exit_pressure) Pa 126626.43
Ejector Exit Temperature (ejector_exit_temperature) K 1039.9478
Ejector Exit Total Pressure (ejector_exit_total_pressure) Pa 235868.76
Exhaust Mach (exhaust_mach) 1 1.1932202
Inlet Static Pressure (inlet_static_pressure) Pa 91080.041
Momentum Relative Residual (momentum_relative_residual) 1 -5.5620175e-11
Primary Area Fraction (primary_area_fraction) 1 0.22490089
Primary Inlet Mach (primary_inlet_mach) 1 2.4697459
Secondary Inlet Mach (secondary_inlet_mach) 1 0.6299157
Thrust Augmentation Ratio (thrust_augmentation_ratio) 1 1.676926

Model notes for this demonstration: - The ideal model requires a supersonic primary-flow inlet, a subsonic secondary-flow inlet, and a choked ejector exit. - Does not include wall friction, shock waves, total pressure loss, fuel mass, secondary flow choke, or outlet unchoked branches. - The ideal ejection punch submodel only, cannot represent the complete RBCC or mode conversion.

ATR · Ideal Air-Turboramjet Submodel

Mode identifier: atr.ideal_air_turboramjet.

Specified primary flow, ideal work balance, and simplified heat addition; no gas generator, pump, or cooling.

Specified primary flow, ideal work balance, and simplified heat addition; no gas generator, pump, or cooling. Ideal air-turboramjet submodel with prescribed primary-stream total state: ideal fan/turbine work balance, low-speed mixing, simplified heat addition, and complete expansion. It excludes the gas generator, pumps, and cooling.

ṁprimary Δh_turbine = ṁair Δh_fan
F = ṁexit Vexit − ṁair V₀

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
ambient static pressure Pa 100000
Ambient static temperature K 300
ambient sound speed m/s 340
Mach number 1 0.5
specific heat ratio 1 1.35
Air-stream total pressure Pa 118000
Air-stream total temperature K 313.2
Primary-stream total pressure Pa 1500000
Primary-stream total temperature K 3000
fan pressure ratio 1 1.5
Heat release parameter ηb·hPR/(cp·T0) 1 485
Total exhaust temperature K 3000
exhaust static pressure Pa 100000
Output Unit Demonstration result
Bypass Ratio (bypass_ratio) 1 36.759324
Exhaust Mach (exhaust_mach) 1 0.95483639
Fan Exit Temperature (fan_exit_temperature) K 347.91651
Fuel Air Ratio (fuel_air_ratio) 1 0.017976935
Mixed Total Temperature (mixed_total_temperature) K 384.35594
Mixing Temperature Residual (mixing_temperature_residual) K 0
Primary Turbine Exit Temperature (primary_turbine_exit_temperature) K 1723.8444
Specific Thrust (specific_thrust) N·s/kg 826.32875
Thrust Augmentation Ratio (thrust_augmentation_ratio) 1 16.641919
Work Temperature Residual (work_temperature_residual) K -4.5474735e-13

Model notes for this demonstration: - The prevailing total state is given by the input; the model does not solve for gas generators, pumps, cooling, or chemical equilibrium. - The ideal model assumes an isentropic fan and turbine, zero Mach mixing and combustion, no total pressure loss, and a fully expanding nozzle. - Exhaust branch: subsonic. The fuel ratio adopts a simplified heat addition formula, ignoring the correction of fuel consumption by the mainstream proportion and fuel outlet enthalpy; no accurate chemical heat balance prediction is made.

Scramjet · Calibrated-Inlet Full Engine · Nonreacting Mixed Flow

Mode identifier: scramjet.calibrated_mixing_engine.

Calibrated inlet–combustor–nozzle system. Given geometry and explicit injection define nonreacting mixing or finite-rate flow; captured flight momentum is subtracted. Ambient back-pressure matching is not automatic.

A calibrated dry-air inlet connects a given-geometry mixing or reacting-flow combustor and nozzle. Each segment may specify injection composition, total enthalpy, and velocity. Net thrust subtracts captured-air flight momentum. There is no fixed-geometry back-pressure matching or automatic transition; no full-engine thrust is reported when the solution is incomplete.

ṁair=ρ0V0Acapture;ṁout=ṁair+Σṁinj;Fnet=ṁoutVe+(pe−p0)Ae−ṁairV0

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
length m 0.1
Exit area m² 0.0012987013
Darcy friction factor 1 0
heat flow per unit length W/m 0
Injection mass flow rate per unit length kg/(s·m) 0.005
Total enthalpy of injection stream J/kg 0
Injection flow axial velocity m/s 0
Number of integration steps 1 20
relative tolerance 1 1e-05
Maximum number of accepted steps 1 10000
Injection relative molar amount 1 1
Nozzlelength m 0.5
NozzleExit area m² 0.0038961039
NozzleDarcy friction factor 1 0
Nozzleheat flow per unit length W/m 0
NozzleInjection mass flow rate per unit length kg/(s·m) 0
NozzleTotal enthalpy of injection stream J/kg 0
NozzleInjection flow axial velocity m/s 0
NozzleNumber of integration steps 1 100
Reference geometric altitude m 34000
Reference freestream Mach 1 10
Reference exit Mach 1 4.15
Reference contraction ratio 1 15.4
Geometric altitude m 34000
Freestream Mach 1 10
Contraction ratio 1 15.4
capture area m² 0.02
Output Unit Demonstration result
Accepted Steps (accepted_steps) 1 139
Area (area) m² 0.0038961039
Captured Air Mass Flow (captured_air_mass_flow) kg/s 0.60478655
Completed (1 = Yes, 0 = No) (completed) 1 1
Specific Heat cp (cp) J/(kg·K) 1109.3345
Element Relative Residual (element_relative_residual) 1 0
Enthalpy (enthalpy) J/kg 494209.19
Exit Mach (exit_mach) 1 5.2396235
Exit Pressure (exit_pressure) Pa 12022.511
Exit Temperature (exit_temperature) K 765.28022
Exit Velocity (exit_velocity) m/s 2881.3009
Flight Pressure (flight_pressure) Pa 663.4107
Flight Velocity (flight_velocity) m/s 3070.5246
Flow Energy Residual (flow_energy_residual) W 9.3132257e-10
Flow Momentum Residual (flow_momentum_residual) N -1.563194e-13
Specific Heat Ratio γ (gamma) 1 1.3562001
Gross Thrust (gross_thrust) N 1788.2689
Injected Mass Flow (injected_mass_flow) kg/s 0.0005
Inlet Area (inlet_area) m² 0.0012987013
Inlet Exit Mach (inlet_exit_mach) 1 4.15
Inlet Total Pressure Recovery (inlet_total_pressure_recovery) 1 0.25138398
Mach Number (mach) 1 5.2396235
Mass Flow (mass_flow) kg/s 0.60528655
Mass Relative Residual (mass_relative_residual) 1 -1.2839474e-15
Mole Fraction Ar (mole_fraction_Ar) 1 0
Mole Fraction Ch4 (mole_fraction_CH4) 1 0
Mole Fraction Co (mole_fraction_CO) 1 0
Mole Fraction Co2 (mole_fraction_CO2) 1 0
Mole Fraction H (mole_fraction_H) 1 0
Mole Fraction H2 (mole_fraction_H2) 1 0.011693531
Mole Fraction H2O (mole_fraction_H2O) 1 0
Mole Fraction N (mole_fraction_N) 1 0
Mole Fraction N2 (mole_fraction_N2) 1 0.78076211
Mole Fraction No (mole_fraction_NO) 1 0
Mole Fraction O (mole_fraction_O) 1 0
Mole Fraction O2 (mole_fraction_O2) 1 0.20754436
Mole Fraction Oh (mole_fraction_OH) 1 0
Net Thrust (net_thrust) N -68.743051
Pressure (pressure) Pa 12022.511
Residence Time (residence_time) s 0.0002136318
Specific Impulse Injected (specific_impulse_injected) s -14019.681
Specific Thrust (specific_thrust) N·s/kg -113.66498
Temperature (temperature) K 765.28022
Velocity (velocity) m/s 2881.3009
Axial Position (x) m 0.6

Model notes for this demonstration: - The calibrated NASA9 inlet feeds nonreacting conservation-based mixed flow. Injection can change composition; reaction rates are zero and external heating is user-specified. - Net thrust subtracts captured-air momentum flux. specific_impulse_injected uses total injected mass; injected oxidizer or air is not relabeled as fuel. - User-specified reaction coefficients and preset dissociation demonstrations are not a substitute for confirmed combustion mechanisms. - Downstream geometry is fixed by the input. Shocks, isolator states, and area are not adjusted to match ambient back pressure. Spillage drag and automatic mode transition are excluded. - If any segment is incomplete, only its valid prefix is exported and full-engine thrust is not reported.

History data: - full_flow_profile: 140 points; charts can select a quantity and JSON/CSV exports retain complete data.

Scramjet · Calibrated-Inlet Full Engine · Finite-Rate Reacting Flow

Mode identifier: scramjet.calibrated_reacting_engine.

Calibrated inlet–combustor–nozzle system. Given geometry and explicit injection define nonreacting mixing or finite-rate flow; captured flight momentum is subtracted. Ambient back-pressure matching is not automatic.

A calibrated dry-air inlet connects a given-geometry mixing or reacting-flow combustor and nozzle. Each segment may specify injection composition, total enthalpy, and velocity. Net thrust subtracts captured-air flight momentum. There is no fixed-geometry back-pressure matching or automatic transition; no full-engine thrust is reported when the solution is incomplete.

ṁair=ρ0V0Acapture;ṁout=ṁair+Σṁinj;Fnet=ṁoutVe+(pe−p0)Ae−ṁairV0

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
length m 0.1
Exit area m² 0.0012987013
Darcy friction factor 1 0
heat flow per unit length W/m 0
Injection mass flow rate per unit length kg/(s·m) 0.005
Total enthalpy of injection stream J/kg 0
Injection flow axial velocity m/s 0
Number of integration steps 1 20
relative tolerance 1 1e-05
Maximum number of accepted steps 1 10000
Pre-exponential coefficient A (m³/kmol)^(0.0) / s / K^(0.0) 1
Temperature exponent n 1 0
Activation energy Ea J/kmol 0
Reactant stoichiometric coefficient 1 1
Product stoichiometric coefficient 1 2
Injection relative molar amount 1 1
Nozzlelength m 0.5
NozzleExit area m² 0.0038961039
NozzleDarcy friction factor 1 0
Nozzleheat flow per unit length W/m 0
NozzleInjection mass flow rate per unit length kg/(s·m) 0
NozzleTotal enthalpy of injection stream J/kg 0
NozzleInjection flow axial velocity m/s 0
NozzleNumber of integration steps 1 100
Reference geometric altitude m 34000
Reference freestream Mach 1 10
Reference exit Mach 1 4.15
Reference contraction ratio 1 15.4
Geometric altitude m 34000
Freestream Mach 1 10
Contraction ratio 1 15.4
capture area m² 0.02
Output Unit Demonstration result
Accepted Steps (accepted_steps) 1 2178
Area (area) m² 0.0038961039
Captured Air Mass Flow (captured_air_mass_flow) kg/s 0.60478655
Completed (1 = Yes, 0 = No) (completed) 1 1
Specific Heat cp (cp) J/(kg·K) 1109.3269
Element Relative Residual (element_relative_residual) 1 1.3113729e-15
Enthalpy (enthalpy) J/kg 494205.26
Exit Mach (exit_mach) 1 5.2397327
Exit Pressure (exit_pressure) Pa 12021.976
Exit Temperature (exit_temperature) K 765.2448
Exit Velocity (exit_velocity) m/s 2881.3023
Flight Pressure (flight_pressure) Pa 663.4107
Flight Velocity (flight_velocity) m/s 3070.5246
Flow Energy Residual (flow_energy_residual) W -1.8626451e-09
Flow Momentum Residual (flow_momentum_residual) N 1.0516032e-12
Specific Heat Ratio γ (gamma) 1 1.3562045
Gross Thrust (gross_thrust) N 1788.2677
Injected Mass Flow (injected_mass_flow) kg/s 0.0005
Inlet Area (inlet_area) m² 0.0012987013
Inlet Exit Mach (inlet_exit_mach) 1 4.15
Inlet Total Pressure Recovery (inlet_total_pressure_recovery) 1 0.25138398
Mach Number (mach) 1 5.2397327
Mass Flow (mass_flow) kg/s 0.60528655
Mass Relative Residual (mass_relative_residual) 1 1.1005264e-15
Mole Fraction Ar (mole_fraction_Ar) 1 0
Mole Fraction Ch4 (mole_fraction_CH4) 1 0
Mole Fraction Co (mole_fraction_CO) 1 0
Mole Fraction Co2 (mole_fraction_CO2) 1 0
Mole Fraction H (mole_fraction_H) 1 4.5678936e-06
Mole Fraction H2 (mole_fraction_H2) 1 0.011691221
Mole Fraction H2O (mole_fraction_H2O) 1 0
Mole Fraction N (mole_fraction_N) 1 0
Mole Fraction N2 (mole_fraction_N2) 1 0.78076033
Mole Fraction No (mole_fraction_NO) 1 0
Mole Fraction O (mole_fraction_O) 1 0
Mole Fraction O2 (mole_fraction_O2) 1 0.20754388
Mole Fraction Oh (mole_fraction_OH) 1 0
Net Thrust (net_thrust) N -68.744307
Pressure (pressure) Pa 12021.976
Residence Time (residence_time) s 0.00021363177
Specific Impulse Injected (specific_impulse_injected) s -14019.937
Specific Thrust (specific_thrust) N·s/kg -113.66706
Temperature (temperature) K 765.2448
Velocity (velocity) m/s 2881.3023
Axial Position (x) m 0.6

Model notes for this demonstration: - The calibrated NASA9 dry-air inlet feeds a combustor and nozzle using user-specified finite-rate reactions. Injection composition and formation-inclusive enthalpy are specified per segment. - Net thrust subtracts captured-air momentum flux. specific_impulse_injected uses total injected mass; injected oxidizer or air is not relabeled as fuel. - User-specified reaction coefficients and preset dissociation demonstrations are not a substitute for confirmed combustion mechanisms. - Downstream geometry is fixed by the input. Shocks, isolator states, and area are not adjusted to match ambient back pressure. Spillage drag and automatic mode transition are excluded. - If any segment is incomplete, only its valid prefix is exported and full-engine thrust is not reported.

History data: - full_flow_profile: 437 points; charts can select a quantity and JSON/CSV exports retain complete data.

Scramjet · Finite-Rate · Quasi-One-Dimensional Reacting Flow

Mode identifier: scramjet.finite_rate_flow.

User-supplied finite-rate reactions coupled to quasi-one-dimensional mass, momentum, and formation-enthalpy energy equations. Explicit Mach branch; third-body and Troe support; no automatic transonic transition.

Mass-action rates close with species mass flow, F/G, and NASA9 formation enthalpy, so temperature is not fixed. The inlet Mach branch is explicit; geometry, friction, and heat source may be specified; injection composition is set per segment or inherited from the inlet. Supports third-body and Lindemann/Troe chemistry, but not transport or transonic matching.

dNᵢ/dx = Aωᵢ + ṁ′Yᵢ,inj/Wᵢ;dF/dx = pA′ − τP + ṁ′Vinj;d(ṁG)/dx = q′ + ṁ′Ginj

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
entrance area m² 0.01
Quiet temperature K 3000
static pressure Pa 100000
Mach number 1 2
length m 0.01
Exit area m² 0.01
Darcy friction factor 1 0
heat flow per unit length W/m 0
Injection mass flow rate per unit length kg/(s·m) 0
Total enthalpy of injection stream J/kg 0
Injection flow axial velocity m/s 0
Number of integration steps 1 20
relative tolerance 1 1e-05
Maximum number of accepted steps 1 10000
Initial relative molar amount 1 1
Pre-exponential coefficient A (m³/kmol)^(0.0) / s / K^(0.0) 1
Temperature exponent n 1 0
Activation energy Ea J/kmol 0
Reactant stoichiometric coefficient 1 1
Product stoichiometric coefficient 1 2
Output Unit Demonstration result
Accepted Steps (accepted_steps) 1 20
Area (area) m² 0.01
Completed (1 = Yes, 0 = No) (completed) 1 1
Specific Heat cp (cp) J/(kg·K) 18392.914
Element Relative Residual (element_relative_residual) 1 0
Enthalpy (enthalpy) J/kg 44015529
Exit Mach (exit_mach) 1 2.0000074
Exit Pressure (exit_pressure) Pa 99999.326
Exit Temperature (exit_temperature) K 2999.9799
Exit Velocity (exit_velocity) m/s 7987.5398
Flow Energy Residual (flow_energy_residual) W -1.4901161e-08
Flow Momentum Residual (flow_momentum_residual) N 9.094947e-13
Specific Heat Ratio γ (gamma) 1 1.289064
Mach Number (mach) 1 2.0000074
Mass Flow (mass_flow) kg/s 0.64553784
Mass Relative Residual (mass_relative_residual) 1 0
Mole Fraction Ar (mole_fraction_Ar) 1 0
Mole Fraction Ch4 (mole_fraction_CH4) 1 0
Mole Fraction Co (mole_fraction_CO) 1 0
Mole Fraction Co2 (mole_fraction_CO2) 1 0
Mole Fraction H (mole_fraction_H) 1 2.5038968e-06
Mole Fraction H2 (mole_fraction_H2) 1 0.9999975
Mole Fraction H2O (mole_fraction_H2O) 1 0
Mole Fraction N (mole_fraction_N) 1 0
Mole Fraction N2 (mole_fraction_N2) 1 0
Mole Fraction No (mole_fraction_NO) 1 0
Mole Fraction O (mole_fraction_O) 1 0
Mole Fraction O2 (mole_fraction_O2) 1 0
Mole Fraction Oh (mole_fraction_OH) 1 0
Pressure (pressure) Pa 99999.326
Residence Time (residence_time) s 1.2519508e-06
Temperature (temperature) K 2999.9799
Velocity (velocity) m/s 7987.5398
Axial Position (x) m 0.01

Model notes for this demonstration: - Quasi-one-dimensional finite rate reaction flow: temperature is closed with the enthalpy of formation and total energy; no additional LHV is added to the reaction heat release. F/G reconstruction retains the selected inlet Mach branch. - Reaction coefficients are user inputs; the default dissociation reaction demonstrates the algorithm only. Supports third-body effects and Lindemann/Troe falloff. Excludes diffusion, shock trains, and automatic transonic matching. - Injection composition can be specified per segment; otherwise inlet composition is used. Injection total enthalpy includes formation enthalpy; explicit heat input represents additional external heating. A valid prefix from an incomplete integration is not a complete nozzle or full-engine result. - Thermal data: NASA9 · 13 species, version: NASA9-c915968268c707d69776909cadd834f1bcb6e44e4aaf1adfc6d5f42f86f6ace4.

History data: - reacting_flow_profile: 21 points; charts can select a quantity and JSON/CSV exports retain complete data.

Scramjet · Seven-State Variable-Specific-Heat · Frozen Flow Segment

Mode identifier: scramjet.variable_cp_flow.

NASA9 seven-state/F–G branch reconstruction and same-composition frozen flow with formation enthalpy in heat and mass injection; no chemical reaction.

NASA9 seven-state inlet reconstruction with explicit subsonic or supersonic F/G roots; G includes formation enthalpy. Flow segments allow area change, heat input, same-composition injection, and friction. Mass and energy residuals are checked; sound-speed or property-range events stop the solution. No along-path chemical reaction.

F = pA + ṁV;G = h(T,x) + V²/2;p = ρRmixT;d(ṁG)/dx = q′ + ṁ′Ginj

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
entrance area m² 0.01
Quiet temperature K 600
static pressure Pa 100000
Mach number 1 2
length m 0.5
Exit area m² 0.01
Darcy friction factor 1 0
heat flow per unit length W/m 200000
Injection mass flow rate per unit length kg/(s·m) 0
Total enthalpy of injection stream J/kg 0
Injection flow axial velocity m/s 0
Number of integration steps 1 200
Relative molar amount 1 0.79
Relative molar amount 1 0.21
Output Unit Demonstration result
Completed (1 = Yes, 0 = No) (completed) 1 1
Exit Mach (exit_mach) 1 1.9430073
Exit Pressure (exit_pressure) Pa 105174.99
Exit Temperature (exit_temperature) K 625.10954
Exit Velocity (exit_velocity) m/s 965.80152
Flow Energy Residual (flow_energy_residual) W 9.3132257e-10
Mass Flow (mass_flow) kg/s 5.6384653

Model notes for this demonstration: - NASA9 seven-state reconstruction and frozen composition flow segment; G=h+V²/2 includes the enthalpy of formation, allowing physically valid negative values. - The injection stream must have the same composition as the main stream; the explicit heat source does not equal the reaction mechanism, and the mixing or chemical rates of different components are not calculated.

History data: - frozen_flow_profile: 201 points; charts can select a quantity and JSON/CSV exports retain complete data.

Scramjet · Reference Calibration · Variable-Specific-Heat Inlet

Mode identifier: scramjet.calibrated_variable_inlet.

NASA9 dry air with explicit reference entropy-rise calibration, three freestream definitions, five inlet closures, and multiple-root selection; an independent inlet model.

A reference point explicitly calibrates Δs/ln(pe/p0). Three freestream definitions and five inlet closures share total-enthalpy, mass, and entropy relations. Uses NASA9 dry air from 0–70 km. Contraction inversion explicitly selects the higher- or lower-Mach root; it is not matched to a complete reacting flowpath.

h + V²/2 = h0;CR = ρeVe/(ρ0V0);Δs = K ln(pe/p0);πt = exp(−Δs/R)

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Reference geometric altitude m 34000
Reference freestream Mach 1 10
Reference exit Mach 1 4.15
Reference contraction ratio 1 15.4
Geometric altitude m 34000
Freestream Mach 1 10
Contraction ratio 1 15.4
Output Unit Demonstration result
Altitude (altitude) m 34000
Calibration Entropy Coefficient (calibration_entropy_coefficient) J/(kg·K) 89.792728
Contraction Ratio (contraction_ratio) 1 15.4
Dynamic Pressure (dynamic_pressure) Pa 46425.299
Energy Residual (energy_residual) J/kg -9.3132257e-10
Entropy Change (entropy_change) J/(kg·K) 397.92924
Exit Mach (exit_mach) 1 4.15
Exit Pressure (exit_pressure) Pa 55772.509
Exit Temperature (exit_temperature) K 1136.2267
Exit Velocity (exit_velocity) m/s 2734.1415
Flight Mach (flight_mach) 1 10
Root Count (root_count) 1 2
Total Pressure Recovery (total_pressure_recovery) 1 0.25138398

Model notes for this demonstration: - Reference calibration uses Δs = K ln(pe/p0), NASA9 dry-air properties with frozen composition, and total-enthalpy conservation. It does not substitute local γ into a constant-γ total-pressure power law. - Reference altitude, flight Mach, exit Mach, and contraction ratio are saved explicitly. High/low Mach branches apply to contraction-ratio inversion only; roots near extrema are rejected when they cannot be bracketed. - Three freestream specifications and five exit constraints are supported over 0–70 km geometric altitude. Calculations use the bundled NASA9 data; numerical equivalence to legacy property implementations is not claimed. - Independent inlet model; it does not by itself match a variable-specific-heat reacting combustor or fixed-geometry ambient back pressure.

Scramjet · Finite-Rate · Constant-Temperature, Constant-Volume Reactor

Mode identifier: scramjet.finite_rate_reactor.

User-supplied mass-action reactions in a constant-volume, externally isothermal reactor with adaptive explicit integration. Supports third-body/Troe and an optional NASA7 hydrogen–oxygen submechanism; no transport.

Constant-volume, externally isothermal mass-action reactor. It can load the 29-reaction hydrogen–oxygen submechanism or custom coefficients, supports third-body/Lindemann/Troe effects, and derives reverse rates from selected thermodynamic data. The initial single dissociation is numerical demonstration only. Incomplete integration cannot be used for extrema analysis.

dcᵢ/dt = Σ νᵢⱼ (kf ∏cᵣ^νᵣ − kr ∏cₚ^νₚ);kf = A Tⁿ exp(−Ea/RuT);kr = kf/Kc

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
temperature K 1500
initial pressure Pa 100000
duration s 0.1
relative tolerance 1 1e-05
Maximum number of accepted steps 1 10000
Initial relative molar amount 1 1
Pre-exponential coefficient A (m³/kmol)^(0.0) / s / K^(0.0) 1
Temperature exponent n 1 0
Activation energy Ea J/kmol 0
Reactant stoichiometric coefficient 1 1
Product stoichiometric coefficient 1 2
Output Unit Demonstration result
Accepted Steps (accepted_steps) 1 177
Completed (1 = Yes, 0 = No) (completed) 1 1
Mass Relative Residual (mass_relative_residual) 1 4.2929024e-16
Mole Fraction Ar (mole_fraction_Ar) 1 0
Mole Fraction Ch4 (mole_fraction_CH4) 1 0
Mole Fraction Co (mole_fraction_CO) 1 0
Mole Fraction Co2 (mole_fraction_CO2) 1 0
Mole Fraction H (mole_fraction_H) 1 0.17378712
Mole Fraction H2 (mole_fraction_H2) 1 0.82621288
Mole Fraction H2O (mole_fraction_H2O) 1 0
Mole Fraction N (mole_fraction_N) 1 0
Mole Fraction N2 (mole_fraction_N2) 1 0
Mole Fraction No (mole_fraction_NO) 1 0
Mole Fraction O (mole_fraction_O) 1 0
Mole Fraction O2 (mole_fraction_O2) 1 0
Mole Fraction Oh (mole_fraction_OH) 1 0
Pressure (pressure) Pa 109516.26
Temperature (temperature) K 1500
Thermostat Heat Input per Unit Volume (thermostat_heat_rate) W/m³ 3171942.5
Time (time) s 0.1

Model notes for this demonstration: - Constant volume, external constant temperature reactor; temperature is not updated by heat release, thermostat_heat_rate is the heat flow per unit volume required to maintain constant temperature. - Reaction-rate coefficients are supplied by the user. The default H2→2H reaction with A=1 s⁻¹ demonstrates the algorithm; it is not a calibrated hydrogen-combustion mechanism. - Arrhenius A uses concentrations in kmol/m³ and temperature in K; Ea is in J/kmol. Reverse rates use equilibrium constants derived from the selected Gibbs-energy data. Third-body effects and Lindemann/Troe falloff are supported; transport is excluded. - Thermal data: NASA9 · 13 species, version: NASA9-c915968268c707d69776909cadd834f1bcb6e44e4aaf1adfc6d5f42f86f6ace4.

History data: - reaction_history: 178 points; charts can select a quantity and JSON/CSV exports retain complete data.

Scramjet · Specified Temperature and Pressure · Gas-Phase Equilibrium

Mode identifier: scramjet.gas_equilibrium_tp.

Fixed T/p, 13-species ideal-gas equilibrium with explicit elemental inventory and chemical-affinity residuals; no ions or condensed phase.

At fixed temperature and pressure, Gibbs energy is minimized for the listed 13 ideal-gas species while conserving elements. Unconverged results are not reported. This mode does not solve adiabatic flame temperature.

Σ νᵢ [gᵢ°/(RuT) + ln(xᵢ p/p°)] = 0;Σ aₖᵢ nᵢ = bₖ

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
equilibrium temperature K 2500
Equilibrium pressure Pa 100000
Initial relative molar amount 1 2
Initial relative molar amount 1 1
Initial relative molar amount 1 3.76
Output Unit Demonstration result
Specific Heat cp (cp) J/(kg·K) 1749.3176
Enthalpy (enthalpy) J/kg 361753.15
Entropy (entropy) J/(kg·K) 11231.471
Equilibrium Residual (equilibrium_residual) 1 7.1054274e-15
Specific Heat Ratio γ (gamma) 1 1.2455563
Gas Constant (gas_constant) J/(kg·K) 344.87071
Iteration Count (iteration_count) 1 8
Mole Fraction H (mole_fraction_H) 1 0.0037750537
Mole Fraction H2 (mole_fraction_H2) 1 0.022467977
Mole Fraction H2O (mole_fraction_H2O) 1 0.31078338
Mole Fraction N (mole_fraction_N) 1 2.334651e-07
Mole Fraction N2 (mole_fraction_N2) 1 0.63940651
Mole Fraction No (mole_fraction_NO) 1 0.003713036
Mole Fraction O (mole_fraction_O) 1 0.0011895522
Mole Fraction O2 (mole_fraction_O2) 1 0.0067471934
Mole Fraction Oh (mole_fraction_OH) 1 0.011917058
Molecular Weight (molecular_weight) kg/kmol 24.108926
Pressure (pressure) Pa 100000
Temperature (temperature) K 2500

Model notes for this demonstration: - Ideal gas-phase reaction equilibrium for a given T, p; uses a 13-species ensemble and does not contain ionic, condensate, or complete hydrocarbon mechanisms. - Reported cp and γ are frozen-composition properties evaluated at the equilibrium composition, not derivatives along a changing chemical-equilibrium path. - Initial species amounts define the elemental inventory only; this mode does not solve adiabatic combustion temperature. Data version: NASA9-c915968268c707d69776909cadd834f1bcb6e44e4aaf1adfc6d5f42f86f6ace4.

Scramjet · Constant-Pressure Energy Closure · Gas-Phase Equilibrium

Mode identifier: scramjet.gas_equilibrium_hp.

Inlet gaseous composition, temperature, pressure, and heat input close equilibrium enthalpy. Zero heat is adiabatic. No liquid or condensed phase.

At fixed pressure and elemental inventory, inlet gas-phase enthalpy and specified heat determine equilibrium temperature and composition. Every temperature trial must converge and the root interval is explicit. No liquid phase, condensed phase, or ions.

h_eq(T,p,b) = h_in(T_in,x_in) + q; Σ aₖᵢ nᵢ = bₖ; q = 0 is adiabatic

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
common inlet temperature K 300
Heat supply per unit mass J/kg 0
lower temperature limit K 1000
upper temperature limit K 4500
Equilibrium pressure Pa 100000
Initial relative molar amount 1 2
Initial relative molar amount 1 1
Initial relative molar amount 1 3.76
Output Unit Demonstration result
Specific Heat cp (cp) J/(kg·K) 1736.964
Enthalpy (enthalpy) J/kg 2572.6057
Enthalpy Residual (enthalpy_residual) J/kg -0.0031265945
Entropy (entropy) J/(kg·K) 11084.304
Equilibrium Residual (equilibrium_residual) 1 1.0658141e-14
Specific Heat Ratio γ (gamma) 1 1.2456833
Gas Constant (gas_constant) J/(kg·K) 342.57751
Heat Per Mass (heat_per_mass) J/kg 0
Inlet Enthalpy (inlet_enthalpy) J/kg 2572.6088
Iteration Count (iteration_count) 1 8
Mole Fraction H (mole_fraction_H) 1 0.0017750149
Mole Fraction H2 (mole_fraction_H2) 1 0.015191703
Mole Fraction H2O (mole_fraction_H2O) 1 0.32355716
Mole Fraction N (mole_fraction_N) 1 7.217441e-08
Mole Fraction N2 (mole_fraction_N2) 1 0.6443166
Mole Fraction No (mole_fraction_NO) 1 0.002478197
Mole Fraction O (mole_fraction_O) 1 0.00052848526
Mole Fraction O2 (mole_fraction_O2) 1 0.0046640961
Mole Fraction Oh (mole_fraction_OH) 1 0.0074886728
Molecular Weight (molecular_weight) kg/kmol 24.270311
Pressure (pressure) Pa 100000
Target Enthalpy (target_enthalpy) J/kg 2572.6088
Temperature (temperature) K 2378.9565
Temperature Evaluations (temperature_evaluations) 1 31

Model notes for this demonstration: - At specified pressure, the inlet gaseous composition and common inlet temperature define the formation-inclusive enthalpy used for energy closure. Zero heat input gives adiabatic gas-phase equilibrium. - Only the 13 species declared in the gas phase; no liquid vaporization, condensed phase, ions, reaction times or combustion efficiencies. Output is rejected for solutions outside the interval and that have not converged. - Reported cp and γ are frozen-composition properties of the resulting equilibrium mixture. NASA9 data version: NASA9-c915968268c707d69776909cadd834f1bcb6e44e4aaf1adfc6d5f42f86f6ace4.

Scramjet · Variable-Specific-Heat · Frozen Nozzle

Mode identifier: scramjet.variable_cp_frozen_nozzle.

NASA9 variable-property frozen composition, isentropic enthalpy drop, and supersonic area matching; not replaced by constant-γ power laws.

NASA9 variable-property nozzle with frozen composition. Mass, total enthalpy, and entropy determine area; the supersonic branch does not cross sonic conditions. Extrapolation outside the property range is rejected.

h(T) + V²/2 = h₀;s(T,p) = s₀;ρVA = ṁ;Fgross = ṁVe + (pe − p₀) Ae

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
Entrance static temperature K 1600
inlet static pressure Pa 200000
Entrance Mach number 1 2
entrance area m² 0.01
Exit area m² 0.03
length m 1
ambient static pressure Pa 10000
Profile point count 1 101
Relative molar amount 1 0.79
Relative molar amount 1 0.21
Output Unit Demonstration result
Completed (1 = Yes, 0 = No) (completed) 1 1
Energy Relative Residual (energy_relative_residual) 1 0
Entropy Residual (entropy_residual) J/(kg·K) 0
Exit Mach (exit_mach) 1 3.0331414
Exit Pressure (exit_pressure) Pa 35341.794
Exit Temperature (exit_temperature) K 1053.796
Exit Velocity (exit_velocity) m/s 1928.2881
Gross Thrust (gross_thrust) N 13741.424
Mass Flow (mass_flow) kg/s 6.7319658

Model notes for this demonstration: - NASA9 variable specific heat with frozen composition and adiabatic, isentropic supersonic expansion. Excludes reactions, friction, separation, and side loads. - gross_thrust is nozzle gross thrust. Full-engine net thrust also subtracts captured-air momentum flux. - Physical property data version: NASA9-c915968268c707d69776909cadd834f1bcb6e44e4aaf1adfc6d5f42f86f6ace4.

History data: - nozzle_profile: 101 points; charts can select a quantity and JSON/CSV exports retain complete data.

Scramjet · Frozen Composition · Variable-Specific-Heat Properties

Mode identifier: scramjet.frozen_gas_properties.

NASA9 frozen ideal mixture with variable heat capacity, formation enthalpy, mixing entropy, and enthalpy inversion; no chemical equilibrium.

NASA9 frozen ideal mixture with explicit formation-enthalpy reference and mixing entropy. It is calculated only within the common temperature range of all selected species and is not chemical equilibrium.

h = Σ xᵢ hᵢ / Mmix;cp = Σ xᵢ cp,ᵢ / Mmix;cv = cp − Rmix;γ = cp/cv

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
pressure Pa 100000
temperature K 1000
Relative molar amount 1 0.79
Relative molar amount 1 0.21
Output Unit Demonstration result
Specific Heat cp (cp) J/(kg·K) 1149.2184
Specific Heat cv (cv) J/(kg·K) 861.02544
Density (density) kg/m³ 0.34698976
Enthalpy (enthalpy) J/kg 752975.25
Entropy (entropy) J/(kg·K) 8169.061
Specific Heat Ratio γ (gamma) 1 1.334709
Gas Constant (gas_constant) J/(kg·K) 288.19294
Molecular Weight (molecular_weight) kg/kmol 28.850334
Pressure (pressure) Pa 100000
Speed Of Sound (speed_of_sound) m/s 620.20457
Temperature (temperature) K 1000

Model notes for this demonstration: - NASA9 ideal-gas properties with frozen composition, including formation enthalpy and ideal mixing entropy; chemical equilibrium is not solved. - Physical property data version: NASA9-c915968268c707d69776909cadd834f1bcb6e44e4aaf1adfc6d5f42f86f6ace4. - Enthalpy includes formation enthalpy and must not be mixed with a cp·T reference convention. Temperature extrapolation is not supported.

Scramjet · Full Engine · Constant-Specific-Heat Flowpath

Mode identifier: scramjet.full_engine.

Seven-state input, fixed-cp explicit heat and mass sources, and a frozen nozzle; no reaction kinetics.

Seven-state input, fixed-cp explicit heat and mass sources, and a frozen nozzle; no reaction kinetics. Constant-specific-heat inlet, prescribed source-term flow segments, and a frozen nozzle. F is the momentum function pA + ṁV and G is total enthalpy per unit mass. Integration stops at sonic events and does not cross singularities.

F = p A + ṁ V
G = cp T + V²/2
Fnet = ṁe Ve − ṁair V₀ + (pe − p₀) Ae

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
specific heat ratio 1 1.4
gas constant J/(kg·K) 287
ambient static pressure Pa 5000
Mach number 1 4
Ambient static temperature K 220
capture area m² 0.02
Total intake pressure recovery 1 0.6
Inlet and outlet Mach number 1 2
length m 0.5
Exit area m² 0.01
Darcy friction factor 1 0
heat flow per unit length W/m 200000
Injection mass flow rate per unit length kg/(s·m) 0
Total enthalpy of injection stream J/kg 0
Injection flow axial velocity m/s 0
Number of integration steps 1 200
length m 1
Exit area m² 0.03
Darcy friction factor 1 0
heat flow per unit length W/m 0
Injection mass flow rate per unit length kg/(s·m) 0
Total enthalpy of injection stream J/kg 0
Injection flow axial velocity m/s 0
Number of integration steps 1 200
Output Unit Demonstration result
Completed (1 = Yes, 0 = No) (completed) 1 1
Energy Relative Residual (energy_relative_residual) 1 4.0723093e-12
Exit Area (exit_area) m² 0.03
Exit Mach (exit_mach) 1 3.6298922
Exit Mass Flow (exit_mass_flow) kg/s 1.8835264
Exit Pressure (exit_pressure) Pa 4059.5974
Exit Temperature (exit_temperature) K 268.71913
Exit Velocity (exit_velocity) m/s 1192.746
Gross Thrust (gross_thrust) N 2218.3566
Inlet Area (inlet_area) m² 0.0052478134
Inlet Mach (inlet_mach) 1 2
Inlet Mass Flow (inlet_mass_flow) kg/s 1.8835264
Point Count (point_count) 1 401
Specific Thrust (specific_thrust) N·s/kg -11.490898
Thrust (thrust) N -21.643409

Model notes for this demonstration: - Fixed specific heat, explicit heat flow, and mass sources; no reaction dynamics, shock trains, cooling coupling, or automatic mode switching. - Inlet total-pressure recovery is specified by the user. Capture area does not predict spillage or installation drag.

History data: - flow_profile: 401 points; charts can select a quantity and JSON/CSV exports retain complete data.

Scramjet · Combustor · Specified Heat Source

Mode identifier: scramjet.combustor_only.

Seven-state input, fixed-cp explicit heat and mass sources, and a frozen nozzle; no reaction kinetics.

Seven-state input, fixed-cp explicit heat and mass sources, and a frozen nozzle; no reaction kinetics. Constant-specific-heat inlet, prescribed source-term flow segments, and a frozen nozzle. F is the momentum function pA + ṁV and G is total enthalpy per unit mass. Integration stops at sonic events and does not cross singularities.

F = p A + ṁ V
G = cp T + V²/2
Fnet = ṁe Ve − ṁair V₀ + (pe − p₀) Ae

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
specific heat ratio 1 1.4
gas constant J/(kg·K) 287
ambient static pressure Pa 5000
entrance area m² 0.01
Quiet temperature K 600
static pressure Pa 100000
Mach number 1 2
length m 0.5
Exit area m² 0.01
Darcy friction factor 1 0
heat flow per unit length W/m 200000
Injection mass flow rate per unit length kg/(s·m) 0
Total enthalpy of injection stream J/kg 0
Injection flow axial velocity m/s 0
Number of integration steps 1 200
Output Unit Demonstration result
Completed (1 = Yes, 0 = No) (completed) 1 1
Energy Relative Residual (energy_relative_residual) 1 0
Exit Area (exit_area) m² 0.01
Exit Mach (exit_mach) 1 1.9373861
Exit Mass Flow (exit_mass_flow) kg/s 5.7026595
Exit Pressure (exit_pressure) Pa 105518.1
Exit Temperature (exit_temperature) K 626.87012
Exit Velocity (exit_velocity) m/s 972.3216
Gross Thrust (gross_thrust) N 6550
Inlet Area (inlet_area) m² 0.01
Inlet Mach (inlet_mach) 1 2
Inlet Mass Flow (inlet_mass_flow) kg/s 5.7026595
Point Count (point_count) 1 201

Model notes for this demonstration: - Fixed specific heat, explicit heat flow, and mass sources; no reaction dynamics, shock trains, cooling coupling, or automatic mode switching. - Inlet total-pressure recovery is specified by the user. Capture area does not predict spillage or installation drag.

History data: - flow_profile: 201 points; charts can select a quantity and JSON/CSV exports retain complete data.

Scramjet · Nozzle · Frozen Constant-Specific-Heat Flow

Mode identifier: scramjet.nozzle_only.

Seven-state input, fixed-cp explicit heat and mass sources, and a frozen nozzle; no reaction kinetics.

Seven-state input, fixed-cp explicit heat and mass sources, and a frozen nozzle; no reaction kinetics. Constant-specific-heat inlet, prescribed source-term flow segments, and a frozen nozzle. F is the momentum function pA + ṁV and G is total enthalpy per unit mass. Integration stops at sonic events and does not cross singularities.

F = p A + ṁ V
G = cp T + V²/2
Fnet = ṁe Ve − ṁair V₀ + (pe − p₀) Ae

Workflow: select this engine and mode in the app, choose Load Current Mode Demonstration, adjust fields, then calculate. The table lists numeric fields visible for the demonstration configuration; the app presents the current full field set after optional-field, freestream, or component changes. All table values are SI.

Input field Unit Demonstration value
specific heat ratio 1 1.4
gas constant J/(kg·K) 287
ambient static pressure Pa 5000
entrance area m² 0.01
Quiet temperature K 600
static pressure Pa 100000
Mach number 1 2
length m 1
Exit area m² 0.03
Darcy friction factor 1 0
heat flow per unit length W/m 0
Injection mass flow rate per unit length kg/(s·m) 0
Total enthalpy of injection stream J/kg 0
Injection flow axial velocity m/s 0
Number of integration steps 1 200
Output Unit Demonstration result
Completed (1 = Yes, 0 = No) (completed) 1 1
Energy Relative Residual (energy_relative_residual) 1 1.4645035e-11
Exit Area (exit_area) m² 0.03
Exit Mach (exit_mach) 1 3.1878837
Exit Mass Flow (exit_mass_flow) kg/s 5.7026595
Exit Pressure (exit_pressure) Pa 16111.673
Exit Temperature (exit_temperature) K 356.13939
Exit Velocity (exit_velocity) m/s 1205.9171
Gross Thrust (gross_thrust) N 7210.2846
Inlet Area (inlet_area) m² 0.01
Inlet Mach (inlet_mach) 1 2
Inlet Mass Flow (inlet_mass_flow) kg/s 5.7026595
Point Count (point_count) 1 201

Model notes for this demonstration: - Fixed specific heat, explicit heat flow, and mass sources; no reaction dynamics, shock trains, cooling coupling, or automatic mode switching. - Inlet total-pressure recovery is specified by the user. Capture area does not predict spillage or installation drag.

History data: - flow_profile: 201 points; charts can select a quantity and JSON/CSV exports retain complete data.