Propulsion System
Analysis Calculator

TRANSPARENT BY DESIGN · v1.5.1

Model, equations & limits

All six engines use a steady, one-dimensional design-point model. Core air flow and total temperatures/pressure ratios are specified; nozzle and combustor areas are inferred. No maps, bleed, cooling, accessory loads, installation drag or fixed-geometry engine matching. Total (stagnation) conditions use station subscripts. SI is used internally; exports identify units.

Gas properties

Constant mode: R = 287 J/(kg·K), cₚ = 1004.5 J/(kg·K), γ = 1.4. Variable mode uses NASA Glenn’s first-order diatomic-air vibrational approximation with θ = 5500 °R = 3055.56 K and z = θ/T:

cₚ(T) = cₚ₀ + R z² exp(−z)/[1 − exp(−z)]²
h(T) = cₚ₀T + Rθ/[exp(z) − 1]
s°(T) = cₚ₀ ln T + R{z/[exp(z) − 1] − ln[1 − exp(−z)]}
γ(T) = cₚ(T)/[cₚ(T) − R]; a² = γ(T)RT.

Energy calculations use h(T); isentropic pressure changes use s°(T₂) − s°(T₁) = R ln(p₂/p₁). The solver bounds temperatures to 30–3500 K. This is an approximate thermally perfect air model, not real combustion products, equilibrium chemistry, dissociation or ionization. Above 2500 K, treat results with particular caution.

Flight, compression & turbine work

h(Tₜ₀) = h(T₀) + V₀²/2. Inlet recovery: pₜ₂ = πd pₜ₀. Compressors use η꜀ = (hₒᵤₜ,s − hᵢₙ)/(hₒᵤₜ − hᵢₙ). Turbines use ηₜ = (hᵢₙ − hₒᵤₜ)/(hᵢₙ − hₒᵤₜ,s).

The turbofan fan processes both core and bypass flow; core compressor ratio is downstream of that fan. ηₘ ṁhot(hₜ₄ − hₜ₅) = compressor power + fan power. Bypass ratio is ṁbypass/ṁcore. Each bypass nozzle remains convergent.

Turboshaft/turboprop use a free power turbine: specified expansion ratio = pₜ₅/pₜ₆. Delivered power = ηgear ηₘ ṁhot(hₜ₅ − hₜ₆); torque = Pshaft/(2π RPM/60). Mechanical efficiency applies to each shaft separately.

Combustion & ramjet

f = [h(Tₜ₄) − h(Tₜ₃)]/[ηᵦQ − h(Tₜ₄)]; ṁhot = ṁcore(1+f). Fuel mass is included downstream. The ramjet has no compressor/turbine and assumes a subsonic, pressure-loss combustor; pₜ₄ = πᵦ pₜ₃. Ramjet and scramjet require Mach > 1. Inlet recovery is user-specified; inlet shocks, capture, start, spillage and external drag are not calculated.

Scramjet · constant-area mass addition

Specify combustor inlet Mach > 1 and below flight Mach. Inlet static conditions follow from total enthalpy and entropy. Fuel is injected with zero axial momentum, with no wall friction. This extends the textbook Rayleigh idealization to include fuel mass addition:

j₄ = (1+f)j₃; p₄ + j₄u₄ = p₃ + j₃u₃; h(T₄) + u₄²/2 = h(Tₜ₄). Solve on the supersonic branch. The sonic limit is found where u₄ = a₄ and the momentum constraint is just satisfied, including f(Tₜ₄). Requested heat addition at or above this limit is rejected.

Scramjet combustor total-pressure change is calculated from the solution; a separate combustor pressure-recovery input is not applied. Ideal-components mode does not remove this heat-addition loss. Mixing, reaction rates, boundary layers, isolator behavior and inlet unstart are excluded. A finite-temperature limit at the 3500 K solver ceiling may truncate the reported choking margin.

Nozzles

Apply total-pressure recovery at unchanged total enthalpy, then isentropic expansion. Continuity gives A = ṁRT/(pV). Throat state is M = 1, hₜ = h(T*) + a(T*)²/2.

Convergent: expand to ambient if unchoked, otherwise exit at the sonic state.
C–D matched design: infer supersonic exit area to make pₑ = ambient. Requires available pressure ratio above critical.
C–D specified area ratio: solve the supersonic area branch (1 ≤ Aₑ/Aₜ ≤ 20). Underexpanded and externally compressed overexpanded cases are supported. Back pressures requiring an internal shock or subsonic nozzle branch are flagged as unsupported; boundary-layer separation is not predicted.

For scramjets, the nozzle must retain supersonic flow and cannot reduce Mach below the combustor exit. Its equivalent sonic throat is a reference sizing area; it is not a prediction of a physical throat downstream of supersonic combustion.

Thrust, power & efficiencies

Each exhaust stream: F = ṁoutVₑ − ṁairV₀ + (pₑ − p₀)Aₑ. Sum core and bypass thrust for turbofan. Specific thrust uses total inlet air flow. TSFC = ṁfuel/F for positive net thrust; PSFC = ṁfuel/Pshaft. Nonpositive thrust gives unavailable TSFC.

Turboprop Tprop = ηprop Pshaft/V₀ for V₀ > 0, plus residual exhaust thrust. At V₀ = 0, propeller thrust, net thrust and overall propulsive efficiency are unavailable. Constant propeller efficiency is a design-point assumption; no low-speed or static propeller model is included.

Energy conversion efficiency = (shaft output + net exhaust kinetic-power increase)/(ṁfuel Q); residual pressure energy is excluded. Overall propulsive efficiency = FV₀/(ṁfuel Q). Turboshaft instead reports shaft thermal efficiency Pshaft/(ṁfuel Q).

Sweeps, comparisons & ideal mode

Each point is a new design calculation with inferred geometry. Invalid states are shown as gaps with explanatory status, not silently omitted. Comparisons apply common altitude/Mach but retain engine-specific flow, gas model, ratios, temperatures and losses. Review displayed base cases; different engines are not automatically normalized.

Ideal mode sets component efficiencies and specified pressure recoveries to one. It retains fuel mass addition, pressure ratios, temperatures and the scramjet momentum/energy constraints. Nozzle mode, gas-property mode and units are independent choices.

References

NASA Glenn · variable specific heats · stagnation energy with vibrational excitation · nozzle design · ramjet/scramjet thrust

Development milestones consolidated in this release

1.2: ramjet + C–D nozzle models. 1.3: scramjet combustor and choking checks. 1.4: variable-air properties across all engines. 1.5: sweeps, common-flight comparisons, four-file offline package and nozzle favicon concept.

ONE FOUNDATION / MULTIPLE PROPULSION FAMILIES

Development roadmap

Version 1.5 implements six airbreathing engine types, atmosphere, variable-air properties, C–D nozzles, parameter sweeps and engine comparison. The following are planned modules, with no calculations implemented yet.

First favicon concept · C–D nozzle and exhaust

Mint nozzle outline, white flow line and amber exhaust arrow on a navy tile. Shown at 16, 32, 64 and 128 pixels for review.