lrekit 0.1.0

Research and preliminary-design toolkit for liquid rocket engine simulation and CAD export.

LREKit

LREKit is a Python research and preliminary-design toolkit for liquid rocket engine simulation and CAD export. It currently covers nozzle, throat, chamber, regenerative-cooling, and pintle-injector workflows, pairing a practical Rao thrust-optimized parabolic (TOP) bell path with quasi-one-dimensional performance estimation, low-order engineering screens, an axisymmetric method-of-characteristics (MOC) solver, a finite-dimensional Rao variational boundary-value problem (BVP), a vendored NASA/JHU reference-code port, and a differentiable JAX backend with exact-Jacobian solves and gradient sensitivities.

The default, trusted path is the chart-based Rao/TOP quadratic-Bézier contour: it is deterministic, endpoint-exact, and benchmarked against published geometry. The MOC and variational solvers are active research implementations — they expose residuals, topology, reference comparisons, and explicit reliability metadata, but they are not promoted to design-validated or hardware-qualified status.

Engineering status. Every generated contour is stamped hardware_qualified = False. Passing the repository's design gates means a result cleared internal preliminary screening. It does not replace independent CFD, conjugate heat-transfer analysis, structural FEA, combustion-stability work, material allowables, manufacturing review, inspection, proof testing, or hot-fire qualification.

All symbols, ratios, and governing equations in this document have been cross-checked against the source code and against the primary literature stored in propulsion_texts/; citations are given inline and collected at the end.

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Table of contents

1. Capabilities and maturity
2. Test and validation status
3. What the tool does
4. Physical model
5. Contour methods
6. Differentiable (JAX) backend
7. Screening models
8. Installation
9. Command-line usage
10. Python API
11. Outputs
12. Validation and reference evidence
13. Repository layout
14. Known limitations
15. Remaining work
16. References

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Capabilities and maturity

Area	Current implementation	Status
Rao/TOP geometry	Upstream + downstream throat arcs and a quadratic Bézier bell using interpolated Rao-chart angles	Trusted preliminary baseline
Ideal performance	Constant-$\gamma$, calorically perfect, quasi-1D isentropic flow; $C_F$, thrust, $I_{sp}$, $c^*$, $\dot m$, exit state	Preliminary
Thermochemistry	Built-in combustion-product constants, or optional RocketCEA chamber $\gamma$, $M_w$, $T_c$, $c^*$	Preliminary; nozzle flow stays constant-$\gamma$
Direct MOC wall optimization	Axisymmetric characteristic march coupled to a monotone spline wall under SLSQP / Nelder–Mead	Experimental
Rao variational / MOC BVP	NASA-topology seed, Rao stationarity, characteristic compatibility, mass + length closure, $D$-state continuity, validity and topology diagnostics	Experimental research path
Differentiable solver	JAX/Optimistix Levenberg–Marquardt residual solve, differentiable NASA-style kernel march, optional solved $\theta_B$, exact $C_F$ sensitivities	Implemented, research-grade
Wall pressure & separation	Quasi-1D wall-pressure estimate; Summerfield, Kalt–Badal, Schmucker separation screens	Screening only
Thermal / cooling / structure	Bartz convection, Sieder-Tate rectangular channels with a circular-duct laminar proxy, fin correction, rough/helical Darcy loss, coolant-chemistry screens, station-wise SP-125 liner stress	Screening / preliminary sizing
Geometry export	CSV/STL, neutral STEP, Inventor manifest, and optional full-N one-solid regen B-rep with patterned ribs plus plenum/port voids	Preliminary manufacturing geometry, not production definition
Validation	Unit/regression tests, literature manifests, NASA/JHU parsers, kernel/topology parity, diagnostic reports	Strong software verification; incomplete physical validation

The maturity column is enforced in code. Each contour carries a design_status keyed by method — preliminary_top_geometry, experimental_moc_geometry, experimental_variational_geometry, or experimental_rao_variational_moc_bvp — and a research-grade ContourReliability level (see Reliability labels).

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Test and validation status

The most recently recorded run of the normal (non-slow) selection, on June 14, 2026, reports:

784 passed, 4 xfailed, 26 deselected in 350.73 s

produced with

MPLCONFIGDIR=/tmp/raosim-mpl \
  .venv-jax/bin/python -m pytest -q -m "not slow"

The repository contains 339 test functions, expanded by parametrization to the counts above. The four expected xfails record known research gaps: the unresolved provenance of one historical NASA TT' fixture, an unpackaged Cuffel–Back–Massier dataset, and literature-promotion tests for the experimental MOC and legacy variational paths. The 26 deselected tests are long JAX solves, convergence studies, NASA fixed-end closure, and the full Rao-chart sweep, all gated behind the slow marker.

This is software and mathematical verification. It demonstrates internal consistency, parity between backends, and agreement with reference fixtures — not physical validation against experiment or CFD. See Validation and reference evidence.

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What the tool does

Given a chamber pressure, ambient pressure, throat size or target thrust, expansion ratio, propellant model, and contour method, LREKit can:

• generate a reduced-length Rao/TOP bell, a conical nozzle, an MOC-optimized bell, or an experimental Rao variational/MOC contour;
• size throat radius from a requested thrust, or size expansion ratio for matched ideal expansion;
• compute ideal exit Mach number and pressure, thrust coefficient, thrust, mass flow, effective exhaust velocity, and specific impulse;
• estimate wall pressure, overexpansion separation, altitude performance, boundary-layer displacement, heat flux, regenerative-cooling capacity, and thin-wall pressure stress;
• generate one injector-to-exit thrust-chamber contour from $L^*$, contraction ratio, shoulder geometry, and a shared throat specification;
• sweep $\varepsilon$, $P_c$, or $R_t$; compare contour families; and run literature-backed benchmark cases with explicit pass / report / xfail policies;
• plot contours, characteristic nets, Mach / pressure / angle fields, wall distributions, exit-plane profiles, topology, residual diagnostics, and JAX sensitivity fields;
• export versioned CSV, STL, STEP, JSON, Markdown, and metadata artifacts;
• compute exact derivatives of the control-surface $C_F$ with respect to the solved node variables via the JAX backend.

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Physical model

Assumptions

The core gas-dynamics and nozzle solvers assume:

• steady, inviscid, adiabatic flow;
• a calorically perfect ideal gas with constant $\gamma$;
• isentropic expansion, except where an empirical loss or separation screen is applied;
• axisymmetry for the active MOC and Rao implementations;
• a choked throat and a fully supersonic divergent section;
• no reacting-flow chemistry evolution, finite-rate kinetics, particles, film cooling, wall roughness, ablation, embedded shocks, side loads, or fluid–structure interaction inside the solved flowfield.

The optional CEA integration supplies a chamber-property snapshot. The cea_frozen and cea_equilibrium modes preserve provenance and configuration intent, but the nozzle flow is still evaluated with a single effective chamber $\gamma$; variable-property MOC is not implemented.

Propellant / thermochemistry table

The built-in database stores nominal combustion-product properties (the exhaust gas at the nominal mixture ratio), not raw propellant properties:

Propellant	$\gamma$	$M_w$ [kg/mol]	$T_c$ [K]	$\eta_{Isp}$	O/F
N2O/Ethanol	1.22	0.0260	2800	0.92	5.5
LOX/RP-1	1.23	0.0235	3400	0.96	2.6
LOX/LCH4	1.24	0.0220	3500	0.96	3.5
LOX/LH2	1.20	0.0100	3250	0.98	6.0

The specific gas constant is $R = R_u / M_w$ with $R_u = 8314.46~\mathrm{J,kmol^{-1}K^{-1}}$. Users may also supply custom $\gamma$, $M_w$, $T_c$, and efficiency values, or request RocketCEA-derived chamber properties.

Isentropic gas dynamics

For Mach number $M$ and ratio of specific heats $\gamma$, the implemented stagnation relations are

$$ \frac{T}{T_0}=\left(1+\frac{\gamma-1}{2}M^2\right)^{-1}, \qquad \frac{p}{p_0}=\left(\frac{T}{T_0}\right)^{\gamma/(\gamma-1)}, \qquad \frac{\rho}{\rho_0}=\left(\frac{T}{T_0}\right)^{1/(\gamma-1)} . $$

The area–Mach relation is

$$ \frac{A}{A^*}=\frac{1}{M} \left[\frac{2}{\gamma+1}\left(1+\frac{\gamma-1}{2}M^2\right)\right]^{\frac{\gamma+1}{2(\gamma-1)}} , $$

inverted with Newton iteration on the chosen (subsonic or supersonic) branch. The Prandtl–Meyer function and Mach angle are

$$ \nu(M)=\sqrt{\frac{\gamma+1}{\gamma-1}}, \tan^{-1}!\sqrt{\frac{\gamma-1}{\gamma+1}\left(M^2-1\right)} -\tan^{-1}!\sqrt{M^2-1}, \qquad \mu=\sin^{-1}!\left(\frac{1}{M}\right) , $$

with $\nu(M)$ inverted by Newton iteration using the analytic derivative $\mathrm{d}\nu/\mathrm{d}M=\sqrt{M^2-1},/,[M(1+\tfrac{\gamma-1}{2}M^2)]$. These relations are standard compressible-flow results (Anderson, Modern Compressible Flow; cross-checked against propulsion_texts/prmeyer.pdf).

Performance model

With $\varepsilon = A_e/A_t$, $A_t=\pi R_t^2$, and $A_e=\varepsilon A_t$, the ideal one-dimensional thrust coefficient is

$$ C_F= \sqrt{\frac{2\gamma^2}{\gamma-1} \left(\frac{2}{\gamma+1}\right)^{\frac{\gamma+1}{\gamma-1}} \left[1-\left(\frac{p_e}{p_c}\right)^{\frac{\gamma-1}{\gamma}}\right]} +\left(\frac{p_e-p_a}{p_c}\right)\varepsilon . $$

The built-in propellant model applies an empirical efficiency multiplier $\eta_{Isp}$ to the complete ideal coefficient:

$$ C_{F,\mathrm{actual}}=\eta_{Isp},C_F, \qquad F=C_{F,\mathrm{actual}},p_c A_t . $$

The characteristic velocity, mass flow, specific impulse, and effective exhaust velocity are

$$ c^=\frac{\sqrt{\gamma R T_c}}{\gamma\sqrt{\left(2/(\gamma+1)\right)^{(\gamma+1)/(\gamma-1)}}}, \qquad \dot m=\frac{p_c A_t}{c^}, \qquad I_{sp}=\frac{C_{F,\mathrm{actual}},c^*}{g_0}, \qquad V_e=I_{sp},g_0 , $$

with $g_0 = 9.80665~\mathrm{m,s^{-2}}$. These are ideal-cycle estimates. The efficiency multiplier is a single lumped factor, not a resolved loss model, and must not be read as a prediction of combustion, boundary-layer, two-phase, or chemical losses. (Formulation: Sutton & Biblarz, Rocket Propulsion Elements; Anderson.)

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Contour methods

Conical reference

The conical utility reuses the bell throat arcs and a straight divergent wall at half-angle $\alpha$. Its length and classical divergence factor are

$$ L_{\mathrm{cone}}=\frac{R_e-R_t}{\tan\alpha}, \qquad \eta_{\mathrm{div}}=\frac{1+\cos\alpha}{2} . $$

The comparison module also estimates a bell divergence loss from an assumed linear exit-plane flow-angle profile,

$$ \eta_{\mathrm{div}}\approx \frac{\displaystyle\int_0^{R_e}\rho u_x,|\mathbf{u}|,r,\mathrm{d}r} {\displaystyle\int_0^{R_e}\rho,|\mathbf{u}|^2,r,\mathrm{d}r}, \qquad C_{F,2D}\approx\eta_{\mathrm{div}},C_{F,1D} , $$

which is a comparison aid, not a resolved exit-plane solution of the Bézier contour.

1. Rao/TOP Bézier baseline — method="bezier" (default, trusted)

The baseline contour has three pieces:

1. an upstream circular throat arc, $R_u = 1.5,R_t$;
2. a downstream circular throat arc, $R_d = 0.382,R_t$;
3. a quadratic Bézier bell from inflection point $N$ to exit point $E$.

The exit radius and reference 15° cone length are

$$ R_e=R_t\sqrt{\varepsilon}, \qquad L_{15}=\frac{R_e-R_t}{\tan 15^\circ}, \qquad L_n=\frac{L_{%}}{100},L_{15} , $$

and the bell is

$$ \mathbf{B}(t)=(1-t)^2,\mathbf{N}+2(1-t)t,\mathbf{P}_1+t^2,\mathbf{E}, \qquad 0\le t\le 1 , $$

where $\mathbf{P}_1$ is the intersection of the tangent leaving $N$ at angle $\theta_n$ and the tangent entering $E$ at angle $\theta_e$.

Chart angles and provenance. The default $(\theta_n,\theta_e)$ are bilinearly interpolated from embedded Rao/NASA chart tables spanning approximately $4\le\varepsilon\le 50$ and $60%\le L_{%}\le 100%$. The tables reproduce Rao's TOP design charts (G. V. R. Rao, Approximation of Optimum Thrust Nozzle Contour, ARS J. 30(6), 1960; as reproduced in Sutton and NASA SP-8120). Rao's underlying optimum study was computed for $\gamma = 1.23$; per Rao, Recent Developments in Rocket Nozzle Configurations (ARS J. 31(11), 1961), the optimal contour is nearly $\gamma$-insensitive at fixed $(\varepsilon, L)$ — only $C_F$ depends strongly on $\gamma$ — so the angle tables remain valid comparison targets at other $\gamma$. Inputs outside the grid are linearly extrapolated by the interpolator and should be treated cautiously.

This method is the trusted preliminary baseline because it is deterministic, smooth, endpoint-exact, benchmarked against explicit TOP geometry, and does not depend on the convergence of an experimental flow solver.

Chamber and convergent geometry

The authoritative contour includes the injector face, cylindrical chamber, rounded chamber shoulder, straight convergent, shared upstream throat arc, downstream throat arc, and bell. Chamber sizing uses contraction ratio $CR=A_c/A_t$ and characteristic length $L^*=V_c/A_t$:

$$ R_c=R_t\sqrt{CR}, \qquad V_c=L^* A_t . $$

The cylindrical length is root-solved against the exact volume of the piecewise-linear revolved contour. Each meridional segment is integrated as a conical frustum, including the shoulder and upstream throat arc. Infeasible combinations are rejected rather than assigned an arbitrary short cylinder.

ThroatGeometrySpec is shared by chamber and nozzle and owns $R_u/R_t$, $R_d/R_t$, convergent angle, and throat location. The minimum cylindrical length and chamber-shoulder radius factor are explicit design inputs; their fallback values are geometric placeholders, not injector- or combustion-qualified limits.

This remains a geometric volume model only: $L^*$ is a residence-time proxy, and its minimum useful value depends on propellants, injector/mixing, pressure, mixture ratio, packaging, stability, cooling, and hot-fire evidence.

2. Direct MOC wall optimization — method="moc"

This path parameterizes the bell as a monotone cubic Hermite spline with decision variables

$$ \mathbf{q}=\left[\theta_n,,r_1,,r_2,\dots,r_{n_c}\right] . $$

For each candidate wall it builds a transonic starting line, marches an axisymmetric characteristic net with wall feedback, samples the exit plane, and minimizes a cost combining negative exit thrust, exit-flow-angle penalties, radius monotonicity, and curvature regularization. SciPy SLSQP is used when available, with a NumPy Nelder–Mead fallback. The exported bell is currently reconstructed as a smooth quadratic Bézier from the optimized entrance and exit angles rather than exporting the sparse spline directly — one reason the method remains experimental_moc_geometry.

3. Legacy direct variational path — method="rao"

The legacy Rao path discretizes a supersonic control surface, evaluates thrust / mass-flow / length functionals, solves a finite-dimensional constrained optimization, and attempts a control-surface-driven MOC wall construction. It is retained for regression and comparison; its public status is experimental_variational_geometry, and literature-promotion tests are expected to fail.

4. Rao variational / MOC BVP — method="rao_variational_moc" (main research solver)

This solver seeds a finite-dimensional BVP from the NASA/JHU topology

$$ T T' ;\rightarrow; B ;\rightarrow; BD ;\rightarrow; D ;\rightarrow; DE ;\rightarrow; E . $$

Its default configuration uses the JAX/Optimistix Levenberg–Marquardt backend with exact autodiff Jacobians, the characteristic residual formulation, a NASA-style fixed-end topology seed, full position / flow-angle / Mach continuity at point $D$, a continuation ladder that raises weights on the mass, length, and endpoint constraints, and separate raw-wall, export-wall, residual, topology, and reliability diagnostics. The solved control-surface unknowns are, schematically,

$$ \mathbf{u}=\left[,M_i,;\theta_i,;r_i ;\middle|; \lambda_2,;\lambda_3,;\log C,;f_D,\right], $$

with optional wall unknowns and an optional live kernel angle $\theta_B$. Here $f_D$ is the arc-length fraction locating $D$ on the kernel characteristic $BD$.

Axisymmetric characteristics

With nodes ordered downstream and the axisymmetric source

$$ S=\frac{\sin\theta,\sin\mu}{r}, $$

the implemented compatibility relations are

$$ C^{+}:\quad \frac{\mathrm{d}r}{\mathrm{d}x}=\tan(\theta+\mu), \qquad \mathrm{d}(\theta-\nu)=-S,\mathrm{d}s, $$

$$ C^{-}:\quad \frac{\mathrm{d}r}{\mathrm{d}x}=\tan(\theta-\mu), \qquad \mathrm{d}(\theta+\nu)=+S,\mathrm{d}s . $$

The $C^{+}$ control surface $DE$ is enforced geometrically by reconstructing its axial coordinates,

$$ x_{i+1}=x_i+\frac{r_{i+1}-r_i}{\tan(\bar\theta_i+\bar\mu_i)}, \qquad x_1=x_D(f_D) . $$

The source term $S=\sin\theta\sin\mu/r$ and the $C^{\pm}$ invariant pairing are taken from Anderson (Modern Compressible Flow §11.4) and Zucrow & Hoffman (Gas Dynamics Vol. 2, Ch. 17), and are oracle-validated against the NASA M3.5Perf grids (the corrected forms hold at RMS $\sim 10^{-6}$–$10^{-8}$ on kernel and Deriv characteristics; see raosim/rao_residuals.py).

Rao stationarity

The critical Mach number is

$$ M^*=\sqrt{\frac{(\gamma+1)M^2}{2+(\gamma-1)M^2}} . $$

The primary algebraic optimum-thrust condition along the control surface $DE$ is

$$ M^*\frac{\cos(\theta-\alpha)}{\cos\alpha}=C, \qquad \alpha=\mu=\sin^{-1}(1/M), $$

implemented in logarithmic form for conditioning. This is Eq. (1) of Rao, Beck & Booth, AIAA 99-2584 (propulsion_texts/rao1999.pdf). Its differential identity, Eq. (2) of the same paper,

$$ \mathrm{d}\ln M^*-(\mathrm{d}\theta-\mathrm{d}\alpha)\tan(\theta-\alpha) +\mathrm{d}\alpha\tan\alpha=0 , $$

is retained as a secondary consistency check. The older direct-method functionals are also available; per unit radial extent their stagnation-normalized forms are

$$ f_1=2\pi r\left[\left(\frac{p}{p_0}-\frac{p_a}{p_0}\right) +\frac{\rho}{\rho_0}\gamma M^2\frac{T}{T_0} \frac{\sin(\phi-\theta)\cos\theta}{\sin\phi}\right], $$

$$ f_2=2\pi r\frac{\rho}{\rho_0}\bar V\frac{\sin(\phi-\theta)}{\sin\phi}, \qquad f_3=\cot\phi , $$

representing axial thrust, mass flow, and axial length respectively.

Mass and endpoint closure

Mass closure compares the surface-normal flux integral on $DE$ and the selected $BD$ segment,

$$ \dot m_\Gamma=\int_\Gamma 2\pi r,\rho V,\left|\sin(\beta-\theta)\right|,\mathrm{d}s, \qquad \dot m_{DE}=\dot m_{BD} . $$

The BVP additionally pins the commanded exit station and radius, $x_E=L_n$ and $r_E=R_t\sqrt{\varepsilon}$, and reports scaled residuals for mass, length, stationarity, characteristic compatibility, geometry, regularization, penalties, wall endpoints, and wall tangency.

Smooth-flow validity

The classical Rao validity inequality is evaluated along $DE$:

$$ b=1-\frac{\mathrm{d}\alpha}{\mathrm{d}\theta}, \frac{\tan(\theta-\alpha)+\tan\alpha}{\tan(\theta-\alpha)-\tan\alpha};\ge;0 . $$

If $b$ drops below tolerance, the requested smooth variational solution lies outside the shock-free Rao region; the construction is flagged invalid_short_nozzle_region and the reliability level is downgraded. This boundary relation is the perfect-gas optimum-thrust boundary of Rao, Beck & Booth (1999) and is discussed in Östlund's KTH thesis (propulsion_texts/fulltext01.pdf, §3).

For the repository's $\varepsilon=10$, 80%-length, $\gamma=1.4$ regression case, the smooth stationary-$DE$ reference is

theta_B = 25.5659 deg
f_D     = 0.15216
D       = (M = 3.40145, theta = 18.5182 deg)
E       = (M = 3.47655, theta = 11.1193 deg)

These are a numerical regression point for the implemented formulation, not a universal nozzle-design result.

Transonic starting lines

The MOC code provides several throat starting-line models:

• kliegel_levine — a third-order toroidal-coordinate Kliegel–Levine series (default; Kliegel & Levine, 1969);
• sauer_modified — a compact leading-order curved-throat approximation;
• area_ratio — a quasi-1D area–Mach starting line;
• hall — a deprecated alias for sauer_modified;
• nasa_visible_kliegel_levine — a source-faithful NASA/JHU compatibility mode used by the reference port.

The theory-correct Kliegel–Levine implementation documents and tests several coefficient-transcription corrections; the source-faithful mode deliberately preserves the historical C++ integer-division behavior required for NASA binary/output parity. The two modes answer different verification questions and are intentionally not collapsed into one implementation.

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Differentiable (JAX) backend

raosim/jax/ provides the default inner solver for the Rao BVP and the gradient API. The design keeps a single boundary (JAX_DIFFERENTIABLE_PLAN.md §2): the NumPy shell in rao_variational.solve_rao_bvp still owns seeding, kernel construction, reliability gating, diagnostics, and output assembly, while the JAX layer owns only the inner least-squares solve.

• Solver. Optimistix Levenberg–Marquardt with the exact jacfwd Jacobian of the assembled residual, replacing SciPy's finite-difference least_squares. Box bounds are handled by a smooth reparametrization $u = \mathrm{lo} + (\mathrm{hi}-\mathrm{lo}),\sigma(z)$ so every iterate stays strictly inside the box. A constraint-weight continuation ladder up-weights the single-element mass/length/endpoint residuals; the reported residual is always the unweighted one, so reliability gates stay comparable across the NumPy and JAX backends.
• Differentiable kernel march and $\theta_B$. The NASA-style kernel march and the live $\theta_B$ secant path are differentiable.
• Sensitivities. rao_sensitivities(config, solution=...) returns exact derivatives of the control-surface $C_F$ with respect to the solved node variables, explicit fixed-solution partials with respect to $p_a/p_0$ and $\gamma$, and the residual-Jacobian condition number.

Not yet provided (v2 deferrals): total re-solved (implicit-function) design derivatives with respect to $R_t$, $\varepsilon$, length percentage, or $\gamma$; a differentiable sensitivity map carried through to the final manufacturable bell wall; and the Hessian. The pinned, tested stack is jax==0.6.2, jaxlib==0.6.2, optimistix==0.0.11, equinox==0.13.8.

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Screening models

These models are deliberately low-order. They are useful for ranking concepts and rejecting obviously unsuitable designs, not for qualification.

Wall pressure

At each contour radius the code sets $A(x)/A_t=\left(r(x)/R_t\right)^2$, inverts the area–Mach relation, and evaluates $p(x)/p_c$ isentropically. A positive downstream pressure increment is flagged as non-monotonic (a check motivated by NASA SP-8120). This is a quasi-1D estimate, not a boundary-layer or shock solution.

Separation

Three empirical overexpansion-separation criteria are exposed (as implemented):

$$ p_{\mathrm{sep}}\approx 0.4,p_a \quad\text{(Summerfield)}, $$

$$ \frac{p_{\mathrm{sep}}}{p_a}\approx\frac{1}{1.88,M_e-1}\quad\text{(Kalt–Badal implementation)}, $$

$$ \frac{p_{\mathrm{sep}}}{p_c}\approx\left(\frac{p_a}{p_c}\right)^{0.8}M_e^{-1}\quad\text{(Schmucker implementation)} . $$

The first contour station whose quasi-1D wall pressure falls below the chosen threshold is reported as the estimated separation location. Side loads, restricted/free shock separation, hysteresis, and transient startup are not modeled. (Criteria surveyed in NASA SP-8120 and Stark, Flow Separation in Rocket Nozzles — An Overview, 2009.)

Boundary layer

The displacement-thickness screen uses a turbulent flat-plate-style correlation,

$$ \delta^*\approx 0.046,\frac{s}{Re_s^{1/5}}\sqrt{\frac{T}{T_w}}, $$

and estimates an effective exit area ratio from $r_e-\delta_e^*$. Gas viscosity uses a Sutherland-type estimate.

Heat flux and cooling

The gas-side model implements the Bartz correlation, including the pressure, area-ratio, throat-curvature, and wall-temperature property factor. Gas transport properties remain estimated unless supplied from CEA or measured data, so it is still preliminary design physics rather than a validated CHT boundary condition. Regenerative cooling is marched station by station in the coolant-flow direction. The coolant-side coefficient uses Sieder–Tate with local rectangular hydraulic diameter, bulk/wall viscosity, a Nu=4.36 circular-duct laminar proxy, and fin area. Rectangular laminar aspect-ratio, heated-wall, and developing-flow effects remain unresolved. The optional curved-channel multiplier is the Niino-Kumakawa/Taylor relation reproduced by Pizzarelli et al. (2011) and Torres et al. (2009). It remains disabled in automatic liquid-coolant sizing because NASA SP-8087 recommends experimental calibration before crediting curvature enhancement; --curvature-correction opts into it. The wall is the series resistance

$$ \frac{1}{H(x)}=\frac{1}{h_g(x)}+\frac{t_\mathrm{hot}(x)}{k_w} +\frac{1}{h_c(x)} . $$

Total absorbed heat and coolant rise satisfy

$$ \dot Q=\int q''(s),2\pi r(s),\mathrm{d}s, \qquad \Delta T_c=\frac{\dot Q}{\dot m_c,c_{p,c}}, $$

while friction pressure loss is integrated with local Darcy factor, hydraulic diameter, velocity, channel roughness, and the actual helical passage length. Smooth passages use Blasius and rough passages use Swamee-Jain. An absolute coolant outlet pressure (or the explicit default $p_{c,\mathrm{out}}=P_c+\Delta p_\mathrm{injector}$) anchors the jacket pressure march. RP-1/kerosene reports a coolant-side wall-temperature margin against a conservative 700 K coking screen and can gate sizing with --gate-coolant-chemistry. --hydraulic-network adds every channel branch, annular inlet/outlet headers, ports, and entry/exit losses to the pressure budget. Methane and LH2 use station-wise CoolProp properties with --coolant-property-backend auto|coolprop. --radiation-model spectral accepts explicit band data, while leccese_gray provides a documented LOX/CH4 or LOX/H2 screen. --boiling-chf reports phase state and a conservative Zuber CHF reference; supercritical heat-transfer deterioration and qualified forced-flow cryogenic CHF remain outside the model.

Structural screen

For a coaxial-shell regen liner, the station-wise combined stress follows NASA SP-125 equation 4-31:

$$ \sigma_c(x)= \frac{\left[p_\mathrm{cool}(x)-p_g(x)\right]r(x)}{t_\mathrm{hot}(x)} + \frac{E\alpha q''(x)t_\mathrm{hot}(x)} {2(1-\nu)k_w}. $$

This exposes the real thickness squeeze: pressure stress wants a thicker liner, while wall temperature and thermal-gradient stress usually want a thinner one. --size-wall searches hot-wall thickness, channel count, and channel width together against thermal margin, yield margin, channel fit, manufacturing minimum, and pressure-drop budget. NARloy-Z uses NASA CR-134627 Coffin–Manson/Basquin data; GRCop-84 uses NASA direct total-strain/life regressions. Both are active sourced screening gates, not chamber-life qualification.

The joint optimizer first selects channels and a feasible uniform $t_\mathrm{hot}$ candidate, then size_wall_profile refines the liner and outer-jacket thickness and channel depth station by station. SP-125 equation 4-29 is reported as an equivalent-tube longitudinal-buckling screen for milled channels and does not gate by default; the separate rib-supported coolant-over-gas liner screen does gate. NARloy-Z and GRCop-84 use sourced stress- and temperature-dependent cyclic tangent-modulus curves instead of the former fixed Et/E assumption. Fatigue still uses a nominal $\alpha\Delta T$ strain range rather than a local cyclic-plasticity solution.

Without --size-wall, the scalar --wall-thickness is only a uniform geometry/reference input and is labeled as unsized in the report. The station-wise solver does not force the throat to be thicker: SP-8087 also recommends thin walls where heat load is highest and nozzle tapering for heat-flux-limited coolants. Local thermal, pressure, buckling, manufacturing, and degradation constraints determine the profile; --t-hot-min supplies the process-specific liner floor.

With --regen-brep, the CAD path exports one OpenCascade STEP solid containing liner, full-count patterned ribs, end seals, jacket, and real channel gaps. --regen-manifolds additionally cuts connected annular plenums and area-sized radial ports. This is a neutral final B-rep, not native Inventor feature history. The optional one-dimensional manifold graph now reports maldistribution and local/network losses; 3-D manifold CFD, jacket buckling, plasticity, creep, weld/braze allowables, stress concentrations, and nonlinear FEA are not yet solved.

How user inputs affect wall sizing

• Rt, epsilon, and length-pct set local radius, heated area, passage length, channel pitch, and the radius multiplying pressure stress.
• gamma and Pc change the gas state and Bartz heat loading; Pc also sets propellant flow and the coolant/gas pressure load.
• pa/p0 primarily changes nozzle performance/separation. It does not directly prescribe thickness.
• O/F sets the fuel share used as coolant in the simplified cycle: $\dot m_c=\dot m_\mathrm{total}/(1+O/F)$. Lower O/F therefore increases available fuel coolant in this model; a real change also requires updated thermochemistry.
• margin and max wall T impose the allowable peak wall temperature.
• pressure-drop budget, channel width/height/count, coolant properties, and helix turns control velocity, heat transfer, and hydraulic loss. Helical channels use their longer 3-D path and the reduced pitch transverse to coolant flow, not merely a visual coil.
• auto-size selects channel geometry at a fixed wall thickness. size-wall co-sizes channels, then refines variable liner and jacket thickness profiles.

The equation provenance, local-PDF inventory, parameter map, and exact CAD scope are collected in docs/regen_wall_model.md.

Atmosphere and trajectory

Altitude performance uses piecewise ISA layers (troposphere −6.5 K/km from 0–11 km, isothermal 11–20 km, +1.0 K/km 20–47 km) with an exponential tail above 47 km. The optional trajectory module integrates a one-dimensional vertical point mass,

$$ m,\dot v=F-\tfrac{1}{2}\rho v|v|,C_D A-m,g(h), \qquad g(h)=g_0\left(\frac{R_E}{R_E+h}\right)^2, $$

with $R_E=6.371\times10^{6}~\mathrm{m}$. It is not wired into the main CLI and does not model guidance, pitch, staging, throttling, winds, or six-degree-of-freedom dynamics.

---

Installation

Python 3.12 is recommended because the differentiable backend is pinned to a tested JAX stack.

For a normal user install after the first PyPI release:

python3.12 -m pip install lrekit

Optional integrations can be requested with extras:

# Optional thermochemistry (variable chamber properties)
python3.12 -m pip install "lrekit[cea]"

# Optional true revolved B-rep STEP export; otherwise a faceted STEP is used
python3.12 -m pip install "lrekit[cad]"

Until the package is published on PyPI, install directly from GitHub:

python3.12 -m pip install \
  "lrekit @ git+https://github.com/ibrahimshahid1/RaoRocketSim.git"

For repository development:

python3.12 -m venv .venv-jax
source .venv-jax/bin/activate
python -m pip install --upgrade pip
python -m pip install -e ".[dev]"

Core dependencies are NumPy, SciPy, Matplotlib, CoolProp, JAX, JAXlib, Optimistix, and Equinox. Optional integrations are not installed by default. The PyPI release checklist is in docs/pypi_release.md.

After installation, the toolbox CLI is available as:

lrekit --help
lrekit

lrekit launches the current nozzle/chamber/regenerative-cooling/pintle runner, the same implementation as python scripts/run_nozzle.py .... The existing RaoRocketSim command remains as a compatibility alias. The older top-level toolbox interface is still available as:

RaoRocketSimLegacy --help

To ensure a triangle-based STEP fallback is never mistaken for editable B-rep CAD:

lrekit --max-nfev 4000 --regen \
  --l-star 1.0 --contraction-ratio 2.5 \
  --material grcop-84 --size-wall --cad step --require-brep --regen-brep \
  --out builds/regen_brep

Add --regen-manifolds to include two connected plenums and radial ports. Port area defaults to total channel flow area and can be distributed with --regen-ports-per-manifold. That flag also enables the matching full-channel hydraulic graph. The fluid/radiation/phase screens can be run without CAD, for example:

lrekit --max-nfev 4000 --regen --thermal \
  --coolant methane --coolant-inlet-temperature 120 \
  --coolant-property-backend coolprop \
  --hydraulic-network --radiation-model leccese_gray \
  --radiation-family methane --boiling-chf

For pintle injector manufacturing geometry, request the machined CAD package:

lrekit --injector pintle --injector-cad machined \
  --injector-face-od 0.10 --injector-face-thickness 0.010 \
  --bolt-count 8 --bolt-circle 0.085 --bolt-hole 0.004 \
  --min-tool-diameter 0.0005 --injector-tolerance 0.00005

This writes pintle/injector_manufacturing_report.json on every run and, when CadQuery/OpenCascade is installed, exports injector_face_machined.step, pintle_post_slotted.step, annular_sleeve.step, and injector_assembly_machined.step.

Without --require-brep, the summary records either brep or faceted_brep. Inventor, Fusion, SolidWorks, and FreeCAD can import the true STEP as a solid body; it will not contain native Inventor feature history.

For repo-local development, python scripts/run_nozzle.py ... remains a thin compatibility wrapper around the packaged runner.

---

Command-line usage

CLI pressure units are bar for $P_c$, kPa for $P_a$, and millimeters for $R_t$ and manufacturing dimensions. Internal APIs use SI units throughout.

Preliminary Rao/TOP design

lrekit \
  --propellant LOX/RP-1 \
  --Pc 45 --Pa 101.325 \
  --Rt 20 --epsilon 10 --length-pct 80 \
  --method bezier --no-plot \
  --output nozzle_profile.csv

Output is written to a versioned directory builds/vNNN_YYYYMMDD_HHMMSS/ together with metadata.txt.

Size the throat from thrust

lrekit \
  --propellant LOX/LCH4 \
  --Pc 60 --target-thrust 10000 --epsilon 12 --no-plot

The sizing relation is

$$ R_t=\sqrt{\frac{F_{\mathrm{target}}}{\pi,C_{F,\mathrm{actual}},p_c}} . $$

Experimental Rao variational / MOC solve

lrekit \
  --propellant LOX/RP-1 \
  --Pc 45 --Rt 20 --epsilon 10 \
  --method rao_variational_moc \
  --rao-moc-n-control 12 --rao-moc-n-kernel 12 \
  --rao-moc-max-nfev 200 --no-plot

This path can be computationally expensive and remains experimental (--rao-moc-max-nfev defaults to 25). --rao-moc-skip-moc skips raw wall/net diagnostics for a faster residual-only study, but that also prevents MOC reliability promotion.

Sweep a design variable

lrekit \
  --propellant LOX/LCH4 \
  --Pc 60 --Rt 25 --epsilon 10 \
  --sweep epsilon 4 50 20 --no-plot

Supported sweep variables are epsilon, Pc, and Rt.

Run a literature benchmark

lrekit \
  --benchmark-case lea_top_schomberg_2014 \
  --benchmark-method bezier \
  --benchmark-report builds/benchmarks --no-plot

Available manifests are lea_top_schomberg_2014, rao_scarfed_moc_1990, and vulcain_s1_separation_similarity. Each metric is classified strict, xfail, or report, so missing physics is recorded rather than hidden behind a single pass/fail number.

---

Python API

Baseline contour and performance

from lrekit.engine import compute_engine_performance
from lrekit.nozzle_geometry import bell_nozzle_contour
from lrekit.propellants import get_propellant

prop = get_propellant("LOX/RP-1")
contour = bell_nozzle_contour(
    Rt=0.020, epsilon=10.0, length_pct=80.0,
    method="bezier", gamma=prop.gamma,
)
performance = compute_engine_performance(
    Pc=4.5e6, Pa=101325.0, Rt=0.020, epsilon=10.0, prop=prop,
)

Design-gated workflow

from lrekit.design import DesignInput, ThermoSpec, design_nozzle_v2

result = design_nozzle_v2(DesignInput(
    thermo=ThermoSpec(mode="constant_gamma", propellant_name="LOX/RP-1"),
    Pc=8.0e6, Rt=0.020, epsilon=8.0,
    method="bezier", mode="preliminary",
))

print(result.performance.thrust)
print(result.gate_report.to_dict())
print(result.report_sections["thermal"])

The API name ValidatedDesignResult and workflow mode validated mean the stricter internal schema and gate set were used. They do not set hardware_qualified = True. Validated mode currently requires RocketCEA, the Bézier method, regenerative-cooling inputs, material/manufacturing inputs, and all internal gates to pass.

Rao BVP and sensitivities

from lrekit.rao_variational import RaoSolverConfig, solve_rao_bvp
from lrekit.jax.api import rao_sensitivities

config = RaoSolverConfig(
    Rt=0.020, epsilon=10.0, gamma=1.4, length_pct=80.0,
    solver_backend="jax", formulation="characteristic",
)

solution = solve_rao_bvp(config)
sens = rao_sensitivities(config, solution=solution)

print(solution.reliability)            # ContourReliability level
print(solution.residuals.max_scaled)   # worst scaled residual
print(sens.cf, sens.condition_number)  # Cf and Jacobian conditioning

Pass solver_backend="numpy" to fall back to the legacy SciPy path.

---

Outputs

Normal CLI runs create builds/vNNN_YYYYMMDD_HHMMSS/ and may contain:

• contour CSV in meters;
• a binary STL closed wall solid;
• a STEP solid (CadQuery revolved B-rep when available, else a faceted AP214 fallback);
• with variable wall sizing, separate liner and closeout-jacket solids;
• optionally, regen.step: one full-channel-count cooling-aware material solid, with connected plenum/port voids when requested;
• optionally, a pintle machined-CAD package with Boolean-cut STEP bodies for the face, slotted pintle post, annular sleeve, and assembly, plus an injector manufacturing report;
• an Inventor conversion manifest pointing to the authoritative STEP file;
• optional regen STL/PNG visualization surfaces for liner, channels, and jacket;
• design-gate JSON and v2 physics-screening sections;
• sweep CSV or benchmark JSON / Markdown reports;
• human-readable metadata.txt with inputs, performance, warnings, gate results, and generated filenames.

Native Autodesk Inventor IPT writing is not implemented. Pintle machined mode models injector bolt holes, manifolds, feed/inlet ports, seal grooves, annulus passages, and slot cut-throughs, but remains preliminary until cold-flow and joint/fitting-specific validation are complete. Throat inserts, weld/braze allowances, and non-pintle injector interfaces are metadata/readiness placeholders, not modeled solid features.

---

Validation and reference evidence

The repository deliberately separates software verification from physical validation.

Software and mathematical verification

The test suite covers gas-dynamics identities and inverse relations; Bézier, conical, chamber, curvature, export, and design-workflow behavior; axisymmetric characteristic pairing and source terms; transonic Kliegel–Levine coefficients and NASA-visible-source semantics; characteristic topology, mass conservation, BDE closure, wall tangency, and crossing checks; NumPy/JAX primitive and residual parity; exact-Jacobian convergence, kernel-march parity, solved-$\theta_B$ derivatives, and $C_F$ sensitivities; literature-manifest parsing with strict/report/xfail policies; NASA/JHU legacy-output and Tecplot parsing; and plotting/diagnostic metadata.

NASA/JHU reference port

Three-Dimensional-Nozzle-Design-Code-master/ vendors the Rice/JHU 2D MOC, streamline-tracing, and 3D MOC source package plus sample outputs. The active Python port implements major pieces of the axisymmetric 2D workflow: the initial throat line and kernel march; arc-wall, interior, special-wall, and axis unit processes; mass flow along right-running characteristics; point-$D$ selection, point-$E$ integration, and fixed-/free-end closure; the $\theta_B$ secant solution; BDE-region and wall-contour construction; and explicit RaoTopology objects for $TT'$, $B$, $BF$, $D$, $BD$, $DE$, $E$, and the wall streamline.

The checked-in M3.5 perfect-nozzle wall comparison is within the repository's $10^{-3}$ RMS regression gate (the perfect-nozzle pipeline currently measures wall $r(x)$ RMS $\approx 1.8\times10^{-4}$ against wall.out). However, the generator provenance of the historical TT'.out fixture is unresolved (see docs/nasa_tt_prime_provenance.md): the visible MOC_GridCalc_BDE.cpp source-port workflow is the canonical reference track, and the orphaned M3.5Perf fixture is a diagnostic overlay only — not promotion authority. Consequently the public solver does not label any contour NASA_REFERENCE_MATCHED.

Reliability labels

The research code defines an ordered ContourReliability vocabulary:

geometric_approximation → moc_compatible → rao_variational_residual_solved → nasa_reference_matched → benchmark_validated → cfd_checked → experimentally_validated.

This is a vocabulary, not a claim that every level has been reached. The rao_variational_moc solver assigns its level from per-solve gates: a clean solve that passes the BVP residual, MOC closure, valid-region, and thrust sanity gates reaches rao_variational_residual_solved. Promotion to benchmark_validated is gated behind the module flag BENCHMARK_VALIDATED_AT_RELEASE, which is False in the current code, so no public contour is benchmark-validated, NASA-reference-matched, CFD-checked, or experimentally validated by this repository.

---

Repository layout

main.py                         Primary interactive/batch CLI
raosim/                         Active Python package
  gas_dynamics.py               Perfect-gas, area-Mach, Prandtl-Meyer relations
  engine.py                     Ideal performance model (Cf, Isp, c*, m_dot)
  propellants.py                Combustion-product property database
  nozzle_geometry.py            Rao/TOP Bezier geometry + chart tables
  conical.py                    Conical reference contour and divergence factor
  chamber_geometry.py           L*/CR chamber + convergent sizing
  design.py                     High-level schemas, gates, artifacts
  validation.py                 Design-status labels and engineering gates
  physics.py                    BL, thermal, cooling, structural screens
  separation.py                 Summerfield / Kalt-Badal / Schmucker screens
  wall_pressure.py              Quasi-1D wall-pressure distribution
  atmosphere.py, altitude_performance.py, trajectory.py
                                ISA atmosphere, altitude sweep, 1-D trajectory
  moc.py                        General axisymmetric MOC march + starting lines
  transonic_kernel.py           Kliegel-Levine transonic series
  nasa_moc.py                   NASA/JHU-style kernel and BDE topology port
  moc_topology.py               RaoTopology objects (TT', B, BD, D, DE, E, wall)
  rao_optimizer.py              Direct MOC wall optimization
  rao_variational.py            Rao functionals, validity, and global BVP
  rao_residuals.py              Characteristic residual primitives
  jax/                          Differentiable primitives, residuals, kernel
                                march, LM solve, and sensitivities
  cea.py                        Optional RocketCEA thermochemistry
  benchmarks.py                 Literature benchmark runner
  benchmark_data/               Manifests and digitized reference curves
  plotting.py                   Geometry, field, topology, residual plots
  export.py                     CSV, STL, STEP, IPT-manifest export
tests/                          Unit, regression, parity, and benchmark tests
scripts/                        Research diagnostics and artifact generators
docs/                           NASA provenance, topology, and audit notes
latex-report/                   Mathematical reference report and figures
propulsion_texts/               Local source literature used by the project
Three-Dimensional-Nozzle-Design-Code-master/
                                Vendored Rice/JHU reference source and outputs
Rocket_nozzle_sim_phase2.py     Legacy monolithic prototype; not the primary API

---

Known limitations

1. No hardware qualification. All results require independent analysis and test evidence.
2. Constant-property nozzle flow. CEA does not yet drive variable $\gamma$, composition, or transport properties through the MOC field.
3. Inviscid MOC. Boundary-layer growth is applied only as a separate screen, not coupled into characteristic marching or contour optimization.
4. Incomplete separation physics. Empirical onset criteria only — no shock/boundary-layer or side-load solver.
5. Experimental exact-Rao path. The BVP is mathematically auditable and heavily tested, but release-level literature promotion is disabled (BENCHMARK_VALIDATED_AT_RELEASE = False).
6. Chart vs. exact-variational angles. Rao 1960 TOP chart angles are parabola-fit design data; the exact variational solution can differ systematically. Those deltas are recorded, not forced to zero.
7. Partial differentiability. The NASA kernel march and live $\theta_B$ path are differentiable, but the complete start-line-to-final-wall design map and total design derivatives are unfinished.
8. Low-order thermal/structural models. Radiation bands, the hydraulic graph, CoolProp properties, fatigue, buckling, and CHF remain preliminary screens—not qualification CHT, 3-D manifold CFD, cyclic plasticity, creep, or FEA.
9. Preliminary manufacturing CAD. The full-N channels, ribs, optional plenums, and ports are solid-modeled, but bolt holes, injector faces, fillets, inserts, welds, tolerances, and process-specific rules are not.
10. No package metadata or stable API guarantee. The project runs from its source tree and research interfaces may change.

---

Remaining work

A practical roadmap, grounded in the current code rather than historical phase labels:

1. Complete and publish the exact-variational chart/reference sweep, define accepted exact-vs-TOP-fit deltas, and set the criteria for flipping BENCHMARK_VALIDATED_AT_RELEASE = True.
2. Make the live differentiable $\theta_B$ solve a routinely exercised production path and finish total implicit design derivatives with respect to $R_t$, $\varepsilon$, $L_{%}$, $\gamma$, and ambient pressure.
3. Differentiate or replace the remaining start-line and BDE/final-wall steps so sensitivities reach manufacturable wall coordinates, not only the control surface.
4. Finish source-port provenance and public reliability wiring for the NASA/JHU reference workflow, including the unresolved historical TT' fixture.
5. Add variable-property frozen/equilibrium thermochemistry and transport properties to the nozzle flowfield.
6. Couple viscous displacement, wall pressure, separation, and side-load physics to the contour solution; validate against published experiments and CFD.
7. Add independent axisymmetric Euler/RANS CFD comparisons with quantitative gates for $C_F$, wall pressure, exit Mach, and flow angle.
8. Replace thermal/cooling/structural screens with conjugate heat transfer, coolant pressure-drop/property models, temperature-dependent materials, and structural analysis.
9. Promote CAD from a revolved screening solid to a manufacturing definition with channels, interfaces, fasteners, tolerances, joints, and inspection features.
10. Retire or clearly isolate legacy paths, add package metadata, and publish a stable API and reproducible release artifacts.

---

References

Primary literature in propulsion_texts/ and the reference notes under docs/ and raosim/benchmark_data/:

• G. V. R. Rao, Exhaust Nozzle Contour for Optimum Thrust, Jet Propulsion, 1958.
• G. V. R. Rao, Approximation of Optimum Thrust Nozzle Contour, ARS J. 30(6), 1960 — the TOP $\theta_n/\theta_e$ design charts.
• G. V. R. Rao, Recent Developments in Rocket Nozzle Configurations, ARS J. 31(11), 1961 — $\gamma$-insensitivity of the optimal contour (RaoRecentDevinRockNozConfig.pdf).
• Rao, Beck & Booth, Rao Variational Optimum Bell Nozzle: A Design Compendium, AIAA 99-2584, 1999 — stationarity Eq. (1)–(2), validity boundary (rao1999.pdf).
• NASA SP-8120, Liquid Rocket Engine Nozzles — chart reproduction, separation and wall-pressure guidance.
• Rice, 2D and 3D Method-of-Characteristics Tools for Complex Nozzle Development, JHU/APL RTDC-TPS-481, 2003.
• Kliegel & Levine, Transonic Flow in Small Throat Radius of Curvature Nozzles, 1969 (prmeyer.pdf and related notes).
• J. Östlund, Flow Processes in Rocket Engine Nozzles…, KTH, 2002 — Rao valid-region discussion (fulltext01.pdf).
• R. Stark, Flow Separation in Rocket Nozzles — An Overview, 2009.
• J. D. Anderson, Modern Compressible Flow — isentropic relations, Prandtl–Meyer, MOC compatibility (§11.4).
• M. J. Zucrow & J. D. Hoffman, Gas Dynamics, Vol. 2, Ch. 17 — axisymmetric characteristics.
• G. P. Sutton & O. Biblarz, Rocket Propulsion Elements — performance relations.

See latex-report/raosim_reference.pdf for the extended mathematical reference and JAX_DIFFERENTIABLE_PLAN.md for the differentiable-solver development record. Those documents contain historical research notes; where any status statement conflicts with the executable code or the current test suite, the code and tests are authoritative.