rockmoc

Industry-oriented Method of Characteristics (MOC) rocket nozzle design for Python.

Design conventional bells (MLN, ideal, TIC, Rao TOP/TOC), planar NASA sharp-throat MLNs, and annular aerospikes from literature-faithful algorithms — with pluggable thermochemistry, boundary-layer correction, field-integrated performance, dark-themed plots, and a multi-regime validation campaign against NASA/NACA/Rao sources.

Website	aboutkvs.vercel.app/rockmoc.html — full portfolio showcase
Version	see src/rockmoc/_version.py
Python	≥ 3.10
Core deps	NumPy, SciPy
License	MIT
Author	shanthoshkv
Repo	https://github.com/shanthoshkv/rockmoc

---

Table of contents

• How to use (full guide) ← start here if you are new
• Project website — interactive gallery, validation, API overview
• What rockmoc is
• Nozzle types
• Capabilities
• Install
• Quickstart
• Dark plots & post-solve dashboard
• Validation
• API map
• Assumptions & limits
• Project layout
• CLI
• References
• Contributing / release checklist
• License

New to rockmoc? Start here:

• Project website — figures, validation, and overview
• How to use (full guide) — install, first design, student helpers, FAQ
• Jupyter tutorials — MLN, compare, altitude, NASA planar
• Homework problems
• Glossary & symbols

---

What rockmoc is

rockmoc is a library + CLI for preliminary-to-production-engineering nozzle contour design using the method of characteristics, not a full CFD solver.

It is built for:

• Propulsion students and researchers who need reproducible MOC contours
• Rocket teams who want MLN / TIC / Rao / aerospike options in one package
• Pipelines that export walls to CAD / CFD and attach CEA / Cantera / CoolProp γ later

Coordinate system: SI meters; geometric throat at (x = 0), wall radius (r = R_t); API angles in radians (summaries often print degrees).

---

Nozzle types

Type	Function(s)	Geometry	Typical use
Planar MLN	design_planar_mln_nasa	2D sharp-throat minimum-length, uniform exit	Turbine nozzles, educational MOC, NASA TM-X-1502 parity
Axisym MLN	design_mln	Axisymmetric sharp-throat minimum-length bell	Short high-ε vacuum stages, upper stages
Ideal	design_ideal	Circular throat arc + elongated canceling region	Full-length “ideal” contoured bell reference
TIC	design_tic	Truncated ideal contour (truncate_fraction)	Flight trade: length vs performance
Rao TOP	design_rao	Thrust-optimized parabolic / engineering TOP	Industry-standard compact high-thrust bells
Rao TOC	design_rao_toc, design_rao_control	Length-referenced / control-surface TOC variants	Advanced TOP–TOC studies
Conical	design_conical	Constant half-angle wall (default 15°)	Textbook baseline vs MOC / TOP
Aerospike (full)	design_spike	Annular plug (Lee / Vernacchia)	Altitude-compensating engines
Aerospike (truncated)	design_spike_truncated, truncated_spike_with_base	Truncated spike + base pressure models	Practical plug nozzles
Spike + cowl	design_spike_with_cowl, design_primary_cowl	Primary cowl + spike stack	Integrated aerospike packages
Production package	design_production	Any of MLN/ideal/TIC/Rao + BL + field Cf + UQ	Recommended “ship the design” path

Contour family (same Me, γ)

Typical length ordering at fixed design point:

MLN  <  Rao TOP (~0.8 × 15° cone)  ≲  TIC (e.g. 80% ideal)  <  Ideal
(+ conical 15° as length/angle baseline)

Use compare_nozzle_designs(spec) (includes cone by default) then:

cmp = compare_nozzle_designs(spec)
print(cmp.to_markdown())   # lab report
cmp.to_csv("compare.csv")

Student helpers: DesignSpec.student, example_gas, result.report(), result.lab_report(), explainer("mln"), KNOWN_LIMITS — see how to use.

---

Capabilities

Design & mesh

• Axisymmetric MOC unit processes (interior / axis / wall) with geometric source terms (Zucrow–Hoffman style)
• Planar NASA MOC (TM-X-1502): θ_max = ν_e/2, y_e = A/A*, mesh Δν control
• Dense defaults for accuracy (n_characteristics ~ 160, planar Δν down to 0.1°)
• Mesh studies: mesh_convergence_planar, mesh_convergence_axisym
• Optional strict canceling wall + robust schedule fallback
• Isotropic area match so geometric ε tracks 1-D A/A*(Me) without warping wall angles

Thermochemistry

Backend	Install	Role
PerfectGas	core	Constant-γ isentropic / PM
VariableGammaGas + expansion tables	core	Multi-γ along M (chamber → throat → exit)
RocketCEA	pip install rockmoc[cea]	Frozen chamber/throat γ, R, Tc from propellants
Cantera	pip install rockmoc[cantera]	Equilibrium / frozen mixtures
CoolProp	pip install rockmoc[coolprop]	Pure-fluid properties

Accuracy stack (production)

design_production(...) chains:

1. Fine MOC design (MLN / ideal / TIC / Rao)
2. Expansion table (perfect-gas or multi-γ)
3. Sauer-style throat IVL metadata
4. Optional BL δ* wall growth (TM-X-2343 spirit)
5. Field-integrated Cf / Isp on the exit station
6. Altitude off-design sweep
7. Optional mesh certificate / UQ hooks

Performance & analysis

• 1-D ideal (C_F), (I_{sp}) (Sutton form)
• Exit-plane divergence / kinetic efficiencies (θ_e-based — no false wall-history penalty)
• off_design_altitude_sweep with ISA-style (p_a(h))
• OF / γ / ε design sweeps for trade plots
• Monte Carlo / one-at-a-time sensitivity / mesh certificate

Plotting (optional rockmoc[plot])

Dark aerospace theme:

• Nozzle contour (mirrored walls, metrics box, wall-angle colormap)
• MOC field: C+, C−, expansion fan, canceling C−, wall nodes
• Wall profiles r(x), θ(x), M(x)
• Mach & p/p_c along wall
• Performance vs altitude
• O/F, γ, ε sweeps
• Family overlay + comparison bars
• Aerospike contour
• BL inviscid vs corrected

result = design_mln(spec, store_net=True)
result.plot()                              # display dashboard
result.plot(show=False, save_dir="out")    # optional PNG save

Export

result.export_csv("wall.csv")
result.export_json("wall.json")
# Contour also: result.contour.export_csv / export_json

---

Install

From PyPI (when published)

pip install rockmoc
pip install "rockmoc[plot]"       # figures (CLI needs no extra)
pip install "rockmoc[fast]"       # Numba-compiled MOC kernels
pip install "rockmoc[viz]"        # interactive Plotly field
pip install "rockmoc[all]"        # all optional extras

From GitHub

pip install "git+https://github.com/shanthoshkv/rockmoc.git"

From a clone (development)

git clone https://github.com/shanthoshkv/rockmoc.git
cd rockmoc
pip install -e ".[plot,dev]"

# Optional chemistry stacks
pip install -e ".[cea]"
pip install -e ".[cantera]"
pip install -e ".[coolprop]"

Requirements: Python ≥ 3.10, NumPy ≥ 1.24, SciPy ≥ 1.10.

Publishing notes for maintainers: see PUBLISH.md.

---

Quickstart

For a slower, more detailed tour (inputs, mesh, exports, FAQ), see the full how-to guide or the project website.

Axisymmetric MLN

from rockmoc import PerfectGas, DesignSpec, design_mln

gas = PerfectGas(gamma=1.25, R=350.0)
spec = DesignSpec(
    gas=gas,
    throat_radius=0.05,      # m
    exit_mach=3.0,           # or area_ratio=... or pressure_ratio=...
    n_characteristics=80,
)
result = design_mln(spec, store_net=True)
print(result.summary())
result.export_csv("mln_wall.csv")
result.plot(show=True)       # needs rockmoc[plot]

Ideal, TIC, Rao

from rockmoc import design_ideal, design_tic, design_rao, DesignSpec, PerfectGas

spec = DesignSpec(PerfectGas(1.25), throat_radius=0.05, exit_mach=3.0, n_characteristics=64)

ideal = design_ideal(spec)
tic   = design_tic(DesignSpec(PerfectGas(1.25), throat_radius=0.05, exit_mach=3.0,
                              n_characteristics=64, truncate_fraction=0.80))
rao   = design_rao(spec, length_fraction=0.80)

NASA planar MLN (TM-X-1502 sample)

from rockmoc import design_planar_mln_nasa

# Paper sample: Me = 4.05, γ = 1.36
r = design_planar_mln_nasa(4.05, 1.36, dnu_deg=0.1, throat_half_height=0.05)
print(r.summary())
r.contour.export_csv("planar_mln.csv")

Aerospike

from rockmoc import design_spike, design_spike_truncated

spike = design_spike(
    Pc=5e6, Tc=3200.0, gamma=1.25, molar_mass=22.0,
    Re=0.15, expansion_ratio=25.0, Pa=0.0, n_points=5000,
)
print(spike.summary())
trunc = design_spike_truncated(spike, length_fraction=0.25)

Production pipeline (recommended)

from rockmoc import PerfectGas, DesignSpec, design_production

prod = design_production(
    DesignSpec(PerfectGas(1.25), throat_radius=0.05, exit_mach=3.0),
    kind="mln",                      # mln | ideal | tic | rao
    apply_bl=True,
    multi_gamma=(1.25, 1.22, 1.18), # optional γ_c, γ_t, γ_e
    pc=5e6,
    Tc=3200.0,
)
print(prod.summary())
prod.plot(show=False, save_dir="figures")
# prod.design.contour  — inviscid wall
# prod.bl.corrected    — BL-grown wall
# prod.field           — field Cf / Isp

Fair comparison

from rockmoc import DesignSpec, PerfectGas, compare_nozzle_designs

cmp = compare_nozzle_designs(
    DesignSpec(PerfectGas(1.25), throat_radius=0.05, exit_mach=3.0, n_characteristics=40)
)
print(cmp.summary_table())

Chemistry-backed gas (optional)

from rockmoc.thermo.rocketcea_backend import RocketCEAGas  # rockmoc[cea]

cea = RocketCEAGas(ox="LOX", fuel="LH2", of_ratio=5.0, Pc_psia=500.0)
gas = cea.solve()  # PerfectGas-like with frozen throat γ, R

---

Dark plots & post-solve dashboard

pip install -e ".[plot]"
py -3.12 tests/generate_all_graphs.py   # writes tests/graphs/*.png

Figure family	Contents
Contour	Mirrored wall, throat/exit markers, metric box
MOC field	C+/C−, fan, canceling C−, wall & axis nodes
Wall profiles	r(x), θ(x), M(x)
Thermo edge	M(x) and p/p_c(x)
Altitude	C_F and I_sp vs h
Sweeps	O/F, γ, ε
Family	Overlay + bar comparison
Aerospike	Spike + lip radius
BL	Inviscid vs δ*-corrected wall

Saving is always optional (save_dir=None → display only).

---

Validation

rockmoc ships an offline, literature-anchored validation campaign.

Run it

# Full unit + regression suite
pytest -q

# Deep multi-regime literature campaign → JSON / CSV / Markdown
py -3.12 tests/run_deep_validation.py

Stored validation artifacts

Path	Role
tests/data/validation_catalog.json	Reference targets, sources, tolerances
tests/data/validation_results/validation_results.json	Full ref vs solver
tests/data/validation_results/validation_results.csv	Flat table with error_percent
tests/data/validation_results/validation_report.md	Human-readable report
tests/data/validation_results/sources.md	Source index
docs/validation.md / validation_deep.md	Methodology

Campaign snapshot (representative)

Regime	Cases	What is checked	Typical error
Isentropic / PM tables (γ=1.4)	6	ν, A/A*, pe/pc at M=1.5…5	≪ 0.02%
Multi-γ round-trip	5	M→ν→M, M→A/A*→M	~0 (machine)
NASA TM-X-1502 sample	1	θ_max=ν_e/2, y_e=A/A*, throat (0,1)	identity-level
NACA planar MLN suite	5	Me=2…4 design rules	≪ 0.1% on rules
Axisym MLN multi-regime	6	ε vs 1-D, θ_e≈0, L/R_t band, diverging	ε match; θ_max ~4% vs planar half-ν by design
Rao TOP	3	L/L_15° cone, θ_n>θ_e, ε	few % on engineering L
Aerospike Lee	2	δ=π/2−ν_e, Me(ε), tip→0	≪ 1% identities
1-D C_F (Sutton)	5	Closed-form C_F	~0
Family ordering	1	ideal > MLN; TIC < ideal; Rao compact	structural

Latest deep run: 43/43 cases, 170 metrics, 12 cited sources, median error ~0%, thermo table errors typically < 0.02% (max ~4% only on documented axisym θ_max vs planar ν_e/2).

Primary literature anchors (12)

1. Anderson — Modern Compressible Flow / γ=1.4 PM & isentropic tables
2. NACA Report 1135 (Ames, 1953) — compressible flow equations & tables
3. NASA TM-X-1502 — Vanco & Goldman (1968), planar sharp-edged MLN
4. NACA RM E8J12 — Shames & Seashore (1948), 2D sharp-edge design data
5. NASA TM-X-2343 — Goldman & Vanco (1971), MLN + BL displacement
6. Rao (1958) — optimum thrust contour / TOP vs 15° cone
7. Lee / Vernacchia — annular aerospike (δ = π/2 − ν_e)
8. Sutton & Biblarz — ideal 1-D thrust coefficient
9. Zucrow & Hoffman — axisymmetric MOC unit processes
10. Huzel & Huang — conical nozzle practice (15° baseline)
11. Sauer / Kliegel — transonic throat IVL
12. Shapiro — Prandtl–Meyer function form & ν_max

Catalog + CSV: tests/data/validation_catalog.json, tests/data/validation_results/.
Local PDFs: refs/*.pdf.

Also covered by pytest

• Planar MOC interior Riemann invariants
• Physics regressions (wall angle vs geometry, canceling schedule, η_n = 1 at θ_e = 0)
• Aerospike, production pipeline, thermo backends (optional skips)
• Graph generation is separate (tests/generate_all_graphs.py)

---

API map

rockmoc
├── DesignSpec / DesignResult / ProductionResult
├── PerfectGas / VariableGammaGas
├── design_mln | design_ideal | design_tic
├── design_rao | design_rao_toc | design_rao_control
├── design_production
├── design_planar_mln_nasa
├── design_spike | design_spike_truncated | design_spike_with_cowl
├── correct_wall_bl | sauer_throat_ivl
├── integrated_performance | field_integrated_cf | off_design_altitude_sweep
├── compare_nozzle_designs
├── monte_carlo_mln | mesh_certificate | sensitivity_one_at_a_time
├── run_all_validation | run_deep_validation | write_validation_outputs
└── plot.*  (optional matplotlib dark theme)

Import surface is re-exported from the top-level rockmoc package for the main designers and utilities.

---

Assumptions & limits

Path	Assumptions
Planar NASA	2D, inviscid, isentropic, constant γ
Axisym bells	Axisymmetric MOC; inviscid isentropic; γ from PerfectGas / frozen table / CEA
Canceling wall	Classic MLN (θ,ν) schedule + streamline integration + isotropic ε match (engineering hybrid, not full inverse CFD)
Aerospike	Lee/Vernacchia constant-γ isentropic annular model; needs ν_e < π/2
BL module	Integral compressible estimate (not full Cohen–Reshotko ODE suite)
Performance	Exit-station / 1-D edge models — validate with CFD before hardware
Chemistry	Frozen-γ surrogates for MOC; not multi-phase reacting CFD

Always: mesh-converge → export wall → CFD / thermal / structural before flight hardware.

---

Project layout

rockmoc/
├── src/rockmoc/
│   ├── thermo/          # Perfect gas, variable-γ, CEA/Cantera/CoolProp
│   ├── moc/             # Equations, unit processes, planar NASA, axisym HF
│   ├── designers/       # MLN, ideal, TIC, Rao, production
│   ├── aerospike/       # Lee spike, base/cowl
│   ├── analysis/        # BL, throat IVL, atmosphere, UQ, compare
│   ├── performance/     # Metrics, integrated & field Cf
│   ├── geometry/        # Contour + export
│   ├── plot/            # Dark-themed figures
│   ├── validate/        # Literature suite + deep benchmark
│   └── cli.py
├── tests/
│   ├── data/
│   │   ├── validation_catalog.json
│   │   └── validation_results/   # ref vs solver + error %
│   ├── run_deep_validation.py
│   ├── generate_all_graphs.py
│   └── test_*.py
├── docs/
│   ├── how_to_use.md    # Friendly end-to-end usage guide
│   └── …                # Theory, validation, production notes
├── refs/                # Primary PDFs (NASA/NACA/Rao/…)
├── examples/
├── pyproject.toml
└── README.md

---

CLI

No extra dependency (standard-library argparse):

rockmoc design --type mln   --Me 2.5 --gamma 1.25 --Rt 0.05 --export csv,dxf --units mm -o out
rockmoc design --type ideal --area-ratio 25 --Rt 0.04 --export csv,openfoam -o out
rockmoc design --type tic   --Me 4.0 --truncate 0.8 -o out
rockmoc design --type rao   --Me 3.0 --gamma 1.25 --length 0.8 --export cad -o out
rockmoc run nozzle.toml          # reproducible TOML spec (see rockmoc/spec_io.py)

Export formats: csv (x, r, θ, M), cad (header-less x y z for SolidWorks/CATIA curve-through-points), dxf (R12 polyline), openfoam (axisymmetric wedge system/blockMeshDict, checked with blockMesh/checkMesh), json (summary).

---

References

• Zucrow, M. J. & Hoffman, J. D. — Gas Dynamics (axisym MOC)
• Anderson, J. D. — Modern Compressible Flow / isentropic–PM tables
• Vanco, M. R. & Goldman, L. J. — NASA TM-X-1502 (1968)
• Goldman, L. J. & Vanco, M. R. — NASA TM-X-2343 (1971)
• Shames, H. & Seashore, F. L. — NACA RM E8J12 (1948)
• Rao, G. V. R. — Exhaust nozzle contour for optimum thrust (1958)
• Lee, C. C. / Vernacchia — annular aerospike contour methods
• Sutton, G. P. & Biblarz, O. — Rocket Propulsion Elements
• Kliegel / Sauer — transonic throat approximations

See refs/README.md and docs/ for mapping from papers → modules.

---

Contributing / release checklist

# 1. Install
pip install -e ".[plot,dev]"

# 2. Tests
pytest -q

# 3. Deep validation (writes tests/data/validation_results/)
python tests/run_deep_validation.py

# 4. Build installable artifacts
python -m build
twine check dist/*

# 5. Optional: regenerate demo graphs (gitignored)
python tests/generate_all_graphs.py

Publish to PyPI: PUBLISH.md.

.gitignore excludes venvs, caches, website/, generated PNGs, secrets — while keeping src/, tests/data/, docs/, examples/.

---

License

MIT — see LICENSE.