This tool supports learning, teaching and early design exploration with documented numerical benchmarks and measured comparisons. The evidence defines its current scope and next validation steps; qualification for real-world engineering use remains to be completed.
If this seems to be a tool error, report it through Feedback in the header.
This tool supports learning, teaching and early design exploration with documented numerical benchmarks and measured comparisons. The evidence defines its current scope and next validation steps; qualification for real-world engineering use remains to be completed. See Benchmarks & validation for details.
Inputs
Hull geometry, actual waterline, physical loading and mass inertia.
Optional: import loading from the Hydrostatics & stability tool
Hull & sections
ComputedStation view
Station cage in mean-waterplane axes. The selected station is highlighted. This view shows the computed wetted contours.
Selected section
Sectional area curve
Checks & convergence
Numerical checks| Base N | Sections sampled | Volume (m³) | Volume difference (%) | LCB (m) | LCB difference (m) |
|---|
Agreement tolerances and frame will be reported after calculation.
Mesh check limits & balance residuals
Mesh checks cannot detect faces touching at a point or edge without crossing, or folds through a vertex shared by non-adjacent faces. Section symmetry is tested at sampled stations; it is not a proof for all hull points.
Run record
Save setup at the end of Inputs stores editable inputs and embedded geometry. Downloads and run record at the end of Analysis & results provides the PDF, complete results JSON, CSV tables and calculation metadata. Saved results are displayed as an archive; checksums detect accidental changes, not authorship or prediction accuracy.
Save setup
Save an editable .json file of the current hull, loading and wave settings. Imported hull geometry is embedded. Results are saved separately on Analysis & results.
Analysis & results
Regular-wave responses, irregular-sea statistics and motion playback.
Compute uses the selected wave heading. Compute 360° map repeats the analysis over the heading grid. Either can run after the hull check; neither depends on the other. Reset clears wave results and keeps your hull and inputs. Open saved results restores a results JSON for viewing; a setup JSON restores inputs.
Wave & response settings
Linear, small-amplitude strip approximation in deep water for a symmetric, rigid hull. Numerical diagnostics and the admitted frequency range are reported with every run. Measured zero-speed heave/pitch comparisons are documented in Benchmarks & validation; wider-hull pitch fails the fixed comparison limits.
If this seems to be a tool error, report it through Feedback in the header.
Inputs changed. Recalculate before using or exporting these results.
Automatic Ikeda damping
| Period (s) | Roll amplitude (°) | Friction | Eddy | Hull lift | Total | Closure |
|---|
Frequency coverage & numerical diagnostics
| Wave ω (rad/s) | Wave period (s) | Encounter ωe (rad/s) | Status | Diagnostics / reason |
|---|
Regular-wave response
Response amplitude operator
Regular-wave point trace
| Wave ω (rad/s) | Wave T (s) | ωe (rad/s) | Sway (m/m) | Sway phase (°) | Heave (m/m) | Heave phase (°) | Roll (rad/m) | Roll phase (°) | Pitch (rad/m) | Pitch phase (°) | Yaw (rad/m) | Yaw phase (°) |
|---|
Irregular-sea response
| Statistic | Value |
|---|
Motion playback
Ship motion in regular waves
The same seed reproduces the same sea and ship motion.
Mouse, touch and keyboard controls
Drag with the left mouse button to orbit the ship. Scroll to zoom toward the pointer. Hold Shift while dragging, or use the right mouse button, to pan. On touch screens, use one finger to orbit and two fingers to zoom or pan. With the view focused, use arrow keys to orbit, Shift + arrows to pan, +/− to zoom, Home to reset the view and Space to play or pause. These controls also work during playback.
Motion is reconstructed from the calculated complex RAOs using exp(−iωe t). Irregular playback sums the discrete components of the selected finite-band spectrum, at one wave heading; it does not add directional spreading. The same random phase drives each wave and its ship response. The plotted regular-wave point trace above stays at its selected frequency. Light-blue water is partly transparent (60% opacity), revealing the submerged hull in a muted blue-grey shade. The dry hull stays sand-coloured, and their boundary follows the incident sea. Visible panels come from the checked geometry; large faces are subdivided only for drawing the waterline. This is a linear motion reconstruction, not a time-stepping hydrodynamic or free-surface CFD solution. Surge is not calculated. Rotations follow right-hand axes: positive pitch is bow down. Magnification affects the display only.
360° directional response map
Inputs changed. Run the directional map again before using or exporting it.
Angle = wave propagation heading, 0° at the bow and 90° towards port. Radius = wave period (s), increasing outwards. Each sector and ring shows a calculated sample, without interpolation; grey hatching means refused or unavailable. Colours share one scale across the whole map. Hover or select a cell to inspect it and view its motion above. The table provides the same values. These are independent long-crested headings, not a spreading sea spectrum.
Directional values and refusal reasons
| Heading (°) | Period (s) | Encounter ωe (rad/s) | Selected response | Status / reason |
|---|
Check the hull and loading before computing.
Preparing the calculation…
The worker solves wave radiation around each immersed hull section, checks boundary error and energy balance, then assembles ship motions and sea-state statistics. Fine meshes and local panel refinement can take several minutes. During a long section solve, the elapsed clock may advance before the next progress update. You can cancel at any time.
Downloads and run record
The PDF presents the completed single-heading analysis and/or directional map, with inputs and references. Its attachments retain the complete results JSON and software notices. Results JSON saves the latest completed calculation for reopening; the CSV files contain response or map tables.
Run record
No completed calculation.
Separate results JSON files
Benchmarks & validation
Numerical benchmarks and measured comparisons document the present evidence. Wigley III heave and pitch meet the fixed comparison limits, as does Wigley IV heave. Wigley IV pitch exceeds three limits and is the next refinement priority. Evidence for other hulls, speeds and motions remains to be established.
Ship-motion experiments20 measured Wigley III/IV rows at zero speed
All 20 measurement rows are compared with the tool: 13 for slender Wigley III and seven for wider Wigley IV. Both hulls come from the same laboratory and report, at zero speed in head waves, with other motions restrained. They do not establish accuracy for other hulls or operating conditions.
| Hull | Calculation | Compared rows | Heave amplitude RMS | Pitch/slope amplitude RMS | Heave complex RMS | Pitch/slope complex RMS | All fixed screens |
|---|---|---|---|---|---|---|---|
| III | Tool strip | 13/13 | 0.04633 | 0.08434 | 0.06067 | 0.10718 | Pass |
| III | External 3D | 13/13 | 0.04228 | 0.07688 | 0.05771 | 0.10324 | Pass |
| IV | Tool strip | 7/7 | 0.06991 | 0.14284 | 0.10034 | 0.18629 | Fail |
| IV | External 3D | 7/7 | 0.07044 | 0.11782 | 0.10059 | 0.15596 | Fail |
In the strip calculation, slender-hull heave and pitch and wider-hull heave meet the fixed comparison limits; wider-hull pitch exceeds the amplitude RMS, maximum amplitude and complex RMS limits. The independent whole-hull calculation exceeds the amplitude RMS and complex RMS limits in wider-hull pitch and both phase limits in wider-hull heave.
These are absolute dimensionless differences, not percentage errors. Limits: amplitude RMS/maximum 0.10/0.20; complex RMS/maximum 0.15/0.30; phase RMS/maximum 15°/30°. Phase is included only when both normalized amplitudes are at least 0.10. Measurement uncertainty is not included in these limits.
The independent calculation used Capytaine 3.0.0 with matched hull, loading and phase conventions. Selected refinement from 1440 to 2880 panels changed normalized motion by less than 0.1%. The outcomes and fixed limits above include the failed wider-hull comparisons. Source: J. M. J. Journée (1992), Experiments and Calculations on 4 Wigley Hull Forms in Head Waves, Report 0909, author reprint 26 November 2003; zero-speed Tables 10-III/IV, pp. 57–58. Tank conditions and measurement uncertainty remain unresolved.
Forced-heave experimentMeasured forces on a short box-shaped body
Thirty sharp-box records from Meyer et al. (2025) cover five periods and six amplitudes. All 90 records across three supplied shapes were reduced and checked; the declared solver comparison uses all 30 base-box records. With L/B = 2, this tests prescribed heave of a short body rather than free-motion ship responses.
| Calculation | Added mass: mean absolute relative difference | Wave vs total damping: mean absolute relative difference | Full filtered-force history: mean NRMSE |
|---|---|---|---|
| Tool strip calculation, 96 panels | 9.74% | 23.39% | 29.86% |
| External 3D, 1944 panels, actual depth | 6.34% | 28.14% | 29.27% |
Measured damping includes viscous effects absent from the calculated wave damping. The independent 3D calculation improves added mass and the smallest-amplitude force comparison, but discrepancies remain across the full amplitude range.
Adjacent measurement windows change inferred added mass by up to 0.1063 of displaced mass. A range qualified by measurement uncertainty is not established. Reference: Meyer et al., Applied Ocean Research 159, 104585 (2025), Eq. (5), Tables 2–3 and Appendix A; experimental dataset, version 0.9. No prospective accuracy tolerance was set for this diagnostic, so no pass/fail qualification is assigned. The 9.74%, 23.39% and 29.86% values above are observed discrepancies. Third-party measurements and meshes are not redistributed.
Independent solver comparisonsSectional coefficients and forces compared with PDStrip
The first comparison covers 24 fixed-section cases: three shapes, four frequencies and two mesh densities. All 792 coefficient and force discrepancies meet the declared limits. Sixteen cases pass the sectional checks; eight near-circular polygon cases are refused in that comparison because their roll boundary checks fail.
| Quantity | Difference |
|---|---|
| Added mass | 0.0199621 |
| Radiation damping (the tool’s wave-energy estimate) | 0.00851111 |
| Froude–Krylov excitation | 0.000998919 |
| Diffraction excitation | 0.00626643 |
Refined roll cases: with the tool’s local section refinement, those eight cases pass the same mode and matrix checks. All 264 discrepancies from a repeated PDStrip comparison of these cases meet the same limits, and the native Python reference repeats all eight cases. This extends the numerically admitted cases. Measured roll comparisons remain the next step in qualifying roll accuracy.
Values use the study’s density, section-area, draught, frequency and beam scales. They are normalized absolute differences, not percentage errors. This is sectional numerical evidence, not whole-ship experimental validation. The reference is PDStrip, December 2014 revision by H. Söding, V. Bertram and G. Thiart. All cases use the predeclared 0.05 normalized absolute discrepancy screen; the observed two-grid-change screen is 0.01. Passing a discrepancy screen does not override a refused sectional solution.
All 24 fixed-section cases and eight refined roll cases
| Study and section | Panels | νT = ω²T/g | Largest difference | Limit and comparison | Section admission |
|---|---|---|---|---|---|
| Original — rectangle | 48 | 0.1 | 0.01996206 | 0.05 — Pass | Pass |
| Original — rectangle | 48 | 0.3 | 0.01556958 | 0.05 — Pass | Pass |
| Original — rectangle | 48 | 0.6 | 0.0158591 | 0.05 — Pass | Pass |
| Original — rectangle | 48 | 0.85 | 0.01659476 | 0.05 — Pass | Pass |
| Original — rectangle | 96 | 0.1 | 0.01526546 | 0.05 — Pass | Pass |
| Original — rectangle | 96 | 0.3 | 0.009865289 | 0.05 — Pass | Pass |
| Original — rectangle | 96 | 0.6 | 0.007927159 | 0.05 — Pass | Pass |
| Original — rectangle | 96 | 0.85 | 0.007799557 | 0.05 — Pass | Pass |
| Original — chamfer | 40 | 0.1 | 0.0166217 | 0.05 — Pass | Pass |
| Original — chamfer | 40 | 0.3 | 0.01190099 | 0.05 — Pass | Pass |
| Original — chamfer | 40 | 0.6 | 0.00993573 | 0.05 — Pass | Pass |
| Original — chamfer | 40 | 0.85 | 0.009728709 | 0.05 — Pass | Pass |
| Original — chamfer | 80 | 0.1 | 0.01533569 | 0.05 — Pass | Pass |
| Original — chamfer | 80 | 0.3 | 0.008698438 | 0.05 — Pass | Pass |
| Original — chamfer | 80 | 0.6 | 0.006644046 | 0.05 — Pass | Pass |
| Original — chamfer | 80 | 0.85 | 0.006591751 | 0.05 — Pass | Pass |
| Original — tangent-polygon | 26 | 0.1 | 0.01540646 | 0.05 — Pass | Refused: roll boundary |
| Original — tangent-polygon | 26 | 0.3 | 0.008781527 | 0.05 — Pass | Refused: roll boundary |
| Original — tangent-polygon | 26 | 0.6 | 0.005487911 | 0.05 — Pass | Refused: roll boundary |
| Original — tangent-polygon | 26 | 0.85 | 0.005058592 | 0.05 — Pass | Refused: roll boundary |
| Original — tangent-polygon | 52 | 0.1 | 0.01562567 | 0.05 — Pass | Refused: roll boundary |
| Original — tangent-polygon | 52 | 0.3 | 0.009114058 | 0.05 — Pass | Refused: roll boundary |
| Original — tangent-polygon | 52 | 0.6 | 0.005545323 | 0.05 — Pass | Refused: roll boundary |
| Original — tangent-polygon | 52 | 0.85 | 0.004600256 | 0.05 — Pass | Refused: roll boundary |
| Refined roll — tangent-polygon | 58 | 0.1 | 0.01398951 | 0.05 — Pass | Pass |
| Refined roll — tangent-polygon | 58 | 0.3 | 0.007262074 | 0.05 — Pass | Pass |
| Refined roll — tangent-polygon | 58 | 0.6 | 0.005287188 | 0.05 — Pass | Pass |
| Refined roll — tangent-polygon | 58 | 0.85 | 0.004143167 | 0.05 — Pass | Pass |
| Refined roll — tangent-polygon | 68 | 0.1 | 0.01540863 | 0.05 — Pass | Pass |
| Refined roll — tangent-polygon | 68 | 0.3 | 0.008941213 | 0.05 — Pass | Pass |
| Refined roll — tangent-polygon | 68 | 0.6 | 0.005785427 | 0.05 — Pass | Pass |
| Refined roll — tangent-polygon | 68 | 0.85 | 0.004422136 | 0.05 — Pass | Pass |
Added mass is scaled by ρATrᵢ+rⱼ, damping by ρωATrᵢ+rⱼ, and force by ρgBTr; A is section area, B is beam, T is draught, and r is 0 for translation or 1 for roll. No measurements or third-party geometry are included in this table.
Refinement and sensitivity checksWhat changing the numerical resolution has established
Twelve section calculations vary hull shape at three resolutions and subdivide each fixed shape at two panel targets. Both hulls meet the section checks at a representative quarter-length section and the frequency with the largest wider-hull pitch discrepancy.
The largest scaled excitation change from shape refinement is 0.000364. The largest fixed-shape panel change across the reported heave quantities is 0.00000136. A separate native Python calculation agrees within 4 × 10−15 on those scales. These are local section checks, not a whole-hull uncertainty estimate; wider-hull pitch remains outside the fixed limits.
The analysis controls also support one or two direct frequency-refinement levels. Sourced non-wave roll coefficients can replace the assumed damping ratio, with separate regular-wave and Gaussian-sea closures. These controls have numerical checks; measured validation remains a separate next step.
The fixed-section studies above use the 0.01 normalized change screen. The smaller local changes reported here are resolution diagnostics, not an experimental accuracy tolerance.
Numerical benchmark catalogueIndividual tests, plots, criteria and references
The catalogue contains fixed, versioned studies. They do not change when you edit the active hull. A passed numerical test applies to its stated conditions and is distinct from experimental validation. Expand an individual study for its inputs, results, limits and sources.
Validation priorities and evidence scopeNext steps from the measured comparisons
- Resolve the wider-hull pitch discrepancy using matched geometry, loading, inertia and experimental conditions.
- Assess independent hulls and experiments, including oblique waves and roll damping.
- Complete and verify the original forward-speed end terms before qualifying operation at speed.
- Extend numerical convergence assessment and compare whole-ship responses with matched independent calculations and measurements.
- Validate irregular-sea spectra and RMS responses against measurements.
No comparison with commercial seakeeping software has been made.
Numerical agreement does not remove the outstanding physical-validation work. The priorities above retain the failed comparisons and the limits of each study.
Catalogue exportsDownload or print the numerical catalogue
The downloads contain the numerical catalogue and the remaining experimental-qualification register. The ship-motion, PDStrip and Meyer comparison outcomes, references and limits are shown on this page; print this page to retain those sections. The detailed verification and validation records are not distributed with the tool.
Print includes the expanded evidence sections. CSV and JSON preserve the numerical evidence and its recorded source versions.
If this seems to be a tool error, report it through Feedback in the header.
About
This tool supports learning, teaching and early design exploration with documented numerical benchmarks and measured comparisons. The evidence defines its current scope and next validation steps; qualification for real-world engineering use remains to be completed.
Methods and limits
Geometry and hydrostatics use an embedded copy of the OpenNAOE hydrostatics and stability engine. A corner-aware linear Frank sectional solver supplies radiation coefficients to the Salvesen–Tuck–Faltinsen linear strip theory, as presented in Principles of Naval Architecture, Vol. III. The symmetric heave/pitch subsystem is the default. Five-mode calculations require the sway, heave and roll section checks to pass. Failed required checks and excluded frequencies are shown as refusals.
The ship model omits the original Salvesen–Tuck–Faltinsen end corrections; forward speed with finite or unconfirmed ends is refused. No surge, slamming or tank dynamics are included. Supplemental non-wave roll damping uses a declared ratio, documented non-wave coefficients or the Ikeda component estimator. Automatic Ikeda requires declared bilge geometry and even keel; irregular statistics require explicit narrow-band Rayleigh opt-in. Bilge-keel wave making and independent validation remain open. A measured zero-speed heave/pitch comparison is documented; it does not qualify other hulls, speeds or motions.
Only symmetric surface-piercing sections with vertical waterline panels and νT<1 are admitted, where ν = ω²/g is the deep-water wave number and T the section draught. The authored Wigley uses circumscribed tangent polygons and reports their area difference from the hull mesh. Below-design Wigley immersion and unsupported imported contours are refused for hydrodynamics. Hull/loading checks remain available separately.
Response amplitude operators (RAOs) use exp(−iωe t), where ωe is the encounter frequency, with propagation heading 0° following and 180° head seas. Motions and point coordinates refer to the physical centre of gravity (CG) in mean-waterplane axes. Spectral integration uses the wave frequency as its variable. Missing response bands prevent total statistics; finite-band statistics need frequency and station refinement before use.
Version & licence
OpenNAOE · OpenNAOE Tool Licence · Copyright © 2026 Mohammed Abdul Hannan. Version 1.0.1. Shared hull engine fca80acee6f3. Build 1.0.1-eaeadcdf13ef. All resources are embedded; source links open online.
If you find an error, use Feedback in the header. Include the build number, inputs and steps needed to reproduce it.
OpenNAOE Tool Licence, version 1.0
OpenNAOE Tool Licence, version 1.0 Copyright (c) 2026 Mohammed Abdul Hannan. All rights reserved. 1. Use. You may use this tool free of charge, for any purpose, and make copies of it for your own use. A school, university or other organization may also install it on the computers it manages, for the people who use them. It is intended for learning, teaching and early design exploration, not for commercial engineering work: if you use it for other work, including consultancy, or rely on its results, you do so entirely at your own risk. 2. Your inputs and results. This licence claims no rights in the inputs you give the tool or in the results it produces for you, and places no conditions on how you use, publish or share them. 3. Restrictions. You may not modify the tool, use any part of its code in other software, or distribute the tool or any part of its code, modified or not. Preparing your own inputs, including by editing copies of the example and configuration files the tool provides, is use, not modification. Others can obtain the tool from opennaoe.org. 4. Other licences. Third-party components are under their own licences, and any part of the tool that a third-party licence requires to be licensed under it is under that licence; the tool's notices list them. Those licences, not this one, govern those parts, and nothing in this licence restricts what they permit. 5. No warranty; no liability. The tool is provided "as is", without warranty of any kind, express or implied, including any warranty of accuracy or of fitness for a particular purpose. Its scope and limits are stated in the tool. The author is not liable for any claim, damage or other liability arising from the tool, its use, its results or any decision made with them. These exclusions apply to the extent permitted by applicable law. 6. Name and logo. This licence gives no right to use the OpenNAOE name or logo.
Third-party and data licences
Bundled shared hydrostatics/stability engine and geometry support
Copyright (c) 2026 Mohammed Abdul Hannan
The author's own code, distributed as part of this tool under the OpenNAOE Tool Licence, version 1.0, whose full terms are on the About page.
Authored explanatory text, synthetic examples and benchmark data retain CC BY 4.0.
External cited studies retain their own rights; source datasets are not licensed by this tool.
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b. To the extent possible, in no event will the Licensor be liable to You on any legal theory (including, without limitation, negligence) or otherwise for any direct, special, indirect, incidental, consequential, punitive, exemplary, or other losses, costs, expenses, or damages arising out of this Public License or use of the Licensed Material, even if the Licensor has been advised of the possibility of such losses, costs, expenses, or damages. Where a limitation of liability is not allowed in full or in part, this limitation may not apply to You.
c. The disclaimer of warranties and limitation of liability provided above shall be interpreted in a manner that, to the extent possible, most closely approximates an absolute disclaimer and waiver of all liability.
Section 6 – Term and Termination.
a. This Public License applies for the term of the Copyright and Similar Rights licensed here. However, if You fail to comply with this Public License, then Your rights under this Public License terminate automatically.
b. Where Your right to use the Licensed Material has terminated under Section 6(a), it reinstates:
1. automatically as of the date the violation is cured, provided it is cured within 30 days of Your discovery of the violation; or
2. upon express reinstatement by the Licensor.
c. For the avoidance of doubt, this Section 6(b) does not affect any right the Licensor may have to seek remedies for Your violations of this Public License.
d. For the avoidance of doubt, the Licensor may also offer the Licensed Material under separate terms or conditions or stop distributing the Licensed Material at any time; however, doing so will not terminate this Public License.
e. Sections 1, 5, 6, 7, and 8 survive termination of this Public License.
Section 7 – Other Terms and Conditions.
a. The Licensor shall not be bound by any additional or different terms or conditions communicated by You unless expressly agreed.
b. Any arrangements, understandings, or agreements regarding the Licensed Material not stated herein are separate from and independent of the terms and conditions of this Public License.
Section 8 – Interpretation.
a. For the avoidance of doubt, this Public License does not, and shall not be interpreted to, reduce, limit, restrict, or impose conditions on any use of the Licensed Material that could lawfully be made without permission under this Public License.
b. To the extent possible, if any provision of this Public License is deemed unenforceable, it shall be automatically reformed to the minimum extent necessary to make it enforceable. If the provision cannot be reformed, it shall be severed from this Public License without affecting the enforceability of the remaining terms and conditions.
c. No term or condition of this Public License will be waived and no failure to comply consented to unless expressly agreed to by the Licensor.
d. Nothing in this Public License constitutes or may be interpreted as a limitation upon, or waiver of, any privileges and immunities that apply to the Licensor or You, including from the legal processes of any jurisdiction or authority.
Creative Commons is not a party to its public licenses. Notwithstanding, Creative Commons may elect to apply one of its public licenses to material it publishes and in those instances will be considered the “Licensor.” Except for the limited purpose of indicating that material is shared under a Creative Commons public license or as otherwise permitted by the Creative Commons policies published at creativecommons.org/policies, Creative Commons does not authorize the use of the trademark “Creative Commons” or any other trademark or logo of Creative Commons without its prior written consent including, without limitation, in connection with any unauthorized modifications to any of its public licenses or any other arrangements, understandings, or agreements concerning use of licensed material. For the avoidance of doubt, this paragraph does not form part of the public licenses.
Creative Commons may be contacted at creativecommons.org.
PDF report layout
-----------------
The report layout code is by Mohammed Abdul Hannan, adapted from the OpenNAOE Hydrostatics & stability tool. The Adobe core-14 font metrics it uses are under APAFML; their complete notices follow below and are also kept with the metrics in the tool's code. The PDF standard fonts are not embedded; reports are tagged but are not claimed to conform to PDF/UA.
Adobe font-metric notices (APAFML)
--------------------------------
Copyright (c) 1985, 1987, 1989, 1990, 1997 Adobe Systems Incorporated. All Rights Reserved.Helvetica is a trademark of Linotype-Hell AG and/or its subsidiaries.
Copyright (c) 1985, 1987, 1989, 1990, 1997 Adobe Systems Incorporated. All rights reserved.
Copyright (c) 1985, 1987, 1988, 1989, 1997 Adobe Systems Incorporated. All Rights Reserved.ITC Zapf Dingbats is a registered trademark of International Typeface Corporation.
Modified by OpenNAOE (2026): only the advance widths (WX) are kept, rearranged by scripts/pdf-fonts.mjs for the
WinAnsi encoding (Helvetica) and for the Unicode characters listed (Symbol, ZapfDingbats); the header values
Ascender, Descender, CapHeight and XHeight of Helvetica are kept. Nothing else is taken from the AFM files.
This file and the 14 PostScript(R) AFM files it accompanies may be used, copied, and distributed for any purpose and
without charge, with or without modification, provided that all copyright notices are retained; that the AFM files are
not distributed without this file; that all modifications to this file or any of the AFM files are prominently noted
in the modified file(s); and that this paragraph is not modified. Adobe Systems has no responsibility or obligation to
support the use of the AFM files.
PDF engineering glyph outlines: Inter Regular 4.000.
Copyright 2016-2023 The Inter Project Authors (https://github.com/rsms/inter).
Modified by OpenNAOE (2026): subset glyph outlines and widths, scaled to thousandths of an em; nabla from Delta and four mapped signs.
This Font Software is licensed under the SIL Open Font License, Version 1.1.
This license is copied below, and is also available with a FAQ at:
http://scripts.sil.org/OFL
-----------------------------------------------------------
SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007
-----------------------------------------------------------
PREAMBLE
The goals of the Open Font License (OFL) are to stimulate worldwide
development of collaborative font projects, to support the font
creation efforts of academic and linguistic communities, and to
provide a free and open framework in which fonts may be shared and
improved in partnership with others.
The OFL allows the licensed fonts to be used, studied, modified and
redistributed freely as long as they are not sold by themselves. The
fonts, including any derivative works, can be bundled, embedded,
redistributed and/or sold with any software provided that any
reserved names are not used by derivative works. The fonts and
derivatives, however, cannot be released under any other type of
license. The requirement for fonts to remain under this license
does not apply to any document created using the fonts or their
derivatives.
DEFINITIONS
Font Software refers to the set of files released by the
Copyright Holder(s) under this license and clearly marked as such.
This may include source files, build scripts and documentation.
Reserved Font Name refers to any names specified as such after
the copyright statement(s).
Original Version refers to the collection of Font Software
components as distributed by the Copyright Holder(s).
Modified Version refers to any derivative made by adding to,
deleting, or substituting in part or in whole any of the components
of the Original Version, by changing formats or by porting the Font
Software to a new environment.
Author refers to any designer, engineer, programmer, technical
writer or other person who contributed to the Font Software.
PERMISSION & CONDITIONS
Permission is hereby granted, free of charge, to any person
obtaining a copy of the Font Software, to use, study, copy, merge,
embed, modify, redistribute, and sell modified and unmodified copies
of the Font Software, subject to the following conditions:
1) Neither the Font Software nor any of its individual components,
in Original or Modified Versions, may be sold by itself.
2) Original or Modified Versions of the Font Software may be bundled,
redistributed and/or sold with any software, provided that each
copy contains the above copyright notice and this license. These
can be included either as stand-alone text files, human-readable
headers or in the appropriate machine-readable metadata fields
within text or binary files as long as those fields can be easily
viewed by the user.
3) No Modified Version of the Font Software may use the Reserved Font
Name(s) unless explicit written permission is granted by the
corresponding Copyright Holder. This restriction only applies to
the primary font name as presented to the users.
4) The name(s) of the Copyright Holder(s) or the Author(s) of the
Font Software shall not be used to promote, endorse or advertise
any Modified Version, except to acknowledge the contribution(s)
of the Copyright Holder(s) and the Author(s) or with their
explicit written permission.
5) The Font Software, modified or unmodified, in part or in whole,
must be distributed entirely under this license, and must not be
distributed under any other license. The requirement for fonts to
remain under this license does not apply to any document created
using the Font Software.
TERMINATION
This license becomes null and void if any of the above conditions
are not met.
DISCLAIMER
THE FONT SOFTWARE IS PROVIDED AS IS, WITHOUT WARRANTY OF ANY KIND,
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT
OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL
THE COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR
CONSEQUENTIAL DAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR
OTHERWISE, ARISING FROM, OUT OF THE USE OR INABILITY TO USE THE FONT
SOFTWARE OR FROM OTHER DEALINGS IN THE FONT SOFTWARE.
Verify the download
SHA-256 is a fingerprint of a file’s contents. Each version of this file is published with its SHA-256 checksum on the tool’s page at opennaoe.org; a version archived on Zenodo also has it in its Zenodo record. Compute the checksum of your copy and compare the two. A matching checksum confirms that the bytes match that version; it does not establish prediction accuracy.
Windows PowerShell: Get-FileHash <file> -Algorithm SHA256
macOS: shasum -a 256 <file>
Linux: sha256sum <file>