Skip to content

References

Jump to bottom
matejhron edited this page May 10, 2026 · 3 revisions

How to cite this wiki

DecoJS Wiki, Hron M., 2026. https://github.com/matej-hron/decojs/wiki

The underlying source code is archived at https://github.com/matej-hron/decojs and deployed at https://decotheory.eu. Where the code implements a published equation, cite both this wiki (for the implementation) and the original source below (for the equation).

At a glance

Cited inline by other wiki pages — the load-bearing references for DecoJS's algorithm and constants:

  • §1.1 — decotengu Decompression Model docs
  • §2.1 — Bühlmann Tauchmedizin (ZH-L16 source)
  • §2.2 — Schreiner & Kelley 1971 (linear-rate uptake equation)
  • §2.3 — Workman 1965 (M-values)
  • §2.4 — Erik Baker GF articles
  • §3 — Mark Powell, Deco for Divers (project's intellectual inspiration)
  • §4.1 — decotengu (numerical oracle for the test suite)
  • §6 — ZH-L16 constant tables

Further reading — context, prior art, and orientation for readers going deeper:

  • §1.2, §1.3 — decotengu Algorithms and Design pages
  • §2.5 — Wienke & O'Leary secondary review
  • §4.2 — divetools.app (another web-based deco planner)
  • §4.3 — eight other open-source ZH-L16 + GF implementations across Python, C, C++, Java, JavaScript, Kotlin
  • §5 — SPČR / CMAS training references and the project's institutional context

1. decotengu — reference implementation and documentation model

Project documentation for Artur Wroblewski's decotengu (Python 3 Bühlmann ZH-L16 + GF implementation, v0.14.1). Hosted at https://wrobell.dcmod.org/decotengu/.

The sidebar TOC:

  • info.html — Project Information
  • usage.html — Using DecoTengu Library
  • cmd.html — Commandline Tools
  • model.html — Decompression Model (the math)
  • algo.html — Algorithms (ascent, first-stop, stop-length)
  • alt.html — Alternative Implementations
  • design.html — Design (engine, data model, dive phases, conveyor)
  • api.html — Classes and Functions (API reference)
  • changelog.html — Changelog

1.1 Decompression Model — https://wrobell.dcmod.org/decotengu/model.html

Sections: Introduction · Parameters · Equations · Calculations · References.

Equations presented symbolically with all variables defined and one worked numerical example per equation:

  • Schreiner equation for inert-gas tissue uptake under continuously changing ambient pressure:

    P = P_alv + R·(t − 1/k) − (P_alv − P_i − R/k)·e^(−k·t)

    with a worked nitrogen-loading example across descent / bottom / ascent.

  • Bühlmann ceiling with gradient factors:

    P_l = (P − a·gf) / (gf/b + 1 − gf)

    plus the trimix extension (weighted a, b from N₂ and He partial pressures) and the gf_low / gf_high linear interpolation between first stop and surface.

The rigour level is equation-with-definition-and-numerical-example, no derivation from first principles — the reader is expected to know Haldane. The DecoJS wiki matches this level.

1.2 Algorithms — https://wrobell.dcmod.org/decotengu/algo.html

Sections: Ascent to Surface · Finding First Decompression Stop · Finding Length of Decompression Stop.

Presented as numbered pseudocode with conditional branches (NDL vs deco), 3 m rounding of ceilings (p_l = ceil(p_l/3) · 3), and a big-O note for stop-length search (O(n/64 + log n) via linear pre-range + binary refine). No external citations — algorithms are presented as library-specific design choices.

1.3 Design — https://wrobell.dcmod.org/decotengu/design.html

Sections: Core Calculations · Data Model · Dive Phases · Dive Profile Expansion · Tabular Calculator. Covers the Engine class orchestrating the ZH_L16_GF model; data classes Step / Data / GasMix / DecoStop; the six-value Phase enum (START, DESCENT, CONST, ASCENT, DECO_STOP, GAS_MIX); the Conveyor that expands profiles at fixed time intervals; TabExp for precomputed exponentials.

2. Academic references

2.1 Bühlmann — ZH-L16 / Keller-Bühlmann

Keller, H.; Bühlmann, A. A. "Deep diving and short decompression by breathing mixed gases." Journal of Applied Physiology, 20(6): 1267–1270, November 1965. https://doi.org/10.1152/jappl.1965.20.6.1267 (Original Keller-Bühlmann multi-gas decompression paper.)

Bühlmann, A. A. Dekompression — Dekompressionskrankheit. Berlin / Heidelberg / New York: Springer-Verlag, 1983. ISBN 3-540-12514-0. (Original ZH-L12 book, German.)

Bühlmann, A. A. Decompression — Decompression Sickness. Berlin / New York: Springer-Verlag, 1984. ISBN 0-387-13308-9. (English translation of the 1983 volume.)

Bühlmann, A. A. Tauchmedizin: Barotrauma, Gasembolie, Dekompression, Dekompressionskrankheit. Berlin: Springer-Verlag, 1992. ISBN 3-540-55581-1 / 978-3-540-55581-0. https://link.springer.com/book/10.1007/978-3-642-97413-7

This is the canonical ZH-L16 reference — the first edition to publish the 16-compartment A / B / C parameter sets. DecoJS's compartment constants in js/tissueCompartments.js trace back to this book through the chain in §6 below.

Bühlmann, A. A. Tauchmedizin. 3rd ed. Berlin: Springer-Verlag, 1995. ISBN 3-540-58970-8. https://link.springer.com/book/10.1007/978-3-642-97623-0

Bühlmann, A. A.; Völlm, E. B.; Nussberger, P. Tauchmedizin: Barotrauma · Gasembolie · Dekompression · Dekompressionskrankheit · Dekompressionscomputer. 5th ed. Berlin: Springer-Verlag, 2002. ISBN 3-540-42979-4 / 978-3-540-42979-1. https://link.springer.com/book/10.1007/978-3-642-55939-6 (Introduces ZH-L8 ADT; still reprints the ZH-L16 tables.)

2.2 Schreiner — exponential gas uptake with changing pressure

Schreiner, H. R.; Kelley, P. L. "A Pragmatic View of Decompression." In C. J. Lambertsen (ed.), Underwater Physiology IV: Proceedings of the Fourth Symposium on Underwater Physiology. New York: Academic Press, 1971, pp. 205–219.

Origin of the linear-rate-of-pressure-change form of the Haldane equation used in iterative dive-computer calculations. This is what "the Schreiner equation" refers to in decoModel.js:125.

Secondary reference which derives and discusses the Schreiner form in modern notation: Baker, "Clearing Up The Confusion About 'Deep Stops'" (§2.4) — contains the worked-out Schreiner equation as it appears in most dive-computer source code.

2.3 Workman — M-values

Workman, R. D. "Calculation of decompression schedules for nitrogen-oxygen and helium-oxygen dives." Research Report 6-65. Washington, D.C.: U.S. Navy Experimental Diving Unit, 26 May 1965. https://pubmed.ncbi.nlm.nih.gov/5295231/ · https://www.semanticscholar.org/paper/eb72db3344bfe9d5bfbc59efe59d68c55bcac6d9

The original U.S. Navy paper that introduced the "M-value" concept — maximum tolerated inert-gas pressure per tissue compartment as a linear function of depth. Foundation on top of which Bühlmann's a / b coefficients were constructed.

2.4 Erik Baker — Gradient Factors articles

All three freely distributed PDFs, archived by Shearwater and other outlets. No formal publication venue; these are the "grey literature" of the GF model, and the central reference for DecoJS's findFirstStopAtGFLow / interpolateGF implementation.

Baker, Erik C. "Understanding M-values." 1998. https://www.shearwater.com/wp-content/uploads/2019/05/understanding_m-values.pdf

Explains M-values, surfacing M₀ and slope ΔM, and Bühlmann a/b coefficient derivation from half-time:

  • a = 2 · ht^(−1/3) (atm)
  • b = 1.005 − ht^(−1/2) (dimensionless)

Baker, Erik C. "Clearing Up The Confusion About 'Deep Stops'." 1998. https://www.shearwater.com/wp-content/uploads/2012/08/Deep-Stops.pdf — mirror: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=eb03802361c6050ec2d0bb250c3db2407602032e

Introduces Gradient Factors as the mechanism for forcing deeper first stops — this is THE Gradient-Factor paper. Contains the complete Schreiner equation form used by DecoJS (decoModel.js:125).

Baker, Erik C. "Oxygen Toxicity Calculations." Sometimes circulated as "Deco Lessons" in the decotengu references. No stable publisher URL; mirrored widely. Used by decotengu as its third Baker reference.

2.5 Community secondary review

Worth citing as a readable secondary source that ties Workman, Bühlmann, Schreiner, and Baker together:

Wienke, B. R.; O'Leary, T. R. "Reduced Gradient Bubble Model in Depth." In Decompression Modelling and Algorithm (Springer chapter). https://link.springer.com/chapter/10.1007/978-3-030-96921-9_5

3. Mark Powell — Deco for Divers

Powell, Mark. Deco for Divers: A Diver's Guide to Decompression Theory and Physiology.

Cited by the DecoJS README as the primary inspiration for the project. Powell is a senior TDI instructor-trainer and one of the most widely cited popular-education authorities on Bühlmann + GFs.

4. Open-source prior art

4.1 decotengu — primary reference implementation

  • Project: https://wrobell.dcmod.org/decotengu/
  • Source (mirror): https://gitlab.com/wrobell/decotengu · also on PyPI as decotengu
  • Language: Python 3
  • License: GPL-3.0
  • Approach: Bühlmann ZH-L16 A/B/C with Erik Baker gradient factors; Schreiner iteration for inert-gas loading; decompression stops located by iteratively finding the shallowest depth at which the tissue ceiling (GF-adjusted) is not violated; stop duration found by linear search + binary refinement. OC air / nitrox / trimix supported.

DecoJS relationship: used as the numerical oracle. DecoJS matches decotengu 0.14.1 exactly on 83.8 % of the 160 Bühlmann-air reference scenarios and within ±1 min on 100 %. See Validation-and-Testing.

4.2 divetools.app

Browser-based dive-planning tool covering Bühlmann ZH-L16 with gradient factors, OC and CCR planning, multi-level profiles, trimix, ppO₂ / CNS / OTU tracking, gas mixer, MOD / EAD / END.

4.3 Additional open-source implementations worth cross-referencing

Verified GitHub projects implementing ZH-L16 + GF, in several languages. Useful as additional numerical sanity checks and for readers wanting reference code in their preferred language.

5. SPČR / CMAS training references

See the project's "Expert review" section in about.html (rendered at https://decotheory.eu/about.html) for the endorsement context.

SPČR = Svaz potápěčů České republiky, the Czech diving federation and CMAS national-federation seat for the Czech Republic. DecoJS is the practical component of Matej Hron's CMAS I3 (International Instructor Level 3) thesis.

5.1 SPČR official sites

  • https://www.cmas.cz/ — SPČR main site (CMAS ČR).
  • https://www.cmas.cz/stranka-pro-instruktory-55 — "Pro instruktory" (For Instructors). Downloadable PDFs include Výcvikové směrnice SPČR 2016 (Training Guidelines), Bezpečnostní směrnice SPČR 2016 (Safety Guidelines), Jak se stát instruktorem (How to become an instructor), CMAS Trimix Blender výcviková směrnice SPČR, and instructor qualification extension / pricing lists. No dedicated decompression-theory PDF is directly linked — deco theory is delivered through the instructor courses and the SPČR 100-question exam bank, not a standalone PDF.
  • https://www.cmas.cz/stranka-archiv-53 — Archive of Training Commission (VK SPČR) meeting minutes and instructor-project documents (2012–).
  • https://www.cmas.cz/mapa-cmas-a-spcr-76 — "CMAS and SPČR" — explains the federation / international-body relationship.

5.2 SPČR / CMAS exam banks

Source for the DecoJS quizzes:

  • SPČR 2018 exam questions — official CMAS ČR examinations (Physics, Anatomy, Accidents, Safety, Training, Equipment, Vessel). Digitised into DecoJS's data/quiz-*.json. The canonical printed / PDF version is distributed by SPČR VK to candidates — not publicly downloadable on cmas.cz.
  • Strany potápěčské — https://www.stranypotapecske.cz/kurzy/syskval.asp?sys=CMAS — independent Czech summary of the CMAS qualification system.

5.3 CMAS international

5.4 SPČR / CMAS endorsers

Per about.html "Expert review" section:

  • Ing. Jiří ("Jirka") Hovorka — SPČR technical instructor; reviewed and endorsed DecoJS. Source of the in-app Gradient-Factor reference table.
  • Petr Hruška — SPČR / CMAS instructor; further endorser.
  • Výcviková komise SPČR (VK SPČR) — the SPČR Training Commission, institutional endorser.

6. ZH-L16 constant tables

Primary (paper) source for the constants is Bühlmann 1992 Tauchmedizin (§2.1); this is the book in which the 16-compartment A / B / C coefficient sets were first published. For citing in a wiki without access to the book, the accepted substitute sources are:

  1. Baker, E. "Understanding M-values." https://www.shearwater.com/wp-content/uploads/2019/05/understanding_m-values.pdf — reprints the full ZH-L16A half-times and a / b values and derives them from the half-time formulas a = 2·ht^(−1/3), b = 1.005 − ht^(−1/2). This is the de-facto open reference most OSS projects cite, including decotengu. The DecoJS wiki cites Baker here.

  2. Wikipedia — Bühlmann decompression algorithm. https://en.wikipedia.org/wiki/B%C3%BChlmann_decompression_algorithm — contains a full ZH-L16C parameter table (half-times and a / b for both N₂ and He, all 16 compartments), citing Bühlmann 1984 / 1992 / 1995 / 2002 as primary sources. Useful as a quick-lookup reference but should not be the sole citation.

  3. dive-tables.com — https://dive-tables.com/buhlmann-en — independent reprint of ZH-L16A/B/C tables side-by-side with a clear GF explanation.

  4. CMAS fact sheet — https://www.cmas.org/fact-sheets/b%C3%BChlmann-zh-l-eng.html — CMAS-endorsed short summary.

  5. HeinrichsWeikamp OSTC firmware source — https://bitbucket.org/heinrichsweikamp/ostc2_code — primary-source-style reference: the ZH-L16 constants as actually shipped in production dive-computer firmware. decotengu cites this for cross-check.

Variant letter meaning:

  • A = Experimental (mathematically derived from half-times; found empirically not conservative enough in middle compartments).
  • B = Printed tables (slightly more conservative; used for table calculations).
  • C = Dive computers (most conservative; used for in-water computers).

DecoJS's defaults follow ZH-L16C — aligned with decotengu — see js/tissueCompartments.js.

Numerical provenance chain:

DecoJS constants ≈ decotengu ≈ OSTC firmware ≈ Baker (1998 derivation) ≈ Bühlmann 1992 Tauchmedizin.

This chain is what the alignment in commits ff06756 and 7f985da established; it is the warrant for calling DecoJS's output a correct implementation of Bühlmann ZH-L16C.

References last verified 2026-04-24.

Clone this wiki locally