libzhl

The ZHL Bühlmann algorithm is a decompression model that simulates theoretical gas exchange dynamics in various body tissue compartments (connective tissue, epithelial tissue, muscle tissue, and nervous tissue) under elevated ambient pressure, enabling the calculation of optimal decompression times ($\Delta{t}$) in response to pressure gradients ($\nabla{P}$) for different gas mixtures.

The gas exchange dynamics in each tissue compartment are modeled using the following differential equation:

$$\frac{\Delta{P}}{\Delta{t}} = \frac{P_{amb} - P}{\tau}$$

where $P$ is the partial pressure of the gas in the tissue compartment, $P_{amb}$ is the ambient pressure, and $\tau$ is the time constant for gas exchange in the tissue compartment.

The decompression time ($\Delta{t}$) is calculated using the following equation:

$$\partial t = \frac{\Delta{P}}{\nabla{P}}$$

where $\Delta{P}$ is the change in pressure and $\nabla{P}$ is the pressure gradient.

The pressure gradient ($\nabla{P}$) is calculated using the following equation:

$$\nabla P = \frac{\Delta{P}}{\Delta{t}}$$

This equation represents the rate of change of pressure $\Delta{P}$ with respect to time $\Delta{t}$.

Optimal gas mixture

The model is based on the Dalton's Law in combination with Partial Pressures constraint optimisation on the pressure limits recommended in the US Navy Diving Manual (Revision 7, 2020):

• PP02 (21,278 Pa - 141,855 Pa) - to eliminate O2 toxicity under high ambient pressure.
• PPN2 (0 Pa - 354,638 Pa) - to amortise N2 narcotic effect under high ambient pressure.

WARNING: Underlying model assumes no hazardous properties of Helium under high ambient pressures:

• PPHe (0 Pa, ∞ Pa)

./mixture --min=1 --max=10 --interval=0.5 --pressure-unit=ata

Ambient Pressure	PP02 (ATA)	VO2	PPN2 (ATA)	VN2	PPHe (ATA)	VHe
1 ATA	0.209998	0.209998	0.790002	0.790002	0	0
1.5 ATA	0.314996	0.209998	1.185	0.790002	0	0
2 ATA	0.419995	0.209998	1.58	0.790002	0	0
2.5 ATA	0.524994	0.209998	1.97501	0.790002	0	0
3 ATA	0.629993	0.209998	2.37001	0.790002	0	0
3.5 ATA	0.734991	0.209998	2.76501	0.790002	0	0
4 ATA	0.83999	0.209998	3.16001	0.790002	0	0
4.5 ATA	0.944989	0.209998	3.5	0.777779	0.0550062	0.0122236
5 ATA	1.04999	0.209998	3.5	0.700001	0.450007	0.0900015
5.5 ATA	1.15499	0.209998	3.5	0.636365	0.845009	0.153638
6 ATA	1.25999	0.209998	3.5	0.583334	1.24001	0.206668
6.5 ATA	1.36498	0.209998	3.5	0.538462	1.63501	0.25154
7 ATA	1.4	0.2	3.5	0.500001	2.1	0.299999
7.5 ATA	1.4	0.186667	3.5	0.466667	2.6	0.346666
8 ATA	1.4	0.175	3.5	0.437501	3.1	0.387499
8.5 ATA	1.4	0.164706	3.5	0.411765	3.6	0.423529
9 ATA	1.4	0.155556	3.5	0.388889	4.1	0.455555
9.5 ATA	1.4	0.147368	3.5	0.368422	4.6	0.48421
10 ATA	1.4	0.14	3.5	0.35	5.1	0.51

DISCLAIMER

WARNING: USE OF THIS LIBRARY FOR UNDERWATER DIVING MAY CAUSE HEALTH PROBLEMS OR DEATH

The use of this library for underwater diving is strictly prohibited. The calculations and algorithms used in this library are not intended for use in life-critical applications, including underwater diving.

RISKS ASSOCIATED WITH UNDERWATER DIVING

underwater diving is a high-risk activity that can result in serious health problems or death. The use of this library for underwater diving may increase the risk of:

• Decompression sickness (DCS)
• Nitrogen narcosis
• Oxygen toxicity
• Carbon dioxide poisoning
• Other diving-related injuries or illnesses

LIMITATIONS OF THIS LIBRARY

This library is not designed to provide a safe or reliable means of calculating dive plans or managing gas mixtures for underwater diving. The calculations and algorithms used in this library are based on simplified models and assumptions that may not accurately reflect the complexities of real-world diving scenarios.

USER RESPONSIBILITY

By using this library, you acknowledge that you understand the risks associated with underwater diving and that you are responsible for ensuring your own safety and the safety of others. You also acknowledge that you have read and understood the warnings and disclaimers provided in this document.

NO WARRANTY OR LIABILITY

The authors and maintainers of this library disclaim any warranty or liability for damages or injuries resulting from the use of this library for underwater diving. By using this library, you release and hold harmless the authors and maintainers of this library from any claims or liabilities arising from the use of this library.

RECOMMENDATIONS

If you are a underwater diver, we strongly recommend that you use a reputable and safety-tested dive planning software or consult with a qualified diving professional to ensure your safety and the safety of others.

ACKNOWLEDGMENT

By using this library, you acknowledge that you have read and understood the warnings and disclaimers provided in this document and that you are aware of the risks associated with underwater diving.