3 - Saturation, halftime and M-value
For this eBook it is assumed that the reader has some basic knowledge about the saturation which always takes place in the human body whenever a diver uses a compressed breathing gas; a proportion of that gas is always being absorbed by our tissues while diving. So the reader of this eBook is expected to know that the human body consists of different "materials" - i.e. tissues - which absorb at different rates the suspected villain for DCS, nitrogen, and other gases in our breathing gas mixture. Usual listings of tissues include blood, which saturates especially fast, brain, spinal cord, skin, muscles, the inner ear, joints, and finally bones, which saturate slowest of the mentioned tissues; the same applies vice versa during the desaturation process. That a hard bone absorbs a gas slower and needs more time to release it again, is obvious and easy to imagine. Also, the reader will know that the mathematical equations (algorithms) of dive tables and dive computers don't work with real tissues of the human body but rather with theoretical tissues, and for clearer distinction these are usually called compartments.
As already noted, the Recreational Dive Planner (RDP) from DSAT and the dive computers which use the original DSAT algorithm is based on 14 compartments, with halftimes of 5 - 10 - 20 - 30 - 40 - 60 - 80 - 100 - 120 - 160 - 200 - 240 - 360 and 480 minutes.
The Buhlmann algorithms ZH-L12 and ZH-L16 are both based on 16 compartments, but Buhlmann has assigned with few exceptions different halftimes to these compartments:
The halftimes of the Buhlmann ZH-L12 model are 2.65 - 7.94 - 12.2 - 18.5 - 26.5 - 37 - 53 - 79 - 114 - 146 - 185 - 238 - 304 - 397 - 503 and 635 minutes.
The halftimes of the Buhlmann ZH-L16 model are 4 - 5 - 12.5 - 18.5 - 27 - 38.3 - 54.3 - 77 - 109 - 146 - 187 - 239 - 305 - 390 - 498 and 635 minutes.
In a later section we will look at that more in detail.
It is not possible in this eBook to explore in-depth the question how the designers of various models arrived at these halftimes (this can be studied in numerous internet articles and other publications), but we need to examine carefully the terms "halftime" and "M-value" as these are central terms for understanding dive computers.
Halftime
Related to diving the complete term of halftime is "saturation halftime". The term halftime alone is usually used to describe the period of time for the decay of radioactive elements and their radiation to its half. In diving the concept of saturation halftimes describes the time in minutes which is needed by a compartment to saturate or desaturate to its half. When nuclear power is the issue, usually the halftimes of Plutonium and Uranium are addressed; examples: the Plutonium Isotope 244 enjoys a halftime of roughly 80 million years, the radioactive Uranium Isotope 238 in comparison can "only" come up with a bit over 4 million years.
Given those hardly conceivable periods of time it is not really surprising that the temporary disposal and the safe permanent disposal of burned out fuel rods of nuclear power plants are unsolved problems of human mankind. In Germany, for instance, in 2014 there has again been initiated the search for such a disposal site - which should be safe for at least one million years .
In diving, saturation and desaturation of tissues and compartments do of course not last that long. Mathematically not absolutely correct but sufficient for practical diving purposes it is assumed, that a full saturation and desaturation is reached after 6 halftimes. In other words saturation halftime is understood as the time in minutes, which is needed by a specific "tissue" so that the initial pressure inside this tissue reaches half of the gas pressure outside the tissue in the new depth; and after 6 of these half-times the tissue is regarded as having reached its surrounding pressure (resp. is back to its initial pressure). Mathematically speaking it is the time in which an exponentially increasing or decreasing value is halved.
During the desaturation or off-gassing process the amount which has remained after one halftime is halved again during the second halftime, so only 1/4 remains, after three halftimes it will be 1/8, then 1/16, 1/32, 1/64 and so forth, or in percent:
50% [100% minus 1/2 of 100]
25% [50 minus 1/2 of 50]
12.5% [25 minus 1/2 of 25]
6.25% [12.5 minus 1/2 von 12.5]
3.13% (rounded) [6.25 minus 1/2 of 6.25 = 3.125]
1.56% (rounded) [3.125 minus 1/2 of 3.125 = 1.5625] - etc.
During the saturation process (gas absorption) accordingly:
50% ["0" plus 50%]
75% [50 plus 1/2 of 50]
87.5% [75 plus 1/2 of 25]
93.8% (rounded) [87.5 plus 1/2 of 12.5 = 93.75]
96.9% (rounded) [93.75 plus 1/2 of 6.25 = 96.875]
98.4% (rounded) [96.875 plus 1/2 of 3.125 = 98.4375] - etc.
Nobody needs to be a mathematical crack to understand that 100% saturation will never be reached this way, because the last value always only changes by half of the difference to the value before - half of the half of the half etc. This has lead to the simplified but for practical diving purposes sufficient assumption that after 6 halftimes a "tissue" can be regarded as completely saturated resp. desaturated. Diving professionals among the readers will know this relationship as an exponential curve, mathematically speaking:
Less well known than this saturation curve will be that the first dive computer, that really deserved this designation according to widespread opinion, also had a curve on its LCD display. This was the EDGE from the US company Orca (1983), and the curve represented the M-values of the EGDE (more on M-values in the next section). This actual seeing how each of the compartments "filled with nitrogen" had a direct effect on the diver. When you saw on the display that one of the 12 compartments with halftimes of 5 - 11...
