Firstly, I'd caution against considering decompression diving unless properly trained. This is unforgiving diving and the medical consequences of mistakes and unforeseen, unmitigated failures are severe.
There are varied algorithms used to calculate deco. . . all are significant mathematic calculations performed in parallel on a variety of tissue models/compartments.
In a nutshell... you cannot manually calculate saturation and decompression. It is way beyond the scope of mental arithmetic unless you're Rain Man. Here's a
basic example:
For a start, there's a myriad of different
algorithms used. So you first need to pick one of those. Some models calculate based on inert gasses saturating into/out from varied tissue compartments at pre-designated speeds. These are called '
dissolved gas models'... and this concept is what most recreational divers are familiar with from scuba courses. An example of this is Buhlmann ZHL16.
Other models also add factors/calculations that attempt to limit the growth of micro-emboli (micro bubbles) on ascent.... these are called '
dual phase models'... as they track nitrogen but also apply some heavy math to limit 'critical bubble radii' based on the mechanics of bubble formation, growth and collapse. Examples of these are VPM-B and RGBM.
Assuming a (more straightforward) dissolved gas model,you need to apply some mathematics for each tissue compartment (i.e. 16 compartments with varying saturation half-times).
Such a formula for saturation level might be:
Buhlmann Saturation Level
Pcomp = Pbegin + [Pgas - Pbegin) x [1-2 -te/tht]
Where:
Pcomp = Inert gas pressure in the compartment before exposure time (bar)
Pbegin = Inert gas pressure in the compartment after exposure time (bar)
Pgas = Inert gas pressure in the mixture being breathe (bar)
tc = Length of exposure time (minutes)
tht = Half time of the compartment
Once you know your saturation level/s, you need to calculate ascent ceiling/s.
Pamb.tol = (Pcomp - a) x b
Where:
Pcomp = Inert gas pressure in the compartment
Pamb.tol = Pressure you could drop to
a and b = a and b values for that compartment and the gas in question
This will give a ceiling for each tissue compartment. The deepest ceiling is where the stop is conducted. The calculation is repeated to provide necessary stops until the surface is reached.
There is a system called Ratio Deco that allows dive planning using some basic maths. This is based on a ratio between depth/time and stops on ascent. The ratio creates an ascent profile that mimics profiles given by decompression algorithms.
Ratio Deco is taught by the agencies GUE and UTD (they both use different versions) and has a debatable level of success.
Most decompression divers use laptop or smartphone software programs to calculate their dives. Examples of these are Multideco, ProPlanner, Z-planner, PastoDeco etc
Try reading this thread for more information:
Tracking Nitrogen in Tec Diving
Once you've worked out your dive plan and ascent schedule, you can work out your gas plan.
Here's an article on gas management:
Scuba Gas Management | Techniques | Course Notes
