Allow me to elaborate.
There may be some confusion about HT: if you start with more of something, even if the rate will be the same, then you need more periods to get to same end quantity, I will demonstrate below.
We are look at the dissolved gas model.
The model is determined by:
Number of compartments;
Half Times of each compartment;
M-Value for each compartment;
Half Times and M0 Values come in pairs, these define a compartment.
The relations are determined by the model in terms of gradients and rates and concentrations,
absolute quantities of gas are never taken in account, in the model.
Why should absolute quantities be taken in consideration by dive computers?
Because: they can, contemporary technology computing power allows; divers have different sizes of tissues; there are more divers; there are more divers who are obese; there is a higher risks of DCS incidence associated with obesity.
Because the size of the compartments does matter.
I will demonstrate now how two divers on same dive end up with different N2.
Peter is 275lbs or 124kg and has Body Fat of 20% (BFP) with 25kg of fat and Paul has 35% BFP at 200lbs or 90kgs, is obese with 31.5 kg fat.
For each diver, how many grams of N2 are dissolved in in 1 liter of compartment F with Half Time 120 minutes (HT) at given constant temperature? Dive depth is 30 meters or 100ft.
Given KH of N2 in aqueous solution = 1600 atm/(mol/liter)
At equilibrium (saturation) the concentration is directly proportional to the partial pressure of N2 in the solution.
P=KHC
C=P/KH
C=4 atm / 1600 atm/(mol/L)
C=0.0025 mol/L
Convert to grams:
mass of one mole of N2=28g
g of N2 = mol N2 x 28
= 0.0025 x 28 g/mol
= 0,07g
1L of fat = 0.9 kg fat
1L of fat will hold 0,063g N2 when saturated at 30 meters or 100ft.
Peter: 25x0.063 = 1.6kg N2
Paul: 31.5x0.063 = 2 kg N2
Once saturation is reached, it is reached, Peter's and Paul's compartment F won't hold more than what they can respectively.
So after 40 minutes of dive time, 30m-100ft, how much is the residue N2?
In this dive one whole HT period is not yet reached, the dive is 40 minutes so far, one half time is 120 minutes.
To build the table we take some values as anchor points:
F initial(g) time HT remains(g)
Peter 1600 120 120 800
Paul 2000 120 120 1000
Then:
120 minute compartment F
minutes %HT
40 20 <---
80 40
120 50
240 75
360 87.5
600 97,76
720 96.80
840 98.44
24h 100?
48h 100
Peter: saturation is 20% of 1.6 kg = 0.32 kg
Paul: saturation is 20% of 2.0 kg = 0.40 kg
Paul has more gas in his body.
Behold! Same HT but different absolute N2 mass or volume between the divers before starting ascent.
Now we look below at when the divers have ascended for 10 minutes to reach 0 meters.
The time they took to ascend is not 40 minutes but 10.
Peter: saturation is 8% of 0.32 kg = 0.30 kg
Paul: saturation is 8% of 0.40 kg = 0.37 kg
Paul has still more gas in his body than Peter.
Behold! Same HT but different absolute N2 mass or volume between the divers at the end of the dive.
So how should the absolute quantity be reflected in the model?
Peter's 30 meter NDL for compartment F with say M0 14.41
(Using DSAT 9 for sake of example because DSAT compartments have HT with nice round numbers):
k (Cpt F) = ln2/half-time = 0.693/120 min = 0.005775
Pi = (Pamb - PH2O)*FN2 = (40 msw - 0.627 msw)*0.79 = 31.1 msw
Po = (Pamb - PH20)*FN2 = (10 msw - 0.627 msw)*0.79 = 7.4 msw
The "No-Stop Time" or NDL for this compartment,
t = (-1/k)*ln[(Pi - Mo)/(Pi - Po)]
t (Cpt F) = (-1.0/0.005775)*ln[(31.1 - 14.41)/(31.1 - 7.4)] = 60.72 minutes
The model predicts NDL for that compartment which is wrong for Paul. Paul needs M0 to be adjusted (decreased) for the compartment.
Adjusting Paul's F to F+ M0 value of one whole increment to next the compartment value of 14.06 (DSAT 10) would give him:
The "No-Stop Time" or NDL for this compartment:
t (Cpt F) = (-1.0/0.005775)*ln[(31.1 - 14.06)/(31.1 - 7.4)] = 57.13 minutes
There are at least 2 implications:
A. At overpressure Paul has more gas than Peter, which could lead to start bubbling before Peter would.
B. Peter and Paul's computers display the same residue N2, which is false!
While for A. there are settings than can be adjusted (GF high, GF low) to mitigate the risk of bubbling, there are no dive planning adjustments for surfacing M-values for B., in the current model.
I put it to you, that divers should be allowed to adjust M0 for F(n=1 to 16), across all compartments.
In the above example the greater compartment size of one diver's compartment 9 has been taken in account by assigning to compartment 9 the M0 of compartment 10. Such setting is easy to imagine and implement.
The adjustment could be made in increments such that for every kg of body fat above 20% (BFP) the compartment saturation be considered holding additional 0,064 kg of N2 at saturation as default adjustable value.
The calculation could be later revised considering KH of N2 in fat as opposed to in water.
Further, it is known that larger changes in depth at deeper depths have equivalent changes in P halving than at shallower depths, when ascending from 50 meters to 20 meters P is halved, when ascending from 10 meters to 0 meters P is halved.
I put it to you, that ascent speed ideally be not linear but should diminish as shallower depths are reached.
Deep stops allow for "slow" compartments to saturate and slow down the ascent rate already at deeper depths, they are not aligned with P halving. Settings with not too low GFlow, not to high GF high determine a DECO schedule which shapes the overall ascent to be not linear, flattening at shallower depths.
Disclaimer: the above contains errors.
Safe diving!
Narke
