CNS calculation headaches

[Willem Ferguson]

On 2019/08/10 15:40, Robert Helling wrote:
> Willem,
>
>> On 10. Aug 2019, at 15:19, Robert Helling <helling at atdotde.de 
>> <mailto:helling at atdotde.de>> wrote:
>>
>> PS: The original problem arose as the interpolated table value is 
>> used in the denominator of the cns += formula and would result in a 
>> pole when the extrapolated table value reaches 0. Maybe we should 
>> redo the whole thing and linearly interpolate the inverses of the 
>> table value rather than the table value. For those an extrapolation 
>> would be more sensible.
>
> here is another idea: With the exception of the values above pO2 of 
> 1.5bar, a power law is actually a pretty good fit to the table:
>
>
>
> This is exp(11.7853 - 0.00193873 pO2).
>
> Maybe, we should give up the idea of the table entirely and use this 
> power law instead?
>
> Best
> Robert

An interesting alternative, Robert. I am not happy with the deviation at 
1.5 and 1.6. One would have to check what the effect of these two points 
are on the power curve. What is the effect on the overall fit of the 
power curve if one omits those two points? What of a 3rd order 
polynomial that could in principle accommodate the inflection at 1.4? I 
am not averse to a mathematical solution because the linear 
interpolation also causes some inaccuracy.

And of course I like your graph because it is the right way round with 
time limit being the dependent variable. Baker's graph is the wrong way 
round.

I would also love to see what it will look like if one interpolates on 
inverses. But it does not in principle avoid the problem at pO2=1.65.

With respect to your idea of NOT calculating CNS when pO2 > 1.65, if I 
understand you correctly, the underestimate will be much higher if those 
points on the dive profile do not contribute to the total CNS toxicity. 
I think in the planner the solution is to incorporate whatever mechanism 
appears prudent and simply add a warning to the dive plan that the CNS 
value cannot be trusted because of the high pO2. In the dive log it is a 
different thing since the dive log has no way of adding system warnings 
except for the red banner at the bottom of the screen. I am not sure 
that a user would like to get past a red banner warning every time 
she/he views that dive.

Kind regards,

willem



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