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#### Arie0510

##### Registered
By now I have been able to exactly reproduce all M0-values for tissues with half times of 20 minutes and more. Only for tissues with half times of 10 and 5 minutes I obtain slightly smaller values than presented in .

For those of you interested in reproducing (almost all of) the M0-values presented in , I summarize below the approach I followed.

Starting point is the differential equation dP(t)/dt = -k ( P_I(t) - P(t) ) where P(t) denotes the pressure in the compartment, P_I(t) the ambient pressure, and k = ln(2) / t_{0.5} is a constant with t_{0.5} denoting the half time of the compartment.

Start with initial pressure P(0)=33 [fsw], descent at a rate of 60 [fsw/min] to a depth D. Stay at depth D for some time, and subsequently ascent at a rate of 60 [fsw/min], surfacing at time t=tsurf. Using a Schreiner equation, followed by a Haldane equation, followed by an other Schreiner equation one can derive that the pressure at surfacing is given by:

P(tsurf) = 33 + 60 * t_{0.5} / ln(2) * ( 2^( - tsurf / t_{0.5} ) - 2^( D / ( 60 * t_{0.5}) ) * ( 1 - 2^( D / ( 60 * t_{0.5} ) ) )

If in this expression one takes for the surfacing time the maximal no-stop time, i.e.,

tsurf = ( ( D - A ) / C )^( - 1 / x ), where A=20.15, C=803, x=0.7476

one can consider P(tsurf) as a function of the depth D (for a given tissue half time t_{0.5} ).
If you want, you can plot this function for D>20.15. This function is increasing for increasing D, until a maximum is reached, after which the function decreases again. In particular for a given half time t_{0.5} one can therefore determine the depth D for which this function is maximal. Determine this optimal depth D and round the value to two digits behind the comma. For this optimal depth, determine P(tsurf) and floor the outcome to two digits behind the comma. This could be interpreted as an M0-value for air, so to obtain an M0-value for nitrogen, multiply the outcome by 0.791 and round again to two digits behind the comma.

Following this procedure on gets
 t_{0.5} D P(tsurf) M0 5 134.11 124.53 98.50 (*) 10 105.02 104.37 82.56 (*) 20 74.23 84.56 66.89 30 57.92 75.52 59.74 40 48.38 70.45 55.73 60 38.37 65.03 51.44 80 33.43 62.21 49.21 100 30.56 60.49 47.85 120 28.71 59.33 46.93 160 26.47 57.87 45.78 200 25.17 56.98 45.07 240 24.32 56.39 44.60 360 22.94 55.39 43.81 480 22.27 54.87 43.40

As you can see the M0-values are exactly the same as presented in  for tissues with half times of 20 minutes and more. However, in  they obtained for a half time of 5 minutes a value M0=99.08, and for 10 minutes: M0=82.63. I was unable to explain this difference...
Any other approach I tried was not able to exactly reproduce the M0-values of the other tissues.

 Hamilton Jr RW, Rogers RE, Powell MR (1994). "Development and validation of no-stop decompression procedures for recreational diving: the DSAT recreational dive planner"

• #### dmaziuk

##### Contributor
I'm not sure I follow: you're back-calculating M-values from RDP no-stop times?

(And if yes, how did you handle the shaded squares on the table where it says "optional stop shall be mandatory"?)

#### Arie0510

##### Registered
I'm not sure I follow: you're back-calculating M-values from RDP no-stop times?

(And if yes, how did you handle the shaded squares on the table where it says "optional stop shall be mandatory"?)
In , they explain how they derived the RDP and its tables. Basis for that are the M0-values. Though they do a lot of explaining, some details for reproducing their work are missing. In section D.a they wrote "The RDP M0-values were back-calculated from the no-stop curve". I want to know how they did this.

Starting point is the no-stop curve: the time a diver can spend at a given depth and ascend directly to the surface. In  they write that RE Rogers, based on data, determined a new expression, that expression with A,C,D and x in my previous post and in the first post of this topic.
From this no-stop curve they determined M0-values, but the question is how. These M0-values form the basis behind the tables. How to go from the M0-values to the diving times at different depth, determining if you are an F-diver of K-diver, etc. (the first table) will be a next endeavor for me. Then you have to take into account all different tissues to determine which one determines the diving time (to that end, the excel spreadsheet that I linked to is illustrative). Typically these are the slow tissues for shallow dives and the fast tissues for deep dives. But as I mentioned that will be a next endeavor for me.

These shaded areas you mentioned is a different story. That has to do with the fact that there is a difference between no-stop and no-decompression. To reduce the risk for decompression sickness, you are strongly adviced to make safety stops of 3 min at 15 fsw.

• wnissen

##### Contributor
Mainly just out of curiosity, true to my education, but also to better understand the tables I am teaching my students as a DM.

#### dmaziuk

##### Contributor
In , they explain how they derived the RDP and its tables. Basis for that are the M0-values. Though they do a lot of explaining, some details for reproducing their work are missing. In section D.a they wrote "The RDP M0-values were back-calculated from the no-stop curve". I want to know how they did this.

Starting point is the no-stop curve: the time a diver can spend at a given depth and ascend directly to the surface.

My point is that no-stop time is determined from M0 values and the only interesting part of back-calculating them from no-stop time is when your result isn't the same M0 value you started with.

#### Arie0510

##### Registered
According to  it is the other way around: for the RDP the M0-values have been back-calculated from the no-stop curve: Replies
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