how to calculate where your first decompression stop is

[rddvet]

There used to be something called Ratio Deco -- a shorthand way to calculate stops; you can probably google the 'secret sauce" -- it worked but it has fallen out of favor. Now most people use tables or more commonly follow the computer.

Ratio deco and some "adjusted" versions of it are taught and in use all the time still. I don't use it a ton at all since I'm doing 99% of my dives in caves, but its nice to be able to do super quick math in your head if you need to.

 

[L13]

so I've talked to a couple of people. what I'm understanding now is the general idea that your first decompression stop is based on how far you want to get between the depth at which the pressure gradient is enough to begin off gassing efficiently, and the M-value that shows the maximum "safe" tissue saturation. So if you use gradient factors of 65/85, your first stop would create a tissue pressure gradient at 65% of that M-value; conversely, you will surface, at most, at 85% of the M-value. if I misremembered, or mis-typed, sorry!
(correct me if I'm wrong)

Correct.

I've been reading through the calculations in Deco for Divers, and for some reason, I'm not figuring out where to get certain values. There's a table, but for some reason, when calculating the b-variable, I keep getting a negative number. Very annoying, but a work in progress.

Hard to guess what what you are missing.

 

[Moerae]

I've been reading through the calculations in Deco for Divers, and for some reason, I'm not figuring out where to get certain values. There's a table, but for some reason, when calculating the b-variable, I keep getting a negative number. Very annoying, but a work in progress.

I'm familiar with the algorithm and math involved. If you post some specific questions about which values you aren't sure where they come from, or how to do a calculation, I'd be happy to help when I get a chance to read and reply thoroughly.

 

[kaylee_ann]

Hard to guess what what you are missing.

Yeah, I’d have to post screenshots or type out the formulas and values I’m given in the deco for divers book

 

[Marie13]

Seriously - download Subsurface (FREE!) and play around with it. I prefer MultiDeco, but it ain’t cheap.

 

[Bowers]

The dive computer is the way to go but i learned ratio deco early on and still keep that in my head as a backup plan and way to help keep planning on track. In most of my diving the offgasing gets good at about 60% average working bottom depth. So for ratio we ascend at 30’/min to the 60% mark then slow to 10’ per minute between stops the rest of the way to the surface. Stops are every 10 feet and get longer durations each step closer to the surface.

 

[EFX]

Here's how I calculate the first stop in my Excel spreadsheet. I believe I got the formula from Baker's fortran code.

'calculate the first stop at GFLo using the formula:
' D = ((P - GF * a) / (GF / b - GF + 1)) - Psb
'where: D = depth, P = total gas pressure, GF = gradient factor = GFLo,
'a = coefficient a, b = coefficient b, Psb = ambient surface pressure
'the first part within parentheses calculates a pressure. Subtracting
'the surface pressure converts the result to a gauge depth.

first_stop = ((p_gas - gf_lo * a_n2he) / (gf_lo / b_n2he - gf_lo + 1)) - sp

 

[EFX]

I've been reading through the calculations in Deco for Divers, and for some reason, I'm not figuring out where to get certain values. There's a table, but for some reason, when calculating the b-variable, I keep getting a negative number. Very annoying, but a work in progress.

Here is the text from the comment header of the subroutine I use to calculate the ceiling in my Excel spreadsheet:

'=============================================================================
' calc_ceiling
'
' For every segment of the dive check that ascents do not violate a deco
' ceiling. Calculate the first deco stop based on GFLo.
'
' This routine works with the a/b coefficients developed from the m-values
' and slope values. The m-values and slope are called Workman values after
' Robert Workman, a captain in the U.S. Navy refined John S. Haldane's work
' in the early 1900's. Workman developed linear equations to describe the
' relationship between depth and tissue pressure. The equation he came up
' with is:
'
' M = S(D) + Mo
'
' where M = m-value pressure of the tissue compartment at the current
' depth, S = slope of the m-value line, D = current depth, and
' Mo = surfacing m-value.
'
' Rearranging this equation and solving for depth gives:
'
' D = (P - Mo) / S
'
' where P = the pressure of the TC at the current depth
'
' Albert A. Buhlmann M.D., a researcher with the University Hospital in
' Zurich, Switzerland developed equations that were useful for diving at
' altitudes. This type of diving was common in the high altitude lakes of
' Switzerland. Dr. Buhlmann in order to get rid of the divisor (S) in the
' equation came up with a and b coefficients. A and b coefficients can be
' derived from Workman's equations where:
'
' a = Mo - S(Ps) ;Ps is the absolute pressure at the surface
' b = 1 / S
'
' As an example in converting from Workman to Buhlmann to get the a/b
' coefficients for TC 1 nitrogen we have: Mo = 106.4, S = 1.9082
'
' a = 106.4 - 1.9082(33) = 43.4294 ;fsw
' b = 1 / 1.9082 = 0.524 ;ft/fsw
'
' Here are alternate formulas for calculating the a and b coefficients:
'
' a = 2 x (HT ^ (-1/3)) ;in ata, x 33 to get fsw, x 10 to get msw
' b = 1.005 - (HT ^ (-1/2)) ;dimensionaless
'
' To convert from Buhlmann to Workman use these equations:
'
' Mo = a + Ps/b
' S = 1 / b
'
' To find the ceiling use the tolerated ambient pressure formula:
'
' Ptol = (Pigas - GF x a) / (GF / b - GF + 1)
'
' where: pigas = inert gas pressure in compartment, GF = the current
' gradient factor, a = a coefficient, b = b coefficient.
'
' pamb = WorksheetFunction.RoundUp(pamb, 0) 'just for reference
'=============================================================================

The b coefficient, as per the above text, is simply 1 divided by the slope. There are tables in the paper "Understanding m-values" that give the slope, M0 (surfacing m-value), and half-time for each of the Buhlmann 16 tissue compartments. All the numbers are positive so I don't understand how you can get a negative result for the b coefficient using the formula. Also included in the paper are various formulas for calculating tissue pressues and depths between Workman and the Buhlmann style formulas. Attached is Baker's paper for your reference.

 

[kaylee_ann]

Here is the text from the comment header of the subroutine I use to calculate the ceiling in my Excel spreadsheet:

'=============================================================================
' calc_ceiling
'
' For every segment of the dive check that ascents do not violate a deco
' ceiling. Calculate the first deco stop based on GFLo.
'
' This routine works with the a/b coefficients developed from the m-values
' and slope values. The m-values and slope are called Workman values after
' Robert Workman, a captain in the U.S. Navy refined John S. Haldane's work
' in the early 1900's. Workman developed linear equations to describe the
' relationship between depth and tissue pressure. The equation he came up
' with is:
'
' M = S(D) + Mo
'
' where M = m-value pressure of the tissue compartment at the current
' depth, S = slope of the m-value line, D = current depth, and
' Mo = surfacing m-value.
'
' Rearranging this equation and solving for depth gives:
'
' D = (P - Mo) / S
'
' where P = the pressure of the TC at the current depth
'
' Albert A. Buhlmann M.D., a researcher with the University Hospital in
' Zurich, Switzerland developed equations that were useful for diving at
' altitudes. This type of diving was common in the high altitude lakes of
' Switzerland. Dr. Buhlmann in order to get rid of the divisor (S) in the
' equation came up with a and b coefficients. A and b coefficients can be
' derived from Workman's equations where:
'
' a = Mo - S(Ps) ;Ps is the absolute pressure at the surface
' b = 1 / S
'
' As an example in converting from Workman to Buhlmann to get the a/b
' coefficients for TC 1 nitrogen we have: Mo = 106.4, S = 1.9082
'
' a = 106.4 - 1.9082(33) = 43.4294 ;fsw
' b = 1 / 1.9082 = 0.524 ;ft/fsw
'
' Here are alternate formulas for calculating the a and b coefficients:
'
' a = 2 x (HT ^ (-1/3)) ;in ata, x 33 to get fsw, x 10 to get msw
' b = 1.005 - (HT ^ (-1/2)) ;dimensionaless
'
' To convert from Buhlmann to Workman use these equations:
'
' Mo = a + Ps/b
' S = 1 / b
'
' To find the ceiling use the tolerated ambient pressure formula:
'
' Ptol = (Pigas - GF x a) / (GF / b - GF + 1)
'
' where: pigas = inert gas pressure in compartment, GF = the current
' gradient factor, a = a coefficient, b = b coefficient.
'
' pamb = WorksheetFunction.RoundUp(pamb, 0) 'just for reference
'=============================================================================

The b coefficient, as per the above text, is simply 1 divided by the slope. There are tables in the paper "Understanding m-values" that give the slope, M0 (surfacing m-value), and half-time for each of the Buhlmann 16 tissue compartments. All the numbers are positive so I don't understand how you can get a negative result for the b coefficient using the formula. Also included in the paper are various formulas for calculating tissue pressues and depths between Workman and the Buhlmann style formulas. Attached is Baker's paper for your reference.

so.... how the heck do you calculate the pressure of a tissue compartment at a certain depth? do you multiply it by a certain number? it seems to be measured in meters on deco for divers, and I'm using 132 feet as a practice example but just cannot figure it out. I ended up just calculating the alveolar pressure of nitrogen on the surface and multiplying it to depth for calculations. which I am sure is not the correct way, but I wanted to at least do something.
when I tried to do gradient factor calculations, I got 2.3 or something like that- book said 1.0 is 100 percent of the M-value line. soooo yeah, something's not quite right LOL.

 

[Wibble]

Not being funny, but use SI units as they work a lot more easily than Imperial measures.

Example: 10 metres (33ft) is 1 atmosphere (ATA). So at 50m it's 6 ATA (5 plus one for the surface pressure).