Decompression – M-Values – Studio Blue Planet

Units

As a diver we like to use bar’s as pressure unit, since we are familiar with the bar. The pressure in this section, however, are presented in msw (meter sea water) to be consistent with literature. 1 msw = 0.1 bar. M-values in bar can be derived by deviding the M-value in msw by 10.

(1) $\begin{equation*} M = M_0 + \Delta M d \end{equation*}$

What M-values describe

The maximum allowed (absolute) partial pressure M of the Nitrogen in a hypothetical tissue compartment, characterized by half-time τ, is defined as:

M: Partial pressure limit, for each tissue compartment (half-time)
M₀: The partial pressure limit at sea-level (zero depth) (msw)
ΔM: Increase of M per meter depth (msw/m)
d: Depth (m)

Next sections present for various models the M-values.

The Workman M-values (1965) for Nitrogen

No.	τ (min)	M₀ (msw)	ΔM
1	5	31.7	1.80
2	10	26.8	1.60
3	20	21.9	1.50
4	40	17.0	1.40
5	80	16.4	1.30
6	120	15.8	1.20
7	160	15.5	1.15
8	200	15.5	1.10
9	240	15.2	1.10

The Bühlmann ZH-L12 model (1983) for Nitrogen

No.	τ (min)	M₀ (msw)	ΔM
1	2.65	34.2	1.2195
2	7.94	27.2	1.2195
3	12.2	22.9	1.2121
4	18.5	21.0	1.1976
5	26.5	19.3	1.1834
6	37	17.4	1.1628
7	53	16.2	1.1494
8	79	15.8	1.1236
9	114	15.8	1.1236
10	146	15.3	1.0707
11	185	15.3	1.0707
12	238	14.4	1.0593
13	304	12.9	1.0395
14	397	12.9	1.0395
15	503	12.9	1.0395
16	635	12.9	1.0395

The a and b parameter Bühlmann originally used in his models can be derived:

(2) $\begin{equation*} b=\frac {1}{\Delta M} \end{equation*}$

(3) $\begin{equation*} a = M_0 - \frac {P_{amb\_sea\_level}}{b} \end{equation*}$

In this equation P_{amb_sea_level} is the ambient pressure at sea level expressed in msw. Remember the Bühlmann equation is now:

(4) $\begin{equation*} P_{t.tol}ig = M = \frac {P_{amb}}{b} + a \end{equation*}$

The Bühlmann ZH-L16 model (1990) for Nitrogen

No.	τ (min)	M₀ A (msw)	M₀ B (msw)	M₀ C (msw)	ΔM
1	4.0	32.4	32.4	32.4	1.9802
1a	5.0	29.6	29.6	29.6	1.7928
2	8.0	25.4	25.4	25.4	1.5352
3	12.5	22.5	22.5	22.5	1.3847
4	18.5	20.3	20.3	20.3	1.2780
5	27.0	19.0	19.0	18.5	1.2306
6	38.3	17.8	17.5	16.9	1.1857
7	54.3	16.8	16.5	15.9	1.1504
8	77.0	15.9	15.7	15.2	1.1223
9	109	15.2	15.2	14.7	1.0999
10	146	14.6	14.6	14.3	1.0844
11	187	14.2	14.2	14.0	1.0731
12	239	13.9	13.9	13.7	1.0635
13	305	13.5	13.4	13.4	1.0552
14	390	13.2	13.2	13.1	1.0478
15	498	12.9	12.9	12.9	1.0414
16	635	12.7	12.7	12.7	1.0359

The DCAP MM11F6 model (1988) for Nitrogen

No.	τ (min)	M₀ (msw)	ΔM
1	5	31.90	1.30
2	10	24.65	1.05
3	25	19.04	1.08
4	55	14.78	1.06
5	95	13.92	1.04
6	145	13.66	1.02
7	200	13.53	1.01
8	285	13.50	1.00
9	385	13.50	1.00
10	520	13.40	1.00
11	670	13.30	1.00

The DSAT Recreational Dive Planner (PADI) model (1987)

No.	τ (min)	M₀ (msw)
1	5	30.42
2	10	25.37
3	20	20.54
4	30	18.34
5	40	17.11
6	60	15.79
7	80	15.11
8	100	14.69
9	120	14.41
10	160	14.06
11	200	13.84
12	240	13.69
13	360	13.45
14	480	13.33