Blending real gases

As mentioned before, gases in diving cylinders are not only not sufficiently well approximated by the real gas equation but also the van der Waals equation, despite its prominence in thermodynamics teaching, is not doing much better.

Subsurface does better than this using a polynomial fit to table data for the compressibility of the three relevant gases. In a discussion at ScubaBoard, the question came up how to use this in gas blending. After an initial version using Mathematica, I sat down and implemented it as a perl script and hooked it up to this web page for everybody’s use and enjoyment. Here it is:

Real Blender

source code is on GitHub. Right now, it does only nitrox. But it computes instructions to up up partly filled cylinders with any pre-existing nitrox mix.

Let me know if you think extending it to trimix would be useful for actual use. I am not sure what the best user interface would be in that case: For nitrox, specifying the initial and target mix and pressure and two top up mixes, the blending problem generally has a solution. But with three gas components to get right, it is in general impossible with only two top up mixes. So you either have to use three (linearly independent) top up mixes or let one thing unspecified. That could be either the oxygen or helium fraction of the final mix or you have to leave open one of the gas fractions of the top up gases.

So what do you do in practice, which component do you leave unspecified?

Update: I updated the script so it can now also handle blending trimix (starting from a partially filled cylinder, you can specify three top up gases it will now calculated the intermediate pressures you have to fill up to). To blend nitrox, specify the target mix as containing no helium and leave one of the top up mixes empty.

The DCIEM model

When the Subsurface mailing list recently received the request if the planner could implement the DCIEM model as well my first reaction what “Whut?” has I had not heard of it before.

Turns out, DCIEM stands for “Defense and Civil Institute of Environmental Medicine” which was a research institution of the Canadian military and is now part of DRDC Toronto according to Wikipedia. The request to Subsurface was apparently prompted by the fact that Shearwater announced to implement the model into their dive computer for commercial divers. The “for commercial divers” sounds to me like this is more to tick some boxes in the health and safety requirements for these people rather than something that the diving world at large should adopt. But still, it might be interesting to see what this model actually does.

Some googling suggests that this model is mainly consumed not in terms of an algorithm in planning software or dive computers but in the for of tables. A 1992 version can for example be found here.

But Google also finds a review paper by Nishi and Tikuisis that explains that the DCIEM model is a non-linear model developed by Kidd and Stubbs. It shows as four compartment discretisation of a slab of tissue together with a ODE for time evolution:

Kidd-Stubbs model according to Nishi and Tikituisis

As written, I cannot make much sense of it but things clear up when the expression is expanded:

\(\dot p = ab \Delta p +a\Delta p^2\)

Here, p is the vector of tissue pressures and Δ is the discrete Laplacian that for a sequence (s) is

\((\Delta s){n} = s{n-1} -2 s_n + s_{n+1}.\)

If there were only the first term on the RHS, that would simply be a diffusion equation that I would also have written if somebody had asked me to write down a model for a slab of tissue. I have no clue where the second, non-linear term comes from but clearly it can safely be ignored as long as p<<b. There is also a paper by Nishi and Kuehn that gives a FORTRAN implementation of the model (doesn’t this sound familiar…). In the source code, I find a value of b=274.5 which is supposedly in units of psi which translates to 19bar, so the non-linear term should will not be relevant for anyone with a depth limit short of 200m. In the review paper it is stated that the constants of the model were fitted to bubble measurements after trial dives but one could wonder how this is would be possible unless compartment pressures at least came near to 20bar…

The paper with the FORTRAN program also explains that the relation between tissue pressure and ambient pressure is pretty much a standard \(p_{amb}\ge c_1 p_{tissue} + c_2.\)

More interesting is that the discretised slab is an example of the interacting tissue models I talked about in the post about those being equivalent to independent tissues. For four tissues, the discretised Laplacian (there is of course also a closed form) has eigen values \(\frac{-3\pm \sqrt 5}{2}, \frac{-5\pm\sqrt 5}{2}\) which numerically range between -3.6 and -0.38.

So, the four independent tissues after diagonalization cover one decade of half-times all proportional to 1/ab.

So, taking everything into account, the DCIEM model is (equivalent to) a Bühlmann type model with four tissues coving a somewhat small range of half-times. So I would expect with an appropriate choice of constants, one can produce somewhat reasonable deco schedules at least for air dives (we have not discussed different gases) with not too long runtimes. But a full blown Bühlmann (possibly with gradient factors) is much more expressive.

Depth dependent color correction

I want to look into using depth information to improve automated color correction (inspired by some new features of some camera products on the market). Problem is, I don’t do underwater photography myself. Therefore I am looking for example pictures with depth information. They should be

  • no color correction applied to yet (manual or automatic)
  • together with a Subsurface file (use the export function, possibly with annonymization) where they are linked to profile (via the import media function)

As I am only interested in color they don’t have to have high resolution (could well be heavily jpeg compressed) or have any artistic value. By sending those you agree to potentially include them as test files in Subsurface where they would be distributed under a GPL2 or CC0 license.

Mail those to robert@thetheoreticaldiver.org

Thanks a lot!

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Testing of No Fly Times in Commercial Off-the-Shelf Dive Computers

Here is another contribution by Doug Fraedrich. This time, the text would probably better fit on theepxerimentaldiver.org: He tests dive computers No-Fly-Times algorithms and compares those to DAN’s recommendations and the respective user manuals. For some more theoretical considerations regarding diving and flying, see this older post.

Introduction

It is well known that divers must wait a certain time after diving before then can safely fly. The current No Fly Time (NFT) “best practices” guidelines from Divers Alert Network (DAN)1 are listed below:

  • For a single no-decompression dive, a minimum preflight surface interval of 12 hours is suggested. 
  • For multiple dives per day or multiple days of diving, a minimum preflight surface interval of 18 hours is suggested. 
  • For dives requiring decompression stops, there is little evidence on which to base a recommendation and a preflight surface interval substantially longer than 18 hours appears prudent

These guidelines are primarily based on a paper by Richard D. Vann, et al2 of Divers Alert Network, which reported an analysis of risk of Decompression Sickness (DCS) results of 802 dives of nine different profiles: four single non-deco dives and five sets of repetitive dives. DAN did not test decompression dives in Reference 2, so the US Navy No Fly Times were used for this category of dives.

Many commercial off-the-shelf dive computers compute and display this time after surfacing from a dive. The level of documentation on how exactly this is computed varies from dive computer to dive computer; most units state in their manual that they use the DAN guidelines.

The objective of this report is to test several representative commercial off-the-shelf dive computers in pressure chamber which simulates different categories of dives and assess the following: 1) does each computer conform to the DAN NFT guidelines? and 2) does each computer conform to what is described in the computer’s owner’s manual? The dive computers tested are shown in Figure 1 and listed in Table 1. 

Fig 1: Clockwise from Top-Left: Suunto Eon-Steel, Mares Icon, Cressi Cartesio, Oceanic VT4.0, Aqualung i300C, Garmin Descent Mk1, SEAC Guru, DeepBlu Cosmiq+

ComputerMain Dive AlgorithmNo Fly Time computations (as stated in User Manual)
Deepblu Cosmiq+Buhlmann ZHL-16cThe No-Fly Time is based on the calculations of your desaturation time according to your actual dive profile. The No-Fly Time will be counted downwards every half hour.
Suunto EON Steel15-tissue Suunto-FusedNo-fly time is always at least 12 hours and equals desaturation time when it is more than 12 hours. If decompression is omitted during a dive so that Suunto EON Steel enters permanent error mode, the no-fly time is always 48 hours.
Oceanic VT4.0Z+/DSATFLT Time is a count down timer that begins counting down 10 minutes after surfacing from a dive from 23:50 to 0:00 (hr:min)
Mares Icon10 tissue RGBMIcon HD employs, as recommended by NOAA , DAN and other agencies, a standard 12-hour (no-deco non-repetitive dives) or 24-hour (deco and repetitive dives) countdown.
Cressi Cartesio“Cressi” 9 -tissue RGBMThe no-fly times as follows: 12 hours after a single dive within the safety curve (without decompression). 24 hours after a dive outside the safety curve (with decom­pression) or repeated or multi-day dives performed correctly. 48 hours…if severe errors have been made during the dive.
SEAC GuruBuhlmann ZHL-16BFor single dives that did not require mandatory deco stops, wait a minimum interval of 12 hours on the surface. In the event of multiple dives in a single day, or multiple consecutive days with dives, wait a minimum interval of 18 hours. For dives that required mandatory deco stops, wait a minimum interval of 24 hours.
AquaLung i300CZ+The Time to Fly countdown shall begin counting from 23:50 to 0:00 (hr:min), 10 minutes after surfacing from a dive.
Garmin Descent MK1Buhlmann ZHL-16cAfter a dive that violates the decompression plan, the NFT is set to 48 hours. (Note: No mention of NFT after a nominal dive.)
Table 1. Dive Computers Tested

Methods

The dive computers were subjected to simulated dives in a small pressure chamber, Figure 2. This chamber was a Pentair Pentek Big Blue 25cm chamber that had a maximum allowable pressure of 6.9 bar. 

Fig 2: Pressure Chamber

The units-under-test are placed in the chamber with the display facing out (as illustrated in Figure 2) and filled with fresh tap water. Air pressure is added from the top of the chamber via a standard bicycle pump (Velowurks Element floor pump.) Even though the relationship between pressure and indicated depth is well-known, several “calibration runs” were performed before the testing to verify repeatabilty of calibration. For these calibration runs, a Shearwater Perdix dive computer was used.

Pressure was released in a controllable way via an added vent valve. This ensured that the simulated ascent rates were not too fast. Figure 3. 

Fig. 3:. “Controlled Ascent” Valve

Figure 4 shows an actual profile using the test chamber.

Fig. 4: Screen Capture of Shearwater Perdix Computer used in “calibration runs”

A run list was prepared based on the dives described in Reference 2; see run list in Table 2.

CategoryProfiles – Number: Depth/Bottom Time
Single Dives#1: 12m/50 min
 #2: 18m/35mins
 #3: 30m/10 mins 
 #4: 12m/70 mins
Repetitive Dives#5: 12m /50mins -1hrSI 12m/50min
 #6: 18m /30 mins 1hr SI, 18m /20mins
 #7: 18m /30 mins 1hr SI, 18m /30mins
 #8:  30m/10min 1hr SI, 18m /30 mins
 #9: 18m /30mins 1hr SI 18m /20min, 1hr SI, 18m /20min
Deco Dives: #10 24m/30 mins with all required deco stops: Group H (11:04)
 #14 37m/30 with all required deco stops: Group L (16:50)
“Violation” Dives#11 18m /30mins no-deco dive with missed safety stop
 #12 24m/30 mins with omitted (all) deco stops
 #13 18m /30 ft w/ fast ascent ( ~15m/min) w/ 3 min safety stop
Table 2. Run List

Some of the dive times needed to be shortened, compared to the original dives in Reference 2; this is because the bottom times in the “old” no-deco dives exceeded the No Decompression Limits on some of the computers tested.  Since decompression dives were not tested in the DAN study in Reference 2, two dives profiles were added to the test matrix:  a “marginal” deco dive, profile #10 (US Navy Repetitive group H) and a deeper, more stressing deco dive, Profile 14 (US Navy Repetitive Group L).3   US Navy recommended No Fly Times are listed in the table. The specific bottom time for the marginal deco dive was chosen by what was required to make the most conservative of all the computers go into decompression mode.  The last category of “Violation Dives” was added to test claims made in some of the manufacture’s User Manuals.  The dive profiles in Table 2 were simulated and the displayed No Fly Time from each computer was recorded. The battery charge level was monitored for each computer and kept at acceptable levels. With the exception of the repetitive dives with a 1 hour surface interval, the interval between consecutive runs was the maximum of: 24 hours, desaturation time and the longest displayed NFT from any computer.

Results

A total of 26 runs were performed in this study; the raw results are shown in Table A1 in the Appendix.  To start off the testing,  Profile #2  was replicated several times to assess that the results were repeatable. For all of the runs, the water temperature varied from17C to 23C; when repetitive dives were simulated, the water was not completely replenished with new tap water, so the second (and third) dives of repetitive sequences tended to have a water temperature about 1-2 C warmer than the first. The ascent rate was monitored using several different dive computers, but the SEAC Guru displayed numerical values with units of ft/min; ascent rates were constantly monitored and were typically in the range of 5-15ft/min (1.5 -5 m/min). 

The results from Appendix A1 are summarized in Table 3. Based on this data, each of the eight dive computers can be assessed as to whether they are compliant with the DAN guidelines and if they actually compute what is described in their manuals. 

ComputerSingle DiveRepetitive DiveDeco Dive“Violation Dives”
Deepblu Cosmiq+12:0018:00Grp H: 12:00Grp L: 12:00Missed Safety Stop: 12:00Omitted Deco Stops: 24:00Fast Ascent: 12:00
Suunto EON Steel12:00- 19:34*19:09-24:17Grp H: 17:35-21:18Grp L: 26:13Missed Safety Stop: 12:00Omitted Deco Stops: 48:00 (locked)Fast Ascent:12:38
Oceanic VT4.024:0024:00Grp H: 24:00Grp L: 24:00Missed Safety Stop: 24:00Omitted Deco Stops: 24:00Fast Ascent: 24:00
Mares Icon12:00- 14:0824:00Grp H: 24:00Grp L: 24:00Missed Safety Stop: 12:00Omitted Deco Stops: 24:00Fast Ascent: 12:00
Cressi Cartesio24:0024:00Grp H: 24:00Grp L: 24:00Missed Safety Stop: 24:00Omitted Deco Stops: 48:00Fast Ascent: 24:00
SEAC Guru12:0024:00Grp H: 24:00Grp L: 24:00Missed Safety Stop: 12:00Omitted Deco Stops: 24:00Fast Ascent: 12:00
AquaLung i300C24:0024:00Grp H: 24:00Grp L: 24:00Missed Safety Stop: 24:00Omitted Deco Stops: 24:00Fast Ascent: 24:00
Garmin Descent MK124:0024:00Grp H: 24:00Grp L: 24:00Missed Safety Stop: 24:00Omitted Deco Stops: 48:00Fast Ascent: 24:00
Table 3. NFT Results Summary (hr:min) (Violations in Red, marginal discrepancies in Orange)

Discussion

Single Dives:

All of the computers were compliant with the DAN guidelines for this type of dive.  It was observed that both Mares and Suunto increased their NFT after the exact same single dive profile (#2) separated by a surface interval of ~ 44 hours. There is little documentation on the Mares RGBM variant, but the Sunnto variants are known to factor in the effects of multi-day diving in bubble growth (and presumably desaturation) calculations. This multi-day factor, known as “F3”, persists for up to 100 hours4, Figure 4. Multi-day diving is not covered in the DAN NFT guidelines.

Fig. 4: Description of Suunto RGBM and how it factors in repetitive dives, reverse profiles and multi-day diving into bubble growth calculations from Reference 4

Repetitive Dives:

All of the computers were compliant with the DAN guidelines for this type of dive.  For the Suunto EON Steel, since this computer based Repetitive NFT on desaturation times, the reported NFT depended on the exact nature of the repetitive dives and presumably the dives in the previous 100 hours.

Decompression Dives:

Two computers registered an NFT of less than 18 hours for the Group H deco dive: Deepblu Cosmiq+  required only 12 hours of NFT, and the Suunto EON Steel required a range of NFT from 17:35 to 21:18, (depending on previous dives and surface interval.) Note that in both User Manuals, they stated that NFT’s were based on internally-computed De-Sat times and not the DAN guidelines.  The Group L dive required significant total decompression time (~60 mins): all of the computers registered the same NFT as the Group H dive, except the Suunto EON Steel which increased the required NFT to 26:13 which is above the DAN guideline.   It should be noted that all computers registered NFT’s that exceeded that suggested by the US Navy for Repetitive group H3, however the Deepblue Cosmiq+ would fall short of the US Navy recommendation if used for deco dive having repetitive group I or more.

Violation Dives:

Some computers mentioned in their User Manual that they added an extra NFT penalty for ascent rate violations. Different computers defined “fast ascent violation” differently, so a target ascent rate of 50ft/min was used in Profile #13, which qualified as a fast ascent for all computers. Profile #13 was executed and the actual ascent rate varied from 9-15 m/min during the ascent from 18 to 5m, which took about one minute. A three minute safety stop at 5m was performed. None of the computers seemed to adjust the NFT, based on a comparison to similar dives with a nominal ascent rate, Profiles 2, 6a, 7a, 9a. Alarms did go off during the fast ascent from several computers. The Safety Stop may have been sufficient to satisfy all of each computers’ Dive Algorithms’ safety requirements. Similarly, none of the computers added an extra NFT penalty for dive Profile #11, which was a no-deco dive, with nominal ascent rate but missed safety stop.

For omitted stops on a deco dive (Run # 20, Profile 12), four computers added additional NFT time, compared to the same profile deco dives with all the required stops (Run # 17 profile 10.) See Table 4.

ComputerNFT for Deco Dive 10 w/ StopsNFT for Deco Dive 10 w/o Stops
Deepblu Cosmiq+12:0024:00
Suunto EON Steel17:35 – 20:4448:00 (Locked)
Cressi Cartesio24:0048:00
Garmin Descent MK124:0048:00
Table 4. NFT Penalty of Omitting Mandatory Deco Stops (times hr:mm)

User Manual Discrepancies:

It was noted that several computers did not conform with the NFT rules stated in their User Manual; see Table 5.

Dive ComputerUser Manual Discrepancy
Mares IconFor single dives, it displays the greater of 12 hours or the De-SAT time
Cressi CartesioDisplays 24 hour NFT for all dives including no-deco dives with safety stop
SEAC GuruDisplays 24 hour NFT for repetitive dives
Garmin Descent MK1Displays 24 hour NFT for all no-deco dives (omitted in manual)
Table 5. Observed discrepancies with User Manuals

Summary

Eight commercial dive computers were tested in a small pressure chamber to assess their computation and display of No Fly Times. All of the dive computers were found to be generally compliant with the standard DAN guidelines with a few exceptions. Several computers used a very simple rule for NFT: Garmin, Aqualung, Oceanic and Cressi simply displayed 24 hours NFT for all nominal dives (both no-deco and decompression).  Some computers added features that handled cases not covered in the DAN guidelines, e.g. multi-day diving (Mares and Suunto) and certain decompression guidance violations such as omitted decompression stops (Garmin, Suunto, Cressi and DeepBlu).

References

  1. https://www.diversalertnetwork.org/medical/faq/Flying_After_Diving
  2. Richard D. Vann, et al Experimental trials to assess the risks of decompression sickness in flying after diving”  Journal of Undersea and Hyperbaric Medicine, 2004
  3. US Navy Diving Manual, Version 7, 2016, Tables 9-7 and 9-6.
  4. Suunto Reduced Gradient Bubble Model. June 2003. Available from: http://www.dive-tech.co.uk/resources/suunto-rgbm.pdf. [cited 2017 August 29].

Appendix A. Raw Test Results by Run

Table A1. Raw data from each run
*Not a valid run. Computer was erroneously set to Gauge Mode
** Not a valid run. Prior to run, the SEAC conservatism factor was adjusted and this dive was considered a decompression dive. Given that the computer categorized this as a decompression dive, the NFT time displayed conformed to the DAN guidelines and is consistent with the User’s Manual.

Subsurface Goes Statistics

You wouldn’t be here if you didn’t enjoy quantitative analysis of anything diving. There is a special treat for you: Thanks mainly to Willem and Berthold of the Subsurface development team, you can now use Subsurface to do all kinds of statistics on you dive log. There are many cool graphical representations of looking at essentially any variable from your log (depth, duration, date, SAC, rating, visibility, gas use, oxygen or helium percentage, location, buddy etc etc) as functions of each other:

Go ahead and see how your SAC changes over time or which buddy you do the longest dives with or if you use less gas on dives with better visibility.

This is still an an alpha testing phase and crashes are still possible and things will change before the next upcoming release. But you can download a test version from our daily builds. There are also mobile version available from Testflight for iOS and the Google PlaysStore beta program. Please comment on the Subsurface mailing list or on Github if you find bugs or have ideas for improvement.

A measure for decompression stress

I was thinking what might be a good measure for decompression quality or stress. This also comes as O’Dive with their end user Doppler Device claim to provide exactly that in their mobile phone application. As said before, I have some doubts about their approach, so let’s try to come up with something better.

As always here on TheTheoreticalDiver, everything is entirely theoretical, I have zero empirical data of my own. But with this disclaimer, here we go:

I think we all agree on the fact that decompression stress comes arises as tissue pressure exceeds ambient pressure and that also the time of this excess pressure is relevant.

But measuring the excess pressure in mbar is probably not very useful as this is not a natural measure of decompression stress (and the relation might as well depend on the tissue under consideration as well as ambient pressure and a million other things). The gradient factor approach is to normalise this excess pressure with the maximally allowed excess pressure (which is the definition of the gradient factor) and this sounds like a good start.

But rather than comparing to plain vanilla 100/100 Bühlmann, I would like to be more flexible and compare to your decompression model of choice. So I would like to take

\(q(t) := max\left(0, \frac{p_i(t) -p_{amb}(t)}{p_{i,max}(t) – p_{amb}(t)}\right)\)

as a measure of momentary stress where p_i,max is the maximal allowed inert gas pressure in tissue number i as given by your decompression model.

This could be plain Bühlmann in which case this expression is just your momentary gradient factor. Or you believe in excess pressure being worse at depth (as the produced bubbles will grow later on in shallower water) then you take p_i,max as given by Bühlmann corrected by your favourite settings of GF_low and GF_high. Or you insist on using VPM-B then you use the maximal momentary M-value as predicted by that model. Strictly speaking this is an extension of that model for real (as opposed to planned) dives, but at least in Subsurface, we have found a way to compute it (such that it pretty much agrees on planned dives).

Obviously, if you decompress exactly as prescribed by you model, q=1 during decompression (possibly a bit lower due to the fact that most people decompress in steps of 10ft/3m rather than continuously). But

\(q\le 1\)

is the definition of not violating the ceiling.

The ceiling being what it is, violating it should be bad and the more the worse whereas staying way below the ceiling gives your additional conservatism which you probably have to pay in terms of extended decompression time.

So, my proposal would be to compute the L^lambda norm of the function q(t) for somewhat large lambda as this punishes going above q=1:

\(\Big(\int q^\lambda dt\big)^{1/\lambda}=\Big(\int max\left(0, \frac{p_i(t) -p_{amb}(t)}{p_{i,max}(t) – p_{amb}(t)}\right)^\lambda dt\big)^{1/\lambda}\)

To me, this seems to be a reasonable measure of deco stress. Maybe it’s worthwhile to compute this for a number of real profiles and compare it deco outcome (risk of DCS, I wish I had access to the DAN data… or at least Doppler results).

What do you think?

In defence of bar l

In a recent article in GUE’s InDepth blog, Richard Walker argues that the correct unit to discuss the amount of (free) gas in a cylinder is l (litre) and not bar l (bar times litre) because that is the correct unit for a volume.

I would like to argue that although the latter is correct the former isn’t: The volume of the gas is not its amount. The amount is measured by counting the number of molecules or (if you don’t like big numbers) the number of moles of gas. Let’s look at the ideal gas law, the mother of all gas calculations (and of course including Boyle-Mariotte):

\(pV=nRT\)

It’s the n on the right hand side (or nR depending on whether you count molecules or moles). As during diving, the temperature stays pretty much constant (or at least we don’t take changes in to account in our calculations) you could include that in the constant as well. Then the RHS (and thus the LHS) describes the diver’s version of amount of gas.

And that is not changed even when feeding it though a compressor (let’s still ignore the temperature change), when emptying the cylinder at the surface or when breathing it at 30m of depth at ambient pressure. This is the amount.

And you should measure it in the unit of this equation which is volume times pressure, which in SI derived unites is conveniently expressed in bar l.

Of course you can compute which volume this amount of gas fills at some pressure (be it 232 bar or 1 bar or 4 bar in the above examples), simply divide by that pressure. But when gas planning, you should plan the amount of gas you need (you will need it at different pressures) and that is measured (invariantly) in bar l.

I am sorry Rich, but I believe you are wrong here.

Gold

Nothing profound to say these days (in which I guess more people practice the theoretical side of diving). But yesterday, I was watching the first few episodes of season 3 of Money Heist (La casa de Papel, Haus des Geldes) on Netflix. And not only the professor is complaining that he had too little time to work out the plan, it seems this also applies to the script writers.

I am willing to forgive questionable approaches to tracking satellite phones and hacking into mobile phones. But when it comes to theoretical diving, there is a limit!!1!

I don’t want to spoiler too much, let’s just say, there is a flooded vault and they are diving to extract bars of gold:

Wasn’t anybody aware that the density of gold is almost twice the density of lead? A good delivery bar weights 12,4 kg, so the woman holding two of whose on stretched out arms has spent a lot of time in the gym. Also, swimming two of those to the exit it will be challenging to maintain neutral buoyancy…

When I was a student at DESY (the German particle accelerator lab in Hamburg), even in the theory building, we used lead blocks the size of half bricks as door stops, monitor mounts etc. Those came from the experimentalists who used those as means of radiation protection. The first time, you tried to pick up one of those, you got the impression it was screwed to the floor as your brain expected to pick up something they weight of a brick. But no, the density of concrete is about twice that of water while lead is about 11 kg per litre while gold is 19 kg per liter.

Rating decompression

How good was the deco of my dive? For those of us who strive to improve their diving this is a valid question to find ways to optimise how we get out of the water. In Subsurface, for example, we give various information including the individual tissues’ ceilings as well as the heat-map.

Recently, on ScubaBoard, I learned about a new product on the market: O’Dive, the first connected sensor for personalised dives. It consists of Bluetooth connected ultrasound Doppler sensor together with an app on your mobile phone. The user has to upload the profile data of the dive to the Subsurface cloud from where the app downloads it and connects it with the Doppler data (for this, it asks for your Subsurface username and password?!?, the first place where you might ask if this is 100% thought through). Then it displays you a rating (in percent) for your deco and offers ways to improve it.

That sounds interesting. The somewhat ambitious price tag (about 1000 Euros for the sensor plus 1,50 Euro per dive analysed), however, prevented me from just buying it to take it for a test. And since it’s a commercial device, they don’t exactly say what they are doing internally. But in there information material they give references to scientific publications, mainly of one research group in southern France.

A fraction is to conference proceedings and articles in very specialised journals that neither my university’s library nor the Rubicon Archive not SciHub have access to, but a few of the papers I could get hold of. One of those is “A new biophysical decompression model for estimating the risk of articular bends during and after decompression” by J. Hugon, J.-C. Rostain, and B. Gardette.

That one is clearly in the tradition of Yount’s VPM-B model (using several of the bubble formulas that I have talked about in previous posts). They use a two tissue model (fitting diffusion parameters from dive data) and find an exponential dependence of the risk of decompression on the free gas in one of the tissues:

Figure 2 from their paper

 Note, however, that the “risk of decompression sickness” is not directly measured but is simply calculated from the

\(PrT = P\sqrt t\)

paramour (P is the ambient pressure in bar during the dive while t is the dive time in minutes, i.e. a characterisation of a dive profile compared to which a spherical cow in vacuum looks on spot, but this seems to be quite common, see also https://thetheoreticaldiver.org/wordpress/index.php/2019/06/16/setting-gradient-factors-based-on-published-probability-of-dcs/) using the expression

\(r_{DCS} = 4.07 PrT^{4.14}.\)

which apparently was found in some COMEX study. Hmm, I am not convinced Mr. President.

The second reference I could get hold of are slides from a conference presentation by Julien Hugon titled “A stress index to enhance DVS risk assessment for both air and mixed gas exposures” which sounds exactly like what the O’Dive claims to do.

There, it is proposed to compute an index

\( I= \frac{\beta (PrT-PrT^*)}{T^{0.3}} . \)

Here PrT=12 bar sqrt(min), T the total ascent time and beta depends on the gas breathed: 1 for air, 0.8 for nitrox and 0.3 for trimix (hmm again, that sounds quite discontinuous). As you might notice, what does not go into this index is at which depths you spend your ascent time while PrT keeps growing with time indefinitely (i.e. there is no saturation ever).

This index is then corrected according to a Doppler count (which is measured by a grade from 0 to 5):

Index correction according to Hugon teal

This corrected index is then supposed to be a good predictor for the probability of DCS.

I am not saying that this is really what is going on in the app and the device, these are only speculations. But compared to 1000 Euro plus 1,50 Euro per dive, looking at ceilings and heat map in Subsurface sounds like quite good value for money to me.de