probability | John Clarke Online

Professional Diving, Truth, and the Uncertainty Principle

Is anything known for sure?

Heisenberg’s Uncertainty Principle applied to quantum events avows that there is no certainty until you look. Well, this morning, I looked, and I’m just as confused as ever.

It was a chilly morning in late November. As we warmed up with coffee, I wondered how cold it was outside. So, in the modern style, my wife and I checked the Weather Channel on our phones. One indicated it was 47°F, but the other showed it was 48°F.

That can’t be, I said. So, with identical phones side by side, both tuned into Panama City Beach, Florida weather on the Weather Channel, one phone said it felt like 45°F, and the other said it felt like 43°F.

As Charlie Brown would say, “Good grief.”

Wanting to find some agreement among our devices, I checked a nested set of humidity and temperatures sensors grouped together in our kitchen. Humidity indicators are notoriously inaccurate, yet amazingly, the measured humidity was in reasonable agreement. But inside temperature varied from 70.3°F to 72.8°F.

According to Segal’s Law, “A man with a watch knows what time it is. A man with two watches is never sure.”

This aphorism is falsely attributed to Lee Segall of KIXL, now KGGR in Dallas. Regardless of the source, it is often repeated because it makes such good sense. If you multiply the number of devices three times, as above, the situation is no more precise. (But that’s where statistics comes in, I suppose.)

Giving up on simple things like local environmental parameters, I turned to the latest news on the VAERs update for the vaccines.

I wish I hadn’t. Yes, there is a chance you’ll be fine, but there’s also a small chance you’ll have heart problems and even a small chance you’ll die.

Frankly, my one-time shot at slot machines and the roulette table in Vegas did not end well. So, is there anything we know that can be guaranteed accurate?

Diving

I’ve spent a long Navy career in diving science, so I know there are serious certainties there. If you consume more air than is in your scuba tank, you’ll drown. If you stay down too long and surface too quickly, you’ll get the bends, aka decompression sickness.

But what if I use a decompression computer to plan my dive and follow its guidance to the letter? Unfortunately, there’s still a chance you’ll end up in a treatment chamber. Both people’s health and the water environment change constantly, and no decompression algorithm is perfect, or omniscient.

From an engineer’s perspective, the tensile strength of a bolt is known within strict limits. If the force applied to that bolt exceeds its limits, then bad things might happen. Buildings might fall, or planes might crash. Or your muffler might fall off.

It’s hard to know what the effect of a broken bolt will be unless you understand precisely the function of that bolt. There is uncertainty in the outcome of a bolt breaking.

Uncertainty vexes some engineers to no end. I’ve watched them squirm as I reveal the role of statistics and probability in acceptance decisions about diving equipment. People are not bolts whose tensile and shear strength can be measured. As Heisenberg predicted (out of context), a dive outcome cannot be predicted with certainty.

Equipment Testing

The same thing applies to diving equipment. The Navy Experimental Diving Unit is entrusted with determining the safety and suitability of underwater breathing apparatus. Both physiologists and engineers envision a line in the sand for a given water depth and diver breathing rate.

If a UBA exceeds that line during testing, it should be rejected for military use. Right? After all, a limit is a limit.

Test and Evaluation Laboratory, Navy Experimental Diving Unit, Panama City, Florida. Photo by Stephen Frink.

Well, not exactly. When translating engineering limits into human terms, things get messy. If a published limit is exceeded, just like taking the COVID vaccine, some people will fare well, while others may pass out. In other words, failure is classified as the probability of an untoward event where untoward translates to anything that threatens a diver or a diving mission.

For any given dive, and any given diver, the probability of a dive failure cannot be known precisely. Dive failure, like decompression sickness, is probabilistic.

One type of untoward event: Ice inside a second-stage scuba regulator.

To illustrate, the following table and text are from NEDU Technical Report 16-04, Physiological Event Prediction in Evaluations of Underwater Breathing Apparatus, October 2016.

Usually, a UBA evaluated at NEDU is suitable for most diving depths and any foreseeable work/ventilation rate, as shown in Table 1.

The only time that limits were exceeded was at the greatest depth and ventilation rate.

But what if the data had revealed a slightly larger “out of limits” region, as in the next table? What decision regarding safety would then be made?

In this hypothetical case, human judgment is required. It is not sufficient to declare the diving equipment unsafe for use. It simply means divers need to pace themselves when working and breathing hard near a depth of 200 feet. Reducing their workload enough to slow their breathing to 62 liters per minute or less (still a high ventilation rate) is a safe way to keep the UBA within limits.

This is nothing new. Every salvage diver knows to occasionally interrupt hard work periods with periods of rest. Catching your breath is kind of important.

Limits are not absolute

As a person with too many watches, or thermometers can attest, you can’t be sure what all the various goal numbers and limit numbers mean. Instead, collectively they should be used as a guide to safe diving.

Whether you’re a sport diver or professional, if an underwater breathing apparatus is functioning normally but doesn’t meet all of the EU (EN250) or U.S. Navy engineering limits under all possible testing conditions, that doesn’t mean it’s not a useful piece of diving gear. You just have to use it judiciously. After all, good human judgment is always required for safely operating life support equipment.

It is a wise diver who remains mindful of their life support system’s limitations and plans their dive to stay within those limitations. That way, the probability of experiencing an untoward event is minimized.

Maintaining Your Respiratory Reserve

The following is a reprint from InDepth: Digital Scuba Diving Magazine by Global Underwater Explorers.

Published on September 6, 2019 By InDepth

by John Clarke

“*JJ on his JJ*.” *Photo by Andreas Hagberg.*

Just like skeletal muscles, respiratory muscles have a limited ability to respond to respiratory loads. An excellent example of this is a person’s inability to breathe through an overly long snorkel (Figure 1.) Our respiratory muscles simply aren’t strong enough to overcome the pressure difference between water depth and the surface.

*This doesn’t work. Her respiratory muscles are not strong enough.*
Illustration by Cameron Cottrill.

The primary respiratory muscle is the diaphragm, (the brown organ lying below the lungs in Figure 2.) The diaphragm is designed for low-intensity work maintained 24/7 for the entirety of your life.

Like the heart muscle, its specialty is endurance. When called upon to maximally perform, the diaphragm needs assistance.

That assistance is provided by the accessory respiratory muscles, primarily the intercostal muscles linking the ribs within the rib cage.

*The human diaphragm separating the lungs from the abdominal cavity. Graphic by John Clarke.*

Unless you’re reading this while running on a treadmill, your body is probably idling. Your heart is beating rhythmically, your diaphragm is methodically contracting and relaxing. But, if some dire event were to happen, you would be primed for action. If you needed to react to an emergency, your heart and lungs would race at full speed.

The difference between idling and full-speed capability is called physiological reserve, which in turn is divided into its components; cardiac, muscular, and ventilatory reserve. As drivers, pilots, and boat captains will attest, it’s always good to have fuel reserves. Likewise, physiological reserve is good to have in abundance.

The Dive

The following is an imaginary tale of a young, blond-haired hipster drawn to the Red Sea for a deep dive. He chose to dive on the wall at Ras Mohammed on the Eastern Shore of the Sinai, which descends quickly down to a thousand feet and beyond. That was his target—1,000 feet.

The previous year he bought a rebreather so gas usage should not be a problem for his deep dive. He also sprang for the cost of helium-oxygen diluent. Trimix would have been cheaper, but he spared no expense. Nothing but the best. To that end, he used loose-fill, fine grain Sodalime in his CO2 scrubber canister.

These were his thoughts as he descended.

Free-falling at three hundred feet. Never been this deep before. The water’s getting cold, so the warm gas from the canister feels good.

800 feet. Wow, the gas is thicker now.

When he reached the bottom, he realized something wasn’t right. He sucked harder and harder, feeling his full face mask collapsing around his face with each inhalation. He was “sucking rubber,” feeling like he was running out of gas, but his diluent pressure gage still read 1800 psi.

Unconsciously, he compensated for the respiratory load by slowing his breathing—easing his discomfort. Concerned, he briefly switched to open circuit bailout gas, but that didn’t feel any better. In fact, it was worse, so he switched back to the bag.

Surprisingly, he couldn’t get off the bottom. In fact, he was slipping further downslope. He needed to drop weights, but they were integrated. He fumbled with his vest, trying to remember how to release the weights, but he couldn’t work it out.

He found the pony bottle to inflate his integrated BC, but after a second’s spit of air, it stopped filling. He would have to swim off the bottom. As he struggled to swim upwards in the darkness, and without bubbles to guide him, he wasn’t sure which way was up.

His heart was beating at its maximum rate, trying to force blood through his lungs, but he couldn’t force enough gas in and out of his lungs to clear his bloodstream of its increasingly toxic CO2 load. The build-up of CO2 in the arterial blood was clouding his thinking. The CO₂ was making him want to breathe harder, but he couldn’t. The feeling of breathlessness—and impending doom—was overwhelming.

————

The accident investigation on the equipment was inconclusive. The dive computer had flooded, but that was irrelevant. Surface pre-dive checks were passed. The rebreather seemed to function normally when tested in a swimming pool. The investigators convinced a Navy laboratory to press the rebreather down to 1,000 feet, but nothing abnormal was found other than a slight elevation of controlled PO₂.

The Analysis

An asthma attack can kill by narrowing the airways in the lung, making the person suffering the attack feel like they’re sucking air through a clogged straw.

A healthy diver doesn’t have airways that constrict, but gas density increases with depth, causing the same effect as a narrowed airway. It becomes increasingly difficult to breathe as depth increases. A previous InDepth blog post on gas density discusses this subject.

Normal human airways compared to airways during an asthma attack. Graphic courtesy of Asthma and Allergy Foundation of America.

If the strength of respiratory muscles is finite, just as it is for all muscles, then any load placed on those muscles will eat away a diver’s “respiratory reserve.” From the diaphragm’s perspective, the total loading it encounters is divided between that internal to the diver and that external to the diver. As gas density increases, internal loading increases. A rebreather is external to the body, so flow resistance through a rebreather adds to the total load placed on the respiratory muscles. If the internal resistance load increases a lot, as it does at great depth, there is very little reserve left for external resistance, like that of a rebreather.

In this fictional tale of a hapless diver, he needlessly added respiratory resistance by using fine-grain Sodalime in his scrubber canister. Compared to large grain Sodalime, such as Sofnolime 408, fine-grain absorbent adds scrubber duration, but it also increases breathing resistance. It thus cut into the diver’s ventilatory reserve.

This fictional diver exceeded his physiological reserves by,

not understanding the effect of dense gas on the “work of breathing,”
not understanding the limitation of his respiratory muscles, and
by not realizing the “best” Sodalime for dive duration was not the best for breathing resistance.

He also didn’t realize that a rebreather scrubber might remove all CO2 from the expired gas passing through it, but it is ventilation (breathing) that eliminates the body’s CO₂ from the diver’s bloodstream. Once CO₂ intoxication begins, cognitive and muscular ability quickly decline to the point where self-rescue may be impossible.

Lessons from The U.S. Navy

Considering the seriousness of the topic, it is worthwhile to review the following figures prepared for the U.S. Navy.

First, we define peak-to-peak mouth pressure, a measure of the pressure exerted by a working diver breathing through the external resistance of a rebreather. Total respiratory resistance for a diver comes in two parts: internal and external. In the following figures, those resistances in the upper airways are symbolized by a small opening, and in the external breathing apparatus, by a long, narrow opening representing a UBA attached to the diver’s mouth.

*High external resistance. In this case, the difference between mouth pressure and ambient water pressure is called ΔP1* Credit with modifcation: “*Direct measurement of pressures involved in vocal exercises using semi-occluded vocal tracts”*.

*Low external resistance. The difference between mouth pressure and ambient water pressure is called ΔP2.* Credit with modification: “*Direct measurement of pressures involved in vocal exercises using semi-occluded vocal tracts”*.

*Mouth pressure waveforms ΔP1 and ΔP2 during breathing with high (P1) and low (P2) external resistance.*

This author reviewed over 250 dives by Navy divers at the Naval Medical Research Institute and the Navy Experimental Diving Unit. These were working dives involving strenuous exercise at simulated depths down to 1500 feet seawater, using gas mixtures ranging from air to nitrox and heliox. Gas densities ranged from about 1 gram per liter (g/L) (air at the surface) to over 8 g/L. Each dive was composed of a team of divers, so each plotted data point had more than one man-dive result included. An “eventful” dive was one where a diver stopped work due to loss of consciousness, or respiratory distress (“dyspnea” in medical terminology.) They were marked as red in the following figure. Uneventful dives were marked in black.

Using a statistical technique called maximum likelihood, the data revealed a sloping line marking a boundary between eventful and uneventful dives.

*Peak-to-peak mouth pressure and gas density conspire to increase a diver’s risk of an “event” during a dive.*

The fact that the zero-incidence line sloped downward illustrates the fact that the higher the gas density, the greater the respiratory load imposed on a diver by both internal and external (UBA) resistance. The higher that load, the lower the diver’s tolerance to high respiratory pressures.

By measuring peak-to-peak mouth pressures, we are witnessing the effect of UBA flow resistance at high workloads. It does not reveal the flow resistance internal to the body. However, when gas density increases, internal resistance must also increase.

The interrupted lines in the figure illustrate lines of estimated equal probability of an event. The higher the peak-to- peak pressure for a given gas density, the higher the probability of an eventful dive.

Figure 7 suggests that at a gas density of over 8 grams per liter, practical work would be impossible. The only way to make it possible would be to reduce gas density by substituting helium for nitrogen, or substituting hydrogen for helium, and then doing as little work as possible to keep ΔP low.

For our fictional 1,000 foot diver, the gas density would have been between 6 and 7 grams per L. Using a rebreather, there would be virtually no physiological reserve at the bottom. Moderate work against the high breathing resistance at depth would be very likely to result in an “eventful” dive.

Image Citation for medical graphics: Robieux C, Galant C, Lagier A, Legou T, Giovanni A. Direct measurement of pressures involved in vocal exercises using semi-occluded vocal tracts. Logoped Phoniatr Vocol. 2015 Oct;40(3):106-12. doi: 10.3109/14015439.2014.902496. Epub 2014 May 21. PMID: 24850270.

John Clarke, also known as John R. Clarke, Ph.D., is a Navy diving researcher in physiology and physical science. Clarke was an early graduate of the Navy’s Scientist in the Sea Program. During his forty-year government career, he conducted physiological research on numerous experimental saturation dives. Two dives were to a pressure equivalent to 1500 fsw.

For twenty- eight years he was the Scientific Director of the Navy Experimental Diving Unit.

Clarke has authored a technothriller-science fiction series called the Jason Parker Trilogy. All three volumes, Middle Waters, Triangle, and Atmosphere, feature saturation diving from depths of 100 feet to 2,500 feet. The deepest dives involve hydreliox, a mixture of helium, hydrogen and oxygen. UFOs, aliens, and an uncaring cosmos lay the framework for political and human intrigue both on and off-planet.

Although now retired, Clarke has worked for NEDU as a Scientist Emeritus. He now runs a consulting company, Clarke Life Support Consulting, LLC. He helps various companies, when he isn’t writing about diving, aviation, and space. His websites are www.johnclarkeonline.com and www.jasonparkertrilogy.com. His thriller series is available at Amazon and Barnes & Noble.

Related Blog Posts – Further Reading for Rebreather Divers

How Much is Too Much? (Carbon Dioxide – The Diver’s Nemesis)

Knock Yourself Out (Carbon Dioxide – The Diver’s Nemesis)

How Long Will Your Rebreather Scrubber Canister Last?

Does Your Rebreather Scrubber Operate in Its Goldilocks Zone?

A Look Inside Rebreather Scrubber Canisters, Part 1

Carbon Dioxide – The Diver’s Nemesis Pt. 1 (Meduna’s Mixture)

A Look Inside Rebreather Scrubber Canisters, Part 2

My Respiratory System is So Embarrassed

Eating Crow – Safe Water Temperatures for Scuba Regulators

Scientists and engineers love to argue, and unlike the case with politicians, compromise is not an option. Technologists speak for nature, for the truth of a universe which does not speak for itself. But when a technologist is wrong, they usually have to eat some crow, so to speak.

Stephen Hawkings, the famous cosmologist, freely admits his brilliant doctoral dissertation was wrong. Crow was eaten, and Hawkings moved on to a better, arguably more correct view of the universe.

Now, on a much less grand scale, this is my time for eating crow.

There has been quiet disagreement over the water temperature above which a scuba regulator is safe from free-flowing or icing up. Those untoward icing events either give the diver too much gas, or not enough. Neither event is good.

Based upon an apocryphal Canadian government study that I can’t seem to put my hands on anymore (government studies are rarely openly available), it has long been believed by the Canadians and Americans that in water temperatures of 38°F or above, regulator icing problems are unlikely. That temperature was selected because when testing older, low flow Canadian regulators, temperatures inside the regulator rarely dropped below 32°F when water temperature was 38°F.

As shown in an earlier blog post, in 42°F water and at high scuba bottle pressures (2500 psi) in instrumented second stage regulators (Sherwood Maximus) second stage internal temperature dropped below zero Celsius (32°F) during inspiration. During exhalation the temperature rose much higher, and the average measured temperature was above freezing. Nevertheless, that regulator free flowed at 40 minutes due to ice accumulation.

Presumably, a completely “safe” water temperature would have to be warmer than 42°F. But how much warmer?

My European colleagues have stated for a while that cold water regulator problems were possible at any temperature below 10°C, or 50°F. However, as far as I can tell that assertion was not based on experimental data. So as we began to search for the dividing line between safe and unsafe water temperatures in another brand of regulator, I assumed we’d find a safe temperature cooler than 50°F. For that analysis, we used a generic Brand X regulator.

To make a long story short, I was wrong.

To understand our analysis, you must first realize that scuba regulator freeze-up is a probabilistic event. It cannot be predicted with certainty. Risk factors for an icing event are diving depth, scuba bottle pressure, ventilation (flow) rate, regulator design, and time. In engineering terms, mass and heat transfer flow rates, time and chance determine the outcome of a dive in cold water.

At NEDU, a regulator is tested at maximum anticipated depth and ventilated at a high flow rate (62.5 L/min) for a total period of 30 min. If the regulator free flows or stops flowing, an event is recorded and the time of the event is noted. Admittedly, the NEDU test is extremely rigorous, but it’s been used to select safe regulators for U.S. military use for years.

Tests were conducted at 38, 42, 45 and 50°F.

Next, an ordinal ranking of the performance for each regulator configuration and temperature combination was possible using an NEDU-defined probability-of-failure test statistic (P_f). This test statistic combines the number of tests of a specific configuration and temperature conducted and the elapsed time before freezing events occurred. Ordinal ranks were calculated using equation 1, where n is the number of dives conducted, E is a binary event defined as 0 if there is no freezing event and 1 if a freezing event occurs, t is the elapsed time to the freezing event from the start of the test (minutes), and k is an empirically determined constant equal to 0.3 and determined to provide reasonable probabilities, i is the index of summation.

Conshelf XIV pic 2 — Click for a larger image.

Each data point in the graph to the left represents the average result from 5 regulators, with each test of 30-min or more duration. For conditions where no freezing events were observed at 30 min, additional dives were made for a 60-min duration.

As depicted, 40-regulator tests were completed, using 20 tests of the five primary second stages and 20 octopus or “secondary” second stages. Regression lines were computed for each data set. Interestingly, those lines proved to be parallel.

file0001735338997 — A second stage of a typical scuba regulator. The bite block is in the diver’s mouth.

The “octopus” second stage regulator (the part going in a scuba diver’s mouth) differed from the primary only by the spring tension holding the regulator’s poppet valve shut. More negative mouth pressure is required to pull the valve open to get air than in the primary regulator.

The test statistic does not provide the probability that a given test article or regulator configuration will experience a freezing event at a given temperature. However, it does provide the ability to rank the freezing event performance of regulator configurations at various temperatures.

Our testing reveals that in spite of my predictions to the contrary, for the Brand X regulator our best estimate of a “safe” water temperature, defined as Pf = 0, is roughly 53°F for the standard or “primary” second stage regulator and 49° F for the octopus or secondary regulator.

For all practical purposes, the European convention of 50°F (10°C) is close enough.

Eating crow is not so bad. Some think it tastes a little like chicken.

Equation 1 came from J.R. Clarke and M. Rainone, Evaluation of Sherwood Scuba Regulators for use in Cold Water, NEDU Technical Report 9-95, July 1995.

On the Odds of Being Struck by Falling Satellites

uars-pre-deployment — UARS satellite before deployment. Photo credit: NASA Johnson Space Center.

NASA says the odds that someone will be struck by falling space debris when the bus-sized NASA Upper Atmosphere Research Satellite comes down this week is 1 in 3200. Which got me to thinking … if I was struck while out walking Friday night, would I be unusually lucky because I beat the odds, or unlucky because I beat the odds?

Would my life insurance company pay off? Arguably it would not be an act of God, or an act of war, so I think the insurance company should pay. But I really don’t know if they would; admittedly, I don’t have a falling space debris clause in my policy. (As the space around our planet becomes increasingly crowded, perhaps space debris insurance would be a good investment.)

Now if the odds were 1 in 3200 for each of us, can you imagine the chaos? That would be a mass casualty event in the making. Those odds would be much higher than the odds of being killed by almost anything else I can think of.

: From Dr. Strangelove. Click to activate the video.

I suspect there would be anti-NASA marches on the capitols of all the nations affected, which would be most of the world’s nations, by people demanding we nuke the satellite before it poses a hazard. Or maybe they’d demand we send space cowboys up to guide the careening space bus to a safer impact. (I’m not sure how those heroic bronco busters would get back; maybe they’d ride it down a la Dr. Strangelove.)

Fortunately, the odds are mighty small (1 in 21 trillion) that you or I would be hit by this particular satellite. There are much greater chances of winning a state lottery.

But assuming a piece did actually hit me without putting a hole through my head or chest, maybe simply winging me, could I profit from it? Would I become an instant celebrity? Would there be book deals? Can you imagine the television talk show questions, like “How did you feel about your impending death when you saw the fire ball heading your way?”

Let’s face it, with burning metal hurtling to Earth at 18,000 miles per hour I likely wouldn’t see it in time to react, and if I did see it, I undoubtedly wouldn’t have time to mentally compute its trajectory. Should I stand still or run? In fact, I think that calculation would be impossible. An incoming missile simply gets larger and larger in your field of view, giving you perhaps just enough time to say “Oh…” but not enough time to finish the four letter expletive you had intended.

But frankly, I’m not at all concerned. If it happens at all, it wouldn’t happen to me. It always happens to the other guy. Which I’m sure is what the insurance companies are hoping – it will be the other guy, and the other guy will be uninsured.

If pressed, I suppose I could see the insurance company’s point; If I did get squashed by supersonic satellite debris it probably would be an act of God.

Now, I’m trying to think, have I done anything to tick Him off lately?