Having recently criticized Tristan Gooley’s explanation of the tides, I felt obliged to try to do better myself. It’s a tricky job, and there are many partial and misleading explanations out there. So here goes.
Tides happen to anything that is orbiting in a gravitational field. I’m going to hone down on the Earth in a minute; but first, an orbit:
Click to enlarge
The orbiting body (“the satellite”) would travel in a straight line if no force was being applied to it. But it is under the influence of the gravity of the central body (“the primary”). The force of gravity pulls the satellite into a curved path around the primary. For a range of speeds, this causes the satellite’s path to curve enough to make it loop right around the primary and then repeat itself. (If the satellite is moving too slowly, its curved path will come close enough to hit the primary; too quickly, and the loop will never close, allowing the satellite to escape.)
In the diagram, the satellite has precisely the right speed to move in a circular orbit at a constant distance from the primary. The primary’s gravity pulls the satellite radially inwards with a force of constant magnitude. This generates an acceleration of constant magnitude, indicated by the blue arrow. Since the acceleration is always at right angles to the satellite’s motion, the satellite’s speed doesn’t change, only its direction of travel. This induces a constant curvature in the satellite’s path, which makes it circle endlessly.
Click to enlarge
For simplicity, I’m going to deal with only circular orbits from now one, but the logic of the tides applies equally well to all orbits.
The model of a satellite whirling in circles around a stationary central body is good enough for any satellite with a mass that’s very low compared to its primary—like the International Space Station in orbit around the Earth, for instance. But if the satellite’s mass is comparable to the primary’s, then the primary has to follow an orbit too:
Click to enlarge
While the satellite follows a large circle, the primary moves in a small circle so that the two bodies staying exactly opposite each other on either side of their common centre of gravity, which is called the barycentre (from Greek barys, “heavy”). I’ve marked it with a little cross in the diagram. Since primary and satellite both complete one orbit in the same time, the primary has a lower speed and a smaller radial acceleration, which is provided by the weaker gravity of the less massive satellite. Like a fat man balancing a child on a see-saw, the more massive primary, huddled close to the barycentre, is in balance with the lightweight satellite moving in its more distant orbit.
The Earth-Moon system has a barycentre that is actually inside the Earth. While the Moon sweeps out its month-long orbit, the Earth describes a gentle wobble during the same time period, with its centre alway on the opposite side of the barycentre from the Moon:
Click to enlarge
The centre of the Earth is therefore always accelerating gently in the direction of the Moon as it moves around its small balancing orbit.
What may not be intuitively obvious is that at any given moment every point on the Earth’s surface and within its bulk must have exactly the same acceleration (in magnitude and direction) as the centre of the Earth does. If that didn’t happen, then the various bits of the Earth would acquire relative velocities, and the Earth would change shape. (To be strictly accurate, a little relative acceleration is allowed, as the Earth flexes under the influence of the Moon’s gravity, but the net acceleration must average out to zero over time.)
Click to enlarge
Even with that logic in place, it’s still a little difficult to see immediately why a point on the Earth’s surface on the opposite side of the barycentre from the centre of the Earth should be accelerating away from the barycentre, when the centre of the Earth is accelerating towards it.
The explanation is that every point on the Earth is tracing out its own circle in space, the same size as the Earth’s orbit around the barycentre, but displaced from it. To see how that works, let’s stop the rotation of the Earth (diagrammatically) and trace the path of a single point on its surface (marked in purple) during the course of a month.
Click to enlargeClick to enlarge
The acceleration of the purple point is always directed towards the centre of its own (purple) circle, even though it may be directed away from the barycentre. The rotation of the Earth doesn’t make any difference to this argument—the instantaneous accelerations remain the same, they’re just handed off to different points on the surface of the Earth as it rotates.
(If you’re having trouble visualizing the circular movement of the non-rotating Earth depicted in the diagram, put a coin flat on a table, put your finger on the coin, and slide the coin around in a small circle.)
So the blue acceleration arrows show what the Earth is actually doing during the course of a lunar orbit. But does the Moon’s gravity apply forces in the right direction, and of the right magnitude, to make the Earth accelerate smoothly throughout its volume in this way?
No, it doesn’t. There are two problems:
1) The Moon’s gravity decreases with distance. While it pulls on the centre of the Earth with just the right force to induce the necessary acceleration to keep the Earth in its orbit around the barycentre, it pulls a little harder on the near side of the Earth, and a little too weakly on the far side.
2) The Moon’s gravity is a central force—it radiates out from the centre of the Moon. So it’s directed a little diagonally when it pulls on parts of the Earth that don’t lie exactly on the line connecting the centres of the Earth and Moon.
That’s all shown in this diagram, with the green arrows representing the force of the Moon’s gravity laid on top of the blue arrows representing the true acceleration:
Click to enlarge
There’s a mismatch, everywhere but at the centre of the Earth, and the difference between the applied force and the necessary force (for uniform acceleration) must be generated by internal forces within the substance of the Earth. The nature of the mismatch between applied force and real acceleration is shown with red arrows below:
Click to enlarge
These residual forces are called tidal forces, and so at last I’ve arrived at the cause of the tides. The Earth is being stretched along an axis that runs through the Moon and the barycentre, and squeezed inwards in a plane at right angles to that axis. (Even though I’ve built this argument around the Earth and its small barycentric orbit, this is a completely general result—it applies to all bodies in orbit around other bodies. They all experience tidal forces of this sort. In fact, it should be evident that it applies equally to bodies that aren’t even in orbit, but are just falling towards each other, or even sitting next to each other—all that’s required for these internal tidal forces to show up is for an object to be maintaining its shape against the forces produced by a central gravitational field.)
Now, if the Earth was a hunk of solid metal, held together by its internal chemical bonds, it would develop a bit of tension along the “stretch axis”, and compression in the “squeeze plane”. Those internal forces would oppose the tidal forces, and ensure that all the parts of the Earth moved together with uniform acceleration.
But objects on the scale of planets aren’t held together primarily by chemical bonds—what keeps them together is their own gravity, and they settle into an equilibrium shape that evens out internal pressures. The red arrows in the diagram show that the Moon’s gravity opposes the Earth’s own gravity along the “stretch axis”, and supplements it in the “squeeze plane”. This slight alteration in the local gravitational force means that the solid body of the Earth shifts slightly in shape in order to equalize its internal pressures.
The same thing happens to the oceans—they pile up under the reduced gravity of the “stretch axis”, and squash down under the increased gravity of the “squeeze plane”:
Click to enlarge
And that’s where tides come from, and why there are two tidal bulges in the ocean, one under the Moon and one opposite it.
As the Earth rotates, it carries us past each tidal bulge in turn, so there are two high tides per day. Or, actually, not quite. By the time the Earth has completed one full rotation, the line between Earth and Moon has shifted a little, and the tidal bulge has shifted with it. The Earth therefore needs to rotate for another 50 minutes at the end of each day, in order to catch up with the position of the tidal bulges:
Click to enlarge
So instead of experiencing a high tide every 12 hours, we get one every 12 hours and 25 minutes.
The situation is actually (you guessed it) a little more complicated—the presence of landmasses distorts the even flow of water suggested in my diagram; the Sun produces its own tidal bulges; and the inclination of the Moon’s orbit to the Earth’s equator introduces its own complexities.
Our journey will begin, like so many great explorers before us, in the kitchen.
Tristan Gooley is, according to his website, a “natural navigator”—by which he means that he navigates using nature, not that he’s just intrinsically good at navigating. He set out his stall with his first book, appropriately entitled The Natural Navigator, which is all about navigating using the sun and stars, the land and water, the plants and animals. And Gooley is an equal-opportunities naturalist—he’s quite prepared to navigate around town using the orientation of satellite TV dishes (they generally point southeast in the UK) and the route of helicopters (they’re legally required to avoid over-flying built-up areas as much as possible, so have a tendency to follow rivers through the city).
How To Read Water is his third book about natural navigation, a successor to the compendious The Walker’s Guide to Outdoor Clues and Signs. As the title suggests, this one zeroes in on water in the environment—and, in trademark style, Gooley is just as happy picking up directional clues from the behaviour of ships as he is from the distribution of puddles. He’s also refreshingly relaxed about what “natural navigation” actually means to the people who read his books—he knows that most of us are going to read this stuff out of curiosity about the outdoor environment, and few will actually throw away their GPS and compass. That’s fine with Gooley—although the book is loosely structure around the “natural navigation” concept, what shines through is a simple delight in just being out in the world, with a heightened awareness of the subtle cues that nature always provides.
The subtitle hints at the structure of the book—Clues, Signs and Patterns from Puddles to the Sea. Gooley starts small, with a glass of water in the kitchen, and expands the view steadily from puddles to rivers to lakes to ocean waves, currents and tides. Interspersed are digressions on the sound of water, the behaviour of fish, navigating at sea using the stars, the marking of ship navigation channels, and many other things.
Indeed, it begins to feel like a bit of a rag-bag. There has to be a diminishing return to this sort of book, and with this third volume I occasionally felt that Gooley was casting around for almost any unused material that he could roughly align with the concept of “water”. The chapter entitled “Rare and Extraordinary” is a case in point, containing a wild assortment of briefly noted phenomena that have something to do with water, but not much to do with navigation—for example, it includes short notes on flying fish, braided rivers, and amphidromes (points in the open ocean that experience a back-and-forth or round-and-round tidal flow, rather than a change in water level). He even mentions the green flash, an atmospheric optical phenomenon which has essentially nothing to do with water at all, and he addresses it so briefly that you can find out much more about it from my own humble offering on the topic. It’s not clear to me why this chapter is included at all.
But the book has taken on such a wide remit that I think there’s something here for everyone, although I also suspect that most readers will encounter a chapter or two that they find themselves skipping through in frustration. (For me, that was the chapter entitled “Shipwatching”.)
That aside, there are two undoubted delights to be had. One is finding out something entirely new, as I did when Gooley discussed the anatomy of a beach, and the origin of rips and undertows. The other (perhaps even more satisfying) is encountering something that you have been vaguely aware of for a long time, but which Gooley sets out in clear detail—a definite “Ah-ha!” moment. For me, that moment came during Gooley’s discussion of the anatomy of rivers. As a hillwalker, I’ve been crossing upland rivers for decades, and am often successful at finding a safe crossing-place over even initially unpromising-looking volumes of water. What I’m doing, it turns out, is exploiting a natural alternation in rivers between riffle and pool—I’m unconsciously seeking out the rapidly moving shallow sections (“riffles”) that are easier to cross than the deeper, slower pools. I’ve also long had an aversion to starting a river crossing on the inside of a meander loop, aware that I’m likely to find myself wading into deeper water as I progress. Gooley explains this phenomenon in terms of the thalweg, the line of maximum flow, which tends to stray towards the outer bank of a curving river.
And I learned some new words, which any reader of this blog will know is a Fine Thing. For instance, the tendency of some deciduous trees to retain their brown leaves throughout the winter (think of all those messy beech hedges, stuffed with dead leaves) is called marcescence. Which, I find after a bit of my own research, comes from the Latin marcere, “to be faint or languid”.
Occasionally things go wrong. If “a cube of water as tall and deep as the average person” weighs “almost three tonnes”, then an average person is about 1.4 metres tall (around 4 feet 7 inches). And I found the explanation of tides a little garbled, mixing gravity and centrifugal force in a way that wasn’t at all clear.
But over all, as with his previous books, there’s much to delight and enlighten. It’s an entertaining gallop through the complexities of hydrodynamics. On which topic, I’ll sign off with a statement attributed (perhaps apocryphally) to the physicist Horace Lamb, which Gooley quotes appreciatively:
I am an old man now, and when I die and go to Heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. About the former I am rather optimistic.
Horace Lamb, at a British Association meeting in 1932
Clear skies here, chez Oikofuge, for Monday’s transit of Mercury, the first in almost ten years.
Mercury and Venus are the two planets that orbit between Earth and the sun, so they are the only two planets that we can occasionally see passing in front of the sun.
If you look at the orbits of Earth and Mercury below (I’ve removed Venus, for clarity), it would seem there should be many opportunities for that sort of alignment.
Click to enlarge
Mercury orbits the sun every 88 days, repeatedly lapping Earth on its slower one-year orbit. Each time Mercury draws level with the Earth (on average, at 116-day intervals) that’s an opportunity for a transit.
But the reason we don’t get three transits a year shows up when we look at the orbits edge on. Mercury’s orbit is tilted at seven degrees relative to Earth’s. So most of the times when Mercury is overtaking Earth, it’s either above or below Earth’s orbital plane, and the alignment is imprecise—no transit.
Click to enlarge
The opportunities for a transit occur only when Mercury is passing through the Earth’s orbital plane. That happens at two precise locations in Earth’s orbit, on directly opposite sides of the sun. If the Earth is at one of those points and Mercury is overtaking at the same time, we have a transit. At any other times, no show.
These two points in Earth’s orbit are (relatively) fixed in space—the orbits of Mercury and Earth do evolve, but only slowly. So Earth reaches them at the same time every year—the start of May, and the start of November. Those are the only times of the year at which transits of Mercury can occur. There’s a little wiggle room, a span of close to a week either side of the exact point, when the alignment is good enough for a transit to occur.
Click to enlarge
If the transit comes early in one of these two-week “transit seasons”, we see Mercury skim across one edge of the solar disc; in the middle of the season, it crosses the middle of the disc; and in late season it crosses the opposite edge. At the extremes, only part of Mercury may overlap the sun, causing a very brief “partial transit”—a little sector of silhouette that comes and goes very quickly along the edge of the solar disc. Under these conditions, where you are on Earth can change the perspective enough to make a difference to what you see. In November 1999, observers in America saw the entire silhouette of Mercury make a short crossing at the very edge of the solar disc; but parts of Australia and New Zealand saw only a partial transit.
Monday’s alignment was a pretty good one. Mercury crossed reasonably centrally, and so spent a long time (seven-and-a-half hours) in transit. Its orbit is marked in red on the diagram below.
Click to enlarge
If you look at the May-November diagram above, you’ll see that Mercury is considerably farther from the sun in May. That’s a bit of a two-edged sword. It means that the geometrical alignment has to be a bit tighter in May before Mercury is actually superimposed on the solar disc from our point of view. So May transits are rarer than November ones. But when there is a May transit, Mercury is closer to us, and appears larger—twelve arcseconds across in May, ten arseconds in November.
Click to enlarge
That’s still tiny, though, as you can see above. It’s well below the resolving power of the human eye, which is conventionally around one arcminute (60 arcseconds). I’ve discussed this issue of optical resolution in a previous post. When Venus is in transit it’s an arcminute across, and so potentially visible to the naked eye for people with good vision and appropriate eye protection, using eclipse-viewing filters. But Mercury needs to be optically enlarged. Usually that means using a telescope with filters in the optical path, which is not something that should be knocked together by an amateur—eye injury is a certainty if you find yourself looking at the unfiltered sun through a telescope.
But there is another way of enlarging the solar image, which keeps your eyes well clear of danger—projecting an image on to a white surface.
So on a half-baked impulse, I trotted out into the garden as the sun was getting low in the sky during the transit, and projected its image on to a piece of paper, using a pair of binoculars. With my back to the sun, I directed the image of the solar disc into the shadow of my own shoulder. You can see the lo-tech (but very safe) set-up below:
Click to enlarge
Difficult to hold steady, and there were blue and red fringes to the image because I was using the optics to do something they weren’t designed to do. But there was a little fleck of shadow! In the photo below it’s a little red-blue smear. (You might need to click on the image to enlarge it for a proper view.)
Click to enlarge
Cool, eh? Excitement reigned, together with a certain smug satisfaction at pulling this off with such rudimentary kit. For a while, at least …
A little sober reflection on the size and position of that fleck of shadow (too big, not quite in the right place); a review of proper photographs of the event … Turns out I had rather neatly projected the image of a sunspot. Mercury is just too small to show up with my gimcrack contrivance.
Oh well. The next transit is on November 11, 2019.
Note: All the diagrams and simulations in this post were generated using Celestia, a free (and highly customizable) space simulator. I recommend it, and not just because I appear on the “Authors” list.
Not to be confused with fairy rings, which are circles of mushrooms and other fungi. These fairy circles were photographed in Namibia, and they’re a feature of the semi-arid margin of the Namib Desert. They form on sandy soil in regions where the annual rainfall is between 50 and 150 mm. They have a bare centre, and a raised rim with a strong growth of grass. And they have a life cycle—appearing at about two metres diameter, growing to 10 or 12 metres over a period of decades, and then dissipating, to be replaced by new circles. There’s a region of (relatively) high soil water content immediately under the bare central area. Rainwater falling in the bare area quickly percolates down into the soil, and the soil here suffers less evaporative loss because the water isn’t being sucked up by plants and lost by transpiration from their leaves. A cross-section of a fairy circle looks like this, with the wetter region marked in blue:
When we saw them in 2009 they were a bit of a mystery, with multiple competing explanations for how they formed. The game guides in the NamibRand told us that an experiment was afoot in the reserve to try to narrow down the possible mechanisms, but they didn’t have any details at that time. It turned out to be a multifaceted, five-year experiment that was reported in PLoS One last year.
More of that in a minute. First, a summary of the competing explanations:
Insect feeding (ants or termites)
Residual plant toxins (from, for instance, Euphorbia)
Poisonous gases
Soil radioactivity
Nutrient deficiency
A “self organizing” emergent property of the vegetation
So Walter Tschinkel’s experiment in the NamibRand reserve was designed to test some of these possibilities. (Tschinkel WR. Experiment Testing the Causes of Namibian Fairy Circles. PLoS ONE (2015) 10(10): e0140099.) He buried an impervious membrane beneath some fairy circles, but this did not alter their density and growth compared to controls. He transferred soil from the circles to a cleared area to see if it would create new circles (it didn’t), and soil from areas outside the circles into the bare zones of existing circles, to see if that would “heal” them (it didn’t). And he tried adding fertilizer to the bare circles, with no effect.
So Tschinkel effectively eliminated hypotheses involving gases seeping from below, toxins in the circle soil, and nutrient deficiencies.
While Tschinkel’s study was on-going, Norbert Juergens published an investigation into the role of insects in the circles. (Juergens N. The Biological Underpinnings of Namib Desert Fairy Circles. Science 2013 339: 1618-21.) Juergens had sampled insect populations associated with fairy circles and had discovered that, although several species of ant and termite appear to be associated with fairy circles, only one species turned up everywhere these fairy circles form: the sand termite Psammotermes allocerus. And P. allocerus turned up frequently in the circles sampled (80-100%) and also early in their development (before the onset of water accumulation and the characteristic grassy rim). So Juergens proposed that the termites were effectively “farming” the circles—creating them by killing a patch of grass, exploiting the water that accumulated in the resulting bare patch, and then expanding the circle by eating the grass on its rim, which thrived because of the additional water in the soil.
But, as Tschinkel subsequently pointed out, association is not causation. Juergens had observed a correlation between fairy circles and P. allocerus nests, but had carried out no test interventions (removing the termites to see if a circle recovered, for instance). It’s possible that the termites were merely exploiting a patch of dying grass and an area of water accumulation caused by something else. It would also be interesting to know whether or not P. allocerus colonies typically develop with a scale and spacing that matches the behaviour of fairy circles.
Because the spacing of fairy circles is quite striking. Here’s a Google Earth view of the fairy circles near Wolwedans Dunes Lodge, where we stayed during our time in the NamibRand:
Click to enlarge
There’s a natural spacing to them, as if each circle somehow repels those around it. And this can be confirmed mathematically—on average, the circles are maximizing their own space in competition with their neighbours. And that’s what leads to the idea that the circles are somehow self-organizing—that simple local rules about how plant grow and utilize water leads to the emergence of a global pattern.
You can see a similar emergent pattern in the convection cells that form in a pan of boiling water:
There’s uniform heating at the bottom of the pan, which makes the water at the bottom less dense than the surface water. But hot water can’t rise to the surface everywhere—there’s got to be room for cold surface water to descend as well. So the water spontaneously sorts itself out into multiple cells with rising water in the middle and sinking water at the edges.
Likewise, we can imagine fairy circles arising because rainfall is insufficient to support a continuous carpet of grass. Instead, bare patches catch enough water to support a surrounding halo of grass, and by doing that inhibit the formation of nearby bare patches. As that situation plays out, a landscape dotted with fairy circles might be one stable solution that could emerge.
Hence the excitement, last month, at the report of fairy circles in Australia (Getzin et al.Discovery of Fairy Circles in Australia Supports Self-Organization Theory. PNAS 2016 113(13): 3551-6). We now have a second, strikingly similar pattern of bare circles with surrounding vegetation, occurring in a near-desert environment. Here’s an image from Google Earth:
Click to enlarge
But this pattern involves different vegetation (spinifex grass), no consistent association with termites, and a different mode of water collection—in the Australian case, the bare circular patch develops a hard crust and sheds water from its surface towards plants at its edges.
This lends credibility to the idea that this pattern is something that can emerge spontaneously when biomass is trying to make the best of scarce water resources. So those Namibian termites might well just be part of the pattern, rather than its cause.
Have you ever seen the sun set at the seaside? Yes? And did you follow it until the top edge of the sun’s disc just touched the horizon and then started to disappear? Probably. But did you observe the phenomenon that occurs at the instant of the last ray of light when the sky is perfectly clear? Perhaps not. Well, the first time that the opportunity for such an observation offers itself (it is very rare), take it and you will see that it is not a red ray, or rather flash, but a green one; a wondrous green that is not found anywhere else in nature. If there is green in Paradise, it must be this green: the true green of hope!
The sequence above consists of three frames from a short sunset video recorded by the Boon Companion in the Caribbean recently. Something odd happens in the last frame—the rim of the sun turns apple green. The effect was visible to the naked eye, and lasted something less than a second.
This phenomenon is called the green flash, and during ten suitable Caribbean sunsets (clear horizon, yellow sun), I managed to see it six times (though four of those were rather feeble offerings). Its cause is superficially simple, but there are complications.
When I wrote about the shape of the low sun recently, I described how light rays travel in a curved path through the atmosphere, lifting the image of the setting sun, like this:
So that, at sunset, the sun is actually below the geometrical horizon, but lifted into view by atmospheric refraction:
What I didn’t mention is the phenomenon of atmospheric dispersion—the refractive index of air is slightly different for different wavelengths of light. Shorter wavelengths are bent more than longer ones. This means that the red image of the sun is lifted slightly less than the green image of the sun. (The blue image of the sun would be lifted even more, but blue wavelengths are very efficiently scattered by the atmosphere before they reach our eyes.) So the true story of atmospheric refraction looks like this:Which means that the image of the sun arriving at our eyes is actually a little smeared in the vertical direction, with more green at top and red at the bottom:In reality, the effect is so small that it isn’t visible to the naked eye under most circumstances. O’Connell calculated that the green rim is only 10 seconds of arc wide—that’s about a 180th of the width of the solar disc, and a sixth of the normal resolving power of the human eye, which is about 60 seconds of arc. (For a discussion of visual resolution see this previous post.) So the green and red rims are simply lost in the yellow overall colour of the solar disc. But when the sun has dropped so far below the visual horizon that only the green rim is visible, then all that can reach our eyes is green light. Even at the equator, with the sun dropping vertically below the horizon, that narrow green rim will be visible on its own for 2/3 of a second. At higher latitudes, with slower sunsets, the visibility will be longer. And that’s the common explanation of the green flash—the momentary visibility of the upper green edge of the solar disc after the rest of it has dropped below the horizon.
But: what can you actually see, if the green rim is narrower than the resolving power of your eyes? You’ll find website claiming that it will simply be invisible, and that there must be some other explanation for the green flash. But a moment’s reflection suggests that’s not true. Every star in the night sky is so far away that its disc is below the resolving power of the human eye, but they’re not invisible. As a concrete example, the star Betelgeuse, in the shoulder of Orion, has a disc 0.05 seconds of arc in diameter—that’s 200 times smaller than the green rim of the setting sun, but we not only see it very well, we can clearly distinguish its orange-red colour. What happens is that your eyes smear out the light of Betelgeuse into a little blob about sixty seconds of arc across, and it becomes apparently dimmer in proportion. If our eyes could resolve its tiny disc, it would be a spark of light with the eye-watering surface brightness of the filament in an old-fashioned incandescent light-bulb.
So that’s what happens to the green rim of the sun. At the horizon, it’s horizontally wider than the eye’s resolving power, but blurred vertically so its apparent brightness is reduced. It forms a horizontal bar of green light, brighter in the middle and fading out towards the ends. And when it’s that close to the horizon, its light is also significantly dimmed by atmospheric scattering. What we see is then determined by how well that blurred bar of green light stands out against the bright background of the sunset sky. Conditions are going to vary from sunset to sunset, but it seems that the green rim could plausibly be responsible for a rather anaemic and very short-lived green flash.
Sometimes, though, the flash is a bright, pure, emerald green. I saw two of these out of my six Caribbean green flashes. So there really must be more to the story.
There’s a hint of the cause in this picture, taken just before the video sequence at the head of this post (you may need to click on it to see the full resolution):
If you look carefully, the setting sun has a tiny flared skirt immediately above the horizon. This is actually a reflection of the solar disc. It’s generated by a mirage—surface air has been warmed by the ocean, producing a low-density layer that refracts light back to our eyes, as if there were a mirror hovering just above the distant waves.
Below are some more extreme examples of the same effect. An “Etruscan vase” sunset:
In each case the sun is setting behind a “reflective” mirage layer positioned just above the horizon.
When I turned my (filtered) binoculars on the sun just as the green flash started to develop, I saw something that looked like this:
The upper part of the ellipse is the direct view of the sun and its green rim; the lower part is a miraged image. As the sun set they closed together like a winking eye, until they formed what Marten Mulder called a green segment.
This green segment is deeper than the green rim—depending on the optics of the mirage, several times deeper. And that’s what increases the intensity of the light so that we see a proper, vivid green flash.
There are other kinds of mirage that similarly enhance the green flash, but this inferior mirage is by far the most common.
If you want to prolong your view of the green flash, you have two options. One is to move upwards to match the speed at which the sun is setting, so that you can keep the green rim continuously in view. Marcel Minnaert describes running (presumably backwards) up the slope of a Dutch dyke while watching the setting sun. He was able to keep the green flash in view for about 20 seconds. The other option is to head to polar latitudes, where the sun rises and sets by skimming along the horizon. In 1929, from Richard Byrd‘s Antarctic camp “Little America“, the green flash was observed during a long polar sunrise—it flickered in and out of existence for 35 minutes as the upper rim of the sun skated along the irregular horizon.
Most people know why the sun looks orange-yellow when it’s rising or setting. Air preferentially scatters shorter (bluer) wavelengths of light—so the more air there is between your eye and the sun, the more short wavelengths are scattered out of the line of sight, leaving yellow/orange/red as the predominant colours reaching your eye. There’s about 38 times more air between your eye and the sun when it’s at the horizon, compared to the zenith, so it’s not surprising it looks progressively yellower the lower it is in the sky.
But what makes it change shape? The setting sun in the photograph above is only 88% as high as it is wide, and ratios down to 80% are commonly seen.
The first thing to know about the sun in that photograph is that it isn’t really there. In fact, whenever you look at the sun on the horizon, it isn’t really there. The sun is actually below the horizon, and what you’re seeing is essentially a mirage, generated by light rays curving towards your eye from beyond the geometric horizon.
Light travels slightly more slowly in denser air. The atmosphere is denser near the ground than it is at altitude. So light passing through the atmosphere is refracted—it follows a slightly curved path, concave to the denser layers of air. That means it curves around the convexity of the Earth, bringing objects into view that would be hidden below the horizon in the absence of air.
This trick of the light means that, in order to calculate the distance to the visible horizon, you need to pretend that the Earth is a little bigger than it actually is. Calculation and observation suggest that multiplying the Earth’s actual radius by 7/6 give the apparent radius produced by refraction. It also means that when objects in the sky are just beyond the curve of the geometric horizon, they are still visible, lifted above the apparent horizon by atmospheric refraction. This applies to the moon (and the stars) as well as the sun, and the tables of rising and setting times you find in newspapers and online contain several minutes allowance for the effects of refraction.
So, going back to the setting sun in the photo, the (approximate) real position of the sun is marked with the white circle below:
Atmospheric refraction is lifting the lower rim of the sun into view above the horizon by an angular distance that is typically around 7/10ths of a degree. But light from the upper rim of the sun takes a trajectory with a slightly different slope through the atmosphere, and its image is lifted a little less—in my sketch, by about a twentieth of a degree less. But that slight angular difference amounts to a tenth of the apparent angular diameter of the sun, and creates the apparent vertical flattening of its disc.
If you watch a sunset or moonset from the International Space Station, you’ll see even more dramatic flattening, because the light rays from the top and bottom edges of the disc have dipped into the atmosphere, producing the amount of flattening we’re used to seeing on the Earth’s surface, and then they’ve come back out again, experiencing a second episode of flattening. Here’s the setting moon photographed from orbit by astronaut Don Pettit:
Image credit NASA, April 16, 2003 (From Don Pettit’s frame ISS-006-E-45773)
That’s a lot of flattening. There’s actually more than just a double dose of standard atmospheric refraction required to account for that very asymmetrical appearance.
If we go back to the original photo at the head of this post, the horizon is about 10 kilometres away. That means that light rays from the top and bottom edges of the solar disc are crossing the horizon only about 100 metres apart, vertically—although their trajectories are slightly different, they’re sampling very similar parts of the atmosphere. But in the ISS photo, the horizon (out of frame just below that flattened lunar disc) is about 2000 kilometres away. Light rays from the top and bottom edges of the lunar disc are crossing the horizon ten or twenty kilometres apart, vertically. So they’re sampling completely different parts of the atmosphere, with very different density gradients, and it’s no wonder the resulting image of the moon is very strongly distorted.
You don’t need to go into space to get that sort of dramatic distortion, however. If the lower few hundred metres of atmosphere contains layers with non-uniform density gradients (alternating bands of hotter and cooler air), then the trajectories of light rays coming from the sun will be deflected in a non-uniform way, and the neat ellipse of the sunset photo above can turn into something like this:
Notice that a single sunspot appears three times in the centre of that solar disc. Light from the sunspot is finding three different curved routes through the atmosphere that all end at the observer’s eye, coming from very slightly different directions.
There’s a critical density gradient (on Earth, corresponding to a temperature inversion of 0.11ºC/m) at which the refracted curvature of a horizontal light ray exactly matches the curvature of the Earth. In an atmosphere with this density structure, light could travel endlessly around the planet. For a while, back in the 1970s, it was thought that the planet Venus might have that sort of atmosphere. In 1975 the science fiction author John Varley wrote a short story, “In The Bowl”, set on Venus, and did a good job of describing what that might look like. (To make sense of the following, you also need to know that Venus rotates in the opposite direction to Earth, and very slowly):
I don’t like standing at the bottom of a bowl a thousand kilometers wide. That’s what you see. No matter how high you climb or how far you go, you’re still standing in the bottom of that bowl. […]
Then there’s the sun. When I was there it was nighttime, which means that the sun was a squashed ellipse hanging just above the horizon in the east, where it had set weeks and weeks ago. Don’t ask me to explain it. All I know is that the sun never sets on Venus. Never, no matter where you are. It just gets flatter and flatter and wider and wider until it oozes around to the north or south, depending on where you are, becoming a flat, bright line of light until it begins pulling itself back together in the west, where it’s going to rise in a few weeks.
But let’s go back to Earth again, and that critical value of refraction at 0.11ºC/m—this implies that, if the temperature gradient is even steeper, rising light rays can be so strongly curved by refraction that they’ll come back down again. This happens readily enough in polar regions, where cold air in contact with ice is overlain by warmer air aloft—at some critical altitude, the temperature can jump by several degrees Celsius in the space of just a few metres, creating an abrupt fall in air density.
So a polar temperature inversion can create a sort of reflective roof, allowing light to reach the observer’s eye from objects well beyond the geometric horizon. In fact, if the temperature inversion is widespread, and the terrain is flat, light rays can “bounce” several times around the curvature of the Earth on their way to the observer, bringing in distorted images from hundreds of kilometres away. If the sun moves into alignment with this “light pipe” then it can become visible despite being four degrees or more below the geometric horizon.
Novaya Zemlya Effect, schematic (Click to enlarge) The yellow light ray moves alternately closer to and farther from the surface of the Earth, “bouncing” off the top of a temperature inversion (in reality, the effect plays out within a layer about 100m deep, spanning just a few degrees of Earth’s curvature)
This is called the Novaya Zemlya Effect, because it was first recorded while members of Willem Barentsz’s 1596/7 expedition were overwintering on the island of Novaya Zemlya in the Russian Arctic. Towards the end of the long polar night, on 24 January 1597, Gerrit de Veer and two other men saw a distorted image of the sun appear on the horizon two weeks before the polar night was due to end, at a time when the sun was still, geometrically, about five degrees below the horizon. This is still one of the most extreme examples of the effect ever observed. Calculations by van der Werf et al.(1.1 MB pdf) in 2003 suggest that it could have involved no less than five successive bounces from an inversion layer at about 80 metres altitude, over a distance of 400 km.
We have a drawing of what the sun looks like under these circumstances, courtesy of Fritjof Nansen, who saw an example of the Novaya Zemlya Effect during his Fram expedition to the Arctic:
Nansen’s sketch of the Novaya Zemlya Effect, 16 Feb 1894 (Click to enlarge) From Farthest North, Vol. 1, George Newnes Ltd., 1898
Those multiple bounces along the “light pipe” completely scramble the image of the solar disc, until what remains is a stack of bright horizontal bands, all of roughly equal width.
You can get a nice impression of what it must have looked like from this beautiful video of a miraged sun, filmed for four minutes after the expected sunset time, in California:
The blue appearance of veins under unpigmented skin is a commonplace observation, to the extent that it has become standard coding in anatomy diagrams to colour arteries red and veins blue:
But that pale blue colour is actually a bit of a puzzle.
Blood gets its colour from the haemoglobin contained in the red blood cells. The haemoglobin changes colour depending on whether it’s bound to oxygen or not. So first of all we want to know what colour venous blood is.
I’m indebted to Scott Prahl, of the Oregon Medical Laser Center, for permission to reproduce this graph of the absorption spectra of haemoglobin bound to oxygen (HbO2) and haemoglobin without attached oxygen (Hb):
The lower the graph dips, the less the absorption, and so the more light at that wavelength the haemoglobin will reflect. And notice there’s a logarithmic vertical scale—those dips mean a big proportional change in light absorption. Below, I’ve edited the graph to show just the visual wavelengths, stretching from 400nm (violet) on the left to 700nm (red) on the right:
HbO2 is absorbing between a hundred and a thousand times more short-wavelength blue than long-wavelength red light. So it’s going to be strongly red in colour—hence the lurid colour of the oxygenated blood that comes out of a cut artery. Without oxygen, Hb absorbs more red light than HbO2 by a factor of ten or so. But it still absorbs ten to a hundred times more light at the blue end of the spectrum than the red—so venous blood, which contains a mix of oxygenated and deoxygenated haemoglobin, is also going to be red in colour, albeit a darker and less saturated red than arterial blood. And we confirm that every time we take a venous blood sample—what flows into the syringe is anything from dark red to deep purple-red; certainly not blue.
So it’s not venous blood that causes the blue colour. Is it the vein wall?
Veins are thin-walled structures. If removed from the body and inflated with saline, they appear translucent pink. When they’re filled with blood, the blood inside shows through, rendered a little paler and pinker by the wall of the vein. Here is a view of a major artery and vein, exposed during surgery (SMV = superior mesenteric vein; SMA = superior mesenteric artery):
A vein full of blood evidently doesn’t look blue, either.
So it must be something to do with the overlying skin and subcutaneous tissues. Keinle et al. (116 KB pdf) investigated this in the journalApplied Optics, back in 1996. To slightly simplify their argument, what they found was as follows.
Unpigmented skin and tissues scatter both blue and red wavelengths back to the eye, with a preponderance of red that makes flesh look pink. But, crucially, red light travels farther into the tissue before bouncing back out again. The blue wavelengths show us the very superficial layers; the red wavelengths probe deeper structures.
And we know that veins, with their translucent walls, bounce back a small amount of light from the dark blood inside, but with red still predominant.But what happens if we put a vein inside the tissues, positioning it deeper than the blue wavelengths typically penetrate, but within range of the red? The superficial tissues scatter away the blue light before it reaches the vein. The vein absorbs more red light than the tissues would have done. Blue predominates!And that’s why most visible veins look blue. If they lie any deeper in the tissues, neither red nor blue light reaches them, and they are invisible. And it’s unusual for them to be so superficially placed that blue wavelengths can reach them—that requires the sort of delicate, thin skin we sometimes find in premature babies and the very old. Those of us whose job involves inserting IV cannulae into veins know from experience that a red-looking vein is thin-walled and lying very close to the surface.
So those blue veins on the back of your hand represent a remarkable conspiracy between optics and anatomy.
Last week, the Boon Companion and I were sipping sundowner cocktails in the British Virgin Islands, leaning back in our chairs, and cloud-watching. Long streets of fair-weather cumulus had been strung out over the Caribbean since midday. Now, half an hour before sunset, the cumulus was growing—boiling upwards to form towering cumulus congestus, which were draping little dark banners of rain here and there across the sunlit sea. At the end of a warm, still day, there was clearly some strong convection building out there on the water.
Quite suddenly, a little finger of grey cloud poked out of the dark base of one of the clouds. I watched it for a minute, as it grew thinner and longer, eventually stretching far enough to catch the rays of the setting sun. It was a funnel cloud. Which meant … Yes, on the sea horizon below the cloud there was a little swirling dark smudge—a spray ring. We were looking at a waterspout, the first I’ve ever seen.
As we watched, the funnel cloud sent down a thin dark streamer that speared into the centre of the spray ring—the waterspout was fully evolved. It stayed that way for about fifteen minutes, idling around gently beneath its parent cloud and slowly moving along the horizon, until it suddenly decayed away—the funnel withdrew into the cloud, and the spray ring collapsed. Show over.
There are actually two different kinds of waterspout. If a tornado moves out over water, it creates a tornadic waterspout. These are big fierce beasts, with all the destructive power of a tornado. They evolve in the fierce updrafts of supercell thunderstorms, and they form by dropping a thick funnel cloud downwards to the ground.
But what we saw in the British Virgin Islands was a fair weather waterspout. They’re generated by air rising into evolving cumulus clouds, and they progress from the surface upwards.
In their early stages, a swirl of wind forms around warm air rising from the water surface, just like a dust-devil spinning through a hot car-park. The wind swirl creates a characteristic disc of rough water with a calm centre—this is the “dark spot phase”, which is best seen from the air. A few spiral lanes of disturbed water then converge on the dark spot, and spray begins to rise into the air as the surface winds intensify. Above this visible spray ring, a column of spiralling, rising winds connects to the base of the cloud overhead. As the spiral tightens and intensifies, the pressure at its core drops by several millibars, and water vapour starts to condense within it—the cloud starts to extend downwards in a visible funnel cloud. In a fully developed waterspout, the funnel reaches all the way down to the centre of the spray ring, by which time it has usually developed a hollow centre—water droplets formed in the low-pressure core are flung outwards to orbit in the zone of highest winds, a few metres from the core.
Ocean Today have put together a nice two-and-a-half-minute video compilation that illustrates the evolution of a fair weather waterspout. It’s full of impressive images, and I recommend it. Here’s a link to the embedding version of the video, which seems reluctant to embed on this website:
Fair weather waterspouts are typically short-lived, persisting for about twenty minutes; and they often occur in groups of two or more when conditions are favourable. (Indeed, we spotted a couple of other tentative funnels appearing and disappearing at the cloud base while we watched our waterspout noodling around the horizon.) The Florida Keys reports more than a hundred a month between May and September, when the surface water temperature is over 25ºC.
They can be relatively benign—people have driven speedboats through them. But with wind speeds of 65 m/s (130 knots), they can also be very dangerous—large vessels have been capsized or dismasted; small vessels have been swamped by the spray ring; and in 1993 a windsurfer was drowned on the Chicago waterfront by a Lake Michigan waterspout.
The updraft is fierce—a waterspout that made landfall on Matecumbe Key, Florida, reportedly lifted a two-ton Cadillac a few feet into the air before setting it down again. So it seems at least possible that they can lift a significant quantity of water from the sea surface, and there are anecdotes to support this. In his book It’s Raining Frogs And Fishes, Jerry Dennis gives a report of a downpour of salty rain on the island of Martha’s Vineyard on August 19, 1896, a few hours after a waterspout had been seen close to shore—the salt water had presumably been incorporated briefly into the parent cumulus cloud. And in the Annals and Magazine of Natural History(January 1929), E.W. Gudger reported that a waterspout had dissipated near an open boat in the Gulf of Mexico, which was then promptly swamped under a torrent of seawater and fish.
Gudger’s article is entitled “More Rains Of Fishes”—he was primarily interested in sporadic reports of fish falling from the sky, and he felt that waterspouts offered a reasonable route by which aquatic creatures might get up there in the first place.
Surprisingly, falls of fish (and frogs) are quite well documented, both before and after Gudger’s time. For instance, on October 23, 1947, a Canadian fisheries biologist was fortuitously on hand to see fish falling from the sky in Marksville, Louisiana:
In the morning of that day, between seven and eight o’clock, fish ranging from two to nine inches in length fell on the trees and in yards […] There were spots on Main Street, in the vicinity of the bank (a half block from the restaurant) averaging one fish per square yard. Automobiles and trucks were running over them. Fish also fell on the roofs of houses.
They were freshwater fish native to local waters, and belonging to the following species: large-mouth black bass (Micropterus salmoides), google-eye (Chaenobrittus coronarius), two species of sunfish (Lepomis), several species of minnow and hickory shad (Pomolobus mediocris). The latter species were the most common.
Following Gudger’s example, waterspouts (and their terrestrial cousins, whirlwinds) are nowadays the usual explanation trotted out for such events—the fish or frogs are presumed to have been hoovered up from surface water, to bounce improbably around in the clouds for a while before falling on some unsuspecting town.
However, these anomalous falls tend to be oddly pure samplings, as in Bajkov’s description above, which seemed to involve nothing but fish. I suppose we can imagine a waterspout picking a shoal of surface fish out of the ocean quite cleanly; but what about the freshwater fish in Bajkov’s example? Or the frogs reported elsewhere? Why are such falls apparently never accompanied by mud, gravel, weeds and battered waterfowl, scooped up incidentally? I’ll give the last word on that topic to Charles Fort:
[…] a pond going up would be quite as interesting as a frog coming down. Whirlwinds we read over and over—but where and what whirlwind? It seems to me that anyone who had lost a pond would be heard from.
Here’s the problem: the tropical year, the time it takes the Earth to go through a complete cycle of seasons, is 365.2422 days long (to four-decimal accuracy).
If every calendar year were 365 days long, then the missing 0.2422 days would add up from year to year, each year starting a little earlier relative to the changing seasons. It would take only 120 years for the calendar to be a month adrift from the season.
The Roman Republican calendar had a standard year of just 355 days. Every few years an additional month was added, bringing the year up to 377 or 378 days. With the right frequency (about 11 long years to every 13 standard years), that system could have kept the calendar year aligned with the tropical year on average, though with pretty large excursion from year to year. Trouble was, the decision whether or not to add additional months was driven as much by politics and superstition as it was by astronomical accuracy, and on occasion the Republican calendar drifted as much as four months away from seasonal alignment.
Julius Caesar came to power when the Roman calendar was awry by more than two months. After taking advice from the Greek astronomer Sosigenes of Alexandria, he came up with a plan to get the calendar back into alignment with the seasons, and to keep it that way. First, he decreed that 46 BC should be 445 days long. He then established the familiar pattern of leap years we know today, by creating a regular year of 365 days, and adding an extra day to February quarto quoque anno, “every four years”. That made the average calendar year 365.25 days long, tolerably close to the desired 365.2422.
Caesar was assassinated in 44 BC, and confusion immediately reigned. Roman counting was commonly inclusive—for instance, they used what we would call an eight-day week, from one market day to the next, but they called it a nundinem, derived from nonus, “ninth”. They counted nine days because they included the market day at the beginning and at the end of the week as being part of the same week. So Caesar’s quarto quoque anno was implemented as a three-year cycle until 9 BC. At that point his successor, Augustus (having had the necessary arithmetic drawn to his attention), started the correct four-year cycle, and tried to get things back the way Julius had wanted them by skipping the leap years in 5 BC, 1 BC and AD 4 in order to get rid of the effect of the excessive leap years that had accumulated so far.
Julius Caesar’s calendar years of 365.25 days (called Julian years, in his honour), then ticked away steadily from AD 8 until 1582. And the difference of 0.0078 days between the Julian year and the tropical year mounted up steadily, so that by 1582 the calendar had moved more than 12 days out of register with its original seasonal position.
This was a problem for the Christian Church. The date of Easter was tied to the seasons—specifically the northern spring equinox—but for the purpose of calculating the specific date of Easter each year, the spring equinox was represented by a date, March 21. This date had been correct at the time of the Council of Nicaea in AD 325, when the standard computation of Easter was agreed, but by the sixteenth century the calendar had drifted so that the vernal equinox was occurring on March 11. Martin Luther pointed out that, in 1538, Easter should have been celebrated on March 17, according to the timing of the vernal equinox, but had been pushed to April 21 because of the slippage in the Julian calendar.
Pope Gregory XIII, advised by astronomers Aloysius Lilius and Christopher Clavius, came up with a solution.* Like Caesar’s calendrical intervention previously, there were two parts to the fix—one to get the calendar back into alignment with the seasons, and the other to prevent it drifting again. The details were promulgated in the papal bull Inter gravissimas. To realign the seasons (specifically, to get the vernal equinox back to March 21) ten days were to be omitted from the month of October—October 4, 1582 was to be followed by October 15.
To tighten the approximation of the calendar year to the tropical year, the rule for leap years was subtly tweaked, by dropping three leap years every four centuries. According to the Julian calendar, every century year was a leap year; according to the new Gregorian calendar, only century years exactly divisible by 400 were to be leap years. So 1600 was a leap year, 1700, 1800 and 1900 were not, and 2000 was (you may remember) a leap year. Having just 97 leap years in every four centuries brings the length of a mean calendar year down to 365.2425 days—just 0.0003 days longer than the tropical year.
Catholic countries all made the change as instructed, though some lagged a little behind the dates set out in Inter gravissimas. Rulers and governments in Protestant and Orthodox countries were keen not to be seen as toeing the papal line, and so in some places the improvement took a long time to be adopted. The two calendars therefore ran in parallel for several centuries, with writers having to be careful to mark their dates “O.S.” (for “Old Style”) or “N.S.” (for “New Style”).
Great Britain and its colonies eventually made the change in the eighteenth century, by which time eleven days† had to be dropped—the Julian calendar had drifted another day ahead of the Gregorian calendar by observing a leap year in 1700. In Britain, September 2, 1752 was followed by September 14. (This eventually led to the renaming of a butterfly. At that time the April Fritillary was so called because of its early hatching; but the change in the calendar shifted its peak hatching period into May. It’s nowadays called the Pearl-bordered Fritillary.)
Russia held out until 1918, by which time the Julian leap years in 1800 and 1900 meant they had to drop a total of 13 days, which they did between January 31 and February 14. This had the unfortunate consequence that the anniversary of the October Revolution had to be celebrated in November.
Sweden tried a different approach, with a plan to drop all leap years between 1700 and 1740, thereby making the necessary eleven-day shift gradually. Unfortunately, after missing the leap year in 1700, they observed leap years in 1704 and 1708, getting stuck a day ahead of the Julian calendar and ten days behind the Gregorian. At this point they seem to have thrown their hands in the air and declared the whole thing to be a bad idea. They shifted back into synchrony with the Julian calendar by having both a February 29 and a February 30 in 1712.
(Sweden eventually made the Gregorian shift in the conventional manner, by dropping eleven days in February 1753.)
* It’s of course depressingly predictable that the calendars have been called Julian and Gregorian, after the powerful men who legislated the changes, rather than Sosigenean and Lilian, after the clever men who worked out the details. † There seems no truth to the story that people rioted in Britain because they believed the eleven days were being removed from their lives. There were riots in the election year of 1754, and the recent calendar reform was one of the political hot potatoes of the time; there was also an issue that some people were paying tax and rent for a full quarter, while being denied wages for the missing eleven days.
In my first post on this topic, I discussed some physics and physiology, in an effort to predict and explain the likely consequences for a person exposed to the vacuum of space.
In this part, I’m going to look at the evidence from animal experiments and human accidents.
ANIMAL DATA
The animal decompression experiments were carried out in the 1960s. The original reports used to be available on-line, but they seem now to have vanished. I suspect the organizations involved have concerns about being associated with these experiments, even though they took place half a century ago. They are, however, summarized in the second edition of the Bioastronautics Data Book, and in a 1968 NASA report entitled Rapid (Explosive) Decompression Emergencies in Pressure-Suited Subjects (5.7 MB pdf). The NASA report (NASA CR-1223) provides more physiological detail, and that’s what I’m using for the information below unless otherwise stated.
Boiling and swelling
Dogs were decompressed to ambient pressures of 2 mmHg—effectively a vacuum, and well below the 47 mmHg pressure threshold that marks the Armstrong Limit, the point at which water boils at body temperature. This decompression was accompanied by
… violent evolution of water vapor with swelling of the whole body of dogs.
The Bioastronautics Data Book adds that the body swelled to “perhaps twice as much as its normal volume”.* How fast did that happen? Experiments in which the gaseous composition of the subcutaneous bubbles was monitored showed:
At first there appears to be a rapid conversion of liquid water to the vapor phase which reaches a peak at one minute and continues at a slower rate for several minutes. There is an initial rush of carbon dioxide, nitrogen, and oxygen into the pocket, but carbon dioxide and the nitrogen soon become predominant.
So these whole-body decompression experiments produced different results from the isolated hand experiments I described at the end of Part 1. When the whole body is decompressed there’s a prompt, extensive formation of water vapour bubbles in the subcutaneous tissue—no sign of the delayed onset of swelling (by up to ten minutes) that was found in the hand experiments. Either there’s something unusual about human hands, or something about being connected to an undecompressed body delayed the onset of swelling in the hand experiments.
As soon as the water vapour bubbles form, gases dissolved in the tissues diffuse into them. These experiments were carried out breathing air, so nitrogen is the major gas to enter the bubbles, with carbon dioxide a more minor component. Oxygen levels in the tissues are falling rapidly, so the oxygen content of the bubble gas will initially rise, and then fall off dramatically.
Did the blood boil? The technical term for this is ebullism (Latin “out-boiling”), and some of the animals were monitored for the formation of bubbles in the circulation. (I don’t have access to the original publication, but I presume this was done fluoroscopically—by continuous X-ray screening—given that this was all happening in the 1960s, before ultrasound became a diagnostic tool.)
Yes, the blood did indeed boil:
Almost immediately after decompression to an ambient atmospheric pressure at which ebullism can occur, vapor bubbles form at the entrance of the great veins into the heart, then rapidly progress in a retrograde fashion through the venous system to the capillary level.
This backward propagation of the bubbles may be because there is a slight pressure gradient along the length of the veins, from the capillaries to the heart, but it might also be because small bubbles are forming at the periphery, washing centrally, and growing or grouping into larger bubbles as they go.
Venous return is blocked by this “vascular vapor lock.” This leads to a precipitous fall in cardiac output, a simultaneous reduction of the systemic arterial pressure, and the development of vapor bubbles in the arterial system and in the heart itself, including the coronary arteries.
As soon as the right side of the heart contains a significant volume of gas, it can’t work as a liquid pump any more—it just compresses and recompresses the gas volume it contains. So flow to the lungs and the left side of the heart is prevented, the left side of the heart has nothing to pump, and the arterial blood pressure begins to fall. As soon as it falls below the critical 47 mmHg, the arterial circulation starts to fill with gas, too.
Systemic arterial and venous pressures then approach equilibrium in dogs at 70 mm Hg. At ebullism altitudes, one can expect vapor lock of the heart to result in complete cardiac standstill after 10-15 seconds, with increasing lethality for exposures lasting over 90 seconds. Vapor pockets have been seen in the heart of animals as soon as 1 second after decompression to 3 mm Hg.
That figure of 70 mmHg for the pressure in the blood vessels at cardiac arrest is interesting. Since it’s higher than the vapour pressure of water at body temperature, it presumably reflects the additional presence of nitrogen in the bubbles.
While the nitrogen in the tissue bubbles isn’t a serious problem, its presence in the circulation is. Recompression quickly causes the big water vapour bubbles to collapse back to the liquid phase. If the heart is still beating, the disappearance of these large bubbles means it can start working as a pump again. But nitrogen takes some time to redissolve, so it persists as small bubbles that are then showered into the circulation:
Upon recompression, the water vapor returns immediately to liquid form but the gas components remain in the bubble form. When circulation is resumed, these bubbles are ejected as emboli to the lungs and periphery. Cardiac arrythmias often occur as do focal lesions in the nervous system. These are probably a result of infarct by inert gas bubbles.
In effect, these animals suffered a case of the bends (nitrogen bubble emboli) as they recovered from cardiac arrest.
Survival
Cardiac arrest evidently occurs in two stages. At first, the heart is still beating, but full of gas and therefore ineffective as a pump. This is called Pulseless Electrical Activity. Recompression at this stage will get rid of most of the bubbles in the circulation, and allow the heart to start working properly again. But in the absence of recompression, rapidly falling oxygen levels and bubbles in the coronary arteries will soon cause the heart to stop beating. The Bioastronautics Data Book reports: “Once heart action ceased, death was inevitable, despite attempts at resuscitation.”
In the dog experiments, after 90 seconds of exposure to near-vacuum the animal’s hearts were still beating, but extremely slowly—about 10 beats per minute. If recompressed at this stage, all the animals survived, but often with transient neurological deficits, presumably from a shower of nitrogen-bubble emboli as the heart started pumping again. Beyond 120 seconds of vacuum exposure, deaths occurred frequently. Squirrel monkeys showed a similar pattern of survival but, interestingly, chimpanzees survived longer, with some making a delayed return to “baseline function” after 3.5 minutes of vacuum exposure.
Consciousness and brain damage
It’s difficult to judge “useful consciousness” from animal experiments. One chimpanzee with EEG monitoring is reported as having useful consciousness of 11 seconds, which I presume means that EEG activity looked normal for that period. The cortex had shut down by 45 seconds, and the whole brain was electrically silent by 75 seconds.
Both squirrel monkeys and chimpanzees showed a range of deficits afterwards, in the form of changes in their behaviour and performance. This sort of thing clearly isn’t good for your brain.
Lung injury
After an episode of decompression, the lungs are affected by bruising and areas of overdistension, presumably caused by gas trapping. The longer the decompression, and the faster its onset, the greater the lung injury. Another problem is atelectasis—regions in which the lung is completely collapsed. During a decompression episode, the airways fill with water vapour. When recompressed, this water vapour collapses back to the liquid phase, and the lung tissue tends to collapse with it.
HUMAN DATA
Someone’s got to have an accident for us to obtain the sort of data we’re interested in here—even in the high days of test-pilot derring-do, no-one was volunteering to be decompressed to vacuum.
We’ve seen from the animals studies that chimpanzees seem to survive vacuum exposure better than dogs. So are humans more like chimps or dogs? We’ve got some survival data that help answer that question.
Survival
In 1966, Jim LeBlanc was the victim of a depressurization accident in a vacuum chamber while carrying out spacesuit tests. A hose disconnection caused his suit to rapidly (but not explosively) depressurize. He lost conscious after about 15 seconds. The last thing he remembers is the saliva on his tongue starting to boil. The chamber was completely repressurized within a minute, he recovered consciousness during the repressurization, and was able to stand up almost immediately. Apart from sore ears, he suffered no ill-effects. There is video of the incident:
In 1971, the Soyuz 11 capsule returned to Earth with all three crewmen dead inside: Georgi Dobrovolski, Vladislav Volkov and Viktor Patsayev. A damaged air vent had opened shortly after the separation of the orbital and descent modules. The crew had been exposed to vacuum for 11 minutes, and could not be resuscitated.
From a 2013 article in Space Safety Magazine, we know that the dead men appeared normal apart from facial bruising and evidence of bleeding from the nose and ears. Dobrovolski and Patsayev had apparently tried to unstrap in order to deal with the emergency. Telemetry recorded the subsequent course of events:
At the instant of separation of the orbital and instrument modules, the cosmonauts’ pulse rates varied broadly: from 78-85 in Dobrovolski’s case to 92-106 for Patsayev and 120 for Volkov. A few seconds later, when they first became aware of the leak, their pulse rates shot up dramatically—Dobrovolski’s to 114, Volkov’s to 180—and thereafter the end had been swift. Fifty seconds after the separation of the two modules, Patsayev’s pulse had dropped to 42, indicative of someone suffering oxygen starvation, and by 110 seconds all three men’s hearts had stopped.
In 1982, Kolesari & Kindwall reported a case in which a technician was accidentally decompressed over several minutes to a pressure less than 30 mmHg, and held there for a minute before recompressing. Total time at pressures less than the Armstrong Limit was estimated at between one and three minutes. His heart did not stop, but on removal from the chamber he was bleeding from his lungs, unconscious and showing a type of abnormal posturing associated with brain injury. He remained unconscious for five and a half hours, at which point he was treated in a hyperbaric chamber. He woke up within twenty-four hours and eventually made a complete recovery without neurological problems. In the first two days he showed a spike in a biochemical marker called creatine phosphokinase, which is an indicator of tissue damage—presumably due to a combination of the initial hypoxia and bubble emboli.
From these very sparse data it appears that humans may perform closer to dogs than to chimpanzees, with cardiac arrest intervening somewhere around or just after the two-minute mark. The technician in the 1982 accident made a full neurological recover, but probably only with the aid of a hyperbaric chamber to improve his tissue oxygenation in the aftermath of the accident.
Breath-holding
The NASA CR-1223 report lists a number of episodes of explosive or rapid decompression (one fatal). In particular, there are notes on three men who were decompressed by about 250 mmHg (from the equivalent of 8,000 ft to 22,000 ft) over two seconds—a relatively mild change by the standards we’re discussing here, which would probably have been relatively uneventful without the attempt at breath-holding.
The first subject was a 42-year-old pilot who inadvertently held his breath at the instant of decompression. He immediately experienced an upper abdominal pain of moderate severity and then lost consciousness. His respirations were noted to be irregular and in the nature of short gasps. Consciousness was regained on reaching ground level about one-half minute after the decompression.
This looks like a fainting episode induced by trying to hold pressure in the lungs that was higher than the pressures in his heart.
A twenty-three-year-old altitude chamber technician is believed to have held his breath at the time of decompression. Almost immediately he noted generalized chest pain and collapsed about twenty seconds later. There were no voluntary respiratory movements. Artificial respiration was begun at once. His skin was cyanotic, cold and clammy. Blood pressure was 126/80 and the pulse was regular at 90 per minute. Voluntary respiration began about two minutes after the rapid decompression but he remained unconscious for about five minutes. On recovering consciousness, he noted weakness of the right arm, numbness of the face, headache and blurred vision. He was nauseated and vomited. The paresis and numbness disappeared rapidly but the clinical picture of shock, an ashen pallor with cold wet skin, persisted for a half hour. His blurred vision cleared about five hours post decompression, the nausea and vomiting lasted six hours and the headache subsided in about eight hours. An x-ray of the chest was normal.
That looks like a near-fatal shower of air emboli that were squeezed into the lung blood vessels by the high pressure in the lungs.
In the third case , a thirty-three-year-old pilot was near the peak of inspiration when decompression started. Initially, he noted the expulsion of air from his nose and mouth. This was followed by a severe left parasternal pain. Within a few seconds he felt weak and giddy and shortly thereafter became unresponsive. His respirations were irregular, shallow and associated with a hacking cough. During the descent to ground level he exhibited several uncoordinated twitching movements of the upper extremities. The pulse was 45 per minute about two minutes after the decompression. He was in shock and had an ashen pallor and cold, clammy skin. The patient was unconscious for about ten minutes. In the meantime the blood pressure and pulse stabilized at 130/76 and 80 per minute, respectively. The patient had a complete quadriplegia, as well as the loss of tactile sensation for the initial twenty minutes following the decompression.[…] Chest x-rays taken about one hour after the incident showed a pneumomediastinum, a small pneumothorax of the left apex and air in the soft tissues of the neck.
There seems to have been temporary damage from emboli, as in the previous case, but accompanied by air squeezing into the chest cavity, into the tissues around the heart, and then up into the neck.
All of the above is a pretty powerful argument for not attempting to hold your breath when decompressing.
And finally … Joseph Kittinger’s hand
Project Excelsior was a series of three simulated high-altitude bailouts that took place during 1959 and 1960. Captain Joseph Kittinger ascended in an open gondola suspended from a helium balloon, and then returned to the ground by parachute. All his jumps were from altitudes well above the Armstrong Limit, so he wore a pressure suit. He described the three jumps in an article for the December 1960 edition of National Geographic.
On his third ascent, Kittinger noted at an altitude of about 43,000 ft that his right hand didn’t feel normal, and realized that his suit glove had failed to pressurize. As he wrote later:
The prospect of exposing the hand to the near-vacuum of peak altitude causes me some concern. From my previous experiences, I know that the hand will swell, lose most of its circulation, and cause extreme pain. I also know, however, that I can still operate the gondola, since all the controls can be manipulated by the flick of a switch or a nudge of the hand. I am acutely aware of all the faith, sweat, and work that are riding with me on this mission. I decide to continue the ascent, without notifying ground control of my difficulty.
He and his depressurized hand then rode up to 102,800 ft and spent 12 minutes at altitude, after which he bailed out of his gondola and took 14 minutes to descend to the ground.
[Dr. Dick Chubb] looks at the swollen hand with concern. Three hours later the swelling will have disappeared with no ill effect.
Since the ascent took an hour and a half, it’s likely that Kittinger’s hand spent more than an hour above the Armstrong Limit of 63,000 ft. And the idea that Kittinger’s hand spent an hour in near-vacuum without suffering lasting damage or causing his death seems to be a powerful internet meme, brought up whenever the topic of human vacuum exposure is discussed.
But what happened to Kittinger’s hand is quite complicated, and probably not very informative about vacuum exposure generally.
It’s difficult to say exactly what pressure Kittinger’s body was at. He was wearing an MC-3A partial pressure suit—an outfit that relied on tight lacing and multiple inflating bladders to apply approximately uniform pressure to the body at altitude. Its main function was to allow pressure breathing—the wearer could breathe oxygen from a source at higher-than-ambient pressure, and the suit would compress his body to prevent dangerous pressure gradients being created within his lungs and circulatory system. Some residual pressure gradient commonly occurred—breathing from a source with a pressure 30 mmHg above the suit pressure was not dangerous, and could be performed for some time. But even breathing oxygen, Kittinger’s suit would need to compress his body by at least 100 mmHg to allow him to breathe at his maximum altitude.
The glove that had failed was made of leather and nylon, with lacing at the back to ensure a snug fit, and an internal bladder across the back of the hand, which should have inflated to generate the necessary counterpressure to balance that in the rest of the suit. It was similar in construction to the pair below:
So as Kittinger’s altitude increased and his suit inflated, his body pressure (and in particular, the pressure in his blood vessels) would ramp steadily higher relative to the tissues in his hand. Critically, the venous pressure in his arm would rise until it was ∼100 mmHg higher than normal venous pressure in his hand. Valves in the veins would prevent blood squeezing backwards down this pressure gradient, but arterial blood was still entering his hand, at an abnormally high relative pressure. The only thing that could happen was for the veins and capillaries to fill with blood until their pressure rose to match the suit pressure in Kittinger’s arm, at which point a trickle of blood flow out of his hand would resume.
So intravascular pressures everywhere in his hand would have very quickly risen to exceed 47 mmHg—there would be no gas formation in the blood vessels of his hand.
And, at those grossly abnormal pressures, his capillaries would have started to leak fluid into the surrounding tissues—he would develop oedema in his hand. The combination of oedema and (above the Armstrong Limit) water vapour bubbles would quickly expand the tissues of his hand until it completely filled the snugly fitted glove. Tissue pressure would then rise further as more oedema squeezed out of the capillaries, and eventually the water vapour bubbles would collapse back into the liquid phase as his tissues pressures exceeded 47 mmHg.
To what extent that process completed during Kittinger’s time above the Armstrong Limit we don’t know—but the fact that his hand was still swollen for a couple of hours after he returned to the ground implies that something other than water vapour was present in the tissues. Although in his National Geographic article Kittinger says he was “breathing oxygen”, Dennis R. Jenkins, in Dressing For Altitude (17.8 MB pdf) writes that the breathing-gas mix for Project Manhigh, the precursor to Project Excelsior, was 60% oxygen, 20% nitrogen and 20% helium, because of concerns about fire hazard. So it may be that Kittinger had a mixture of residual inert gas bubbles and oedema in the swollen hand Dr Chubb examined with concern.
SUMMARY
Tissues do swell with gas, promptly, and up to approximately double their normal size. Evidence of blood boiling can appear as early as one second after depressurization, and gas bubbles will get big enough within 10-15 seconds to prevent the heart pumping blood. Prompt repressurization will immediately fix this pump problem but, if you’ve been breathing nitrogen, you may then endure a shower of residual nitrogen emboli into your circulation, causing transient neurological problems. After a couple of minutes depressurized your heart will stop, and it will then become much more difficult to resuscitate you. At about the same time, the neurological insult and tissue damage from hypoxia become so severe that it’s likely you’ll need advanced medical facilities and access to hyperbaric medicine to recover unimpaired. Transient attempts at breathholding (or even being caught at the top of a deep breath in) are likely to have nasty consequences due to lung injury and air leaks into the blood vessels and tissues. It seems likely that the actual Time of Useful Consciousness will be established by a race between falling oxygen concentrations in the blood and the onset of cardiac arrest because of gas bubbles filling the heart—there’s not much hope of anything longer than ten seconds, and (as I described in Part 1) reason to believe it might be significantly shorter than that.
For me, it’s interesting that there are two opposing schools of speculation about vacuum exposure out there, neither of which is accurate. In one, people are imagined to explode or freeze within seconds of exposure to space—certainly untrue. In the other, which seems to be almost a reaction to the excesses of the first, there’s the idea that the skin and blood vessels are somehow tight enough to stop widespread and immediate gas formation in the blood and tissues—again, as demonstrated by experiment, also untrue.
The truth, as ever, lies somewhere in the middle.
* This prompts the question of whether all that internal evaporation of water might not cause a significant fall in body temperature. If we take a doubling of body volume as a ball-park figure for the volume of water vapour evolved, we could put it at about 80 litres. Steam tables tell us that, at an absolute pressure of 47 mmHg (that’s -713 mmHg on the “gauge” scale used in steam tables), a gram of water generates about 22.8 litres of vapour—so doubling an adult human’s size under these conditions requires the evaporation of only about 3.5 g of water. Our trusty steam table also tells us that, at 37ºC, this will require about 8.5 kJ of energy. But the specific heat capacity of water is 4.2 kJ/kg/ºC, making the heat capacity of an 80-kg person about 336 kJ/ºC. So all that internal evaporation is only enough to cool a person by a fortieth of a degree Celsius.
In reality, the effect is so small that it isn’t visible to the naked eye under most circumstances. 
