I think I’ve finally found the problem to how to refresh the memory in the Egg of the Phoenix: use daily tidal atmospheric pressure swings to power programs to periodically rewrite NAND Flash.
The problem is that the device, by definition, needs to be able to retain its memory when buried for a century or more; that’s its entire raison d’être. But modern Flash is not designed for such a requirement; instead, it’s designed for memory retention of 20 or even 10 years. And it’s very likely that Flash memory will gradually lose its memory as charge tunnels away from its floating gate, at a rate which is IIRC exponential in temperature.
It doesn’t take very much energy to refresh Flash; Low-power microcontrollers for a low-power computer says the Adesto AT25SF041-SSHD-T NAND chip requires 100 mA for 500 ms to erase 32 kB ≈ 500 nJ per byte, and presumably some smaller amount to write the erased memory; Keyboard-powered computers says Flash uses 2 μJ per 32-bit write, which is exactly equal. FeRAM also exists and is about 2000 times more energy-efficient than Flash, and MRAM is apparently about 500 times more energy-efficient than Flash, but both are dramatically more expensive.
(Other possibilities besides Flash, FeRAM, and MRAM exist, but nothing that we can confidently predict will survive a century.)
The power needed is thus proportional to the amount of data archived.
This means that preserving, say, 100 gigabytes of Flash requires about 50 kJ every 10 years or so, which works out to an average of 160 μW. If we take that over 100 years, it’s 500 kJ; converted to milliamp hours at the 3.7 V of a lithium-ion battery, it’s 37000 milliamp hours. This would be a very reasonable-sized lithium-ion battery, one you could hold in your hand. So why not just use that?
Well, all batteries have a self-discharge rate, and typically it’s enough to discharge them completely within five years. Lead-acid batteries have a somewhat longer shelf life, perhaps 10 or 20 years. But no commercially made battery has a shelf life of a century.
One possible alternative is a Zamboni pile such as, it is believed, the Clarendon Dry Pile that powers the Oxford Electric Bell, which has been ringing almost continuously since 1840, on about 1 nA and 2000 V (2 μW). Unfortunately, although long-lived Zamboni piles do exist, they are not very well characterized; we don’t know very much about the ways they can fail, particularly after decades. We don’t even know for sure that the Clarendon Dry Pile is in fact a Zamboni pile. And, as far as I know, nobody has ever built a Zamboni pile that yields tens of microwatts, let alone hundreds.
Earth’s atmospheric pressure varies tidally by a few millibar (a few hundred pascals) around its average of 101.325 kPa at sea level, varying from 87.0 kPa (during Typhoon Tip in 1979) to 108.48 kPa (during the Siberian High in Mongolia in 2001). (The vertical variation is larger than this, at about 11.3 Pa/m, so reaching the record low typhoon sea-level pressure only requires going a bit over a kilometer up.)
As I write this, the pressure is some 103 kPa, and tomorrow it’s forecast to fall to 102 kPa, then as low as 100 kPa the next day as a rainstorm comes through. For most of the next week, the trend is almost perfectly flat, staying between 101 and 102 kPa. There are tidal-looking wiggles in the forecast of about 100 Pa above and below the trend line. The NWS says Boston currently has 101.51 kPa, but earlier today it’s been as low as 101.05 kPa and as high as 101.62 kPa; yesterday was from 100.91 kPa to 101.56, with a bit of rain. So, although the dependable tidal variations are only around 100–200 Pa, working out to a total of 400–800 Pa per day absolute change, it’s common to have a bit more than that, like 1 kPa or more per day of change in one direction or the other.
Common soils and even rocks are not sufficiently rigid and impermeable to prevent this pressure variation from reaching underground, even to a depth of tens of meters, a phenomenon known in some contexts as “barometrically induced variability”. So an energy-harvesting device that harnesses these tidal pressure variations will work even if it’s buried, as long as it doesn’t get all crudded up with sand or something. Even if it’s filled with water, it should continue to work.
Such energy-harvesting computational devices date back to the seventeenth century; one of the greatest engineers of all time, Cornelis Drebbel, built several clocks powered by such pressure changes at that time, starting in 1610. Cox’s Timepiece, built in the 1760s, ran exclusively on atmospheric pressure until being acquired by the Victoria & Albert museum in 1961, and the Beverly Clock, built in 1864, is still running today, 154 years later, though it also harvests thermal energy.
Jaeger-LeCoultre currently sells the Atmos clock, which harvests energy from temperature and pressure variations to run without winding; some half a million have been produced so far since their 1929 début. Although, like the Beverly Clock, it primarily harvests thermal energy, a pressure variation of 3 mmHg = 0.4 kPa is sufficient to energize it for two days; although typical tidal pressure variation is slightly smaller than this, it shows that pressure variations in this range are suitable for harvesting even with a tabletop-sized device with no electrical parts, by pressing an ethyl chloride bellows against a spring. Michael P. Murray, a specialist in Atmos clocks, claims that they use about 250 nW; Adam Sacks claims they should have a service life of about 600 years.
Aside from the few hundred pascals of tidal variation, when it rains, the soil may saturate with water and go to higher pressures. If the Egg is buried 2 meters deep, for example, it will experience an extra 20 kPa of hydrostatic pressure if the water table rises past it to the surface. This is some two orders of magnitude larger than daily tidal variations, but only somewhat larger than the 15 or so kPa of difference between world records. So it’s important to design the Egg to withstand such pressures, even if it can’t harvest the energy they present.
The surface tension of water in the soil can also produce soil suctions up to some 30 MPa, which I interpret as pressure below atmospheric pressure and indeed below zero pressure, despite cautions that that’s not exactly what is meant. Apparently typical soil suction for agricultural soils is 25 kPa or less.
“Barometrically induced variability” is a term used for variability in subsurface gas concentrations, of concern in monitoring of toxic waste. One paper reported pressure variation over a range of some 25 mb (2.5 kPa) during a few days, tens of meters below the soil surface, which was inversely correlated with CCl₄ concentrations.
Even higher-frequency pressure variations, such as those caused by wind vortices, can penetrate deep underground; Takle and colleagues in 2004 measured about 6 dB of attenuation of 2 Hz pressure variation by 600 mm of soil, if I’m reading the paper right, which suggests that the ≈20 μHz tidal pressure swings should be able to penetrate many, many meters of soil with no real attenuation.
How much power is available from these air pressure variations? It seems like the limit is somewhere around 100 μW/ℓ, but it may be hard to approach that limit.
Suppose we have a cubic decimeter of air (a liter) with one flexible or bellowed face, to which we couple some kind of harvesting device, piezoelectric or mechanical or whatever. Suppose the air pressure changes by 200 Pa. If that device provides no resistance to the pressure variations, then the volume of the cube will increase and decrease by 0.2%, which is some 200 μm. But this is doing no work on the device, because there is no force. At the other extreme, suppose that the harvesting device is absolutely rigid. Then the force on it will vary from +1 N to -1 N, but the volume of the cube will not vary, and so it will do no work on the device, because there is no movement.
In between these extremes, we can harvest energy. For example, suppose that the harvesting device will rigidly resist a maximum of 0.5 N and thereafter move, winding a spring or something at constant force. Then the flexible face will move by only 100 μm, but it will be exerting 0.5 N over that distance, providing 50 microjoules, about every 6 hours. This works out to about 2 nW, which is two orders of magnitude smaller than what Murray claims the Atmos clock runs on. And the Atmos clock bellows does not appear to occupy an entire liter. We can perhaps conclude that using air, as the Beverly clock does, is quite disadvantageous.
Dividing the cube into slices to get more faces does not help, because the slices will expand and contract by correspondingly less distance. Making the cube larger does help, as the energy available is proportional to the expansion distance and piston area.
What’s the maximum work we could potentially extract from air pressure on our liter? Suppose it’s still a cube, but filled with vacuum and with four bellows sides, with a constant-force spring pulling on it producing 1013.2 N. Now, whenever the air pressure falls below 101.32 kPa, the spring will expand the cube to its full 1ℓ volume, and whenever the air pressure rises higher, the spring will contract the cube down to a little square pancake, which we can suppose has insignificant volume compared to 1ℓ. The work that can potentially be extracted is a function of the height of the peak at the point that we allow the harvesting device to move; supposing that, as before, it’s 200 Pa from trough to peak, we have 2 N over 100 mm, which of course yields 200 mJ. This is a quite respectable 9.3 μW, though still considerably smaller than the 160 μW we need. And, of course, if we somehow know that the pressure will fall from 103 kPa to 102 kPa tomorrow, then we can leave the cube fully extended until the pressure reaches its minimum, and then extract 10 N over 100 mm, a total of 1 J, some 100 μW over 24 hours.
(And of course we can use multiple liters to multiply the power; use a longer, thinner cylinder to get a longer stroke at proportionally less force; or use a fatter, flatter cylinder to get a shorter stroke at proportionally more force.)
Note that 9.3 μW is some 4000 times larger than the 2 nW we’d get from the air cube.
How close could we come to this ideal in practice? Presumably the Atmos uses ethyl chloride because the pressure range is enough to cause much of it to condense and evaporate at room temperature, enabling much larger volume variations than an air tank could manage. At a given temperature, the equilibrium pressure within such a mixed-phase, single-material container is absolutely constant at the vapor pressure of the liquid at that temperature, so a liquid whose vapor pressure is 101.32 kPa at whatever your temperature is would actually behave precisely like the vacuum-and-constant-force-spring gedankenexperiment above, expanding to an almost arbitrarily large volume when the pressure drops, and contracting to almost none when the pressure rises. (For water, the liquid to vapor density ratio is a few thousand to one; it’s a bit lower for ethyl chloride.) Unfortunately, that experiment assumes that the tidal swings center precisely on that known pressure, which, as described above, is far from true; day-to-day shifts are commonly several times the amplitude of the dependable tidal pressure swings.
It isn’t yet obvious to me how, but I suspect that something close to the ideal behavior described above is feasible. So only a few liters (perhaps less than the 28 used by the Beverly Clock) should be necessary to provide the refresh power. I think the Atmos compromises its ability to harvest energy at any given pressure/temperature combination by using its “counterweight” Hookean spring to spread its response curve over a wide range of pressures and temperatures in a purely static fashion. That is, at a given pressure and temperature, I think the Atmos’s expansion chamber will always have the same volume, plus or minus a small constant bit of hysteresis.
Efficiently converting the mechanical power to electrical power is, I think, the easiest part of the problem; piezoelectric, electromagnetic, and electrostatic techniques are all applicable, though it seems likely that the fairly rigid piezoelectrics are the best fit for the likely small displacements involved.