[kragen]

A thing I forgot to calculate: with 75m of wire dissipating 533 watts per meter, how thick should the wire be? Suppose we divide it into three 25m circuits so that we still have most of our heat if a wire burns out, and suppose we're using 48Vdc. So E²/R = 13.3kW, R = E²/13.3kW = 0.173Ω, and each of those elements is carrying an astonishing 277 amps. So we want 7 milliohms per meter. It turns out that that's about 12-gauge copper wire, nominally 5 milliohms per meter. 2 millimeters across. A higher-resistivity metal like iron or nichrome would have to be even thicker.

Better idea: put 9 2.7-meter wires in parallel on each of the three circuits, so each wire can have 9×0.173Ω = 1.56 Ω = 0.58Ω/m. That's 32-gauge copper magnet wire, 0.2mm diameter, 0.54Ω/m; or its thicker equivalent in other metals. Iron's resistivity is 5.7 times copper's, so you need a 5.7 times thicker wire: 0.5mm, 24-gauge. Nichrome is 11 times the resistivity of iron, so you'd need 1.6-mm-diameter nichrome.

I don't know, I think the copper would probably melt faster than the sand could conduct the heat away from it, and the nichrome would definitely be fine, but too expensive. But you can extrapolate from this how to solve the problem: by shortening the distance along the heating wires to low-resistance busbars (possibly made of rebar or leftover angle iron) and thus increasing the number of parallel paths, you allow the use of higher-resistance-per-unit-length and thus cheaper and more workable heating elements; the limit of this lightweighting is that the wires' surface area in contact with the sand must cool them enough to prevent melting. By this method you can use a small amount of a conductor of any resistivity at all, limited mainly by the temperature.

All these metals are fine at 700°, or for that matter 1000°. Copper will have less of a tendency to oxidize than iron, which would require a reducing atmosphere, and nichrome will oxidize but remain protected by its oxidation. (A reducing atmosphere will destroy nichrome.) But, at a lower temperature still, like 600°, you could use 10μm thick household aluminum foil, which is much easier to work with than any kind of 20μm wire, but has a similar ratio of surface area to volume. It has 54% more resistivity than copper, so a 10μm × 1mm strip is 2.7 ohms per meter. Our previous objective of 0.58Ω/m is a 4.6mm-wide-strip, which transfers heat to the sand along its 9.2mm perimeter, like a 10-gauge wire. 75m × 4.6mm is the size of about 5 or 6 pages of A4 paper cut into strips.

[sandy234590]

Maybe stainless steel for the heating elements and busbars?

Cheaper than nichrome and copper. I feel like mild steel would not last long in practice.

Copper plated MIG welding wire might be good enough?

Probably want to think about thermal expansion also, especially configured as "walls", and with skins considerably colder than cores.

[pfdietz]

Austin Vernon claims they have a very cheap resistor material for Standard Thermal but hasn't said what it is. I look forward to hearing that detail when it leaks out. A good chunk of their work while in stealth was on the resistors, I understand.

[kragen]

I think I've shown above that you can make the resistor material itself almost arbitrarily cheap, calculating for example how you can get 40 kilowatts out of 9.3 grams of aluminum foil, and showing that with more busbars you can use even less resistor material than that. Aluminum itself wouldn't work for Standard Thermal's target temperatures, but you can make an arbitrarily thin foil out of any metal, supporting it as a thin film on an insulating ceramic such as porcelain if necessary. Copper, gold, silver, mild steel, nickel, nichrome, other stainless, titanium, platinum, and platinum/iridium, could all be made to work, and in no case would the material cost be significant. Metal film resistors supported on ceramic are being used to convert electrical energy into heat in probably every electronic device in your house.

And the old standby for resistive heating of giant piles of dirt, for example to bake it into carborundum, isn't a metal at all—it's plain old carbon, which you can if necessary bake in situ. Carborundum itself can also work, though it's not malleable, and controlling its resistivity can be tricky.

MIG welding wire is an interesting possibility.

The main potential obstacle, I think, is the manufacturing cost, and as sandy234590 was saying, potentially durability in use. Vernon said resistor durability had been one of their major problems; I'd think that sand would impose less stress on the resistors than generic dirt, but, with quartz in particular, you could greatly reduce the risk by not crossing the quartz dunting temperature at 573°: https://digitalfire.com/glossary/quartz+inversion That obviously isn't an option for Standard Thermal, but it would be completely viable for household climate control, just requiring somewhat more sand.

Sandy points out, implicitly, that mild steel such as the baling wire I suggested typically does not last long at high temperatures. But that's because it oxidizes. The same vulnerability is present in most metals, though not silver, gold, platinum, and platinum/iridium alloys, and only to a limited extent for nickel, nichrome, and other stainlesses. That oxidation can only happen in an oxidizing atmosphere; the thin iron ballast wires in Nernst lamps last indefinitely because they're sealed in a reducing (hydrogen) atmosphere. As I said, I think you can maintain a reducing atmosphere in the sand pore space by just including a little charcoal, which will scavenge any oxygen that gets close to the heating elements when they're hot, and may even be able to reduce any oxide that does form, at the cost of carbon monoxide emission.

If the atmosphere inside the sand is oxidizing, you'd probably want to either use something that won't be damaged by oxidization, such as gold or nichrome, or use a very thick heating element such as carbon so that it will have an adequate service life despite the oxidation. Most stainless steels will start to oxidize at a few hundred degrees, even though they're fine at room temperature.

(The main heating element in Nernst lamps, cubic zirconia, was also immune to oxidation, but it had some other drawbacks; for example, it needed to be preheated into its conductive range with a platinum preheat wire, and its rather aggressive negative temperature coefficient of resistance made it prone to thermal runaway when operated on a constant-voltage source—thus the iron ballast wire.)