by kragen | 2025-10-24 02:28:33+00:00
I haven't seen pfdietz's proposed system design, but a so-called "sand battery," consisting of a box of sand with a heating element running through it, should work fine. You can PWM the heating element with a power MOSFET to keep it from overheating; you can measure its temperature with its own resistance, but also want additional thermocouple probes for the sand and to measure the surface of the box. A fan can blow air over or through the sand to control the output power within limits.

I'll work out some rough figures.

Let's say your house is pretty big and badly insulated, so we want an average of 5000 watts of heating around the clock with a time constant on the order of 10 hours, and we don't want our heating element to go over 700°. (Honest-to-God degrees, not those pathetic little Fahrenheit ones.) That way we don't have to deal with the ridiculous engineering issues Standard Thermal is battling. There's a thermal gradient through the sand down to room temperature (20°) at the surface. Suppose the sand is in the form of a flat slab with the heating element just heating the center of it, which is kind of a worst case for amount of sand needed but is clearly feasible. Then, when the element is running at a 100% duty cycle, the average sand temperature is 360°. Let's say we need to store about 40 hours of our 5000W. Quartz (cheap construction sand) is 0.73J/g/K, so our 720MJ at ΔT averaging 340K is 2900kg, a bit over a cubic meter of sand. This costs about US$100 depending mostly on delivery costs.

The time constant is mostly determined by the thickness of the sand (relative to its thermal diffusivity), although you can vary it with the fan. The heating element needs to be closely enough spaced that it can heat up the sand in the few hours that it's powered. In practice I am guessing that this will be about 100mm, so 1.5 cubic meters of sand can be in a box that's 200mm × 2.7m × 2.7m. You can probably build the box mostly out of 15m² of ceramic tiles, deducting their thermal mass from the sand required. In theory thin drywall should be fine instead of ceramic if your fan never breaks, but a fan failure could let the surface get hot enough to damage drywall. Or portland cement, although lime or calcium aluminate cement should be fine. You can use the cement to support the ceramic tiles on an angle iron frame and grout between them if necessary.

7.5m² of central plane with wires 100mm apart requires roughly 27 2.7m wires, 75m, probably dozens of broken hair dryers if you want to recycle nichrome, though I suspect that at 700° you could just use baling wire, especially if you mix in a little charcoal with the sand to maintain a reducing atmosphere in the sand pore spaces. (But then if it gets wet you could get carbon monoxide until you dry it out.) We're going to be dumping the whole 720MJ thermal charge in in under 9 hours, say 5 hours when the sunshine is at its peak, so we're talking about maybe 40kW peak power here. This is 533 watts per meter of wire, which is an extremely reasonable number for a wire heating element, even a fairly fine wire in air without forced-air cooling.

If we believe https://www.nature.com/articles/s41598-025-93054-w/tables/1 the thermal conductivity of dry sand ranges from 0.18 W/m/K to 0.34 W/m/K. So if we have a linear thermal gradient from our peak design temperature of 700° to 20° over 100mm, which is 6800K/m, we should get a heat flux of 1200–2300W/m² over our 15m² of ceramic tiles, so at least 18kW, which is more than we need, but only about 3×, so 200mm thickness is in the ballpark even without air blowing through the sand itself. (As the core temperature falls, the heat gradient also falls, and so does the heat flux. 720MJ/18kW I think gives us our time constant, and that works out to 11 hours, but it isn't exactly an exponential decay.) Maybe 350mm would be better, with corresponding increases in heating-element spacing and decreases in wire length and box surface area and footprint.

To limit heat loss when the fan is off, instead of a single humongous wall, you can split the beast into 3–6 parallel walls with a little airspace between them, so they're radiating their heat at each other instead of you, and cement some aluminum foil on the outside surfaces to reduce infrared emissivity. The amount of air the fan blows between the walls can then regulate the heat output over at least an order of magnitude. (In the summer you'll probably want to leave the heating element off.)

The sand, baling wire, aluminum foil, lime cement, angle irons, charcoal, thermocouples, power MOSFETs, microcontroller, fans, and ceramic tiles all together might work out to US$500. But the 40kW of solar panels required are about US$4000 wholesale, before you screw them to your siding or whatever. At US prices they'd apparently be US$10k.

720MJ is 200kWh in cursed units, so this is about US$2.50/kWh. Batteries are about US$80/kWh on the Shanghai Metals Market.

What do you think?