Espacio de César posted a video demonstrating how to make a usable 40-watt soldering gun out of a heavy mains transformer (rewound with a low-voltage secondary) and some heavy steel wire, saying he was looking for about ½ volt on the secondary. This seems like a very reasonable strategy to me but I can’t salvage transformers — invariably they are already recycled before I encounter a discarded electronic item. Probably even something like an ATX power supply would be easier to find.
½V and 40W is about 80 amps, though, which is a bit more than ATX power supplies can usually provide.
That also implies about 0.006Ω. Is that about the right resistance? Iron’s resistivity at room temperature is about 100 nΩm; guessing that César’s heating element is about 100 mm long and 1 mm², we get 0.01Ω, so yeah, that’s about right. 1010 carbon steel is about 143 nΩm, while stainless is several times higher at some 700 nΩm. Nichrome would be much better, at 1100 nΩm, and I’ll probably find some sooner or later, since people constantly throw out broken hair dryers and space heaters.
We could get the same power out of a thinner wire at a higher voltage
and lower current, but at more risk of burning the wire out. The
wire fusing current estimates from Powerstream that I used in
file balcony-battery in Dercuano suggest that 86 A is already
enough to melt 11-gauge iron wire (2.3 mm), 43 A is enough to melt
15-gauge iron wire (1.5 mm), 21 A is enough to melt 19-gauge iron wire
(0.9 mm), and 10.7 A is enough to melt 23-gauge iron wire (0.57 mm).
So really César is already past the edge of safety and will melt his
soldering tip if he holds the trigger down long enough.
Can you do it with simple electronics instead of a transformer?
You can’t just PWM the AC line current through a 6-milliohm heating element; you’ll trip the house’s circuit breaker, and even if you don't, you're dropping the line voltage to zero temporarily, and other nearby appliances won't like that. But you ought to be able to PWM it into a hefty inductor with a hefty freewheel diode or ten, at least if they have enough ballast to prevent thermal runaway. Very crudely guessing, if you have a duty cycle of 0.01% or more and a PWM frequency of 10kHz, then your inductor just needs to prevent the current from rising to too much more than 80 amps in 10 ns, or 8 billion amps per second, at less than 340 V (the peak voltage). That only requires 43 nanohenries, which you might get without asking for it. But it also requires subnanosecond switching times for that current. Also, you need an input capacitor bank that can handle 80 amps of ripple current, which is doable but nontrivial.
You probably could PWM the AC line current into a high-frequency stepdown transformer, which could handle the 40 watts or whatever in a much smaller core. This is basically a flyback supply I think, just with a stepdown instead of a stepup? I don’t know, I have to think about this stuff later.